USFDC Home  USF Electronic Theses and Dissertations   RSS 
Material Information
Subjects
Notes
Record Information

Full Text 
PAGE 1 Closure Between Apparent and Inhere nt Optical Properties of the Ocean with Applications to the Determin ation of Spectral Bottom Reflectance by James Edward Ivey A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy College of Marine Science University of South Florida Major Professor: Kendall L. Carder, Ph.D. Paula G. Coble, Ph.D. Margaret O. Hall, Ph.D. Pamela Hallock Muller, Ph.D. Gabriel A. Vargo, Ph.D. Date of Approval: April 6, 2009 Keywords: absorption, irradiance, oc eanography, backsc attering, albedo Copyright 2009 James Edward Ivey PAGE 2 Dedication This work is dedicated to my sons Heath and Wyatt. Their curiosity and enthusiasm as they learn more about this world is a virtue that everyone should keep throughout their life. Their excitement at seeing a new bug for the first time or their fascination with the shape of a leaf is an insp iration to me. If I can exhibit even half their enthusiasm for discovery I will be a better scientist. PAGE 3 Acknowledgements The most important acknowledgement is rese rved for my wife a nd partner, Angie. She has supported me in this endeavor thr ough the month long cruises, late nights getting equipment prepped, and years of working nights and weekends on my dissertation. Without her help, I would not have made it this far. The support from Dr. Carder and the o cean optics lab at USF made this study possible. Ken Carder is my major profe ssor and mentor. David English and Jen Cannizzaro worked collecting and processing data and provided input on ideas for this study. Tom Peacock taught me instrumenta tion. Bob Chen, Dave Costello, Zhongping Lee, Flip Reinersman, Chris Cattrall, Andy Farmer, Steve Butcher, and Dan Otis all contributed to this work with eith er ideas and/or da ta collection. The members of my committee helped me in several ways. I participated in cruises with and learned a gr eat deal from Pamela Hallo ckMuller, Gabe Vargo, and Paula Coble. Margaret Hall deserves thanks for plunging into middle of this dissertation after a committee member dropped out at the last moment. Cindy Heil is both my chair and my supervisor at FWRI. The Office of Naval Research, Enviro nmental Optics Program, provided the majority of funding for my resear ch under grants N000149615013, N000149710006, and N000140210211. Chuanmin Hu funded my salary for several months. Kent Fanning invited us on the FSLE crui ses and HOBI Labs invited us on two cruises. NRL funded the Friday Harbor optic s cruise. The two Jims in the shop helped me get equipment built and designed. Charlie Mazel collected the W FL shelf albedo data used in this study. I worked with so many people here at the College of Marine Sciences that there is not room to acknowle dge them all. I'll end with a thank you to everyone. PAGE 4 i Table of Contents List of Tables iv List of Figures v Abstract xv 1. Introduction 1 1.1. Light, Water, and Life 1 1.1.1. Global Scales of Ocean Optics 1 1.1.2. Local Scales of Optical Oceanography 3 1.1.3. Application of Optical Oceanography to Coastal Problems 4 1.2. The Path of Light Through Water 6 1.2.1. Light Through a Beam Transmissometer 6 1.2.2. Sunlight Entering the Ocean 7 1.2.3. Effective Optical Path Length 9 1.3. Main Focus of Study 11 1.4. Hypotheses 12 2. Background 14 2.1. Introduction 14 2.2 Definitions of Optical Terms 14 2.3. Progress in Ocean Optics 18 2.4. Optical Closure 22 2.5. Spectral Bottom Albedo Through Optical Closure 24 2.6. Locations and Descriptive Optics 26 2.7. Morel Case of Study Sites 29 3. Instruments and Algorithms 35 3.1. Introduction 35 3.2. SlowDrop Package 35 3.2.1 ac9 35 3.2.2. Spectrix Hyperspectral Downwelling Irradiance Meter 38 3.2.3 Hyrdoscat6 40 3.3. Rrs( ) Measurement with Spectrix 40 3.4. Spectrophotometer Measurements 40 3.5. Rrs( ) Inversion Models 41 3.5.1 QAA 41 3.5.2 MODIS 42 PAGE 5 ii 3.5.3. Optimization Model 42 3.6. Kd( ) inversions 44 3.6.1. Kirk 44 3.6.2. Loisel 3.6.3. Kd Optimization 45 3.7. Note on recent progresses in instruments and algorithms 48 4. Statistical Methods 49 4.1. The Unbiased Approach 49 4.2. Interpolation and Integration 50 4.3. Statistical Tools 51 4.4. Determining the Filters 52 4.5. Test for Normality After Applying a Log Transform 55 4.6. Statistical Comparisons to the Ideal Values 55 5. Optical Closure Results 62 5.1. How to Interpret Results 62 5.2. Determination of Filte rs Based on Bottom, Clouds, and Zenith Angle 64 5.3. Nonparametric Analysis for Ideal Data Set 70 5.3.1. KW Nonparametric Analysis of anw( ) 76 5.3.2. KW Nonparametric Analysis of bbp( ) 77 5.3.3. KW Nonparametric Analysis ag( ) 78 5.3.4. KW Nonparametric Analysis aph( ) 80 5.4. Comparisons of anw( ) to Idealized Values 81 5.4.1. Unfiltered and No Bottom Filters anw( ) 81 5.4.2. Ideal Conditions anw( ) 87 5.4.3. Bottom Reflectance Only anw( ) 93 5.4.4. Discussion of anw( ) Comparisons with Ideal 98 5.5. Comparisons of bbp( ) to Idealized Values 100 5.5.1. Unfiltered and No Bottom Filters bbp( ) 100 5.5.2. Ideal Conditions bbp( ) 107 5.5.3. Bottom Reflectance Only bbp( ) 112 5.5.4. Discussion of bbp( ) Comparisons with Ideal 117 5.6. Comparisons of ag( ) to Idealized Values 119 5.6.1. Unfiltered and No Bottom Filters ag( ) 119 5.6.2. Ideal Conditions ag( ) 126 5.6.3. Bottom Reflectance Only ag( ) 131 5.6.4. Discussion of ag( ) Comparisons with Ideal 136 5.7. Comparisons of aph( ) to Idealized Values 138 5.7.1. Unfiltered and No Bottom Filters aph( ) 138 5.7.2. Ideal Conditions aph( ) 144 5.7.3. Bottom Reflectance Only aph( ) 149 5.7.4. Discussion of aph( ) Comparisons with Ideal 154 PAGE 6 iii 5.8. Absolute Percent Error Co rrelations with Parameters 5.8.1. Correlations with anw( ) 157 5.8.2. Correlations with bbp( ) 178 5.8.3. Correlations with ag( ) 190 5.8.4. Correlations with aph( ) 202 5.9. Problems with Making Comparisons Between Methods 212 5.10. Best Methods 216 6. Improvements to Instruments and Algorithms 218 6.1. Analytical versus Empirical Models 218 6.2. Improvements to Kd( ) optimization 221 6.3. Improvements to Loisel Kd( ) inversion 226 6.4. Improvements to Hydroscat6 226 6.5. Improvements to MODIS Algorithm 227 6.6. Improvements to the ac9 228 6.7. Improvements to Quantitative Filter Pad Method 232 6.8. Improvements to Spectrophotometric ag( ) 233 6.9 Improvements to Rrs( ) Optimization Algorithm 234 6.10. Improvements to Kirk and QAA models 235 7. Bottom Albedo 237 7.1. Introduction 237 7.2. Bottom Albedo Inversion Method 239 7.3. Inversion Results 242 7.4. Accuracy of the Albedo Inversion Method 250 7.5. Sources of Error 255 7.6. Applications for Albedo inversions 258 8. Conclusion 261 References 265 About the Author End Page PAGE 7 iv List of Tables Table 2.1. Common symbols used in optical oceanography and this study. 15 Table 2.2. Common subscripts fo r symbols used in optical oceanography and this study. 15 Table 2.3. Study sites: dates, locati ons, and chlorophyll concentrations. 26 Table 5.1. Acronyms for di fferent filter groups. 70 Table 5.2. Mean absolute percent error for anw( ) from 412 to 555 nm. 217 Table 5.3. Mean absolute percent error for bbp( ) from 442 to 589 nm. 217 Table 5.4. Mean absolute percent error for ag( ) from 412 to 555 nm. 217 Table 5.5. Mean absolute percent error for aph( ) from 412 to 555 nm. 217 Table 7.1 Mean values of inherent optical properties from study locations. 240 PAGE 8 v List of Figures Figure 1.1. The simple path of li ght through an attenuation meter. 7 Figure 1.2. The complex path of sunlight through ocean waters. 8 Figure 1.3. Response of instruments to different optical path lengths. 10 Figure 2.1. Station locations in Puget Sound, Washington, USA. 27 Figure 2.2. Stations locations near Lee Stoc king Island, Bahamas. 28 Figure 2.3. Station locations on the West Florida Shelf. 29 Figure 2.4. Analysis of Puget Sound data to determine Morel Case. 31 Figure 2.5. Analysis of Bahamas data to determine Morel Case. 32 Figure 2.6. Analysis of West Florida Sh elf data to determine Morel Case. 33 Figure 3.1. The "simple" path of light through reflective tube absorption meter. 36 Figure 4.1. Method to determine filters for bottom reflectance, cloudiness, and solar zenith angle. 53 Figure 4.2. Summary of steps used to determine ideal data set. 56 Figure 4.3. Examples of how combina tions of mean pe rcent error and absolute percent are used to give more information about differences from ideal values. 58 Figure 4.4. Example of slopes for +/10% of the ideal data. 59 Figure 4.5. Steps used in determinat ion of outlier by comparison against slope values. 60 Figure 4.6. Statistical method for an alyzing study data to determine closure. 61 PAGE 9 vi Figure 5.1. Nonparametric st atistical analysis of anw( ) values of each method under different le vels of bottom reflectance ( = 0.05). 65 Figure 5.2. Nonparametric st atistical analysis of anw(676) of each method under different levels of cloudiness ( = 0.05). 65 Figure 5.3. Nonparametr ic analysis of anw( ) data from each method under different solar zenith angles ( = 0.05). 66 Figure 5.4. Nonparametric st atistical analysis of bbp( ) values of each method under different leve ls of bottom reflectance ( = 0.05). 67 Figure 5.5. Nonparametr ic analysis of bbp( ) data from each method under different levels of cloudiness ( = 0.05). 68 Figure 5.6. Nonparametric analysis of bbp( ) data from each method under different solar zenith angles( = 0.05). 69 Figure 5.7. Percent agreement for anw( ) to determine ideal data. 71 Figure 5.8. Percent agreement for bbp( ) to determine ideal data. 72 Figure 5.9. Percent agreement for ag( ) to determine ideal data. 74 Figure 5.10. Percent agreement for aph( ) to determine ideal data. 75 Figure 5.11. Regression and co rrelation analysis of anw( ) versus ideal values using the NF filter. 83 Figure 5.12. Percent error and outlier analysis of anw( ) under the NF filter. 84 Figure 5.13. Regression and co rrelation analysis of anw( ) versus ideal values using the NB filter. 85 Figure 5.14. Percent error and outlier analysis of anw( ) under the NB filter. 86 Figure 5.15. Regression and correlation analysis of anw( ) versus ideal values using the NBLCLZ filter. 89 PAGE 10 vii Figure 5.16. Percent error a nd outlier analysis of anw( ) under the NBLCLZ filter. 90 Figure 5.17. Regression and co rrelation analysis of anw( ) versus ideal values using the MODNB filter. 91 Figure 5.18. Percent error and outlier analysis of anw( ) under the MODNB filter. 92 Figure 5.19. Regression and co rrelation analysis of anw( ) versus ideal values. 94 Figure 5.20. Percent error and outlier analysis of anw( ) under the BT filter. 95 Figure 5.21. Regression and co rrelation analysis of anw( ) versus ideal values using the BTLCLZ filter. 96 Figure 5.22. Percent error and outlier analysis of anw( ) under the BTLCLZ filter. 97 Figure 5.23. Regression and co rrelation analysis of bbp( ) versus ideal values using the NF filter. 103 Figure 5.24. Percent error and outlier analysis of bbp( ) under the NF filter. 104 Figure 5.25. Regression and co rrelation analysis of bbp( ) versus ideal values using the NB filter. 105 Figure 5.26. Percent error and outlier analysis of bbp( ) under the NB filter. 106 Figure 5.27. Regression and co rrelation analysis of bbp( ) versus ideal values using the NBLCLZ filter. 108 Figure 5.28. Percent error and outlier analysis of bbp( ) under the NBLCLZ filter. 109 Figure 5.29. Regression and co rrelation analysis of bbp( ) versus ideal values using the MODNB filter. 110 PAGE 11 viii Figure 5.30. Percent error a nd outlier analysis of bbp( ) under the MODNB filter. 111 Figure 5.31. Regression and co rrelation analysis of bbp( ) versus ideal values using the BT filter. 113 Figure 5.32. Percent error and outlier analysis of bbp( ) under the BT filter. 114 Figure 5.33. Regression and co rrelation analysis of bbp( ) versus ideal values using the BTLCLZ filter. 115 Figure 5.34. Percent error and outlier analysis of bbp( ) under the BTLCLZ filter. 116 Figure 5.35. Regression and co rrelation analysis of ag( ) versus ideal values using the NF filter. 122 Figure 5.36. Percent error a nd outlier analysis of ag( ) under the NF filter. 123 Figure 5.37. Regression and co rrelation analysis of ag( ) versus ideal values using the NB filter. 124 Figure 5.38. Percent error and outlier analysis of ag( ) under the NB filter. 125 Figure 5.39. Regression and co rrelation analysis of ag( ) versus ideal values using the NBLCLZ filter. 127 Figure 5.40. Percent error and outlier analysis of ag( ) under the NBLCLZ filter. 128 Figure 5.41. Regression and co rrelation analysis of ag( ) versus ideal values using the MODNB filter. 129 Figure 5.42. Percent error and outlier analysis of ag( ) under the MODNB filter. 130 Figure 5.43. Regression and co rrelation analysis of ag( ) versus ideal values using the BT filter. 132 Figure 5.44. Percent error and outlier analysis of ag( ) under the BT filter. 133 PAGE 12 ix Figure 5.45. Regression and co rrelation analysis of ag( ) versus ideal values using the BTLCLZ filter. 134 Figure 5.46. Percent error and outlier analysis of ag( ) under the BTLCLZ filter. 135 Figure 5.47. Regression and co rrelation analysis of aph( ) versus ideal values using the NF filter. 140 Figure 5.48. Percent error and outlier analysis of aph( ) under the NF filter. 141 Figure 5.49. Regression and co rrelation analysis of aph( ) versus ideal values using the NB filter. 142 Figure 5.50. Percent error and outlier analysis of aph( ) under the NB filter. 143 Figure 5.51. Regression and co rrelation analysis of aph( ) versus ideal values using the NBLCLZ filter. 145 Figure 5.52. Percent error and outlier analysis of aph( ) under the NBLCLZ filter. 146 Figure 5.53. Regression and co rrelation analysis of aph( ) versus ideal values using the MODNB filter. 147 Figure 5.54. Percent error and outlier analysis of aph( ) under the MODNB filter. 148 Figure 5.55. Regression and co rrelation analysis of aph( ) versus ideal values using the BT filter. 150 Figure 5.56. Percent error and outlier analysis of aph( ) under the BT filter. 151 Figure 5.57. Regression and co rrelation analysis of aph( ) versus ideal values using the BTLCLZ filter. 152 Figure 5.58. Percent error and outlier analysis of aph( ) under the BTLCLZ filter. 153 PAGE 13 x Figure 5.59. Effective path length fo r the quantitative filter pad method as a function of the volume filtered and assuming a beta factor of 2. 155 Figure 5.61. Percent error correlations with environmental parameters under the NF filter for anw( ) inversion from Rrs( ). 161 Figure 5.62. Percent error correlations with environmental parameters under the NF filter for anw( ) inversion from Kd( ). 162 Figure 5.63. Percent error correlations with environmental parameters under the NF filter for anw( ) direct measurements. 163 Figure 5.64. Percent error correlations with environmental parameters under the NB filter for anw( ) inversion from Rrs( ). 164 Figure 5.65. Percent error correlations with environmental parameters under the NB filter for anw( ) inversion from Kd( ). 165 Figure 5.66. Percent error correlations with environmental parameters under the NB filter for anw( ) direct measurements. 166 Figure 5.67. Percent error correlations with environmental parameters under the NBLCLZ filter for anw( ) inversion from Rrs( ). 167 Figure 5.68. Percent error correlations with environmental parameters under the NBLCLZ filter for anw( ) inversion from Kd( ). 168 Figure 5.69. Percent error correlations with environmental parameters under the NBLCLZ filter for anw( ) direct measurements. 169 Figure 5.70. Percent error correlations with environmental parameters under the MODNB filter for anw( ) inversion from Rrs( ). 170 Figure 5.71. Percent error correlations with environmental parameters under the MODNB filter for anw( ) inversion from Kd( ). 171 Figure 5.72. Percent error correlations with environmental parameters under the MODNB filter for anw( ) direct measurements. 172 Figure 5.73. Percent error correlations with environmental parameters under the BT filter for anw( ) inversion from Rrs( ). 173 PAGE 14 xi Figure 5.74. Percent error correlations with environmental parameters under the BT filter for anw( ) inversion from Kd( ). 174 Figure 5.75. Percent error correlations with environmental parameters under the BT filter for anw( ) direct measurements. 175 Figure 5.76. Percent error correlations with environmental parameters under the BTLCLZ filter for anw( ) inversion from Rrs( ). 176 Figure 5.77. Percent error correlations with environmental parameters under the BTLCLZ filter for anw( ) inversion from Kd( ). 177 Figure 5.78. Percent error correlations with environmental parameters under the BTLCLZ filter for anw( ) direct measurements. 178 Figure 5.79. Percent error correlations with environmental parameters under the NF filter for bbp( ) inversion from Rrs( ). 180 Figure 5.80. Percent error correlations with environmental parameters under the NF filter for bbp( ) from HS6 and Kdopt. 181 Figure 5.81. Percent error correlations with environmental parameters under the NB filter for bbp( ) inversion from Rrs( ). 182 Figure 5.82. Percent error correlations with environmental parameters under the NB filter for bbp( ) from HS6 and Kdopt. 183 Figure 5.83. Percent error correlations with environmental parameters under the NBLCLZ filter for bbp( ) inversion from Rrs( ). 184 Figure 5.84. Percent error correlations with environmental parameters under the NBLCLZ filter for bbp( )from HS6 and Kdopt. 185 Figure 5.85. Percent error correlations with environmental parameters under the MODNB filter for bbp( ) inversion from Rrs( ). 186 Figure 5.86. Percent error correlations with environmental parameters under the MODNB filter for bbp( ) from HS6 and Kdopt. 187 Figure 5.87. Percent error correlations with environmental parameters under the BT filter for bbp( ) for QAA and HS6. 188 Figure 5.88. Percent error correlations with environmental parameters under the BTLCLZ filter for bbp( ) Rrsopt, QAA, and HS6. 189 PAGE 15 xii Figure 5.89. Percent error correlations with environmental parameters under the NF filter for ag(l) from AOP inversions. 192 Figure 5.90. Percent error correlations with environmental parameters under the NF filter for ag( ) from Specag. 193 Figure 5.91. Percent error correlations with environmental parameters under the NB filter for ag( ) from Specag. 193 Figure 5.92. Percent error correlations with environmental parameters under the NB filter for ag( ) from AOP inversions. 194 Figure 5.93. Percent error correlations with environmental parameters under the NBLCLZ filter for ag( ) from AOP inversions. 195 Figure 5.94. Percent error correlations with environmental parameters under the NBLCLZ filter for ag( ) from Specag. 196 Figure 5.95. Percent error correlations with environmental parameters under the MODNB filter for ag( ) from AOP inversions. 197 Figure 5.96. Percent error correlations with environmental parameters under the MODNB filter for ag( ) direct measurements. 198 Figure 5.97. Percent erro r correlations with envi ronmental parameters under the BT filter for ag( ) from AOP inversions. 199 Figure 5.98. Percent error correlations with environmental parameters under the BT filter for ag( ) direct measurements. 200 Figure 5.99. Percent error correlations with environmental parameters under the BTLCLZ filter for ag( ) from AOP inversions. 201 Figure 5.100. Percent error correlations with envi ronmental parameters under the BTLCLZ filter for ag( ) from Specag. 202 Figure 5.101. Percent error correlations with envi ronmental parameters under the NF filter for aph( ) from AOP inversions. 204 Figure 5.102. Percent error correlations with envi ronmental parameters under the NF filter for aph( ) filter pad method. 205 Figure 5.103. Percent error correlations with envi ronmental parameters under the NB filter for aph( ) filter pad method. 205 PAGE 16 xiii Figure 5.104. Percent error correlations with envi ronmental parameters under the NB filter for aph( ) from AOP inversions. 206 Figure 5.105. Percent error correlations with envi ronmental parameters under the NBLCLZ filter for aph( ) from AOP inversions. 207 Figure 5.106. Percent error correlations with envi ronmental parameters under the MODNB filter for aph( ) from AOP inversions. 208 Figure 5.107. Percent error correlations with envi ronmental parameters under the MODNB filter for aph( ) filter pad method. 209 Figure 5.108. Percent error correlations with envi ronmental parameters under the BT filter for aph( ) filter pad method. 209 Figure 5.109. Percent error correlations with envi ronmental parameters under the BT filter for aph( ) from AOP inversions. 210 Figure 5.110. Percent error correlations with envi ronmental parameters under the BTLCLZ filter for aph( ) from AOP inversions. 211 Figure 5.111. Percent error correlations with envi ronmental parameters under the BTLCLZ filter for aph( ) filter pad method. 212 Figure 7.1. Measured albedo values compared to albedo inversion results. 241 Figure 7.2. Comparison of ratio me thod to polynomial method using Hydrolight generated data. 243 Figure 7.3. Measured West Florida Shelf albedos and Hydrolight sand albedo normalized to their 550 nm values. 243 Figure 7.4. Albedo inversion result s and similar measured albedos: 1998 Bahamas stations. 245 Figure 7.5. Albedo inversion results and similar measured albedos: 19981999 Bahamas stations. 246 Figure 7.6. Albedo inversion result s and similar measured albedos: 11/99 to 07/00 West Florida Shelf stations. 247 Figure 7.7. Albedo inversion result s and similar measured albedos: 07/00 to 11/00 West Flor ida Shelf Stations. 248 PAGE 17 xiv Figure 7.8. Albedo inversion result s and similar measured albedos: 2001 West Florida Shelf Stations. 249 Figure 7.9. Absolute percent erro r for albedo at 440 nm using the Hydrolight genera ted data set. 251 Figure 7.10. Plot of absolute per cent difference from best match measured albedos versus albe do inversion results at 440 nm. 252 Figure 7.11. Cumulative percentage of matches that are 20% or less than the given optical depth at 440 nm. 252 Figure 7.12. Absolute percent error ve rsus optical depth as calculated using attenuation for Hydro light generated data set. 253 Figure 7.13. Rrs(440) and belowsurface Q f actor at 440 nm versus albedo values for middle quintile IOPs and 10 m bottom depth. 254 PAGE 18 xv Closure Between Apparent and Inheren t Optical Properties of the Ocean with Applications to the Determination of Spectral Bottom Reflectance James Edward Ivey ABSTRACT This study focuses on comparing six diffe rent marine optical models, field measurements, and laboratory measurements. Inherent Optical Properties (IOPs) of the water column depend only on the constituents within the water, not on the ambient light field. Apparent Optical Pr operties (AOPs) depend both on IOPs and the geometric underwater light field resulting from solar irradiance. Absorption (a) and scattering (b) are IOPs. Scattering can be pa rtitioned into backscattering (bb). Remote Sensing Reflectance (Rrs), the ratio of radiant li ght leaving the water to the light entering the water surface plane (Ed), is an AOP. Rrs is proportional to bb/(a + bb). Using this relationship, Rrs is inverted to determine both absorption and backscattering. The constituents contributing to both absorption and backscatte ring can then be further deconvolved using modeling techniques. The in situ instruments usually have a fixed path length while AOP measurement path length depends on the penetration and/or return of downwelling solar irradiance. As a consequence, AOP measurements use a longer path length than in situ instruments. If the path length of a direct IOP measurement instrument is too short, there may not be sufficient signal to determine a change in va lue. While the AOP inversions require more empirical assumptions to determine IOP values than in situ instruments, they provide a higher signal to noise rati o in clearer waters. This study defines closure as the statis tical agreement between instruments and methods in order to determine the same optical property. No method is considered absolute truth. An Rrs inversion algorithm was best under most of the test stations for measuring IOP values. One exception was wh en bottom reflectance was significant, an inversion of diffuse attenuation (the change in the natural log of Ed over depth) was better for determining absorption and a field instrument was better for determining backscattering. The relationships between AOPs and IOPs provide estimates of unmeasured optical properti es. A method was developed to determine the spectral reflectance of the bottom using IOP estimates and Rrs. PAGE 19 1 1. Introduction 1.1. Light, Water, and Life Light and liquid water are the basic requirements for life on a planet. Exobiologists recently discovered water on Mars (NASA 2008). The discovery was highly reported because it presents the potential for extraterrestrial lif e. Light and liquid water on Earth were part of the necessary conditions for the evolution of singlecelled photosynthetic organisms that led to an incr ease in atmospheric oxygen and to higher life forms. These single celled organisms evolved into the phytoplankton th at are the basis of the food web in oceanic environments. The ab sorption of solar radiation by the ocean provides a moderating force on global climat e by acting as a reservoir and transport mechanism for heat. Light reaching the bent hos supports algae, sea grasses and coral reefs that are nursery grounds for sea life. O cean optics can be used to study light, heat, and photosynthesis in the ocean, all of whic h are necessary for life on this planet. 1.1.1. Global Scales of Ocean Optics The absorption of downwelling solar irradi ance by the oceans is critical to global climate. Ninetyseven percent of the world' s water supply is in th e oceans. The oceans supply the majority of the water for rain on land (Libes 1992). Water has the second highest heat capacity of any liquid (4 j C1 g1 at 17.5 C) and the highest thermal conductivity. The thermal propert ies of the ocean result in heat being diffused over a large area through vertical and horizontal convection. Ocean currents transport heat from the equator to the poles warming temperate regions along its path. The thermal gradients within the ocean are more pronounced than on land. If the atmosphere were static and there were no oceans the mean temperature of the earth would be 67C (Philander 2004). Without the interaction between solar irradi ance and the ocean, life might not exist on Earth. While the physics of the ocean affects its biology, the biology can also affect the physics through feedback mechanisms that de termine the depth and quantity of solar irradiance absorbed by the ocean. Seasonal phy toplankton blooms can affect the depth of penetration of solar irradiance. The changes in depth of penetrati on of solar irradiance can affect the depth of the mixed layer, heat storage, ocean currents, and meteorology of a region. A 0.1 mg m3 change in chlorophyll concen tration results in a 10 W m2 change in solar flux through the upper 20 m of the equatorial Paci fic (Lewis et al. 1990). Upwelling can produce a phytoplankton bloom closer to the surface that results in greater heat absorption and increased stratification, re ducing the depth of the mixed layer (Sathyendranath et al. 1991). A westerly wind burst in the we stern equatorial pacific can PAGE 20 2 lead to upwelling which results in a phytoplan kton bloom that eventually increases sea surface temperatures. The increase in sea su rface temperature incr eases the atmospheric vertical convection resulting in a decline in the winds producing th e upwelling (Siegel et al. 1995). If the phytoplankton biomass is lowe r in the mixed layer, then some of the light can penetrate below it resulting in heat storage that may not interact with the atmosphere for up to 9 months (Ohlmann et al. 1996). If transported by slow moving current like the North Atla ntic Drift Current (0.03 m s1), this trapped thermal energy could travel 700 km before wint er overturn brings it into co ntact with the atmosphere. A 10 to 18% increase in 1% downwelling irradian ce depths can result in a mixed layer depth increase of 3 to 20 m (Sweeney et al. 2005). Studies based on coupled ocean and atmospheric general circulation models indica te that an increased mixed layer depth at higher latitudes results in lower heat transport back to the equatorial regions (Sweeney et al. 2005). In the ocean, a biological response to the physical events that bring nutrients into the euphotic zone can result in a change in wind, ocean currents, and heat transport. The ocean is an integral part of the global carbon cycle. It contains an estimated 50 times the amount of carbon found on land. Oceanic primary production represents about 50% of the total global primary produc tion (Field et al 1998). Photosynthetic organisms take up dissolved inorganic carbon an d are in turn consumed by higher trophic oceanic organisms. The progression of car bon through the oceanic food web results in losses to the system as organic carbon sinks out of the euphotic zone to depth. Some of the small fraction of the carbon reaches the be nthic regions, is incorporated into the sediments, and is sequestered geologically. The benthic oceanic sequestration of carbon is a significant mechanism controlling at mospheric carbon dioxide concentration over geological time. The carbon cycle of the ocean can be a ffected by anthropogenic increases in carbon dioxide in the atmosphere affecting the global climate. With changes in global climate, feedbacks occur that can affect oceanic primary production. The increases in global ocean surface temperatures may result in changes in ocean circulation, reducing the upwelling of nutrients resulting in lo wer primary production (Wood et al. 1992). A study based on Satellite observa tions concluded that global productivity has declined by 6% since 1980 (Gregg et al. 2003). Longterm satellite observations exhibit an inverse relationship between global ocean primar y productivity and sea surface temperature (Behrenfeld et al. 2006). Th e effects of climate change on ocean productivity are not settled in the scientific community. To predict the effects of climate change such as sea level height, environmental parameters are input into coupled general ci rculation models. The absorption of solar irradiance by the ocean is an important parame ter in determining the input of heat to the global ocean. The upper 700 m of the ocean ha ve increased in heat content by 16 3 x 1022 J from 1961 to 2003 (Catia et al. 2008). The increase in heat cont ent results in the thermal expansion of oceanic waters contributing to an estimated rise of 1.5 +/0.4 mm yr1 sea level rise (Catia et al 2008). To better determine the effects of sea level rise, knowledge of the global optical properties of the ocean are required. According to the PAGE 21 3 National Snow and Ice Data Center, the sea ice in the Arctic reached its lowest level of coverage in 2007 and second lowest in 2008. With the decline of the Ar ctic ice sheet, the albedo of the Arctic ocean decreases allowing more solar irradiance to be absorbed. The decline in Arctic sea ice perm its additional input of solar ir radiance to the ocean and will increase the heat content of the ocean. Observations on both global and basin scal es indicate that anthropogenic climate change is affecting the circula tion of the oceans. Infrared sate llite reflectance data can be used to track the paths of the currents and regions of upwelling providing information on the changes in ocean circulat ion (Vastano and Borders 1984). The increase in oceanic temperatures affecting wind patterns combined with fresh water runoff may have resulted in decreases in oceanic circulation. Global circulations models have predicted that freshwater inputs as the resu lt of increased precipitation and ice melt due to climate change could affect North Atlantic D eep Water formation (Rahmstorf 1994). Measurements of equatorial upwelling in the Pacific indicate that it may have slowed by 25% (McPhaden and Zhang 2002). Measuremen ts in the North Atlantic indicate meridional overturning slowed 30% between 1957 & 2004 (Bryden et al. 2005). There are indications of slowing in meridional ove rturn in the Pacific (McPhaden and Zhang 2002). Satellite measurements and estimates of in situ optical properties aid in the determination of climate change effect s on the global ocean circulation. 1.1.2. Local Scales of Optical Oceanography The interaction between solar irradi ance and the oceans can affect the environment on local scales. The sea breezes from the ocean in co astal regions act to moderate climate in those areas as air is a dvected across temperature gradients. The land has a higher temperature during the day resu lting in the wind moving onshore to replace the vertical convection over land. Since the heat capacity of th e land is much less than of water, the air cools more rapidly at night resulting in sinking air masses with winds moving offshore. In addition to moderati ng the atmospheric climate, the winds in conjunction with the tides can affect water tr ansport into bays a nd estuaries. Winds moving along shore can produce up welling increasing productivity in a near shore region. The optical properties of the coastal waters can affect the coastal climate even on local scales. Coastal regions make up only 7% of the US territory but contain half of the human population. About 40% of the world's population lives with 100 km of the ocean. Coastal regions are important both economically and environmentally but can be difficult to study due to higher variabili ty and larger gradients in environmental properties as compared to the open ocean. With increas ing populations alo ng the global coastal regions, anthropogenic pollution cont ributes to eutrophication. The natural process of riverine input bri ngs fresh water, sediment, and nutrients into the coastal oceans. The euphotic zone can extend to the be nthic region providing enough irradiance for primary production on the ocean floor. Upwelling along many PAGE 22 4 coastal regions provides nutrients for primary production resulting in productive fisheries. Estuarine regions provide nurseries for oceanic organisms. Coral reefs provide a productive benthic region in areas of low nutrient input. The environmental diversity along the coastal region contributes to the variab ility in the optical pr operties of the water column making its general characterization more difficult than for open ocean waters. Optical properties in oceanic regions are less complex to quantif y since they often covary with chlorophyll con centrations due to the phyt oplankton populations. Most coastal regions do not exhib it that covariance due to the dynamic nature of their environments, containing suspended sedime nts and humic and fulvic acids. Waters where optical properties covary with chlorophy ll are referred to as Case I waters while other types are labeled Case II (Morel 1974). Case I waters often have low attenuation, are far from the coast, and have no bottom contributions. Numeric models of optical properties for Case I waters are simpler in form ulation since the main factor that has to be considered is absorption of light by phytoplan kton, which is correlated with chlorophyll concentrations. In Case II wa ters, the light leaving the wate r can be modified by several factors other than phytoplankton absorption. Dissolved organic compounds from riverine sources can absorb shortwavelength light. Light can be scattered and absorbed by suspended minerals. The bottom can absorb and reflect light th at would otherwise propagate deeper. Despite the challenges, characterization of the optical properties of the coastal Case II regions is necessary to pr oduce accurate numerical simulations of the effects of water column constituents on h eat budgets (Warrior and Carder 2007) and primary production. Coastal regions exhibit great er primary production relativ e to their area due to higher nutrient input and recyc ling. If the coastal region is characterized as out to the 200 m isobath then they represent about 10% of the primary production with 8% of the surface area of the ocean (Smith and Hollibaugh 1993). If the entire continental shelf is defined as the coastal region, then the prim ary production is 24.9% of the global ocean with only 16.1% of the area (Walsh 1991). About 30 to 40% of the benthic regions of the coastal zone have a net positive community production (Gattuso et al. 2006). The coastal regions, while constituting a small portion of the global ocean, are important to the global carbon cycle. 1.1.3. Application of Optical Ocea nography to Coastal Problems Seagrass meadows are some of the most productive of coastal environments. One acre of seagrass can produce te n tons of leaves supporting fo rty thousand fish and fifty million invertebrates (Dawes 2004). Seagrass acreage in Florida has declined by about 60% from 1950 as Florida's population has in creased six fold (Dawes 2004). Dredging and eutrophication led to incr eased water turbidity reducing the available light for sea grasses (Zieman and Zieman 1989). The ar ea covered by seagrass around Florida has been semiquantitatively estimated by aerial photography in the past. Recent advances in airborne spectral imaging systems have result ed in a more quantitative measurement of PAGE 23 5 seagrass coverage (Dierson et al. 2003). The importance of seagrass to the coastal ecosystem requires accurate assessments of their health a nd coverage. Changes in the optical properties of the ocean waters over cora l reefs are one of the many factors contributing to their decline. The existence of coral reefs depends on solar energy reaching the benthic substrate. Scleractinian corals generally require a suitable substrate in warm, clear, shallow waters. Several of the causes for the decline in coral reefs are ocean warming, ozone deplet ion, nutrification, over fishing, invasive species, light limitation, disease, recreational divers, and commercial harvesting (Hallock et al. 1993, Yentsch et al. 2002, Bellwood et al. 2004, Hallock 2005, Bartow et al. 2005). The optical effects are too much heat, too mu ch ultraviolet to blue light, or not enough irradiance. Optical monitori ng of reef regions, either in situ or remotely, can aid in determination of changes in the environment th at might lead to a decline in coral reef health. The ultimate goal for the remote sensing of a coral reef is to go beyond identifying bottom types and identify the major species on the reef. The first order of the problem is to remove the effects of absorption and scattering of the water column (Holden and LeDrew 2001). While correction for absorption is possible if the optical properties are known or can be id entified, the scattering of light poses a larger problem. Scattering can mix the upwelling irradiance from adjacent bottoms with different signatures. This is further complicated by a bottom where the reflectance is not uniform from all angles and the depth is variable ove r scales of less than a meter (Mobley et al. 2003, Mobley and Sundman 2003). Most curren t methods have focused on coral cover and algal species. The change in total cora l cover can be identified through remote sensing through the use of in struments like the Landsat thematic mapper that have a smaller pixel size (Andrfout et al. 2001, Paland ro et al. 2008). Identification of certain reef algal species is possible with hyperspectral imagery. A lookup table of combinations of bottom types, depths, and optical prope rties can estimate bathymetry and bottom classification on coral reefs (Lesser and Mobely 2007). The goal of identifying major coral species via satellite will possibly have to wait until a satellite with appropriate wavelengths and spatial resolu tion is launched. The current satellites with narrow band filters over estimate coral coverage while th e satellites with broad bandwidth filters underestimate algal coverage while also ove restimating coral coverage (Hochberg and Atkinson 2003). The launch of a hyperspectral imagery satellite that is capable of small pixel sizes could possibly lead to at least identification of the major types of coral species on a reef. Remote sensing techniques have shown so me promise especially when combined with other in situ techniques for identifying and tr acking harmful algal blooms. Harmful algal blooms were observed to have a low chlorophyll specific backscattering value (Carder and Steward 1985). Further research with in situ optical instruments revealed that there was a relationship between the chlorophyll specific backscattering and the presence of Karenia brevis (Cannizzaro et al. 2008). Th e low backscattering of the bloom relative to chlorophyll is due to the bloom's origins in optically clear offshore PAGE 24 6 waters (Walsh et al. 2006, Cannizzaro et al. 2008). The lower backscattering allows the blooms to be better identified in using sate llite reflectance measurements (Cannizzaro et al. 2008). The precursor to the red tide is Trichodesmium (Walsh and Stiedinger 2001) and it can be identified from satellite due to it's high backscattering (Subramanian et al. 1999). The iron rich dust that contributes to a Trichodesmium bloom can be detected using satellite imagery (Carder et al. 1991, Lene s et al. 2001). Using satellite imagery, it is now possible to estimate the c onditions that might lead to a K. brevis bloom and track the bloom once it occurs. 1.2. The Path of Light Through Water Optical oceanography is simple in basic th eory but complex in practice. In its simplest case, light passing through pure water is either absorbed (a ) or scattered (b) by the water molecules. The sum of the absorption and scattering equals the total attenuation of light along a pe rfectly straight path from the source (c). This sounds simple enough but two different cases of li ght passing through wa ter illustrate how complex it really is. The tr avel of light through a beam trassmissometer can serve to illustrate the path of light under controlled conditions. The travel of sunlight from above the surface of a water column to the bottom and returning can serve to illustrate the path of light in a natural environmen t. These two cases demonstrat e some of the difficulties of measuring the optical properties of a water column and how the path length of light affects these measurements. 1.2.1. Light Through a Beam Transmissometer A beam transmissometer measures the at tenuation (c) by projecting a collimated beam of light over a known di stance through the seawater to a detector that only accepts light at a narrow angle (P ettersson 1934, Jerlov 1957, Aus tin and Petzold 1977). The basic design for this instrument (Figure 1.1) involves a light source (a) that passes through an aperture and lens system (b) that collimates the beam. The light source is either an LED that covers a sp ecific wavelength or it has an optic al filter that limits it to a specific wavelength. A beam splitter (c) directs part of the light into a detector (d) to determine the power of the s ource light. The light exits into the water column (e) where two things can happen, it is either scattered out of the direct path (f) or absorbed (g). The reduced light (h) enters through a window (e) on the other side of the instrument. The light passes through another apertu re (i) and enters a detector (j). This second aperture limits the angle of light to only the light traveling straight alo ng the path from the source. Most transmissometers accept light that is approximately 1 from the straight path because the construction of an in strument that can detect light at the low level of a photon traveling directly from the source and the ali gnment of the optics to accept such a narrow beam would be extremely difficult. PAGE 25 7 a b d c ee h f g i j Figure 1.1. The simple path of light through an attenuation meter. The pale red color represents the light. The stepped shape repres ents absorption. The dashed lines represent scattering. The attenuation value from a beam tran smissometer is calc ulated (Equation 1.1) by taking the natural log of the fractional change from the reference detector ( 0) to the measurement detector ( ) and dividing it by the distance between the two windows (zz0). The light level declines logarithmically with increases in path length according to Beer's law (Kirk 1994, Mobley 1994). Using th is coefficient the change in light over a known distance of seawater for a collimat ed beam of light can be calculated. 0 0ln z z c Equation 1.1 Beam transmission is one of the simplest measurements made by optical oceanographers, but it is not a simple task to construct beam transmissometers. They require very precise alignment of the optical path. They require precise regulation of the light source, and precise measurement of the light. The path length of the instrument limits the sensitivity of the measurement. For very turbid waters, a longer path might attenuate light below the level of the detect or. For a shorter path, there might not be sufficient change in signal to register in th e detector. The compromise path length for most oceanographic measurements is usually 25 cm. 1.2.2. Sunlight Entering the Ocean The more complex consideration is looki ng at light entering the water column itself and the different directi ons and paths it travels (Fig ure 1.2). Assuming no clouds in the sky, direct sunlight enters the water (thi ck solid lines) along w ith skylight (dotted lines). The direct sunlight en ters the water at an angle relative to the solar zenith and azimuth angles. Skylight is sunlight scatte red by the atmosphere and can enter the water at many different angles. As the light enters the water the path of its angle is changed PAGE 26 8 following Snell's law due to the difference in index of refraction between the air and water (Kirk 1994, Mobley 1994). As in the beam transmissometer, two things can happen to the light below the water's surface. Light is either absorbed (a, arrow ends) or scattered (c, dashed arrow). The path actual sunlight takes in the ocean is infinitely complicated. Figure 1.2. The complex path of sunlight th rough ocean waters. The thicker solid lines above the water represent direct sunlight and the dotted lines represent diffuse sunlight. The thin solid line represents the path of li ght below the water before scattering and the dashed lines represent the path after scattering. Arrows that end represent absorption in water column. The letters a through d represent possible path s of the light and are detailed in the text. The letter e labels a downwelling irradi ance meter. This case is simplified and several optical paths including surface interactions are not listed but will be discussed in chapter 2. Downwelling irradiance from above the su rface (a) can take several paths before reaching a detector below the surface. The lig ht can either be absorbed (b) or scattered (c). Light that is scattered back towards th e surface can either leav e the water column or be reflected back down towards the bottom (d ). The irradiance detector (e) has a cylindrical collector on the top that will collect light from different scattering angles in the downward direction. The scattered light doe s not take a straight path to the detector so it travels further than the simple geomet ric change in depth. A photon can scatter multiple times resulting in a further lengthening of its path. Like the calculation of the attenuation coefficient (see section 1.2.1), the calculation of the diffuse attenuation e d c a b PAGE 27 9 coefficient of downwelling irradiance (Kd) is the natural log of the fractional change in light between two depths divided by the distance between the two depths. The Kd value is proportional to the absorption and backscattering (bb) of light over the depth measured. This indirect measurement of absorption a nd scattering is an apparent property of the water instead of an inherent propert y such as attenuation measured by a beam transmissometer. The disadvantage of these appa rent optical properties (AOP) is that they depend on the sun for a light source and all th e natural variability associated with the transfer of solar radiation acro ss the air water interface. The main advantages are that the path taken by the solar radiation is much greater than the path of an artificial light source used by the devices that measure inherent op tical properties (IOP). This longer path length means these measurements have a much greater sensitivity to changes in the absorption values than the instruments that m easure those properties directly. The other advantage is that the direct measuring instru ments, like the attenuation meter, have to use separate detectors for measurement and refere nce while the AOP values are the result of ratios that divide out multiplicative errors. While inverting inherent values from apparent optical properties requires more assumptions to compensate for changes in the geometric light field, it has some advant ages in longer path length a nd lower instrument related errors. 1.2.3. Effective Optical Path Length A beam of light only takes a perfectly st raight path in a va cuum. When passing through air, light is scattered in different directions. Atmo spheric scattering is why the sky has a color instead of appearing black. Th e result is that it gives light more chances to be modified by the medium it is traveli ng through. If the medium absorbs light then there is greater chan ce of a photon of light striking a molecule being absorbed over a longer path between two points. Path length is also crucial to the sensitivity of the measurement method. For an absorption determin ation, the path length can vary from a 1 cm cuvette in a spectrophotometer to 10's of meters using an irradiance meter to measure Kd. If the signal loss from the measurement is low, then a longer path length can increase the loss to a determinable level. The path length the light travels in seawater, whether based on a controlled light source or th e sun, affects all optical oceanographic measurements. The effect of path length will depend on the sensitivity and resolution of the instrumentation making the measurement. Th e resolution is affected by the range of analog output and the number of bits used in analogtodigital conversion. Older instruments had outputs in eightbit resolution (0 to 255) values, wh ile newer instruments have analog to digital conversi ons (ADC) of twelve bits (0 to 4095) or higher. This means that for an instrument with an output of 0 to 5 volts will have 16 times the resolution at 12 bit as compared to 8 bit. An 8 bit ADC is comparable to a yard stick with only inch marking. A 12 bit ADC adds the sixteenths of an inch markings. Because of the lower sensitivity of older instrument s sufficient, path length for the signal was more important. PAGE 28 10 Figure 1.3. Response of instruments to different optical path lengths. Graph A is for a 12bit instrument and graph B is for an 8bit in strument. It is assumed in the example that the instruments are accurate to these resoluti ons and do not adjust gain settings. The value is the change in counts over the path length of the meas urement, not the output of the photocell. Using both the 8bit and 12bit ADC scales the effect of path length for an absorption measurement can be demonstrated. The absorption coefficient is calculated the same as the attenuation coefficient in Equation 1.1. Figure 1.3 shows the change in Path length (m) 0.010.10.251102550100 Change in Counts (8 bit) 0 50 100 150 200 250 300 0.002 m 1 0.01 m 1 0.22 m 1 0.5 m 1 1.0 m 1 No Signal Absorption Path length (m) 0.010.10.251102550100 Change in Counts (12 bit) 0 1000 2000 3000 4000 5000 0.002 m 1 0.01 m 1 0.22 m 1 0.5 m 1 1.0 m 1 No Signal Absorption A. B. PAGE 29 11 value for 12bit and 8bit analog to digital c onverters. The lower the resolution of the sensors due to it's ADC, detector, or other electronics, the more critical the path length of the sensor becomes. A 1cm cell is useless at a low absorption of 0.01 m1 even for a 12bit ADC. A 10cm cell doesn't function much better, having only a 4count difference over that path length for a 0.01 m1 absorption value. The 25 cm cell is better, with 10 counts of difference out of 4095, when using a 12bit converter. This is the reason that modern instruments like the ac9 (a reflectiv e tube absorption meter detailed in Chapter 3) use a 24bit ADC along with very stable electronics and sensitive detectors to compensate for their shorter path length. At the other end of the scale, a 50 m pa th length can result in a maximum signal loss for waters with absorption coefficients greater than 0.01 m1 but has no measurable signal at 0.22 m1. There is a trade off for instruments with longer path lengths. A shorter path length has a greater range of measurem ent while a longer path length has greater sensitivity. In Figure 1.3A, the onemeter pa th length can measure within an absorption coefficient range of 0.002 to 1 m1 but the 10meter path has no measurable signal at 1 m1. Beer's law predicts this relationship. Path lengths longer than a meter typically use the sun as a light source and the light is measured using irradiance meters or radiometers. Measurements such as diffuse attenuation have a variable pa th length that decreases as the water column attenuation increases. Looking back at Figure 1.2, th e maximum sensorseparation depth for the irradiance meter will be less for higherattenua tion waters. Most irradiance meters and radiometers also have the capability to adju st their integration time based on the light intensity, resulting in low incidences of sa turation and higher sensitivity at depth. Therefore, an irradiance meter or radiometer with comparable electronics to a reflective tube absorption meter (Chapter 3) will have a greater sensitivity to changes in absorption in very clear waters like t hose of the Bahamas but still be able to detect changes in absorption values in turbid coastal wa ters such as those of the Puget Sound. 1.3. Main Focus of Study The main regions in this study are highly variable in optical properties. They range from the very turbid Puget Sound to the crystal clear wate rs over the Bahamas coral reefs. The type of instrument that is suited to measure the op tical properties of the seawater over a sea grass bed on the West Florida shelf may not be best for an absorption profile in a harmful algal bl oom. The selection of the instrument will depend on the expected range and types of op tical values that will give th e best information about the study location. A primary goal of this study will involve assessing the best method or model to determine an optical property under the highly variable environments of these study sites. With advancements in sensor technology and algorithm development, can an apparent optical property meas urement substitute for a more direct measurement of a particular optical property? While AOP measurements like Kd have a greater sensitivity PAGE 30 12 in response to changes in the inherent optic al properties, they al so require a greater number of assumptions to determine the optical path length and to separate the effects of the different inherent optical properties. Early modeling efforts were limited by lack of knowledge about the factors affecting the unde rwater light field, limited computational capabilities, and instruments th at only measured at a few wave lengths of light. Advances in the past three decades have minimized th ese sources of error resulting in greater accuracy in apparent optical property model inversions. Under the right conditions, an inversion of an apparent property may be an even better measurement than some of the more direct techniques (e.g., path limitations). Closure in optical oceanography usually means statistical agreement between a new model or measurement and a more tr usted measurement (Truper and Yentsch 1967, Ivey 1997, Maffione and Dana 1997, Kirk 1981, and IOCCG 2006). Usually studies are trying to prove some model or method by comp aring it to another approach that gives a similar result. The confusion with this is that the researcher often makes an assumption that one particular method is more accurate th an another for a particular environment. For different environments, that is not always the case. In low attenuation waters, an inversion of an apparent optical property may be more accurate than a profile by an instrument that measures inherent optical pr operties due to the longe r optical path of the AOP measurement. The best way to address th is is to have as a first assumption that all methods can potentially be accurate under the right conditions. First, the methods are compared to determine what condition has the greatest effect on the results. By limiting each group of data based on environmenta l conditions, each method can then be compared to determine where they exhibit the best agreement with the other methods with no bias towards one particular method. This approach aids in determining which method performs best under which environmental condition. By studying relationships betw een apparent and inherent optical properties under conditions where the two methods agree, additional optical pr operties can be determined. The color of the bottom is one of these pr operties that would have many environmental uses like determining sea grass coverage or co ral reef health. The color of the bottom is based on the amount of light at the visible wa velengths reflected from the bottom towards the direction of the observer. The overall di ffuse reflectance from an object, such as the benthic substrate, is referred to as albedo. A goal of this research is utilize the mathematical relationships between the differe nt optical properties to estimate the albedo of the bottom in shallo w marine environments. 1.4. Hypotheses Closure among all methods is expected when conditions are favorable to all methods. The ideal conditions expected for the AOP measurements are clear skies with low solar zenith angle and no significant botto m reflectance. The main criteria for the in situ IOP instruments are signifi cant signal noise in the IOP measured and proper function of the instrument. The laboratory measurem ents based on water samples require that the PAGE 31 13 depth of the sample be representative of most of the water column. Closure is expected under the conditions where the best c onditions for each method intersect. In comparison of the different AOP inve rsion algorithms, the more analytical models based on the AOP measur ement with the longest path length are expected to be the best in determining the IOP values. Th e trade off between analytical and empirical approaches is that the more analytical methods typically have greater computer requirements and need more a priori knowledge of the study area. The more analytical models are expected to be be st but do require some tradeoffs in computer power and a priori knowledge of the study site. The combination of longer path length a nd more analytical approach gives AOP inversions models sufficient accuracy to be used in place of more direct in situ IOP measurements. Previous closure studies have started with the assumption that the direct measurement is the more accurate. This study will compare all AOP algorithms and IOP direct measurements with equal weighti ng to determine under what environmental conditions each method is most accurate. Fo r oceanic waters with low attenuation, low solar zenith angle, low cloudiness, and no significant bottom influence, the AOP inversions are expected to provide mo re accurate results for absorption and backscattering when compared to direct IOP measurements. Preisendorfer (1961) presented an equati on that details relationships between absorption and backscattered light to Kd. This approach can be used in an iterative type model to invert Kd at multiple wavelengths of light to give IOP values. Applying corrections for the angle of the sun and sky light (Gordon 1989) will lo wer the error in the inversion. This model should provide the better results over the other tested Kd inversions models in this study sinc e it uses a semianalytical approach. Most inversion algorithms of ocean co lor do not take into account the solar induced fluorescence due to chromophoric di ssolved organic material (CDOM). This fluorescence can result in errors by estimati ng the amount of light leaving the water larger than it should be in the blue to green wavelengths of light. This error can lead to over estimates and under estimates of differe nt optical properties. By assuming a function that initially underestimates the abso rption of light by CDOM in the blue to green light region, the error in retrievi ng optical properties from ocean color measurements can be reduced. The bottom albedo can be determined th rough the mathematical relationships between the apparent optical properties a nd the inherent optical properties. By determining how these propertie s are related through closure, the spectral reflected light from the bottom can be determined. This method would use common measurements from standard ocean optics instruments instead of complex specialized instruments. This method will not require an initial estimate of th e bottom type or a best guess as to how its magnitude varies spectrally. PAGE 32 14 2. Background 2.1. Introduction The first section is primarily for the reader with little backgro und in ocean optics. It will present a brief discussion of co mmon optical oceanography terms and theory. A more detailed discussion of ocean optic s can be found in the texts Ocean Optics (Spinrad, Carder, and Perry (Ed.) 1994), Light and Photosynthesis in Aquatic Ecosystems (Kirk, 1994), and Light and Water: Radiat ive Transfer in Natural Waters (Mobley, 1994). A short summary of the evolution of optical oceanography methods and instrumentation is presented to demonstrate the advances that have made the research in this paper possible. A discussion on closure of optical properties provides an overview of past efforts and why the approach of this research is unique One of the importan t results of optical closure is the ability to indirectly determ ine optical properties by combining different types of optical measurements. The measuremen ts taken in the shallow sites of this study are used to determine the spectral bottom reflectance, using an evaluation of the closure levels achieved among different measurement approaches. The study sites and optical variability among th em are presented 2.2 Definitions of Optical Terms Closure in the field of optical oceanogr aphy has typically involved comparing a direct measurement of an inherent optical pr operty to results from a model that inverts an apparent optical property to pr ovide an inherent optical pr operty. An inherent optical property (IOP) is one that is based solely on the constituents within the water column so it is independent of the solar irradiance (P reisendorfer 1961). An apparent optical property (AOP) is dependent on al l the inherent optical proper ties and the characteristics of the geometric light field due to solar irradiance. Cl osure between more directly measured IOP values from in situ instruments or water sample s and the results of an AOP inversion algorithm is usually don e with the directly measured IOP values considered the measurement closest to the actual value. This assumption will be tested. The IOPs used in this study are scattering (b( )), absorption (a( )), and attenuation (c( )) coefficients. Absorption is light at a given wavelength ( ) taken in by matter, raising it to a higher energy state. Sc attering is light at a given wavelength where its path is altered by particles or molecule s. The sum of absorption and scattering is attenuation (c( )). Each of these coefficients is a f unction of the logarithmic loss in light over a linear path from the source, giving them the units of per meter (m1). All three of these IOPs represent the light lost along a si ngle straight path. Th ese properties can be separated into categories depending on the type of material interacting with the light: PAGE 33 15 absorption by particulate matter ap( ); by dissolved organic matter ag( ); and by water itself aw( ). The particulate absorption is furthe r split into absorption due to pigmented particles like phytoplankton (aph( )) and absorption due to non living matter referred to as detritus (ad( )). Table 2.1 provides a list of the symbol s used in discussions of light in the ocean that are defined in this chapter. Table 2.1. Common symbols used in optical oceanography and this study. Symbols that are used in only one section are defined in that section. Symbol Quantity Units a Absorption m1 b Scattering m1 c Attenuation m1 Wavelength nm K Diffuse attenuation coefficient m1 Rrs Remote sensing reflectance sr1 R Radiance reflectance Unitless L Radiance W m2 sr1 E Plane irradiance W m2 Average cosine of irradiance Unitless Table 2.2. Common subscripts for symbols used in optical oceanography and this study. These symbols can be used in different combinations. For example, Ed0+ is the planar downwelling irradiance just below the surface. Subscript Meaning Example d Downwelling Ed, d u Upwelling Eu, u b Backwards direction bb f Forwards direction bf p Particulate ap, bbp ph Pigmented aph g Chromophoric dissolved organic matter ag (gelbstoff) w Water Lw nw No water values included anw, cnw o Scalar values Eo 0+ Just above the surface Ed0+ 0Just below the surface Ed0 PAGE 34 16 The use of symbols to repr esent terms in science se rves as a shorthand among researchers to avoid overly verbos e exchanges. For example, Ed0( ) represents the downwelling irradiance just below the surface at all wavelengths of light. If the author of a research paper had to repeat the text descri ption of that symbol every time they referred to it, it would substantially in crease the length of their paper. Early pioneers in optical oceanography often used symbols that were first used by astronomers and theoretical physicists (Austin 1974, Jerlov 1976, Prei sendorfer 1976). However, there was significant ambiguity in the symbols for the di fferent values. Mobley (1994) published a text that suggested a series of common sy mbols for optical oceanography. Morel and Smith first developed most of these (M orel and Smith 1982). These symbols have becomes the most common in optical oceanogr aphy and are used in databases for these values. Table 2.1 lists the commonly used sy mbols used throughout this study and Table 2.2 lists the commonly used subscripts. R eaders unfamiliar with these terms should bookmark the preceding page as a reference to aid in later discussions in the text. Scattering is a more complex measuremen t than absorption because the flux of light scattered by the particle is not the same in all directi ons. The direction is measured as a solid angle that is based on a unit sphere just as a radian is based on a unit circle. Instead of a circumference of 2 radians times the circle ra dius, the unit sphere has a surface area of 4 steradians (sr) times the spherical radius. Similar to latitude and longitude for coordinates on the Earth, th e solid angle has two angles: theta ( ) represents the zenith angle and phi ( ) represents the azimuth angle. The change in solid angle ( ) about a direction ( ) is given as d ( ) = sin d d Equation 2.1 This represents the incremental area element sin d d on a sphere of radius = 1.0. Scattering through a given solid angle ( ) is referred to as the volume scattering coefficient ( ( )) and has the units per meter per steradian. The volume scattering function is very difficult to measure, especially in situ, so most research focuses on measurements of either total scattering integr ated over the entire unit sphere or scattering integrated over the hemisphere of the unit circle with the source at 2 (backscattering, bb( )). Integrating over the hemisphere centered at the direction of the light path (0 sr) is forward scattering (bf( )). An additional subscript is also added to the scattering terms to denote the scattering due to particulates (bp( ), bbp( )) and water (bw( ), bbw( )). The scattering by dissolved substances is consid ered not significantly different from the scattering to water so it is not referenced separately. The absorption (Pope and Fry 1997) and scattering (Morel 1974) coefficients due to water are well known, and removing them from the attenuation (cnw( )) and absorption (anw( )) values, provides a better comparison to the other methods. The partitioning of th ese values represents the IOPs that are directly measured or inverted from AOP algorithms (Mobley 1994). The light energy measured at a particular point over a specific time at a given solid angle, wavelength, and area is the radiance (L). Radiance can be used to derive all PAGE 35 17 radiometric measurements. A single radian ce measurement below the surface is not an optical property of the water column. By its elf, it tells us nothi ng about the underwater light field but only provides us information a bout light at a particul ar point from a given direction. When multiple measurements of ra diance are integrated over a sphere (scalar irradiance, E0, Eq. 2.2) or downward over a flat pl anar surface (pla nar irradiance, Ed, Eq. 3), then we can learn more a bout the underwater light field. It still only represents a point measurement and not the entire water column. A single radiometric measurement still doesn't qualify as an optical property of the water column (Mobley 1994) though some opinions differ regarding irra diance in a particular di rection (Zaneveld 1994). The scalar irradiance at a particular position (x ), a particular time (t) and wavelength of light ( ) is defined by the integration of radiance at x t, and direction ( ) over the unit sphere ( ) for the change in solid angle ( ). The units are watts (W) per square meter (m2). d t x L t x Eo; ; ; ; ; Equation 2.2 Downwelling irradiance is calculated by integrating radiance at a given x t, and for direction over the complete azimuth angle and co sine of the upper hemisphere from the zenith angle. The units are watts (W) per square meter (m2). d d t x L t x Edsin cos ; ; ; ; ;2 0 2 Equation 2.3 Determining scalar or planar irradi ance by integrating individual radiance measurements would be a difficult task. Fo rtunately, the design of the instrument collector can result in an integration of the radiance for scalar or planar irradiance. A spherical collector with a shield blocking light from other directions can measure downwelling scalar irradiance (Eod). A disk shaped cosine collector can measure planar downwelling irradiance (Ed). To get the upwelling light returning from depth the instrument can be flipped over or a second instrument used (Eou and Eu). With multiple measurements at different de pths and wavelengths of radi ance and irradiance now it is possible begin to learn something about the water column. Combining measurements, such as change in Ed over depth or the ratio of water leaving radiance (Lw) to the solar irradiance entering the water (Edo+), results in measurements that are related to the inherent optical properti es of the water column, since the light units have been normalized. These measurements are then referred to as apparent optical properties or AOPs. The logarithmic change of downwelling planar irradiance over depth is the diffuse attenuation coefficient (Kd). The ratio of Lw to Edo+ is referred to as remote sensing reflectance (Rrs). These two measurements are commonly made by optical oceanographers, and algorith ms relating them to inherent optical properties are explored in this research study. PAGE 36 18 Rrs measured just above the ocean surface is particularly useful because it is similar to the ocean color measurement ma de by orbiting satellites without having to correct for the attenuation and backscattering of the light passing through the atmosphere. In addition, using the same radiometer for measuring both Lw and Edo+ ratios out most calibration errors. This measurement is pr oportional to a ratio of the backscattering divided by the sum of backscattering and abso rption for the water co lumn (Gordon et al. 1975, Morel and Prieur 1977). Radiometers th at measure at several wavelengths (hyperspectral) combined with advances in the understanding of ocean optics have resulted in model inversion al gorithms that are much more analytical and accurate for inversion of Rrs( ). The diffuse attenuation coeffici ent of downwelling irradiance (Kd( )) is proportional to the inherent optical properties. The value of Kd( ) can be expressed in terms of the inherent optical prop erties (Eq. 4, Preisendorfer 1961). ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( R b b a Ku b d b d d Equation 2.4 The terms d and u both represent the average cosine of the angles of the light in the downward and upward directi ons. The average cosine is the average of the cosine of the zenith angle at a particular point in th e water column. The arccosine of the average cosine is the average angle of the path of th e different beams of ra diance along the up and down directions in the water column. For ex ample, a solar beam penetrating the ocean surface with a zero zenith angle has an aver age cosine of 1.0. After being absorbed and scattered down to 100 meters in the Sargasso Sea, it has a downwelling average cosine of less than 0.75. In other words, the slant pa th through the water of the average downwelling photon now is ~40 degrees ra ther than 0 degrees. Finally, R( ) is belowwater irradiance reflectance which is a ratio of Eu( ) to Ed( ) Using this relationship, it is possible to retrieve IOPs from Kd( ) values (Preisendorfer 1961). 2.3. Progress in Ocean Optics The theoretical relationshi ps behind optical oceanogra phy were discovered first but had to wait for progress in instrument ation to verify them. Early optical measurements of attenuation were Secchi De pths (Hou et al. 2007). They were very crude methods of getting the vertical attenu ation coefficient with simple equipment by visually observing the disappearan ce of a white disk as it was lowered to depth. This data could then be related to the depth of li ght penetration below the surface of the ocean and the diffuse attenuation coefficient. As technology advanced, submersible single wavelength radiometers became available (Poole and Atkins 1926). By adding filters to these radiometers to balance the response, it was possible to measur e the quanta of light available for photosynthesis (PAR) at depth by balancing out the spectral response of the detector. Specific narrow band pass filters on individual photocells made it possible to determine the downwelling irradiance at several wavelengths. Submersible grating PAGE 37 19 spectrometers were developed that allowed m easurement of the irra diance at hundreds of wavelengths (Tyler and Smith 1966, Morel and Priuer 1977, Carder and Steward 1985). The inversion from theory a pplied to AOP measurements leads to estimates of the inherent optical properties aff ecting the underwater light field. Ocean color detection advanced from a qualitative measurement to the quantitative approach used t oday. Originally color was dete rmined by visually comparing a series of vials of mixtures of different co lored chemicals to determine the color of the ocean. This method was called the Fore lUle scale and was introduced around 1892 (Wernand 2008). The observation was best when compared to the color observed during the decent of a white Secchi disk. Later methods included photographing the water to estimate the color. Like the spectral i rradiance meters, radian ce both below and above water was later measured by spectral techniqu es. The first sensors like the underwater irradiance sensors, were limited to speci fic wavelengths. Late r radiance sensors incorporated small grating spectrometers that allowed a handheld de vice to measure the radiance leaving the water at hundreds of wavelengths of light. To minimize the instrument error, downwelling irradiance wa s measured by aiming the same radiance meter at an isotropic reflecting target illumi nated by sunlight (Carder et al. 1985). Ocean color detection evolved from simple visual estimates to hyperspectral sensors capable of quantitative measurement. Some of the greatest interest in ocean optics occurred when satellites capable of measuring upwelling radiance were launched. The first instrument on a satellite specifically dedicated to dete ction of ocean color was the Coastal Zone Color Scanner (CZCS). The CZCS for the first time allowe d synoptic data about the ocean to be collected over a large region (Gordon et al 1983). Oceanography went from discrete shipboard measurements that only covered a po int in the ocean to ai r borne sensors that were able measure 10's of square miles to satellites that could cover 1000s of square miles. The success of the CZCS led to the development of the Seaviewing Wide Fieldofview Sensor (SeaWiFS) in 1997 (O'Reilly et al. 1998). The CZCS was a proof of concept instrument that had only six wavele ngth bands (channels). SeaWiFS added three additional channels providing more spectra l information. SeaWiFS was the default operational satellite until the 36channel Moderate Re solution Imaging Spectroradiometer (MODIS) was launched in 1999 (Esa ias et al. 1998). The measurement of ocean color by spectral satellite measurements revolutionized the study of oceanography by providing largearea coverage of th e ocean at single points in time. The early algorithms relied on empirical band ratios to estim ate chlorophyll in open ocean waters (Gordon et al. 1980). A benef it from this approach is that it allowed rapid processing using th e slower computers of the time. This led to some of the first closure experiments between in situ chlorophyll concentrations and Rrs( ) inversions to retrieve chlorophyll values (G ordon et al. 1983). The SeaWi FS satellite had three more spectral channels than the CZCS, and the algo rithms were further improved to provide a larger number of water optical properties and we re more analytical (Gordon et al. 1988). This led to more analytical models that m oved away from simply estimating chlorophyll PAGE 38 20 concentration and instead focused on determin ing the IOPs that could be related to constituents in the water column. With th e MODIS sensor and its 36 total channels, the algorithm development turned to the more comp lex models that are in use today (Carder et al. 1999). The progression naturally followed the progression of the satellite capabilities and computational power that is currently available. The relationship between the AOP reflectan ce and the IOP values of ocean water was established well before satellites we re considered (Duntley 1942), leading to algorithms that rapidly progressed to their pr esent semianalytical incarnations. Before CZCS went up, a simplification was determin ed so that irradiance reflectance was directly proportional to the backscattering divided by the ab sorption (Gordon et al. 1975; Morel and Prieur 1977) and it used a consta nt based on the geometric underwater light field. This constant is a function of the volumescattering coefficient and the radiance distribution as well as the wave length of light. For the blueg reen portion of the spectrum, however, the spectral variation of the proportionality coefficien t is low. The constant can be separated into a value that representws th e angle of the light entering the water and the angle of the light due to the di rection of scattering by the water and constituents within it over depth (f). To further carry the upwelli ng irradiance through the surface, and convert it to radiance, terms for the transmittance ac ross the air water interface (t), index of refraction of water (nw), and ratio of irradiance to ra diance (Q) were introduced (Austin 1974). Finally it was realized that the loss due to backscattering in turbid coastal waters needed to be included. The result is equation 2.5 (Carder et al. 1999). b b w rsb a b Q n f t R2 2 Equation 2.5 The backscattering and absorption terms c ould be broken up into their contributing components resulting in a semianalytic al approach to the inversion of Rrs( ) to IOP values that could be related to cons tituents within the water column. Most of the terms that are not IOPs in equation 2.5 are relate d to factors that affect the path length of light as it travels to depth. If the lig ht has to take an angular path to depth versus a nadir path, it will have a greater chance of being attenuated before it reaches a given depth. Backscattered light wi ll also have a greater chance of attenuation coming up from depth with a longer path length. The path length is a concern for all types of optical measurements in oceanography sin ce a longer path can increase the signal to noise ratio of the measurement. The averageco sine is a parameter that can provide some compensation for path length elongation. The progress in AOP measurement and mode ling ran parallel to the progress in IOP measurement. The goal of a true IOP measurement based on principles of optical physics is difficult to achieve since most IOP measurements require some sort of empirical correction for errors. One of the fi rst methods for separating the absorption due to particulates from the other absorbing constituents was the quantitative filter pad method (Yentsch 1962, Truper and Yentsch 196 7, Kishino 1985). This method involves filtering a sample on to a glass fiber filter, where smaller particles become embedded in PAGE 39 21 the pores of the filter. Previ ously, particulates were filtered onto a smallpore filter to concentrate them and then carefully scraped off into a solution to be measured in a spectrophotometer cuve tte to determine ap( ). The quantitative filter pad technique resulted in an increased path length for the absorption measurement by taking the volume for a section of the water column and concentr ating the particulate matter in a thin layer over a small area. However, the path through the filter resulted in sc attering of the light requiring an empirical correction to determine the increased path length. Even the more direct measurements required a correction ba sed on empirical means (e.g., see Keifer and Mitchell 1988). The problem with m easuring absorption in situ was a need for a long path length without interference from ambi ent light or loss of signa l due to scattering. The development of a reflectivetube absorption me ter allowed for increasing the path length while capturing the light lost to scatteri ng (Zaneveld 1990). This instrument became commercially available using a nine channel rota ting optical filter wheel and is capable of measuring both absorption and attenuation (ac9, WET Labs Inc). There were still losses due to backscattering towards the light sour ce, forward scattering near the gap between the reflective tube and the dete ctor window, and path length elongation due to reflections off the tube (Kirk 1992). To correct for thes e it was assumed that at 715 nm the only absorption was due to water and by calibrati ng the media to pure water any measurement beyond 715 nm is due to internal scattering loss es. By taking the ratio of the apparent scattering at a given wavelength to that at 715 and multiplying it by the absorption at 715 nm, the scattering loss can be extrapolated to other wavelengths (Zaneveld 1994). This correction makes the assumption that the scattering loss is proportional over the wavelengths measured and is very small relati ve to overall scattering. This presents an analytical approach to measuring absorption bu t it still relies on an assumption that may introduce some errors. While the ac9 made the measurement of in situ absorption values possible it still is not a completely direct measurement. The backscattering coefficient is one of the more difficult measurements to make in situ due to the complexity of measuring all of the different angles of scattering and the low signal over short path lengths. Early measurements were performed in a laboratory with a complex instrument called the BricePheonix that measured the scattering at several different angles from a sample in a cuvette (Carder 1970). Petzold (1972) performed an experiment where through an elaborate submersible device operated by divers, they were able to measure the vol ume scattering function at several angles. Maffione and Dana (1997) discovered that the backscattering coefficient could be related empirically to a measurement of the volume scattering function at a single angle. The Hydroscat6 (HOBI Labs) was developed to measure the volume scattering at six wavelengths of light at 140 and to then c onvert that measurement to total backscattering by multiplying it by a factor of 2* *1.08. While a profile of the backscattering coefficient is possible, it depe nds on an empirical calculation. While the IOP measurements are a more di rect method of determining an optical property due to a particular constituent in th e water column, they still are not a perfect measurement. All methods require some assumptions, corrections, and empiricism. PAGE 40 22 Clearly a 10cm path length is inadequate for measuri ng absorption and scattering by extremely clear waters such as in the Sarga sso Sea, while it is certainly too long for turbid Mississippi River water. While the AOP inversions require more assumptions and empiricism, they can benefit from a greater si gnal to noise ratio due to the increased path length of the light th at is possible. Rrs( ) measurements made just above the sea surface do not have to be corrected for the effects of passing through the atmosphere resulting in greater signal to noise than a satellite Rrs( ) value. The atmosphere can account for over 80% of the radiance received by a satellite (Kirk 1994). With modern algorithms and instruments, it is possible that AOP inve rsions can be more accurate under certain conditions than more direct IOP measurement techniques. 2.4. Optical Closure There are several different definitions of closure but few fit the closure attempted in this research. Curt Mobley discusses thre e types of closure in his treatise, Light and Water (Mobley 1994). The three types of closur e, according to him, are measurement, scale, and model closure. The first type is to get accurate measurements by comparing them against a measurement commonly accepted existing practice. The scale closure is to make the transition from the properties of single particles to a bulk property of the water column. Model closure is to determin e if AOP inversion algorithms can accurately produce the values of the IOPs in the water column. Zane veld (1994) defines optical closure as matching theoretical relationships to independent measurements and is the closest to what is attempted in this study. None of these definitions fit exactly what needs to be done to determine which is the best current method, but parts of each are necessary A particular oceanographic measurement can vary from an individual particle to 100s of square miles. A measurement based on a discreet sample from a particular depth can only give information about that particular point. For example, if a researcher is interested in primary produc tion based on chlorophyll, a specific sample measured by extracted pigments in a laboratory grade, ca librated fluorometer will be most accurate. The second most accurate approach would be to profile the water column with a calibrated fluorometer. Less accurate would be to invert satellite Rrs( ) to get chlorophyll concentrations. Each technique represents a different size scale. The water sample approach will give a point in the water colu mn, the profile will give one dimension, and the satellite measurement will give a watercolumnintegrated value for 2 dimensions in the horizontal direction. Becau se of the differences in scales, comparisons become difficult. To achieve closure the three methods need to be set to a similar scale so they can be fairly compared to each other. The best way to set a similar scale to co mpare methods is to have a water column profile for each method. By using an a bovewater handheld radiance sensor, the Rrs( ) measurement is limited in horizontal scale to th at particular point. An inversion of the Rrs( ) to get a( ) then represents a verti cally integrated value. The IOPs of water just below the surface have the greatest influence on Rrs( ), decreasing logarithmically as the depth approaches one attenuation depth (1/Kd( )) (Smith 1981, Barnard et al. 1999). PAGE 41 23 Since 90% of the affect on the Rrs( ) values is from the first attenuation depth, comparison win an IOP profile measurem ent requires integration over depth by weighting it to Kd( ). For water sample measurements of absorption such as the filterpad method, the extrapolation of seve ral samples at depth weighted to Kd( ) would be best. Since it is timeconsuming to collect and process that many samples, the best alternative would be to use the sample clos est to the surface si nce it has the highest weighting in the Rrs( ) measurement. An inversion of Kd( ) from one attenuation depth would be similar to the Rrs( ) in weighting of IOPs so no additional weighting is needed for those two to be compared. By integr ating IOP profiles and using a nearsurface sample for the laboratorybased techniques, th e methods are now set to similar scales and can be statistically compared. The three definitions of optical oceanogr aphic closure by Mobl ey need to be updated for a comparison to determine wh ich method is best for a particular oceanographic environment. The developers of a particular met hod generally do scale closure to determine the accu racy of the method. Measurement closure has been achieved for individual measur ement techniques by previous studies (Truper and Yentsch 1967, Ivey 1997, Maffione and Dana 1997). Th e developers of the AOP inversion algorithms have conducted several studies tested for model closure (Kirk 1981, IOCCG 2006). The difficulty in Zaneveld's (1994) proposal is that to achieve closure between measurement and theory requires some difficu lt radiometric measurements. To test the relationship between theory and measurement it would require a data set that includes profiles of such difficult measurements as sc alar irradiance. Scalar irradiance requires a very sensitive photocell with a spherical collector that ha s view angles both towards the surface and downwards. Some modern instruments approach the accuracy necessary for this type of measurement but have not been su fficiently widely used to test for closure. The approximate methods mentioned in Zaneve ld (1994) are much easier to obtain and use for closure. That is closer to the approach used in this study. The remaining test for closure is closer to the mathematical definition of closure. According to the MerriamWebster 2009 dictionar y, that definition is a set that consists of a given set together with al l the limit points of that set. The best test will compare all the methods for a particular IOP under di fferent conditions and environments to determine when they agree with the other methods and where they diverge from the other methods. The type of closure here is to determine which are the best techniques and under what conditions they are be st. This type of closure co uld be considered set closure where there are groupings of overlapping sets based on environmental conditions. The closure between the models and the mo re direct IOP measurements indicates a closure between the AOP measurements and th e IOP values. This indicates that the relationship between the AOP model results and the in situ IOP values are significant enough that they can be substituted for one another. In oceanic environments where attenuation is very low, the ac9 (25cm pa th absorption and attenuation meter) may have low signal to noise for anw( ) values. In these cases, an inversion al gorithm of Rrs( ) can PAGE 42 24 be used to determine anw( ). In cases where the Rrs( ) measurements is suspect, the ac9 value may be used instead. In areas where met hods are expected to give the same result, they can be compared to determine if there is an error in a particul ar measurement. If there are three independent methods that meas ure or can be inverted to measure an IOP and two agree, then the other measurement or method may be retroactively corrected based on the differences. If correction is not possible, then the value from the other more reliable methods can be used. The collecti on of both AOP and IOP da ta that have been determined to agree, allows for a more robus t, accurate, data set of optical properties. Determining the conditions where the met hods agree has the a dditional benefit of extrapolation to other optical properties based on the mathem atical relationships between the AOPs and IOPs. Using the radiative tran sfer equation (e.g., see Mobley 1994 for a summary) the relationships between measurements such as Rrs( ), Kd( ), anw( ), and bbp( ) permit calculation of other parameters such as scalar irradian ce, scattering phase functions, and bottom reflectance. Scalar irradiance can indicate the amount of light available to a phytoplankton cel l at a given depth. Scatte ring phase functions are indicative of the types, sizes and population distributions for particulate matter in the water column. The percent of sea grass c overage can be indicated by a spectral bottom reflectance. Difficult to measure optical pr operties can be estimated using AOPs and IOPs under conditions of agreement to give mo re parameters that are of interest for oceanographic studies. Closure by treating all methods as equally weighted, points out potential sources for improvement in these methods. If one me thod has traditionally be en accepted as best, then it may be ignored when it obviously produ ces errors. Errors may not occur under all environmental conditions, so filters have to be applied to separate out the different conditions. The Rrs( ) are expected to have more errors for determining anw( ) under high solar zenith angles while the instruments that have their own li ght source, such as the ac9, will not be affected by zenith angle. Once errors are quantif ied, then correlations with other parameters can be investigated. Cloudiness might affect the AOP inversions while scattering might affect the ac9derived absorption coefficients. Analysis of these errors will be used to derive correction factors or modifications in the measurement procedures. By treating all methods as equa lly likely of error, instead of initially assuming one method is best can yield inform ation useful about all the method, in this study. 2.5. Spectral Bottom Albedo Through Optical Closure The bottom albedo would be a useful pa rameter to obtain from mathematical relationships between the different measuremen ts. Bottom albedo is the fraction of light leaving the bottom relative to the light reaching it. It is a difficult parameter to measure due to the types of instruments required for its measure and the methods involved (Hochberg et al. 2003). The bottom albedo co uld be useful for applications ranging from environmental to defense. Several publishe d algorithms have attempted to deconvolve bottom albedo from Rrs( ) measurements (Maritorena et al. 1994, Lee et al. 1999, 2001, PAGE 43 25 Werdell and Roesler 2003, and Dierson et al 2003). If a deconvolution of the bottom albedo signal can be achieved from common measurements, determination of bottom albedo would be more common. The way that albedo could be determined from Rrs( ) measurements is illustrated in the Rrs( ) optimization inversion algorithm (Lee et al. 1999). They point out that rrs( ) below the surface can be separated into two pa rts. One portion is due solely to the downwelling light passing through the water column and the return of that light due to backscattering. The second part is due to the light reachi ng the bottom, being reflected and returning up to the surface. His equation is basically the irradiance reflectance from the water column plus the ir radiance due to light reflected off the bottom. The second term includes the albedo as a factor. The rrs( ) values can be calculated within the Hydrolight model (Mobley 1994) using the best IOP values as input. The water column value can be removed by subtracting from measured rrs( ) value, a Hydrolight result using a black bottom. The resulting value is the rrs( ) due to bottom reflectance. A second Hydrolight run using an albedo valu e of one could be corrected for the water column rrs( ) and divided into the measured value to get the albedo. The approach is simple in practice but requi res very good measurements for the input values and reflectance. A spectral bottom albedo could aid in envir onmental studies of sea grasses. Sea grass has made a come back in the in Ta mpa Bay since a large decline in the 1970s (Dawes et al. 2004). Anthropogenic pollution re sulted in large algal blooms that limited light availability to sea grasses and led to th e decline in coverage. Careful monitoring is still necessary to determine areas that mi ght be at risk. High resolution spectral Rrs( ) measurements from air craft could determin e the bottom albedo of sea grass areas at different times of the growing season. This would allow accurate estimations of coverage with little ship time required for monitoring. Spectral bottom albedo over coral reef ar eas could be used to indicate coral health. The rapid decline in reefs over the wo rld has puzzled coral reef ecologists as to the various reasons for the decline (Bellwood et al. 2004). With spectral albedo images of the reef area, zones of al gal coverage, coral bleaching, a nd coral growth could possibly be identified. This knowledge could lead to a better determination of the timing and perhaps the causes of decline. The changes in the images over time could be used to identify regions that are in distress and fo cus mitigation efforts on those areas. With spectral Rrs( ) images from a low flying air craft combined with side scan sonar measurements of depth, 3dimension spectral maps could be made to aid coral reef ecological management. The Navy and port security could benefit from hyperspectral images of bottom albedo. It is very difficult to spectrally ma tch the albedo of a changing bottom. Painted camouflage may be difficult to determine us ing a video camera that only uses red, green, and blue wavelengths. The human eye is most sensitive to green light so it can be fooled by camouflage. A spectral image of the bottom would be very difficult to fool since the PAGE 44 26 target would have to match several wavele ngths of the spectrum exactly. Using the spectral image, a threat to s ecurity or planted mines could be identified using a passive reflectance sensor instead of a sonar system that could be detected. An image of spectral bottom albedo would make even active cam ouflage difficult to achieve. At certain wavelengths the object would contrast prominently against the bottom. 2.6. Locations and Descriptive Optics Data from 126 stations are utilized in th is study covering a wide range of optical values with several different types of synchronous measurements (Table 2.3). Rrs( ) measurements were collected at 115 stations. The ac9 was deployed at all 126 stations. Subsurface downwelling irradiance measurem ents were collected at 119 stations. Filtered ac9 ag( ) was collected at 114 stations for water color. Hydroscat6 bbp( ) values were collected at 119 stations. Filter pad ap( ) values were collected at 82 stations. Spectrophotometric ag( ) data were collected at 84 stations. Filter pad ad( ) were collected at 84 stations. The difference between ap( ) and ad( ) resulted in aph( ) for 79 stations. All the Rrs( ) and Kd( ) measurements produced acceptable inversion results within normal ranges so none were considered erroneous measurements. The majority of stations have a variety of AOP and IOP measurements that are used in comparing the different methods in this study. Table 2.3. Study sites: dates, locatio ns, and chlorophyll concentrations. Cruise Name Date Range for Data Used Number Stations Median Chl g l1 SW Corner Lattitude by Longitude NE Corner Lattitude by Longitude CoBOP 98 05/20/1998 to 05/29/1998 13 0.15 23.78N by 83.06W 23.84N by 80.88W Friday Harbor 08/04/1998 to 08/05/1998 7 8. 60 48.50N by 123.00W 48.65N by 122.86W CoBOP 99 05/22/1999 to 06/03/1999 15 0.07 23.77N by 76.10W 23.87N by 75.92W ECOHAB NOV 99 11/06/1999 to 11/07/1999 4 1.53 26.31N by 83.05W 27.50N by 82.27W ECOHAB Mar 00 03/01/2000 to 03/03/2000 9 0.19 26. 10N by 83.80W 27.50N by 82.87W CoBOP 00 05/20/2000 to 05/29/2000 10 0.12 23.79N by 76.14W 24.21N by 76.03W FSLE 3 07/02/2000 to 07/10/2000 9 0.47 27.15N by 83.12W 27.26N by 82.93W FSLE 4 11/05/2000 to 11/13/2000 13 0.36 26.85N by 83.50W 27.28N by 82.87W HOBI 1 02/07/2001 to 02/07/2001 5 0.30 27.13N by 83.01W 27.21N by 82.82W HOBI 2 04/17/2001 to 04/17/2001 5 0.22 27.12N by 83.00W 27.21N by 82.82W Link (aka FSLE 5) 04/19/2001 to 04/25/2001 36 0.19 26.09N by 83.72W 27.30N by 82.09W Data were collected in the Puget Sound of Washington state during a threeday cruise in the summer of 1998. The area provides attenuations much la rger than most of the other regions. This area is included as a test to the upper atte nuation limit of the models and techniques used in this paper. The Rrs( ) from this area has a lower signal than the clearer regions and has a higher proportion of the signal from the longer wavelengths of the visible spectrum. The signal to noise in the ac9 and other direct IOP measurements is highe st in this region. PAGE 45 27 The stations from Puget Sound had the highest absorption values at 440 nm ranging from 0.227 to 0.568 m1. The attenuation values at 440 nm were higher than most other areas overall with a median of 0.98 m1. The maximum chlorophyll levels were highest reaching 10.07 mg m3 at one station. The ag(412) values were higher than most areas ranging from 0.168 to 0.232 m1. The bbp(442) values ranged from 0.005 to 0.01 m1, but, unlike the absorption values, they were not the highest. Th e stations in the Puget Sound represented the upper range in values except for backscattering. Figure 2.1. Station locations in Puget Sound, Washington, USA. Black dots represent the stations sampled. The area around Lee Stocking Island, Bahamas (LSI), was part of an oceanographic study that emphasized the optical properties of the waters. The study was titled Coastal Benthic Optical Properties (C oBOP) and was sponsored by the Office of Naval Research. The area was surveyed during May for the years 1998 to 2000. The main constituent contributing to the optical pr operties of these clear waters is the water itself. The water near the island was different from Sargasso Sea wate r in that it had high ratios of ag( )/aph( ) and bbp( )/bp( ). The remote sensing reflectance (Rrs( )) in this region has a higher signal and re ceives a greater portion of its signal from the shorter wavelengths of the visible spectrum. The signal to noise in the ac9 and spectrophotometric measurements is low in this region. Longitude (degrees) 123.2123.1123.0122.9122.8122.7122.6122.5 123.2123.1123.0122.9122.8122.7122.6122.5Lattitude (degrees) 48.45 48.50 48.55 48.60 48.65 48.70 48.45 48.50 48.55 48.60 48.65 48.70 PAGE 46 28 The stations near Lee Stocki ng Island of available data had the lowest attenuation. These measurements challenged the lower ra nge of the methods. The attenuation had a median value of cnw(440) of 0.11 m1 with a range from 0.04 to 0.24 m1. These waters also had the lowest chlorophy ll with a median of 0.11 mg m3. The median anw(440) value was low at 0.034 m1 with a range of 0.009 to 0.071 m1. The median ag(412) value was 0.035 m1 and is equal to the median value for the West Florida Shelf data set. The ag(412) range was 0.007 to 0.101 m1. The median bbp(442) value was also the lowest at 0.0017 m1, but the area had a wide range of 0.0008 to 0.0478 m1. The stations from the Bahamas provided the lowest attenua tion range for testing the methods. Figure 2.2. Stations locations near Lee Stocking Island, Bahamas. Black plus signs represent the st ations sampled. The most diverse area studied is the West Florida Shelf, covering from the mouth of Tampa Bay and offshore, to areas off Char lotte Harbor. Most stations were along a track leading out from Sarasota, FL. The cruises cover a period from March of 1999 to April of 2001. The bottom depths ranged from 10 m to 76 m. The optical properties in this area were widely varying depending on the bottom depth and season of collection. Chlorophyll concentration ranged from 0.09 to 2.36 g l1. Typically the attenuation and Rrs( ) values from this area represent a midpoint in optical values between the waters investigated in the CoBOP and Friday Harbor cruises. The West Florida Shelf data had values in between the Puget Sound and CoBOP data, and also had the largest range of valu es. In some cases the offshore water had Lattitude (degrees) 76.2576.2076.1576.1076.0576.0075.9575.90 76.2576.2076.1576.1076.0576.0075.9575.90Longitude (degrees) 23.65 23.70 23.75 23.80 23.85 23.90 23.95 23.65 23.70 23.75 23.80 23.85 23.90 23.95 LSI PAGE 47 29 attenuation values as low as the waters o ff Lee Stocking Island and sometimes the near shore waters had higher atte nuation values than found in the Puget Sound Waters. The attenuations range from 0.07 to 2.19 m1 with a median value of 0.24 m1. The anw(440) values have a median of 0.04 m1. While the median anw(440) value is not much higher than the CoBOP waters, the range (0.02 to 0.24 m1) is much larger. The low absorptions and high attenuations probably reflect a lot more scattering particles fr om local rivers and resuspension of bottom sediments. The We st Florida Shelf data set provided an intermediate range to test the methods. Figure 2.3. Station locations on the West Florida Shelf. Di fferent cruises are indicated by different symbols. 2.7. Morel Case of Study Sites Andre Morel (1974) published a definiti on for open ocean waters by defining them as having all optical properties deri ved from phytoplankton and their degradation products. Examining the in situ ac9 and Hydroscat6 data for the stations in this study indicates that most of the waters do not fit Morels definition. Recent studies have questioned whether these definitions are va lid (Lee and Hu 2006, Mobley et al. 2004). Improved Rrs( ) inversion techni ques have indicated that the ratio between CDOM absorption and phytoplankton concentrations may not be as well establ ished as originally theorized (Siegel et al. 2005). The categories of the data in this study are examined to determine where they fall in the Morel classification method. Longitude (degrees) 84.083.583.082.582.081.581.0 84.083.583.082.582.081.581.0Latitude (degrees) 26.0 26.5 27.0 27.5 28.0 28.5 26.0 26.5 27.0 27.5 28.0 28.5 Eco99 Eco00 f3 f4 link hobi1 hobi2 PAGE 48 30 The Morel definitions for Case II water are broken down into three groups for this test; CDOM Case II, scattering Case II, a nd CDOMscattering Case II. His Case I definition is essentially cons istent with all the optical parameters correlating with chlorophyll concentrations. C DOM Case II is defined as C DOM absorption greater than pigmented particulate absorption at 440 nm. Scattering case II is defined as scattering not correlating with pigmented particulat e absorption. Morel has an equation that empirically determines b(550) from chlor ophyll concentrations for Case I waters (Equation 2.6). The waters that have b(550) va lues above this equa tion would be Case II scattering waters. CDOM and scattering Case II waters would have a combination of the two criteria deviating fro m the Case I definition. b(550) = 0.45C0.62 Equation 2.6 The waters in Puget Sound were high chlo rophyll and were case II CDOM waters. The chlorophyll values did correlate with par ticulate absorption but did not correlate at a high level with scattering or CDOM (Figure 2.4 A and B). The ratios for ag(440) to ap(440) or aph(400) were mostly above one (Figure 2.4 C). The b(550) values were below the Morel equation (Figure 2.4 D. ). The only exceptions were the stations closer to the mouth of Puget Sound, which may have mixed with some open ocean water. None of the Puget Sound data correspond to Morel Case I waters. The waters in the Bahamas Sound, while optically clear, were dominated by CDOM. The CoBOP IOP data from both the ac9 and the spectrophotometric methods do not exhibit a correlati on with chlorophyll (Figur es 2.5 A & B). The ag(440) to ap(400) or aph(400) ratios indicate that even the clear offshore stations are CDOM rich (Figure 2.5 C). Two stations fall above th e Morel line for scattering (Figure 2.5 D). These stations scattering Case II stations were either at or near N. Perry or S. Perry reef in the Bahamas. It appears that some pr ocess in the reefs is producing both higher CDOM and scattering. Probably the local reef organisms are producing the CDOM while resuspension or carbonate precipitation is increasing the scattering. The CoBOP waters are CDOM Case II except for the reef s on the sound side, which are CDOM and scattering Case II. PAGE 49 31 Figure 2.4. Analysis of all Puget Sound data to determine Morel Case. A. chlorophyll correlations with in situ measurements, B. spectrophotomet ric absorption data versus chlorophyll, C. ratios of ag to ap and aph, D. Measured in situ scattering (points) as compared to Morel value modeled from chlorophyll concentrations (line). Station b3b4b5h3h4h5n3n4n5 a g (440)/a (p or ph) (400) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 ag to ap ag to aph ratio = 1 Chlorophyll (mg m 3 ) 110 b(550) (m 1 ) 0.1 1 10 Chlorophyll (mg m 3 ) 024681012 absorption and scattering (m 1 ) 0.0 0.2 0.4 0.6 0.8 1.0 Backscattering (m 1 ) 0.000 0.002 0.004 0.006 0.008 0.010 0.012 a nw (440) r 2 = 0.67 b nw (440) r 2 = 0.41 a nw (412) r 2 = 0.78 b b (442) r 2 = 0.28 A. Chlorophyll (mg m 3 ) 024681012 absorption (m 1 ) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 a p (400) spec r 2 = 0.79 a g (440) spec r 2 = 0.21 a d (400) spec r 2 = 0.63 a ph (400) spec r 2 = 0.54 B. C. D. PAGE 50 32 Figure 2.5. Analysis of all Bahamas data to determine Morel Case. A. Chlorophyll correlations with in situ measurements, B. spectrophotomet ric absorption data versus chlorophyll, C. ratios of ag to ap and aph, D. Measured in situ scattering (points) as compared to Morel value modeled from chlorophyll concentrations (line). Station a p 2 4 0 0 2 a p 2 4 0 0 3 2 9 0 0 1 2 6 0 0 3 2 7 0 0 1 2 5 0 0 2 2 6 0 0 2 a p 3 1 0 0 2 a p 2 2 0 0 3 2 2 0 0 3 a p 2 2 0 0 4 a p 2 2 0 0 2 1 0 3 a p 2 6 0 0 3 2 2 0 0 1 a p 2 2 0 0 1 a p 2 7 0 0 1a p 2 4 0 0 1 1 1 9 a p 2 7 0 0 2 1 1 8 a p 2 8 0 0 2 a p 2 9 0 0 1 a p 1 0 0 1 a p 3 0 0 2 2 3 0 0 1 2 3 0 0 2 a p 2 3 0 0 1 a p 2 5 0 0 1 a p 3 0 0 3 a p 2 6 0 0 1 2 0 0 0 2 a p 2 7 0 0 3 a p 2 8 0 01 2 0 0 0 1 1 0 2 1 0 8 2 0 8 1 1 2 1 1 3 1 1 4 1 1 5 1 1 6 a p 3 0 0 0 2 a p 3 0 0 0 1 1 1 7 a p 3 1 0 0 1 2 1 0 0 1 2 5 0 0 1 2 1 0 0 2 o r 1 1 0 1 1 0 9 1 1 0 3 0 4 1 0 5 1 0 7 2 0 7 2 0 5 1 0 4 2 04 1 0 6 1 1 1 a g (440)/a (p or ph) (400) 0 2 4 6 8 10 12 14 ag to ap ag to aph ratio = 1 Chlorophyll (mg m 3 ) 0.000.050.100.150.200.25 absorption and scattering (m 1 ) 0.0 0.1 0.2 0.3 0.4 Backscattering (m 1 ) 0.000 0.002 0.004 0.006 0.008 0.010 a nw (440) r 2 = 0.48 b nw (440) r 2 = 0.38 a nw (412) r 2 = 0.48 b b (442) r 2 = 0.30 A. Chlorophyll (mg m 3 ) 0.000.050.100.150.200.25 absorption (m 1 ) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 a p (400) spec r 2 = 0.14 a g (440) spec r 2 = 0.06 a d (400) spec r 2 = 0.11 a ph (400) spec r 2 = 0.43 B. C. Chlorophyll (mg m 3 ) 0.010.11 b(550) (m 1 ) 0.01 0.1 1 D. PAGE 51 33 Figure 2.6. Analysis of West Florida Shelf (Link, Table 2.3) data to determine Morel Case. A. Chlorophyll correlations with in situ measurements, B. spectrophotometric absorption data versus chlorophyll, C. ratios of ag to ap and aph, D. Measured in situ scattering (points) as compar ed to Morel value modeled fr om chlorophyll concentrations (line). Station 1 0 1 2 0 1 3 0 1 1 0 2 4 0 2 2 0 3 5 0 3 6 0 4 2 0 5 4 0 5 5 0 6 b 1 0 6 3 0 7 a g (440)/a (p or ph) (400) 0.0 0.5 1.0 1.5 2.0 2.5 ag to ap ag to aph ratio = 1 Chlorophyll (mg m 3 ) 0.010.1110 b(550) (m 1 ) 0.1 1 10 Chlorophyll (mg m 3 ) 0.00.51.01.52.0 absorption and scattering (m 1 ) 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Backscattering (m 1 ) 0.00 0.05 0.10 0.15 0.20 0.25 a nw (440) r 2 = 0.82 b nw (440) r 2 = 0.79 a nw (412) r 2 = 0.80 b b (442) r 2 = 0.79 A. Chlorophyll (mg m 3 ) 0.00.51.01.52.0 absorption (m 1 ) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 a p (400) spec r 2 = 0.79 a g (440) spec r 2 = 0.97 a d (400) spec r 2 = 0.91 a ph (400) spec r 2 = 0.91 B. C. D. PAGE 52 34 The West Florida shelf varies from Case I to Case II according to April 2001 cruise data. The IOPs correlate very well with chlorophyll concen tration. Based on the correlation with chlorophyll c oncentrations along the West Florida Shelf, waters would qualify as Case I (Figures 2.6 A and B). The ag(440) to aph(400) ratios are above the 1:1 ratios but not much higher, and 4 stations had ag(440) to aph(440) ratios that were below 1 (Figure 2.6 C). Some stations border on Case I water ba sed on CDOM absorption. The stations along the 10 m isobath along with one 20 m station border on a Case I CDOM classification (two black squares closest to shore in Figure 2.3). The scatteringtochlorophyll curve shows a different story (Fig ure 2.6 D). All the 10 m isobath stations are above the Morel line. About half the 20 m isobath stations are also above the Morel line. Many of the offshore stations are also above the Morel line for scattering for Day 1 and 2 of a April 2001 cruise when the winds were about 7 to 9 m s1. After Day 3 the winds died down and the seas were almost fl at calm for the last couple of days of the cruise. The scattering appears to be related to resuspension of particulates into the water column as the stations deeper than 20 m fell close to or below the Morel scattering line when the winds subsided. Based on correlati ons with chlorophyll c oncentration and the ag(440) to aph(400) ratios of nearly one, the stat ions at the 50 and 60 m isobaths border on Case I. The nearshore stations are s cattering and CDOM Case II but not strongly CDOM Case II. The scattering at the othe r stations appears to depend on the wind resuspension of sediments. If the cruise had continued another few days, the waters might have turned Case I as suspended sediment dropped out of the water column. The West Florida Shelf stations ranged from Case II at less th an 20 m depth to Case I at greater than 50 m depth. The regions in this study are not ideally suited for older empirical bandratio AOP inversion models. Most inversion models are parameterized with data for open ocean conditions. The older band ratio algorithms do not perform as well in Case II waters. The statistical comparisons in this study are expected to show signi ficantly bette r results for models that used parameters more suited to the region. In CDOM Case II waters, the models not tuned to these regions were postulated to underes timate the amount of CDOM. The CDOM near shore is expected to have a more humic component than the offshore waters due to terrigenous input from rivers. The CDOM fluorescence at 440 nm may result in an underestimate of the magnitude of aph(440). If the model separates out aph( ), it may not have parameters appropriate for the packaging or pigments found in these particular case II waters. The bbp( ) values and spectral bbp( ) shape may be different in case II waters due to larger particle size and an increased mineralgenic component in the detritus absorption. Since most of the areas are not the typical openocean Morel Case I waters, they should provide a good test of the AOP inversion algorithms under varying but realistic conditions. PAGE 53 35 3. Instruments and Methods 3.1. Introduction The techniques for measurement and analyt ical quality of the various methods in this research are a very important part of th is study. A technician can read a manual, and then go deploy an instrument, but it takes years of collective experience for the measurement to be properly made by a scie ntific group. Simply put, an instruction manual is no substitute for handson traini ng and field experience. Likewise, most technicians can perform a regre ssion on data in Excel and call it an inversion algorithm. However, it will likely only apply to that pa rticular data set unless the two sets in the regression are known to have a linear relations hip. The way the data are collected and the analytical methods are of primary importa nce for optical closure, especially in the diverse environments of coastal regions. 3.2. SlowDrop Package The instrument package used in this study had a suite of 13 core oceanographic instruments and up to 4 additional instruments. The data from most of the instruments were merged together based on elapsed time. The data used for this paper from this package come from the ac9 (a 9channel ab sorption and attenuation meter), an ac9 with a filter attached, a 512wavele ngth downwelling irradiance sp ectrometer, a Hydroscat6 (a 6channel backscattering meter) and a CTD (a conductivity temperature, and depth sensor). The instrument was deployed with floatation devices that put the package near neutral buoyancy. The near neut ral buoyancy allowed to the package to drop at a slow steady rate independent of th e motion of the boat and the se as. This also allowed the package to drift out from the shadow of the ship to prevent shading of the irradiance sensor. 3.2.1 ac9 A WET Labs, Inc., ac9 measures attenuati on and absorption of all constituents in the water at wavelengths of 412, 440, 488, 510, 532, 555, 650, 676, and 715 nm (Zaneveld 1990). The ac9 uses a reflective tube to meas ure absorption in the water column. It accomplishes this by having most of the light that is scattered reflected forwards off a quartz flow tube and into a de tector (Figure 3.1.). This is simple in concept but complex in practice. Figure 3.1 show s the basic layout of one of these meters. The light leaves the lamp (a), passes through a pair of apertures (b), a focusing lens (c), a narrowbandpass filter on a rotating wheel (d), and another aperture producing a collimated beam. This light then goes th rough a beam splitter (e) with some going to a PAGE 54 36 detector (f) to take a measurement of how much light is entering the water in the reflective tube. The light beam then passe s through a window (g) and travels through 25 cm of water to illuminate a diffuser (k) and is measured by a photocell (l). According to Beer's law, the change in light over a pa th short enough that only single scattering can take place, is a natural log function using the log of the loss of light over the path to the distance traveled. The measurement would be ex act if all the light entering the reflective tube was either absorbed or detected by th e photocell but the actua l path of the light complicates this measurement. Figure 3.1. The "simple" path of light through re flective tube absorption meter. a. light source, b. aperture, c. collimating lens, d. filter wheel, e. beam splitter, f. reference detector, g. window, h. initial light path, i. light scatter at 41 or less, j. light scattered at > 41, k. diffuser, and l. photocell. The light entering the reflective tube in Figure 3.1 can either be absorbed or scattered (h). The majority of light that is scattered at an angle 41 or less from the straight path (i) will make it to the detector with a minimal change in the length of the path it travels. However light that is scattered at higher angl es is usually lost (j). The difficulty is estimating how much light is lo st to prevent overes timating absorption by including these losses due to scattering. The losses due to scattering not collected by the detector can vary greatly depe nding on the optical properties of the constituents within the water sampled. The scattering efficiency an d direction of scattering of an individual constituent can vary greatly w ith size of the constituent a nd it's index of refraction. The efficiency of scattering can be low for a Karina brevis cell with an index of refraction near water but high for suspended aragonitic particles. The proporti on of scattering in a given direction can vary from evenly in the forward (bf) and backwards (bb) direction for a water molecule to a majority in the forwar d direction for a large diatom cell. This means that the losses due to scattered light not recovered in a refl ective tube absorption meter are impossible to exactly determine wit hout absolute knowledge of the scattering constituents within the water sample. Howeve r, if absolute knowle dge of the scattering constituents was already available then there would be no need for using a reflective tube absorption meter. The only way to compensa te for this loss is through an empirical estimate that will introduce some error in the measurement. This simple case of a reflective tube absorption meter is more complex than it first appears. 0.25 m a b c D e f g h i j k l PAGE 55 37 The optical arrangement of the attenuati on tube is the same as that of the absorption tube for the light entering the flow tube. However after the light enters, the attenuation tube has a black wa ll that absorbs the scattered light and the detector has a narrow aperture before it that rejects almost all of the light except that traveling almost the same path as the source light. The result is the change in power in the collimated source beam along a path straight from the s ource due to both abso rption and scattering or attenuation. Subtracting th e absorption tube result from the attenuation tube result gives the scattering coefficient. The data from the ac9 were calibrate d using highly purified water from a deionized water system. The water blank is subtracted from the in situ measurement of a( ) and c( ) to determine the constituent values and correct for shifts in instrument calibration. The optical properties of water va ry with changes in temperature and salinity and the values from the ac9 were corrected for this shift (Pegau et al. 1997). The absorption values in the ac9 have to be co rrected for losses due to light scattered at angles greater than 41 (Figure 3.1). Absorpti on at 715 nm is assumed to be zero and the value is scaled spectrally by using the ratio of apparent scattering at a given wavelength to the scattering at 715 nm (Zaneveld et al. 1992 ). With all these co rrections and careful deployment technique, the ac9 can meas ure absorption at an accuracy of 0.01 m1. This calibration using pure water is very important with this instrument because the filters in the rotating wheel degrade ove r time, as does the output from the lamp. While the 25 cm path length makes this instrument more sensitive than similar instruments, it also makes it vulnerable to slight shifts in the path due to a slight flexing of the instrument. The ac9 is so sensitive that vibrations from stamping on the floor will cause shifts in its readings. This sensitivity to vibration is one of the reasons why it is best to deploy it on a slowdrop package that is free from surges due to the roll of the ship. The surges can also result in changes in water density within the flow tube of the ac9 resulting in increased scattering. Bubbles can increase scatte ring within the flow tubes so the instrument must be properly cleared of them be fore a profile can be started. All this adds up to an instrument with a sensitive direct measurement of a( ) and c( ) but with several sources of error due to deployment techniques (Ivey 1997). A 0.2 m canister filter was atta ched to an ac9 to collect in situ measurements of the absorption due to CDOM. The filter wa s a highflow Gelman Suporcap with a 0.8 m outer filter. This filter was selected becau se of a very high flow rate and the large outer filter to keep the pores of the 0.2 m filter from rapidly clogging. To prevent problems with bubbles in the lines, the plas tic cannister of the filter was sawed off, exposing the filter membranes directly to the water. The filter was soaked in deionized water until deployment. The deionized water se rved two purposes. It saturated the filter so that few bubbles were caught within it and it helped rinse the filter if it was to be reused at a later deployment. The filter was only placed on the inlet of the absorption tube for the ac9. The calibration and correctio ns for temperature and absorption are the same as for the unfiltered ac9. Scattering by dissolved substances is similar to that of water so losses should be zero due to the wa ter calibration. However, like in a laboratory PAGE 56 38440440 s g ge a aspectrophotometer, there are some losses. Th is is mostly corrected by subtracting the 715 nm value where absorption is usually zero. Wh en values are below the accuracy of the instrument, they are extrapolat ed using the equation below. Equation 3.1 The shorter wavelengths (gener ally 412 to 510 nm) were fit to this equation using a regression model to solve for the coefficient "s" (Bricaud et al. 1981). The values at the longer wavelengths were then extrapolated. A filtered ac9 can usually only be deployed effectively on a slow drop package because th e slower rate of pumping through the filter results in a lag time for the measurement re lative to the depth of measurement so the values can smeared over several dept hs if the descent is too rapid. 3.2.2. Spectrix Hyperspectral Downwelling Irradiance Meter A 512channel radiometer with a cosine collector in a waterresistant housing (Spectrix) was used to measure the subsur face downwelling solar irradiance (English and Carder 2006). This meter measures irradi ance at wavelengths from about 340 to 890 nm. It is radiometrically and spectrally calibrate d by comparison to a standard lamp, a Licor 1800 irradiance meter, and the RADTRAN modeli ng program (Cattrall et al. 2002). The calibration of the Spectrix includes a coeffici ent for an immersion factor determined by carefully submerging it in deionized water in a laboratory tank (M ueller and Austin 1992). The instrument was then mounted clear of all other instruments on a slow drop package. The slowdrop package could drift away from the shadow of the ship limiting the possibility of shading the instrument. The sl ow descent allowed it to record a greater number of measurements at each depth than a much faster descending package connected to the ship's wire. The downwelling irradiance data and diffuse atte nuation coefficients (Kd( )) were processed according to the protoc ols outlined by Costello et al. (2002). While this instrument predates some of the commercial hyperspectral instruments, it still has extremely high accuracy because of the attention to calibration and deployment. The processing of the downwelling irradian ce data required a s ubstantial Matlab routine to correct for wave focusing. Wave focusing is exactly what it sounds like; the light near the surface is focused and defocuse d as waves pass over the sensor (Zaneveld et al. 2001). The resulting li ght field can vary greatly in irradiance and spectrum. The alternating bright and dark lines seen on the bottom of a swimming pool on a sunny day are a perfect illustration of this effect. Ideal ly the instrument would simply be held at several depths below the surface to average many measurements. This is only possible if it is mounted on an expensive platform such as an ROV or AUV (e.g., English et al. 2005) or if the slow drop package had some method of buoyancy control. The wave focusing even from a slowly descending p ackage can be enough that the nearsurface values can be skewed either too high or too low. The correction for wave focusing invo lved first taking an abovewater measurement of Ed( ). This surface value can be converted to a belowsurface value PAGE 57 39 using algorithms for the loss across the airwater interface (Austin 1974, Carder et al. 1999). The Hydrolight model using the Radt ran model (Gregg and Carder 1990) for its solar input value was used to calculate the factors for transmittance below the surface for each cast. If a surface value was not availabl e, a nearsurface va lue was modeled using the Hydrolight program. When the abovewater measurement was taken with a different instrument or calculated by the Hydrolight model, the spectral Fraunhoffer lines were different for two highresolution Ed( ) sensors. To compensate for this difference the routine did a fifthorder fit of Ed( ) versus wavelength for the calculated subsurface value. This polynomial was then statistically compared to a 5thorder polynomial fit for the Ed( ) scans in the upper 5 meters. The measured belowwater scan with the closest statistical match was then scaled using th e polynomial fit so that it matched the magnitude of the calculated va lue but had the spectral shape and resolution of the inwater measurements. Without these calculated values, the Kd( ) value could have severe errors. Spectral scans with more than 75 channe ls saturated (values at maximum raw counts of 4095) due to wave focusing were de termined to be irrecoverable since there was not enough spectral information and were de leted by the routine. Because of the lack of good data near the surface, every possible sc an was needed so scans with fewer than 75 values saturated were corrected with inte rpolated data from near by depths. This interpolation routine used the data from a scan at a close depth by taking a ratio of unsaturated values at 550 nm as a factor. If the individual values at a given wavelength were below the accuracy of the instrument (whe re the dark current is 95% or more of the reading), they were set to a value of 1 x 106 W m2 nm1 (Chris Cattrall personal communication). These values were not simply set to zero so that mathematic errors would not occur when the natural logarithm was calculated. Despite all this automatic filtering and smoothing of the data, there were still some spectral scans that were affected by wave focusing and would bias the Kd( ) value. To remove these, the Matlab routine plotted the data and an observer was able to remove the erroneous values by clicking on the plot at that point. The resulting depth profile of Ed for each wavelength was ready for the final smoothing. To smooth the data, the routine fit a 3rdorder polynomial over depth for each wavelength. For each value deleted during the filtering one of the just below surface Ed( ) values were added to the data array. These values fo rced the polynomial fit near the surface to go through a value unaffected by wave focusing. The fit only went to the depth where the values were above the noise level value. A thirdorder polynomial was selected because sometimes the Ed( ) value would slightly increase at depth. This increase in Ed( ) at depth was due to Raman scattering, fluorescence, or (in shallow regions) bottom reflectance (Cos tello et al. 2002). The Kd( ) values were finally calculated by taking the natura l log of the change in Ed( ) over depth using the smoothed curve from the 3rdorder polynomial fit. PAGE 58 40 3.2.3 Hydroscat6 The Hydroscat6 is one of the firs t commercial spectral backscattering instruments that can be used for water co lumn profiles (Maffione and Dana 1997). The instrument deployed on the slow drop p ackage measured at wavelengths of 442, 488, 532, 589, 620, and 671 nm. The volume of water measured by the instrument is calibrated by slowly moving a Spectralon refl ective plate through its field of view while immersed in a water bath. Th e instrument only measures bb( ) at 140 instead of through the entire hemisphere. This angle of b ackscattering was selected because modeling studies indicated that the va lue at this angle was most proportional to the overall backscatter value (Maffione and Dana 1997). The bb(140, ) is converted to bb( ) by multiplying it by 2* *1.08. This empirical relationship is within 10% of the total measured backscattering. Additional empirical corrections are applied to compensate for losses due to attenuation along the optical path of the instrument. 3.3. Rrs( ) Measurement with Spectrix A 512channel Spectrix radiometer was used to determine the abovewater remote sensing reflectance. The spectrometers ar e calibrated spectrally using an integrating sphere at quarterly intervals and annually calibrated against the solar constant. The downwelling radiance was measured by aiming the spectrometer at a gray Spectralon calibrated Lambertian panel as close to the vertical as possible without shadowing the card (Carder et al. 1985). The gray card measurement was multiplied by Pi and divided by the percent gray card reflectance to convert it to downwelling irra diance. The angular reflectance of the gray card has been calibrated and is upda ted annually (Cattrall 2002). The instrument was then directed at the wate r at a 60 angle to vertical and 90 to the solar plane and the water leaving radiance re corded. The instrument was then directed 30 from the vertical and 90 from the sola r plane and the sky radiance was recorded. Both the water and sky radiance are divided by the gray card irra diance measurement. The sky reflectance is then multiplied by the Fresnel reflectance of the water and subtracted from the above water remote sensi ng radiance of the water (Lee et al. 1998) to correct for refletance off the sea surface. 3.4. Spectrophotometer Measurements Surface samples of water were colle cted and particulate absorption (ap( )) determined using the Quantitative Filter Pad Method (Yentsch 1962, Kiefer and Soohoo 1982). To determine the absorbance of th e filter, a special box was used that incorporated a Spectrix radiometer (Car der et al. 1995). After taking a spectral absorbance reading of the filter, a wetted blank filter was scanned. A few milliliters of hot methanol were passed through the particul ate filter to dissolve the pigments within the cells. The bleached filter was measured for absorbance a second time to determine the light absorbed by nonliving particles or detritus (ad( ))(Kishino et al. 1985) again followed by blank filter. Th e difference between the ap( ) and ad( ) values represented the absorption due to pigmented particles (aph( )). The filter pad absorption values were PAGE 59 41 corrected for optical path lengt h elongation due to internal scattering within the filter (Carder et al. 1999). To convert the measured absorbance into per meter absorption, the absorbance value was multiplied by 2.303 to conver t from a log base of ten to a natural log, multiplied by the area of the filter pad covered with particles, and divided by the volume of water filtered. The dissolved organic absorption (ag( )) was determined by filtering some of the collected seawater through a 0.2 m filter. The filtrate was then measured for absorption in a 10 cm quartz cell with a PerkinsElmer Lambda 18 Spectrophotometer. Due to the low signal to noise in wavelengths above 500 nm the values at longer wavelengths had to be extrapolated using equation 3.1 for some of the lower attenuation samples. The ag data were added to the ap data to determine the anw from spectrophotometric measurements. 3.5. Rrs Inversion Models Most reflectance inversion models star t with the relationship that irradiance reflectance is proportional to th e ratio of the backscattering to absorption for a particular medium (Duntley 1942). This relationship si mply means that the light observed leaving the water relative to that entering the water is a function of what se nds the light back up to what removes the light. For turbid waters a second term of backscattering is usually added to the denominator to account for the returned light that is scattered back down again (Morel and Prieur 1977, Gordon et al. 1988). b b rsb a b C R Equation 3.2 Like most concepts in optical oceanography the theory is simple but application to the real world is more complex. The models in this study are much more complex than the original models and have many more terms. The models have techniques for separation of a( ) and bbp( ) into the various components th at contribute to them. Some of the models attempt to take into account al l the possible analytical equations to provide the highest accuracy. Others use some empirical terms so that large satellite images with millions of pixels, each representing a spectra l reflectance, can be rapidly processed. A brief overview of these models follows in or der from the most empirical to the most analytical. 3.5.1 QAA The QAA (quasianalytical algorithm) rapidly inverts Rrs( ) for only few wavelengths (Lee et al. 2002). By a series of empirical models and analytical steps, the QAA model calculates a( 440), a(555), and bbp( ). Using an equation to estimate the transmittance across the air water interface, inte rnal reflectance and the ratio of upwelling irradiance to radiance, the above water remote sensing reflectance is converted to a below PAGE 60 42 water irradiance reflectance (rrs( )). The rrs( ) is related to the ratio of backscattering to the sum of backscattering and absorption ( u ) through an empirical equation (Gordon et al. 1988). This equation is solved for u as a function of rrs( ). The empirical algorithms are used to initialize the model by estimati ng a(555) and the spectral coefficient of backscattering. The a(555) value is then used to se mianalytically calculate bbp(555) using the u (555) value. With the bbp(555) value determined, the u (555) can be used to solve for a(555). This approach can be repe ated for as many wavelengths as needed. The model includes a technique for separating the a( ) value into its components. The QAA model was in the process of being published during this study. Since this model was added last to the analyses only the values of 440 nm, 555 nm, and bbp( ) were included in the study. Th e techniques for deconvolving the a( ) into aph( ) and ag( ) were not yet settled, as noted in pers onal communication from the author of the model. In addition, adding a third Rrs( ) inversion model for aph( ) may have weighted the statistical comparison towards the Rrs( ) inversions. Therefore, this model was used solely as originally communi cated and recent changes in it were not included in this study. 3.5.2 MODIS The MODIS algorithm (Carder et al. 2004) is a combination of empirical and analytical equations. The aph( ) factors for the equations are determined from a lookup table set for the specific c onditions. The sea surface temperature is used to determine whether the pigment absorption portion of the algorithm uses parameters for packaged selfshading or unpackaged phytoplankton pigments. The term bbp( )/Q is empirically determined as a function of Rrs( ) values. The aph( ) is determined through a hyperbolic tangent function using aph(675) with empirical factors fo r each wavelength and packaging case. Equation 3.1 with an estimated ag( ) coefficient is used as a function of ag(400). The IOP values are now defined with aph(675) and ag(400) as the two unknowns. Ratios of Rrs( ) are used to solve for the tw o unknown values. The model makes the assumption that bbp( ) is small for most conditions and can be ignored in the denominator of equation 3.2 since it would have little effect on that ratio. The "C" in equation 3.2 is assumed to be constant across each wavelength and divides out. The resulting ratios can then be used to determine aph(675) and ag(400) algebraically. When the modeled chlorophyll absorption value is too high to use this method, the model switches to an empirical algor ithm. This results in a simple, computationally rapid model. 3.5.3. Optimization Model The Rrs( ) inversion algorithm by Lee et al. 1999 is the most detailed and analytical. It is the only model that compen sates for the bottom albedo in shallow water. The basic formulation of the model is the sum of the reflectance due to the water column PAGE 61 43P P a a a ln *1 0 Y bpX b 400 and the reflectance due to light reflected fr om the bottom. If the bottom contribution is not significant, a deepwater model is used instead. This model uses a single parameter model for phytoplankton absorption at each wavelength (Equation 3.3). Equation 3.3 The parameters a0( ) and a1( ) are determined for each area by a curve fit to the natural log of the ratio of aph(440) to aph( ) at each wavelength versus the aph( ) at each wavelength. The filter pad absorption data from the CoBOP 00, West Florida Shelf, and the Friday Harbor cruises were used to determine the parameters for each of these regions. Equation 3.1 models the absorpti on due to dissolved organic matter. Back scattering is modeled by the equation from the MODIS algorithm (Equation 3.4). Equation 3.4 The Y coefficient for Equation 3.4 is estimated by an empirical relationship with the ratio of Rrs(440) to Rrs(490). Equation 3.1 was used to model the adg( ) by iterating the adg(440) value with a slope coefficient (s) of 0.018. The known values for the absorption due to water (aw( )) from Pope and Fry (1997) and back scattering due to water (bbw( )) from Morel (1974) are used for those terms. The total absorption coefficient for the model was calculated by summing all the modeled constituents (Equation 3.5): a( ) = aw( ) + a( ) + adg( ) Equation 3.5 The total back scattering coefficient (bb( ) ) was calculated by summing bbp( ) and bbw( ). The resulting a( ) and bb( ) are inserted into equations that take into account the transfer across the air water interface, path length elongation, bottom reflectance, and conversion from rrs( ) to Rrs( ) (Q factor). The bottom reflectance equation introduces parameters of bottom de pth (H) and a factor (X) for the bottom reflectance. The bottom reflectance shape curve is selected based on a white sand curve. The measured Rrs( ) curve is corrected with an offset ( ) to take into account errors due to environmental conditions such as sun glin t and cloud reflectance in the measurement. Combining all the terms gives a very complex equation that is computationally intensive and requires more a priori knowledge but usually gives the most accurate inversions. The six unknown parameters (aph(440), ag(440), X, H, bbp(550), and ) are iterated to minimize the difference in the RM S error between the measured and modeled Rrs( ). If the model results in a bottom reflectan ce that is greater than 20% of the total irradiance reflectance, then the model is iterat ed a second time. If af ter the first iteration, PAGE 62 44 the irradiance reflectance from the bottom is not above 20% of the total irradiance reflectance, the model is reset and iterated using an equation that doesn't include the terms for the bottom reflectance. Unlike the QAA model this model was changed several times throughout this research and the changes were adopted so as to present the most complete analytical model for Rrs inversions. One of these changes to the deep water rrs( ) "g" factor involved the partitioning of it into effects due to molecular backscatte ring and particulate backscattering (Lee and Carder 2002, Lee et al. 2004). 3.6. Kd() inversions The Kd optimization algorithm is the most complex of the three models and originated from this research. The development of this algorithm was based on a similar approach as that used for the Rrs optimization algorithm. While a Kd( ) measurement does not have as long of a path length as a Rrs( ), it is very sensitive to absorption and has little influence from bottom reflectance. The order of the three models presented will proceed from most empiri cal to most analytical. 3.6.1. Kirk The factors used to invert Kd( ) to get a( ) from the Kirk empirical model were formulated from a series of MonteCarlo runs (Kirk 1991). 5 0 2 1440 440 1 a b g g K aw w d Equation 3.6 The w is calculated using Snell's law. The "g" factors corr espond to pathlengthelongation factors from model runs based on phase functions from San Diego Harbor (Petzold 1972). Their values are g1 = 0.425 and g2 = 0.19. The b/a ratio is assumed to be 2.8 based on the mean ratios of ac9 measurements used in this study. 3.6.2. Loisel The Loisel Model is an empirical mode l that uses the below water irradiance reflectance and diffuse attenuation to calculate absorption (Loisel et al. 2001). Since R( ) was not collected in this study, it was ca lculated by the method of Carder et al. (1999) using the above water Rrs( ) and a Q factor of 3.9 sr (Morel and Gentili 1993). 5 0 2) ( 1 ) ( 89 19 54 6 54 2 1 R R K aw w w d Equation 3.7 PAGE 63 45 rs rsR R R 7 1 52 0 9 3 Equation 3.8 Kd( ) is the value calculated from the Spectrix belowwater irradiance sensor without normalization. The w is the subsurface average co sine calculated using Snells law. This model can also determine b( ) and bb( ) but since it relies on the below water reflectance and was not designed to work in the shallow waters with high bottom reflectance, it was only used to determine anw( ) in this study. 3.6.3. Kd Optimization The Kd( ) optimization model is a combinati on of several other models and is solved with an iterative process using the so lver function in an Excel spreadsheet. The goal of this model is to use a co mmon oceanographic measurement and known relationships between AOPs and IOPs to de termine hyperspectral de pth profiles of IOP values. The diffuse attenuation coefficients ar e normalized to a black sky and sun at zenith by using the correction factors of Gordon (1989). sky E sun E sun E Fd d d Equation 3.9 The symbol "F" is the fraction of direct sunlight in the inci dent radiation. Ed(sun) and Ed(sky) are both obtained from the output of the Radtran solar irradiance model (Gregg and Carder 1990). The angle of the incident radiation be low the sea surface is calculated using Snells law. 34 1 sin sin1 s sw Equation 3.10 The symbol sw is the angle below the surface and s is the above surface angle. A normalization factor (D0) can then be calculated for Kd at each wavelength converting it to an approximate value for th e sun at zenith and black sky. F F Dsw 1 197 1 cos0 (Gordon 1989) Equation 3.11 The Kd(normalized) is calculated by dividing the Kd(measured) by D0. A modeled Kd( ) for comparison to the Kd( ) normalized is calculated by Preisendorfers equati on (Preisendorfer 1961). PAGE 64 46 ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( R b b a Ku b d b d d Equation 3.12 The adg( ), aph( ), and bbp( ) are modeled by the same method used in the Rrs( ) optimization model (Equations 3.1, 3.3, and 3.4 respectively). The aw( ) is adjusted for in situ temperature differences from the values measured by Pope and Fry (1997) using the correction coefficients determined by Pega u et al. (1997). The average cosine due to scattering ( us) of upwelling irradiance and is allowe d to vary in the iterative process, is limited to values between 0.35 and 0.5 in value (Kirk 1994), and assumed to be constant across all wavelengths. The average cosine of downwelling irradiance due to scattering ( ds) is determined by iteration and varied spectra lly by an empirical equation. Gordon's normalization theoretically removes the effect s of the sun angle, diffuse sky light, and refraction on the Kd( ) value. The dvalues in Preisendorfer' s (1961) equation should equal a columnintegrated average cosine of scattering in the forward direction ( ds) after the light field effects are removed by Gordon's (1969) normalization. Ratios of bbp( ) to bp( ) were calculated using integrated in situ values from the study sites at wavelengths from 400 to 700 nm at 50 nm increments. The ratios were used in an inversion of the HenyeyGreenstein (1941) phase function to determine the average cosine of scattering in the forward direction. The resulting ds values were close to linear versus wavelength over the 400 to 700 nm range allowing a linear regression model to estimate its value. The regre ssions have a correla tion of 0.95 between ds and wavelength. Values of 0.000025 for the slope and 0.95 for the intercept were used to initialize the iterative model. Absorption values were initialized at 440 nm by using Kirk's (1981) empirical model (Kirk 1981). KruskalWallis (Zar 1994) statistical comparisons between Kirk's model and other methods and models for determining anw(440) showed that it was statistically the same. Unde r certain environmental conditions, Kirk's model was found to produce overestimates. A test of the Kirk a( ) result was determined by subtracting the quotient of the normalized Kd(440) value as divided by an assumed ds of 0.95. If the result was greater than zero, the initial value of aph(440) was estimated at 50% of the anw(440) value from Kirk's model. If the va lue was less than 0, 40% of the value from Kirk's model was used. If this was not done the model would occasionally iterate to a local minimum. The initial value of ag(440) was estimated as being equal to the aph(440) initial value. The influence of the final set of terms in Equation 3.12 (R( )*bb( )/ u) is very small on the overall model and could po ssibly be ignored. In cluding it does improve accuracy of the model especially in highly scattering waters. The R( ) is estimated by using the values of bb( ) and a( ) from the inversion and ente ring them into the equation PAGE 65 47 for deep rrs( ) from Lee et al. (1999) and converting the rrs( ) to irradiance reflectance using a Q factor (Morel a nd Gentili 1993, Equation 3.12). b b b bb a b b a b R * 68 0 336 0 Equation 3.13 The backscattering coefficient can be dete rmined by solving for it analytically. To smooth out measurement noise, Kd(500) and a(500) are binned over a 10 nm range. An estimate of bb(500) is determined by assuming that the last term in Preseindorfer's (1961) equation (Equation 2.9) is small in value relative to bb(500), and by subtracting the a(500) from Kd(500)/ 500d The estimated bb(500) is then inserted into Equation 3.13 to estimate R(500). Since all other terms are now known, bb(500) can be determined using Preisendorfer's equation as a functi on of the three iterated values. The bbp(500) value is calculated by removing bbw(500). This eliminates the need for iterating bb(500) and adding another source of error in the model. By solving for bbp( ) at another wavelength and applying the power function equation for bbp( ) (Equation 2.4), it would theoretically determine the coefficient for bbp( ). However, the spectral Kd( ) values would have to be much more accurate than those in this study. Attempts to do an analyt ical solution resulted in unrealistic values for some stations. The bbp( ) Y coefficient is instead iterated over an expected range of 0 to 2. The optimization involved minimizing the sum of the absolute value of the measured minus modeled values divided by th e modeled values for 400 nm to the lowest error longer wavelength. The lowest error upper wavelength was determined by taking the percent difference between the normalized Kd( ) and aw( )/ ds for wavelengths greater than 600 nm. Above 600 nm, Kd( ) is dominated by the absorption due to water. This also results in low signaltonoise rati os if there are not a significant number of measurements in the upper 5 meters of the water column. If the percent difference was greater than 10%, the wavelengt h is set as maximum wavelength for the curve fit. This allowed the model to use the largest number of wavelengths to get the best fit. The iterations were calculated using the so lver routine in Microsoft Excel but this model could be used with other iterative code such as in Matlab. Using the macro feature of the spreadsheet the entire data set coul d be processed automatically. The values iterated were aph( ), ag(440), Y, us, the ds slope, and the ds intercept. The coefficient for ag( ) was iterated through a Visual Basic macro that tested the fit of the modeled Kd( ) using 3 different coefficients. If the percent error was lowest for the median coefficient, it was selected. If the percent error was lowest for the higher or lower coefficient, it was set as the median and the testing repeated Testing continued until the median value had lowest percent erro r or a limit was reached. Improvements to this model along with better measurement techniques could eventually eliminate several more of the iterated variables. PAGE 66 48 3.7. Note on recent progresses in instruments and algorithms Most of the instruments and models repr esented the state of the art for optical oceanography at the beginning of this st udy but because of the rapid change in technology and advancements in understanding of ocean optics, they will likely not be state of the art at the time of this study's pub lication. The best approach is to use these references as a starting point and go forward fr om there. However, the latest method or model has yet to go through the rigorous tes ting that these have been through and may have some faults not yet revealed. It is hope d that the testing perf ormed in this study can act as an approach for testing of the next advancement in optical oceanography measurement or modeling. PAGE 67 49 4.0 Statistical Methods 4.1. The Unbiased Approach The approach to optical closure as disc ussed in the backgroun d chapter can vary depending on the objective of the oceanographer. Some are testing their models. Others are comparing instruments. Most are compar ing an instrument or algorithm against some commonly accepted optical measurement method. The objective of closure in this study is to determine which method gives the best result under different c onditions. No method or model is assumed to be the absolute truth but all are assumed to be close to the truth. By using this method, the results should be more objective than the common approach. Bias towards a particular instrument or algorithm can potentially influence a researcher's interpretation of the results. Th is bias sometimes results in the clich, "You can make anything true with st atistics". Actually nothing can be further from the truth. Statistics are simply a mathematic form ula and if applied correctly according to mathematically proven methods, they can provi de a wealth of information about a data set. The "lies" occur when the statistics ar e incorrectly applied or the input data set is manipulated to bias it towards one particular outcome. This "lie" is a failure of the researcher and not the statistics. It is lik e blaming a hammer because the nail was bent. The statistics are fairly complex so th e methods in this se ction will cover the approach in some detail. Unless otherwise not ed, all statistical methods were taken from Zar (1994). All the processing of the stat istics was through the Matlab programming language. If Matlab did not have a required statistical method, the method was coded into Mat Lab and debugged using the example da ta given for the particular method in Zar (1994). The results following the statistics are pr esented primarily in graph form. After the initial testing to determine the proper numerical filters based on environmental conditions, the results will be presented by IO P and filter type. The first filter under absorption and the first filter under backscattering will have a detailed analysis of the results. The rest of the sections will have a page summary only mentioning the major observations for each IOP and filter type. The ta bles of results and statistics are given in the appendix. PAGE 68 50 4.2. Interpolation and Integration The IOP values derived from the hypers pectral instruments and methods were spectrally binned to match the wavelengths of the instrument with the lowest spectral resolution. For the absorption values the ac9 wavelengths of 412, 440, 488, 510, 532, 555, 650, and 676 were used. These wavelengths correspond to those measured by ocean color satellites and the important chlorophyll a absorption peaks. The center bandwidths for MODIS aph( ) values required some interpolation to the match the ac9 wavelengths. The MODIS algorithm derives the ag(400) value and uses a constant coefficient so Equation 3.1 could be used to calculate a value at any wavelength. However, output for the MODIS algorithm for aph is at 412, 443, 490, 510, 555, and 675 nm so it involved only a slight li near interpolation from 443 to 440 nm, 490 to 488 nm, and 675 to 676 nm. This interpolation resulted in slightly better agreement for the MODIS anw( ) with the other methods. MODIS aph( ) were interpolated to 532 and 650 nm and that interpolation may lead to some error for aph( ) and anw( ) at those wavelengths since these inter polations were more than a just a few nanometers. An aph(750) of zero was added to the data set to aid in the interpolation fit. A Matlab routine using a 4thorder polynomial fit interpolated the aph(532) and aph(650) values for each MODIS output. This interpola tion of MODIS values improves the statistical comparison between it and the other met hods by putting all the values at consistent wavelengths. The bbp( ) values are compared at the Hydroscat6 wavelengths. The Hydroscat6 provides the only in situ measurement of bb( )and has measurements at 442, 488, 532, 555, 620, and 675 nm. The models use a power function to spectrally model bbp( ) so extrapolation to the Hydroscat6 wavelengths will not require any interpolation. The three Rrs( ) inversions all use a sim ilar approach to modeling bbp( ) so the Rrs inversions bbp( ) values may be similar in results. Kd( ) optimization is expected to have the most error since bbp( ) is a small contribution to the signal compared to anw( ). The anw( ), ag( ), and bbp( ) from the depth profiles by the in situ instruments had to be integrated over depth weighted to Kd( ) to compare the values from the Rrs( ) and Kd( ) inversions. According to the BeerLambe rt law, light intensity will decline logarithmically as it passes through a material. A simple mean of the IOPs values will not work because the contribution by IOP values near the surface should have a higher weight for their absorption and scattering valu es. Light is absorbed near the surface so there is less light at depth than at the su rface. Less light at depth means less to be scattered back towards the surface. Once the light is scattered back towards the surface, it takes a longer path, increasing its chances of being absorbed as it passes back through the surface layer. The equation assumes that the downwelli ng diffuse attenuation is close to the value of upwelling diffuse attenuation (Equation 4.1). The path is assumed to be double the change in depth (dz) since the light travel s down to that depth then returns upward. PAGE 69 51 Equation 4.1 The IOP value (a) is integrated to one attenuation depth (1/Kd( )) because about 90% of the contribution to the Rrs( ) signal comes from this de pth (Gordon and McLuney 1975). Unless the IOP properties are constant over de pth, integration with weighting to the diffuse attenuation coefficient better represents the value returned from an Rrs( ) or water column Kd( ) inversion algorithm (Smith 1981, Bana rd et al. 1999, Ivey et al. 2002). 4.3. Statistical Tools Since statistics is a box of tools that ca n be easily misapplied, it is important to first access what is required. This study is comparing separate popul ations of data and not trying to determine something about a la rger population based on a sample. The first task is to see whether the results of th e different instruments and algorithms are statistically similar and when they are not similar, to determine what environmental conditions cause these differences. The next goa l is to determine what is closest to the actual value for each IOP. Finally the algorith ms and models will be compared to this "ideal" value and analyzed fo r the conditions where they ag ree and disagree. The method or model that gets closest to the "ideal" va lue for given environmental parameters at a given wavelength is judged to be th e best method under those conditions. One objective of this analysis is to a void preconceptions about the methods and where they may be affected by different en vironmental parameters. However, data collected that were less than 0 in value were obviously not real da ta. Negative absorption or backscattering values are not possible. A ny values less than or equal to zero were assumed to be due to an error in the measurem ent or model. To include these data could also cause errors in the statistical calcul ations. A filter was first used before each statistical test to remove these values. Si nce these values represent an error for that particular method, they had to be accounted for. Failure to account for outliers would make a method that produced erroneous va lue under certain cond itions appear more accurate than it should. Each value removed was added to a calculation of the percent outliers for each method under the tested filter and wavelength. Parametric statistics are more powerful th an nonparametric statistics but cannot be applied if a set of data is not normally distributed or transformable to a normal distribution. To select the right statistical tool, a test for normality was required. The D'Augustino and Pearson K2 statistic combines tests for kurtosis and symmetry resulting in a Chi square value that can indicate nor mality (Zar 1994). Most of the histograms of d o d d o dK z z dz k K z z dz ke e a/ 1 0 2 / 1 0 2 ) (1 1 rs R) ( ) ( a PAGE 70 52 IOP values tended to be extremely peaked at one area and skewed towards the lower range values. The testing of the IOP output va lues from the different methods at the study wavelengths determined that they did not ha ve a normal distribution. Therefore, the KruskalWallis rank sum test with pair wise comparison was determined to be the best nonparametric test to intercompare the different values (Zar 1994). 4.4. Determining the Filters Solar zenith angle, cloud cove rage, and significant bottom re flectance are external factors that can affect an AOP measurement. Sea surface conditions and sun glint can also contribute to errors in AOP measurements but are difficult to quantify. For this reason, this study will focus on the affects of the prior th ree conditions to filter the results so that the model inversions are compared in fair manner. Absolutely perfect conditions for AOP measurements are cloudless skies, solar zenith angles less than 45 (but not high enough to result in sun glint), low attenuation waters and no bottom reflectance. If the stations in this study were filtered to perfect conditions there woul d not be enough measurements to have a valid statistical comparison. To determine the maximum acceptable solar zenith angle, cloud cover, and bottom contri butions, a series of comparisons were performed for anw( ) and bbp( ) using the KruskalWallis nonparametric test. The steps for determining the proper filters are listed in Figure 4.1. Significant bottom contribution is we ll known as a problem in algorithms inverting Rrs( ) to determine IOPs (Lee et al. 1999). Of the Rrs( ) inversion methods, only the Rrs( ) optimization model includes bottom al bedo as one of the inputs so bottom reflectance is expected to be a factor for th e MODIS, QAA, and Kd Loisel algorithms. The bottom contribution is usually greatest in shallow clear waters such as those in the Bahamas. While the reflectance should not be a significant effect on the other methods, shallow clear waters could cause errors in Kd( ) inversions, as well as the ac9 and the Hydroscat6 measurements. Shallow waters mean that the irradiance measurements used to determine Kd( ) could experience more wave fo cusing throughout the profile. The irradiance sensor might never get to a de pth where light scattering had minimized the effects of wave focusing. In very shallo w water the ac9 may have troubles clearing bubbles that can be compressed and expelled when the instrument is sent to a depth of around 30 m. Even though the source light on the Hydroscat6 is modulated so that ambient light interference is minimized, a bright white sand bottom in the Bahamas may reflect enough light to cause so me errors in its measurement. While the algorithms that include Rrs( ) as an input are expected to have the greatest problems with a significant bottom contribution, all methods and instrume nts will be tested fo r agreement under the different conditions. PAGE 71 53 Filter set to best conditions for bottom, cloudiness, and zenith anw( ) and bbp( ) data from all methods at a given wavelength Remove missing and less than or equal to zero values Filter based on bottom reflectance: = 0%, <= 1%, <= 5%, <= 10%, <= 20%, <= 30%, <= 50%, and > 0% Filter based on cloudiness: < 3%, < 5%, < 10%, < 20%, <40%, < 50%, < 80%, and <= 100% Filter based on solar zenith angle: < 35, < 43, < 46, < 48, < 55, < 60, < 68, and < 90 KruskalWallis Pair wise comparison to determine agreement between methods Plot to determine when agreement drops Filter data using maximum allowable level of bottom reflectance KruskalWallis Pair wise comparison to determine agreement between methods Plot to determine when agreement drops Figure 4.1. Method to determine filters for bottom reflectance, cloudiness, and solar zenith angle. Before cloudiness or solar zenith angle could be tested, it was first necessary to determine the maximum contribution from the bottom that could be tolerated and still achieve agreement among the methods. The output from the Rrs( ) optimization model gives an estimated rrs( ) due to bottom reflectance. A ratio of this output to the total belowwater radiance reflectance was used to filter the stations. The data were filtered to where there were 0%, <= 1% bottom, <= 5% <= 10%, <= 20%, <= 30%, <= 50%, and PAGE 72 54 >0% bottom contributions. The unfiltered data we re also included in the test. A KruskalWallis pair wise comparison ( = 0.05) was performed to determine the best agreement among the methods. The maximum acceptable bottom percentage was based on where there was decline in agreement between the IOP results from each method. After removing the stations where bottom contribution was significant, the next two conditions were expected to have influence on both Kd( ) and Rrs( ) measurements. The stations were filtered by cloudiness usi ng less than 3%, 5%, 10%, 20%, 40%, 50%, 80%, and 100% cloudiness. Cloudiness was a subjective estimate based on a visual observation of the sky while collecting an Rrs( ) measurement. The reason that 0% was not selected is that there were only 2 stations where there we re completely clear skies. The data were filtered according to solar ze nith angle. Angles le ss than 35 were not considered since shallower angles are usually not considered to be a major problem for Rrs( ) (if sun glint is not seve re) and were not expected to be a problem for Kd( ). However, in hindsight, filters for lower solar zenith angles probably should have been included as some errors were revealed at lower angles for some of the AOP measurements. Solar zenith angles were calculated using a formula based on the location, date, and time (Gregg and Carder 1990). The stations were filtered by less than 35, 43, 46, 48, 55, 60, 68, and 90 zenith angles. Using a KruskalWallis pair wise comparison with ranks ( = 0.05), the groups of different le vels of solar zenith angle and cloudiness were tested to determine agreement with each other. Based on the levels of agreement a filter was determined to remove stations that did not meet the criteria. The IOP output data were categorized into anw( ), ag( ), bbp( ), and aph. Each IOP group was filtered for comparisons. The filt ers were all the data (NF); all the data with minimum bottom influence (NB); minimum bottom, low clouds, and low zenith angle (NBLCLZ); MODIS semianalytical only with minimum bottom (MODNB); all stations with greater than 0% (BT); and great er than 0% bottom with low clouds and low zenith (BTLCLZ). The MODNB stations were selected because the MODIS algorithm in high chlorophyll waters defaults to a simple empirical algorithm instead of the iterative model. The MODIS algorithm was designed to work on large pixel per kilometer satellite images and not for highchlorophyll ne ar shore waters. Including the empirical values would have not been a fair test for th e most effective part of the algorithm. One filter that probably should have been included was for stations where attenuation was significantly higher. The ac9, Hydroscat6 and laboratory spectrophotometer methods may have performed better under this filter th an under the other filters. A group is defined as all the stations from a method for an IOP value (either anw( ), bbp( ), ag( ), or aph( )), at a one of the tested wa velengths, filtered to remove values less than or equal to zero, and with a filter applie d to remove stations that do not meet certain environmental criteria. With the filters in place, the methods can now be compared under different environmental conditions. PAGE 73 554.5. Test for Normality After Applying a Log Transform A log transform may result in normal distribution for data that has multiplicative increases in value (Zar 1994). Previous st udies have presented evidence that a log normal distribution may apply to biooptic al properties (Campbell 1995) for a given location and time. The primary reason for knowing a distribution for measurement values is to interpolate values with high vari ability over small scales to compare to data collected over larger scales. A l og transform was attempted on the anw( ) data to determine if it would be normally distributed and allow the use of parametric statistics. Statistical testing using th e D'Augustino and Pearson K2 test for normality ( = 0.05) demonstrated that much of the logtransforme d data was not normally distributed. Out of 58 combinations of methods and wavelengths for anw( ), 29% under the NF filter, 59% under NB filter, and 72% under NBLCLZ data are normally distributed. A parametric statistic will not be vali d even with a log transform for this data set. It appears that as the data set moves to more ideal conditions, the da ta become closer to a normal distribution with a log transform. However, even under the best conditions 28% of the data is not normally distributed so using this transfor m would result in comparing data with a normal distribution to those not normally dist ributed. The lack of normal distribution was not unexpected since the data used for th is study were collected from three different areas during different seasons a nd years. If the data were from one area at a single time and included not just near shore data but several deep offshore transects, then a log normal distribution might be valid. 4.6. Statistical Comparison s to the Ideal Values The KruskalWallis pairwise comparison with ranks was computed between the methods for each IOP type, filter set, and test wavelength ( = 0.05). The results were used to determine which data at which wavele ngth could be used to calculate an idealized data set for each IOP type and filter. The assumption was made that no technique was better than the other. The exception was the Kd( ) Loisel, Kd( ) Kirk, Rrs( ) MODIS and Rrs( ) QAA inversion algorithms were not includ ed for the two filters with significant bottom contribution. The Loisel, MODIS, and QAA models do not take into account significant bottom reflectance. The Kirk Kd( ) inversion is an empi rical model that did not perform well at longer wavele ngths and was left out of the anw( ) with bottom data because it might bias the result towards the Kd( ) inversions for the ideal data set. The assumption was made that, if for each group there was agreement with over 50% of the other methods in the group, then that techni que was close to the actual value. If for a given wavelength there were no methods that reached the level of 50% agreement under the filter, then the methods with the highest level were selected for determining the ideal value. For each sample station in the groups that met the agreement criteria, a median value was calculated and labeled as the ideal value for that group. Because of occasional outliers due to a bad measurement or fault in an algorithm, a median is a better statistic than a mean because it does not factor in large outliers like a mean. Figure 4.2 summarizes the steps to determine the ideal value. PAGE 74 56 Figure 4.2. Summary of steps used to determine ideal data set. The idealized data for each IOP type we re compared to all techniques for each wavelength and filtered subset. While some models were left out of the ideal data set calculation when bottom contribu tion was significant, all models were tested against the ideal data set. Regression analysis versus the ideal value was performed to determine how close each group matched the ideal line with a slope of one and an intercept near zero. The correlation coefficient was calculated for each group based on the correlation between the group and ideal data, not with the regression line. The mean percent error and the mean abso lute percent error from the ideal value were calculated. Mathematics and physics text s sometimes refer to both absolute and the nonabsolute error statistics as percent error. Since both are used in this study, they will be referred to as percent error and absolute percent error. In equation (4.2) for the mean absolute percent error, IOPmj is the method value, IOPij is the ideal value, and n is the Data at a single wavelength Remove missing and values le ss than or equal to zero Filters applied for either NF, NB, NBLCLZ, MODNB BT, or BTLCLZ All data from IOP to be tested [(anw( ), bbp( ), ag( ), or aph( )] KruskalWallis Pair wise comparison to determine agreement between methods Method agrees with 50% or more of other methods? Yes Method included in ideal data set No Method not in ideal data set Ideal data is the median va lue for a given station, IO P, wavelength, and filter type for those methods that have 50% or greater agreemen t with each other PAGE 75 57 number of samples after filtering. The mean percent difference is calculated the same way except the absolute value is not take n for the difference between the method and ideal values. The use of several different st atistics allowed for better determination of how each method performs under different conditions. Mean Absolute Percent Error n IOP IOP Iopn j ij ij mj 1100 Equation 4.2. The percent error calculated two different ways reveals both the magnitude and direction of the difference from the ideal value. If the absolute value were not used, errors due to accuracy that are even in magnitude about the ideal value would result in an artificially low value for the percent differen ce. However, because there is no sign to the absolute percent difference, it is not clear whether the error is under, over, or around the actual value. In figure 4.3 a series of numbers increase linearly from 0.025 to 1 by 0.025 steps as an example of ideal data. If 10% error occurs in evenly in both positive and negative directions (Figure 4.3A ), then the mean percent error is 0 but the mean absolute percent error is 10%. If the values vary evenly between a 5% overestimate and a 15% underestimate (Figure 4.3B) then the mean perc ent error is 5% and the absolute percent error is still 10%. This lets us know that on average this method will slightly underestimate the values and has an error of 10%. The linear regression by itself doesn't give a good idea of the overall error. The regres sion in Figure 4.3A results in a slope of 1 and an intercept of 0.0037 with a correlation of 0.96. This regression looks pretty good but the mean absolute percent difference gives us an error of 10%. Combining the mean percent error and mean absolute percent error gives a lot more information about agreement to the ideal value than regression analysis alone. PAGE 76 58 A. Method Value 0.0 0.2 0.4 0.6 0.8 1.0 1.2 One to one line Test data Regression B.Ideal 0.00.20.40.60.81.01.2 Method Value 0.0 0.2 0.4 0.6 0.8 1.0 Figure 4.3. Examples of how combinations of mean percent error and absolute percent are used to give more information about differences from ideal values. PAGE 77 59 Determination of outliers for normally distributed data is fairly straight forward, but tests for outliers under othe r distributions for data can be more difficult. A test was devised to determine what stations needed to be removed from each group to achieve a match to the ideal data that was within 10% of the ideal values. The maximum and minimum slopes of the idealized IOP data for each group were calcul ated for variations of plus or minus 10% in the data (Figure 4.4) The stations used in the ideal group were first filtered to match the same stations in the group tested. The maximum slope was calculated assuming the maximum value of th e idealized data was 10% greater and the minimum value was 10% less. Decreasing the maximum value by 10% and raising the minimum value by 10% calculated the mini mum slope. The slope of each group was compared to determine if it fell within the range of slopes. If it did not, then the station with the highest absolute percent error was excluded and marked as an outlier. The slope was then recalculated and compared to th e minimum and maximum slopes. This was repeated until the slope fell within range of minimum and maximum slopes. This technique allowed identification of outliers at individual stations for each group. The percentage of outliers was calculated by adding the number of rejected values to the number of negative and zero valu es and dividing the total by the total number of values for that group. The flow chart for th is method is summarized in figure 4.5. Figure 4.4. Example of slopes for +/10% of the ideal data. A) Minimum and maximum slopes are covered by +/10% lines. B) En larged section that shows the minimum and maximum slope lines (dotted) at low values. Ideal 0.00.20.40.60.81.0 Test Values 0.0 0.2 0.4 0.6 0.8 1.0 Ideal Values 1 to 1 line +/10 % Ideal 0.040.060.080.10 Test Values 0.04 0.06 0.08 0.10 Idea Values One to one line Min and max slopes +/10% A. B. PAGE 78 60 Figure 4.5. Steps used in determination of outlier by comparison against slope values. The absolute percent errors for each station within a group were tested for correlation with environmental factors and IO P values to determine the possible sources of error for each method under those c onditions. An initial test for anw() and bbp() values found that possible contributions to uncertainty were highest for chlorophyll concentration, percent cloud cover, solar zenith angle, maximum percentage bottom reflectance, cnw(440), and anw(440). Ratios of bp(440)/cnw(440), bbp(440)/bp(440), and bbp(440)/anw(440) were also used to help diagnose factors contributing to signals. The correlations were tested for significance using the Fisher z transfor mation for correlation ( = 0.05, Zar, 1994). Only the significant corr elations were published in this study. Figure 4.6 provides an overview summary of the statistical method used this study to compare the different methods to the ideal values. IOP from a single method at a single wavelength Filtered to remove missing and values less than or equal to zero Filtered for different environmental conditions Ideal values filtered to match same stations as data tested Values less than or equal to zero equals outliers Slope for +/10% of ideal value calculated Is slope of data vs ideal within 10% range? Yes. Total outliers divided by total number of non missing data points x 100 to get percent outliers. No. Remove data point with highest absolute percent difference. Add 1 to outliers PAGE 79 61 Data from a single method at a given wavelength Filtered to remove missing and values less than or equal to zero Filtered to test different conditions Ideal values filtered to match same number stations as filtered data Linear regression vsideal values Percent error Slope Intercept Correlation Mean of Percent error Mean of absolute percent error Correlation vsparameters for each data group Correlation tested for significance Value Significant Value not significant Outlier Analysis Absolute percent error Figure 4.6. Statistical method for analyz ing study data to determine closure. PAGE 80 62 5.0 Optical Closure Results 5.1. How to Interpret Results To aid in the presentation of the results, labels are used to represent each method. The Rrs() optimization model (Lee et al. 1999) is referred to as Rrsopt, the Kd() optimization model is referred to as Kdopt, the Kirk Kd() inversion model is referred to as KdKirk (Kirk 1991), and the Loisel Kd() inversion model is referred to as KdLoisel (Loisel et al. 2001). MODIS and QAA Rrs() inversion results will be called MODIS and QAA. The quantitative filter pad met hod is referred to as Specaph, the spectrophotometric chro mophoric dissolved organic abso rption or CDOM measurements are referred to as Specag, and the nonwate r absorption value from the sum of Specaph and Specag is referred to as Spec. The 9channel attenuation and absorption meter is referred to as ac9 and the 6 channel backsca ttering meter is referred to as HS6. These abbreviations should make presentation of th e results less verbose and help graphics labels fit within limited space. In examining the results of these stat istical tests, there are a couple of considerations. The KruskalWallis Pairwise comparison with tied ranks (KW) determines statistical agreement between groups Agreement under this statistic does not always mean that it is the closest to the act ual value but means that it is statistically similar to some of the other methods. For example, it is known that Rrs() inversions are affected by bottom reflectance (L ee et al. 1998). All the Rrs() inversions in this group use a similar approach to determine bbp(). Bottom reflectance has a similar effect on the Rrs() curve as bbp() since both can contribute to in Rrs() in the 500 to 600 nm region. If all the Rrs() inversions are overestimating bbp() in a similar manner then they may agree with each other and have good results unde r the KW test but they may not be close to the actual value. The methods that return a bbp() value are three Rrs() inversions, a Kd() inversion, and the HS6. The pote ntial for a bias by errors in Rrs() inversions is why only Rrsopt, Kdopt, and HS6 were used to determine the ideal value for bbp() when bottom was present. Because of potential agre ement between methods with errors in the same direction, this study does not rely on only one statistic to test these methods. The percent error term resu lts can cause a little conf usion because of the method for determining the ideal value. Only the st ations with 50% or greater agreement for the combination of filter, wavelength, and IOP valu e are included. A median of those values was used instead of a mean. A median was necessary to minimize the influence of large outliers in a particular method for a particul ar station that could introduce error in the ideal value. Comparing this ideal to the actua l data can result in percent difference values that would look much different than if all data were included in the ideal value and a PAGE 81 63 mean of those data were used. An even di stribution about zero woul d be expected if the mean of all the methods was used for each statio n but is not expected under this statistical approach. Further complicating interpretation of these data is that a mean of the percent error values is used instead of another medi an. The reason a mean value of the percent error is necessary is because taking the medi an would result in va lues of zero percent error for some of the methods since their valu e represented the median value for over half the stations. Testing the percent error statistic s shows that they are normally distributed for most groups so using a mean is not too fa r outside limits of sta tistics. The values are going to be different from th e percent difference from the mean but will give more information about errors in the methods. The outlier analysis is based solely on wh ether the slope is clos e to a slope of one. This statistical method was devised to attemp t to test for outliers under a case where a normal distribution does not apply. There can still be some outliers based on the intercept. The outlier analysis should be ta ken with the caveat that it removes data that would cause a multiplicative error but not data that might cause a bias. The best way to look at this statistic is if the method has a low number of outliers and intercept near zero under the initial regression but a high absolute percent error, then there are probably a few really large outliers that are causing the er ror. If the intercept is high, outliers are low, and the absolute percent error is high then the method probably has a constant bias. The case where outliers are high bu t the other regression, correl ation, and error statistics are good may indicate a consistent factor that causes a small error in these values. None of these statistics are definitive by themselves and all should be examined to get the complete picture. The absolute percent error values were examined as to their correlation with certain parameters. The correlation only indi cates a possible relationship between that parameter and the error. Two things must be considered when examining these results. First, a high positive correlation with a para meter does not mean a high percent error when that parameter is larger. It simply means that the source of error may be that parameter but has no indication on the magnitude of the percent error. Rrsopt may have a large correlation with bottom contribution to reflectance but it may only cause a 5% change in percent error. Secondly, correla tion does not mean causality. A correlation between absolute percent error and bp/cnw(440) occurred along with correlations with significant bottom contribution to reflectance. Th is correlation is more a factor of the shallow stations during the CoBOP cruise ha ving a significant bottom reflectance while coincidentally having high ag() to aph() ratios. The bottom re flectance is correlated with bp/cnw(440) for these regions. The correla tion with causality is the increased proportion of light from these sh allow bright bottoms not the bp/cnw(440) value. While it can be stated that the magnit ude of the correlation can explain that proportion of the error, the sum magnitudes of all the correlations for a given group can sometimes be above one. A correlation above 1 is because some of the parameters have interdependencies. The b ackscattering ratios of bbp/anw(440) and bbp/bp(440) both depend on the magnitude of the backsc attering so they may have si milar correlations values. PAGE 82 64 Chlorophyll concentration can be a surrogate for anw(440) since, generally, higher chlorophyll concentratio ns lead to higher aph(440) values. Sometimes there are parameters that will affect all of the othe r methods biasing the ideal value. A large correlation between the ac9 and cloudiness or zenith angle indicates that the AOP methods are affected in the same way resulti ng in a possible error in the ideal value not the ac9 value at that wavelength. By exam ining these results there can be valuable information for improving the methods but re lying just on the correlation value without examining causation and the magnitude of the percent error would not be a valid approach. The results from each test and the disc ussion about those specific results are presented in this chapter. E ach statistical test is followed by a discussion of the results. The first section will cover the determination of filters. The next section will cover the nonparametric tests to determin e the ideal data. The compar isons to the ideal data are sectioned accord to the IOP value tested. Th e filters are grouped together according to similarities. The unfiltered data and bottomfiltered data are grouped together (NF and NB). The ideal AOP conditions are groupe d together (NBLCLZ and MODNB) and the two filters that include only stations with significant bottom contri bution are grouped (BT and BTLCLZ). The percent error correlations are presented by IOP type with a focus on major spectral correlations. 5.2. Determination of Filters Based on Bottom, Clouds, and Zenith Angle In Figure (5.1), the ac9, Rrsopt, KdKi rk, and KdLoisel all demonstrate less agreement for anw when the percent bottom reflectan ce is greater than 10%. The agreement in the other models does not necessa rily mean that they perform better when bottom is present. It may mean that they have errors in the same direction. An indication of this is the error in the ac9 and KdKirk anw(). The ac9 is not affected by bottom reflectance and only bright shallow bottoms s hould affect the KdKirk model. However the ac9, anw(), and Kd() values may be affected by shallow clear waters. The ac9 may not be able to get deep enough to clear th e small bubbles within the instrument. The downwelling irradiance sensor may not be able to get deep enough to avoid wave focusing. Since all three methods have less agreement when the bottom contribution is above 10%, the filter is set to th is value. This filter was applied to the data before testing for affects of cloud c over or zenith angle. PAGE 83 65 Figure 5.1. Nonparametric statistical analysis of anw() values of each method under different levels of bottom reflectance ( = 0.05). The left axis is the mean percent agreement of each method with the other met hods averaged over all the wavelengths. The =>0% bottom contribution value repr esents the entire data set. Figure 5.2. Nonparametric statistical analysis of anw(676) of each method under different levels of cloudiness ( = 0.05). The left axis is the percent agreement of each method with the other methods at 676 nm. All other wavelengths exhibited good agreement among the methods. Type ac9MODISKdoptRrsoptSpecKdKirkKDLoiselQAA Percent agreement 0 10 20 30 40 50 60 70 80 90 100 110 = 0% <= 1% <= 5% <= 10% <= 20% <= 30% <= 50% => 0% Type ac9MODISKdoptRrsoptSpecKdKirkKDLoisel Percent agreement 0 10 20 30 40 50 60 70 80 90 100 110 <= 3% <= 5% <= 10% <= 20% <= 40% < 80% <= 100% PAGE 84 66 The percent cloudiness has a minimum affect on anw() at levels below 80%. This consistency resulted from an effort to only take measurements when the solar path was cloudfree. It doesn't appear to have much affect except for Kd() inversions at longer wavelengths (Figure 5.2). At 676 nm, the KdKirk and KdLoisel exhibit a drop in agreement for cloud coverage greater than 40% The Kdopt model al so exhibited similar problems in earlier tests but changes to the model appear to have minimized those problems. The difference between 80% and 40% clouds is 10 stati ons so a significant number of data would be removed to benef it those two models at longer wavelengths. The filter was set for removal of stations where cloud cover was greater than 80% to retain the maximum number of reasonable data points. Zenith angle did not exhibit any clear affect on anw() (Fig 5.3). The biggest difference for a single angle was at 55. However, the overall agreement exhibited improvement when all zenith angl es were included. All the Kd() inversions and the Rrsopt models included factors that took into account solar zenith angle. There is no clear reason to filter the data based on zenith angle and agreement for anw(). Figure 5.3. Nonparame tric analysis of anw() data from each method under different solar zenith angles ( = 0.05). The left axis is the mean percent agreement of each method with the other methods averaged over all the wavelengths. The percentage of bottom reflectance di d have a significant effect on derived values of bbp() (Fig 5.4). A bottom contribution of 0% is best for bbp() but would result in a very small number of stations when combined with filters for both zenith angle and clouds. The smaller number of stations would lower the si gnificance of statistical comparisons. The HS6 possibly exhibited lo wer agreement because it is the only method measuring bbp() that is independent of th e light field. All the Rrs() inversions use a Type ac9MODISKdoptRrsoptSpecKdKirkKDLoiselQAA Percent agreement 0 10 20 30 40 50 60 70 80 90 100 110 <= 35 <= 43 <= 46 <= 48 <= 55 <= 60 <= 68 All PAGE 85 67 similar method to determine bbp() and may have errors caused by bottom contribution that are similar in magnitude in the same direction. The low agreement by the HS6 could also be that the instrument was near its acc uracy limit in very clear water while the Rrs() inversions still have sufficient signal due to a longer effective path length. The filter was kept at 10% maximum bottom contribution si nce it provided an acceptable agreement while retaining the largest number of stations. Figure 5.4. Nonparametric statistical analysis of bbp() values of each method under different levels of bottom reflectance ( = 0.05). The left axis is the mean percent agreement of each method with the ot her methods for all the wavelengths. There was no noticeable effects below 80% on bbp() for cloud coverage (Figure 5.5). Kdopt and MODIS have some improve ment by limiting the cloud cover to less than 5% but the number of stations when combin ed with the other filters was too low (18 stations) for the small gain in agreement. AOP measurements were generally collected only when the sun was not behind clouds and this technique aided in the agreement between methods. Based on this result, the filter was kept for cl oud coverage less than 80%. Type HS6ModisKdoptrrsoptQAA Percent agreement 0 10 20 30 40 50 60 70 80 90 100 110 = 0% <= 1% <= 5% <= 10% <= 20% <= 30% <= 50% <= 100% > 0% PAGE 86 68 Figure 5.5. Nonparame tric analysis of bbp() data from each method under different levels of cloudiness ( = 0.05). The left axis is the mean percent agreement of each method with the other methods aver aged over all the wavelengths. With the exception of MODIS, there is a definite drop in bbp() agreement for solar zenith angles greater than 46 (Figure 5.6). Except for the HS6 and QAA, there is no further change in bbp() agreement for zeniths greate r than 46. The HS6 and QAA show a drop in agreement for zenith angles greater than 68. However the HS6 is the only method independent of ambient light field conditions so the agreement may be a bias in the other methods. Most Rrs() measurement protocols require that measurements take place when zeniths are less than 45. Filtering for Zeniths less than 35 leaves too few stations (21 stations) when combined with the other filters. The optimum filter was set at zeniths below 46. Type HS6ModisKdoptrrsoptQAA Percent agreement 0 10 20 30 40 50 60 70 80 90 100 110 <= 3% <= 5% <= 10% <= 20% <= 40% <= 80% <= 100% PAGE 87 69 Figure 5.6. Nonparame tric analysis of bbp() data from each method under different solar zenith angles( = 0.05). The left axis is the mean percent agreement of each method with the other methods averaged over all the wavelengths. The data were filtered in 6 different ways to fairly test each method (Table 5.1). The total unfiltered data set is 126 stations (No Filter, NF). The no bottomreflectance filter (No Bottom, NB) was set for bottom cont ributions less than 10% which resulted in 90 stations. The ideal cond itions filter (No Bottom Low Clouds, Low Zenith, NBLCLZ) was set with bottom contribution less than 10%, percent cloud cover less than 80%, and solar zenith angles less than 46 resulting in 46 stations. The MODNB filter removed all the stations where MODIS switched to th e empirical default algorithm and bottom contribution was less than 10% resulting in 59 stations. The next filters were set for only stations where bottom is detected based on the Rrs optimization algorithm (Bottom, BT) resulting in 49 stations. This includes even bottom contributions below 10%. The BTLCLZ (Bottom Low Clouds Low Zenith) fi lter used stations where bottom was present but clouds were less than 80% and so lar zenith angle was le ss than 46 resulting in 30 stations. Type HS6ModisKdoptrrsoptQAA Percent agreement 0 10 20 30 40 50 60 70 80 90 100 110 <= 35 <= 43 <= 46 <= 48 <= 55 <= 60 <= 68 All PAGE 88 70 Table 5.1. Acronyms for different filter gr oups. Book mark this page for reference regarding discussions of different filter groups. Acronym Description NF Unfiltered represents the entire data set NB No Bottom contribution to reflectance >10% NBLCLZ NB filter + cloudiness < 80% + Solar zenith < 46 MODNB NB filter + MODIS uses the semianalytical model only BT Bottom contribution to reflectance > 0% BTLCLZ BT filter + cloudiness < 80% + Solar zenith < 46 KW KruskalWallis pairwise comparison with tied ranks statistical test 5.3. Nonparametric Analysis to Determine the Ideal Data Set Agreement between most methods was highe st at the shortest wavelength for anw() (Fig. 5.7). At 412 nm, all methods agr ee (only Rrsopt, Kdopt, Spec and ac9 compared under BT and BTLCLZ filters). At 440 nm, only the ac9 has agreement problems using the BT filter. At 488 nm a nd higher, the ac9 shows disagreement for filters NF, BT, and BTLCLZ. At 532 a nd 555 nm, KdKirk shows disagreement using filters NF, NB, NBLCLZ, and MODNB. At 555 nm, KdLoisel shows disagreement under filters NF and MODNB. At 650 and 676 nm, KdKirk and KdLoisel do not show agreement under filters NF, NB, NBLCLZ, and MODNB. At 650 and 676 nm, the ac9 does not show agreement under any of the filters. At 650 nm, Kdopt did not show agreement under filters NF and BT. For the BT filter at 650 nm only Spec and Rrsopt exhibited any agreement with each other but were below the 50% mark. Except for 650 nm under the NF and BT filters, Rrsopt, MODIS, QAA, Kdopt, and the Spec have agreement above 50%. These 5 methods are best for anw() according to the nonparametric test. For bbp() Kdopt has the lowest agreement (Fi gure 5.8). It exhibits no agreement for NF, NB, and NBLCLZ at any wavelengt h. For the MODNB filter Kdopt only has agreement at 671 nm. The HS6 has the next lowe st agreement. It ex hibits less than 50% agreement for NF at 488 and 589 nm. The HS6 has no agreement for NB filter at 488, 532, 589, and 620 nm. For NBLCLZ the HS6 only shows no agreement at 488 nm. MODIS demonstrates no agreement for the NF filter at 589, 620, and 671 nm. Rrsopt has disagreement at 589 nm under the NF filter. The QAA model does not have a problem with agreement under an y of the filters. For the BT a nd BTLCLZ filters only the HS6, Kdopt, and Rrsopt are considered since th e QAA and MODIS algorithms do not take into account bottom albedo. Under the BT and BTLCLZ filters, the HS6 performs the best with the highest agreement, and no method ha s less than 50% agreement. The QAA is best for determining bbp() in deep water while the HS6 is best when there is significant bottom influence according to agreement with a majority of the other methods under the nonparametric KW test. PAGE 89 71 A. 020406080100Wavelength (nm) 412 440 488 510 532 555 650 676 ac9 MODIS Kdopt Rrsopt Spec KdKirk KDLoisel QAA C. Wavelength (nm) 412 440 488 510 532 555 650 676 E.Percent agreement 020406080100 Wavelength (nm) 412 440 488 510 532 555 650 676 B. 020406080100 412 440 488 510 532 555 650 676 D. 412 440 488 510 532 555 650 676 F.Percent agreement 020406080100 412 440 488 510 532 555 650 676 Figure 5.7. Percent agreement for anw() to determine ideal data. A. NF Filter, B. NB Filter, C. NBLCLZ Filter, D. MODNB Filter, E. BT Filte r; and F. BTLCLZ Filter. PAGE 90 72 Figure 5.8. Percent agreement for bbp() to determine ideal data. A. NF Filter, B. NB Filter, C. NBLCLZ Filter, D. MODNB Filter, E. BT Filte r, and F. BTLCLZ Filter. bbp NBLCLZ Wavelength (nm) 442 488 532 589 620 671 bbp BTPercent agreement 020406080100 Wavelength (nm) 442 488 532 589 620 671 bbp NB 020406080100 442 488 532 589 620 671 bbp MODNB 442 488 532 589 620 671 bbp NF 020406080100Wavelength (nm) 442 488 532 589 620 671 HS6 MODIS Kdopt rrsopt QAA bbp BTLCLZPercent agreement 020406080100 442 488 532 589 620 671 PAGE 91 73 MODIS data agree with the major ity of the other methods for ag() under the KW nonparametric analysis (Figure 5.9). At 412 nm, all methods agree with at least 50% of the other methods for all conditions. At 440 nm, Rrsopt does not agree under filters NF and MODNB. At 488 nm, only the ac9 s hows disagreement under filters NBLCLZ, MODNB, and BTLCLZ. For Wavelengths 510 and greater, the ac9 did not show agreement under any filter. At 650 nm, Rrs opt shows disagreement for NF, MODNB, BT, and BTLCLZ. The Specag shows disagr eement at 650 nm for both BT and BTLCLZ for 650 nm. At 676 nm, only Kdopt shows agre ement with 50% of the methods for filter NF. Rrsopt shows disagreement at 676 nm for filters NF, NB, MODNB, and BT. The Specag also shows disagreement for BT at 676 nm. MODIS is the best method under this nonparametric analysis, only failing to agree with 50% or more of the methods at 676 nm under filter NF. MODIS was only method not tested using the BT and BTLCZ filters where Kdopt did the best. Kdopt has the worst agreement for aph() (Figure 5.10). U nder filter NF, Kdopt shows disagreement for 440, 488, and 510 nm. However, under filter NB, Kdopt only shows disagreement at 676 nm. Under MODNB Kdopt shows disagreement at 440, 488, 510, 532, and 676 nm. Under BT and BTLCLZ filters, Kdopt shows disagreement at 412, 440, 488, and 510 nm. Rrsopt has the seco nd most disagreements. It exhibits disagreements at 440 and 555 under the MODNB filte r. Rrsopt also has disagreements at 650 nm for filters NF, NB, NBLCLZ, and M ODNB. MODIS only has disagreements at 555 nm for MODNB and 676 nm for NF. At 412 nm under the NF and MODNB filters for NF none of the methods reached 50% all four methods tied at agreement with one other method. Specaph shows no disagreement except for 412 nm under the NF and MODNB filters, making it the best method under the KW statistic. Based on the results from the KW test, an ideal data set was created by taking the median value of the methods that have agreem ent of 50% or more at a given wavelength and filter. There were 3 cases out of 180 where no method reached the 50% or greater mark where those with the highest value of agreement were used. This data set was compared to the different methods using st atistical techniques of linear regression, correlation, and percent error, and outlier anal ysis. Before comparing the methods to the ideal, the results from the KW nonparametric te st bear further examination. This test can provide some evidence about which me thod is best under the different filters. However, the KW test should not be consider ed conclusive about which method is best because it only tests agreement based on ranks not the actual values. PAGE 92 74 Figure 5.9. Percent agreement for ag() to determine ideal data. A. NF Filter, B. NB Filter, C. NBLCLZ Filter, D. MODNB Filter, E. BT Filte r, and F. BTLCLZ Filter. Wavelength (nm) 412 440 488 510 532 555 650 676 Percent agreement 020406080100 Wavelength (nm) 412 440 488 510 532 555 650 676 020406080100 412 440 488 510 532 555 650 676 412 440 488 510 532 555 650 676 020406080100Wavelength (nm) 412 440 488 510 532 555 650 676 ac9ag MODIS Kdopt Rrsopt Specag Percent agreement 020406080100 412 440 488 510 532 555 650 676 A. C. E. B. D. F. PAGE 93 75 Figure 5.10. Percent agreement for aph() to determine ideal data. A. NF Filter, B. NB Filter, C. NBLCLZ Filter, D. MODNB Filter, E. BT Filte r, and F. BTLCLZ Filter. Wavelength (nm) 412 440 488 510 532 555 650 676 Percent agreement 020406080100 Wavelength (nm) 412 440 488 510 532 555 650 676 020406080100 412 440 488 510 532 555 650 676 412 440 488 510 532 555 650 676 020406080100Wavelength (nm) 412 440 488 510 532 555 650 676 MODIS Kdopt Rrsopt Specaph Percent agreement 020406080100 412 440 488 510 532 555 650 676 A. C. E. B. D. F. PAGE 94 76 5.3.1. KW Nonparametric Analysis of anw() Path length of the measurement was ke y for best performance for determining anw(). The KW nonparametric statistical anal ysis showed that the ac9 did poorly for anw() for wavelengths greater than 488 nm. With the except ion of the Puget Sound data and some near shore West Florida shelf data most of the areas in this study had low absorption values. The ac9 had problems where the signal to noise was lower in the longer wavelengths because of its shorter path length. The Kd() optimization method performed best where bottom reflectance was not significant (NB, NBLCLZ, and MODNB). The processing of the Ed() values to get Kd() involved using a th ird order polynomial curve fit to aid in reducing the effects of wave focusing. As depth increased, wave focusing became less of a problem due to scattering by the constituents in the water co lumn. In a shallow water column it was not easy to get to depths where wave focusing wa s low and mixing of rays from more wave facets in view. This led to spectral inaccuracies in the Kd() curve. MODIS performed best for the unfiltered (NF) data set. MODIS uses fewer optimizations to determine anw() than the Rrs() Optimization method. The lower number of iterations and fewer variables iter ated by the MODIS algorithm keep it from getting stuck in local mini ma as can occur under the Kd() and Rrs() optimization algorithms (Chen et al. 2004). Cloudiness and zenith angle can affect the other methods by giving spectral errors that emulate CDOM absorption, backscattering, or bottom albedo. MODIS locks bbp() at a fixed ratio to Rrs(550) and uses fewer iterations, preventing it from getting stuck at an errone ous value. The addition of the new method of using a higher CDOM spectral coefficient to determine the initial values followed by a lower coefficient to calculate ag() was hypothesized to compensate for CDOM fluorescence. The change may have aided the agreement of MODI S under the less than ideal conditions. With significant bottom reflectance the results for anw() were mixed under the KW nonparametric analysis. The spectrophotome tric methods did best under nonideal conditions, besting Rrsopt at 440 nm. The Rrs() optimization algorithm fared best when under ideal conditions with significant bottom contribution, besting the spectrophotometric method only at 412 nm. However, when inverting to achieve spectral bottom albedos (details in chapter 7), the Kd() optimization method anw() produced the best result. With the excepti on of 650 nm under the BT filter, Kdopt had agreement with at least 50% of the other methods. Almost all of the ideal conditions were from the COBOP cruises where there was low absorption and the bottom was white sand. This clear water and white sand possibly improved the inversion for anw() using Rrs() optimization. The bottom reflectance would be very dominant in these Rrs() scans from the Bahamas and the input bottom PAGE 95 77 albedo would most resemble that of the white sand albedo used in the Rrs() optimization models. The spectrophotometric method does better under conditions of high bottom reflectance since there is usually a higher si gnal to noise ratio clos er to shore and the water column is usually well mixed. Th e spectrophotometric methods were affected more using the other filters since Spec repr esents a sample from only a near surface depth. The other methods represent an inte grated value of the water column optical properties. If there are changes in optical properties near the su rface then the other methods may reflect these while the spec trophotometric methods will not. With significant bottom reflectance, Rrs() optimization and the sp ectrophotometric methods were best according to the KW nonparametric statistics but the Kd() optimization provided the best results wh en using Hydrolight runs to determine bottom albedo. 5.3.2. KW Nonparametric Analysis of bbp() There are only 5 methods for determining bbp() in this study. All of the Rrs() inversions have bbp() as an output, the Kd() optimization algorithm outputs bbp(), and the Hydroscat6 gives a more direct measurement of bbp(). All the Rrs() inversion algorithms use similar empirical approaches for determining the spectral shape of the bbp() curve. The intercept value for bbp() is determined iteratively by the Rrsopt and QAA but empirically by MODIS. The proportion of the contribution by bbp() to the Kd() value (about 5%) is much smaller than to the Rrs() value. If the Kd() measurements were perfect, then it should produce a good inversion of bbp(). However, with such a small contribution by bbp() along with sources of error in the Kd(), it means the Kd() inversion is the least reliable of the group. The HS6 measures () at 140 and then empirically determines the total value by assuming that bbp() is 8% greater than a hemispheric integration of the (,140). While this method is close to the actual value, the instrument also has an accuracy that can limit it in very clear waters. Of the 5 methods, the Rrs() inversions should have the best signaltonoise ratio in deep low attenuation waters due to the long path length of light in an Rrs() value, but the Hydroscat6 should be better in more turbid waters and those with bottom influence. The nonparametric tests show that Rrs() optimization and QAA produce similar results under conditions with low bottom in fluence. Both methods use similar approaches to determine bbp(). This agreement may indi cate that they will bias the median bbp() ideal value favoring an Rrs() inversion. This potential bias may make the statistical comparisons with the idealized bbp() value not as valid. However, the Rrs() measurements do have the longest path lengt h so they are probably the most accurate under conditions without signifi cant bottom reflectance. Under the filters that included only botto m contribution to reflectance, only the Rrs() optimization, Kd() optimization, and Hydroscat6 were compared using the KruskalWallis analysis for bbp() values. All three methods agreed when all conditions were included. Under the ideal conditions including bottom reflectance (BTLCLZ), only the Hydroscat6 agreed with all the others. This agreement may mean that the HS6 value PAGE 96 78 was centered between the Kdopt and Rrsopt values. Under the BTLCLZ filter, more bottom reflectance is present in the Rrs() measurement since more direct sunlight has a greater penetration to depth. The bottom al bedo would be more like ly to influence the Rrs() optimization routine affecting bbp() during the inversi on. While the Rrs() optimization generally does better due to a longer path in deep water, the Hydroscat6 is best for shallow water according to this test. 5.3.3. KW Nonparametric Analysis ag() MODIS performed best for determining ag() under most filters in the KW nonparametric tests when there was not a bottom present. MODIS, for this test, uses a higher CDOM slope coefficient for the initial iterations to invert anw() in presence of CDOM fluorescence (Carder et al. 2006). When the final anw() and ag() were calculated, MODIS used a lower coefficient that is closer to the slope coefficient for a coastal ag() spectra. Bottom reflectance appeared to affect the Rrs() inversion for ag() similar to the affect on bbp(). Kd() optimization is the only inversion that did not use a set ag() coefficient and iterated the value to de termine it. While it did not perform as well as MODIS under conditions without bottom contribution, Kdopt did give the best result under the BT filter. The spectrophotometer ag() was best under the BTLCLZ filter. The ac9 performed the worst of the methods for determining ag() spectrally. The ac9 ag() was good for shorter wavelengths but ra pidly dropped in agreement at longer wavelengths. The ac9 was probably limited by a shorter path length than the AOP inversion methods and problems with the clearance of bubbles from the filters. The spectrophotometric method had the best ag() value for the MODNB filter using the KW nonparametric statistics. This result was surprising since the spectrophotometric method has a fairly high error compared to other methods due to having the shortest path length. A near surface single sample taken from a Niskin bottle or surface sample from a bucket wa s used for the spectrophotometric ag() so it only represents a point near the surface and not deeper. The MODNB filtered data set has the lowest chlorophylls and is closer to Morel Case I waters so the Rrs() inversions were expected to do best. It a ppears that the accuracy of the spectrophotometric method was underestimated. This good performance may be due to determination of ag() in visible where it has low accuracy by extrapolation fr om the near UV wavelengths where signal to noise is much higher using Equation 3.1. An ag(400) value of 0.01 m1 with a slope coefficient of 0.017 nm1 would have a value of 0.055 at 300 nm giving it sufficient signal. The Specag has the benefit of not havi ng to estimate the coefficient for the slope like the AOP inversions. The spectrophotometric method for ag() has the smallest correction for errors due to sca ttering of any of the methods. The method is more direct and not influenced by other parameters such as solar zenith angle or cloudiness. While these environmental parameters did not greatly affect the Rrs() and Kd() inversions in the determining anw() under the MODNB filter, they may affect the inversion for ag() by introducing spectral changes. Both parame ters would influence the spectral shape of the average cosine and might in fluence the magnitude of the ag() values from an AOP PAGE 97 79 inversion. The performance of the spectrophotometric ag() under the lowest attenuation conditions was surprising due to the short path length of th e technique. However, the Specag may not perform as we ll under the other statistics. Kdopt provided the best ag() measurement for the BT filter and Specag was best for BTLCLZ. Significant bottom reflectance from a bright sand bo ttom could affect the magnitude of the ag() value from Rrsopt, resulting in lower agreement. A sand bottom has a linear slope for its albe do that increases with increasi ng wavelength. This spectral albedo may act against the decreasing values of ag() with wavelength in a way that underestimates either the magnit ude of the bottom albedo or ag(). Kdopt is the only AOP inversion algorithm that did not lock the ag() spectral coefficient but allowed to iterate over a limited range to achieve the best fit. The Kd() values are more susceptible to spectral changes due to wave focusing and did not perform as well under the BTLCLZ filter. Wave focusing is more likely to occur under ideal conditions like the BTLCLZ filter as opposed to conditions where solar zenith angle or cloudiness is high. Under those cloudy and low zenith conditions the subsurface downwelling irradiance is likely to be more diffuse and would not be as easily focu sed as direct sunlight. Wave focusing may have caused Kdopt to have gr eater error under ideal conditions but was not a factor under the less than ideal conditions for ag() inversions. The ac9 only had reasonable values for the first 2 to 3 wavelengths. The ac9 has a 25 cm path length versus the spectrometer, which has a 10 cm path length. It appears that the ac9 would be more accurate than the Specag, but the signal was usually below the accuracy of the ac9 at longer wavelengths. The spectro photometer was able to make measurements in UV where the absorption by CDOM is higher. This allowed the spectrophotometer data to be interpolated for the longer wavelengths by fitting to a logarithmic slope. The same technique can be applied to the ac9 to improve the values of longer wavelengths but it does not have th e channels in the UV range so only the 412 to 488 wavelengths can be fit. The ac9 also performed poorer than expe cted under conditions where bottom was present under the KW nonparametric analysis for ag(). One of the difficulties with the deployment of the ac9 for ag() was clearing the flow tube with a 0.2 m filter attached. For deeper casts lowering the ac9 to dept h to compress the bubbl es can clear bubbles. The stations where bottom reflectance was signi ficant were often too shallow to compress the bubbles resulting in some errors for the ac9 ag() values. The data from the ac9 improved for ag() measurements in later cruises due to a change in technique. The filter was presoaked in deionized water and left in a container of deioni zed water until just before the ac9 went over the side. This ai ded in bubble clearance by saturating the filter pores with water instead of air resulting in improvement in ag() measurements. The filters are expensive and to conserve resources, they were often used for multiple casts. When reusing the filters, th ere is a greater chance of the filter pores becoming filled resulting in a lower flow rate. The lower flow rate results in changes in scattering within the flow tube due to di fferences in turbulence from the standard PAGE 98 80 calibration flow rate. The best method would be to replace the filters and leave the ac9 and filter filled with deionized water until the instrument is submerged, but the high cost of the filters (>$100 each) make this a costly approach. The problems with the ac9 ag() were the result of deployment techniques that improved over the studies but were limited due to the cost of the filters used for sampling. 5.3.4. KW Nonparametric Analysis aph() This is the only analysis where there was not a profile of the IOP to compare to the other methods. The filterpad method onl y represents a single point in the water column while the other methods represent an in tegrated value. This use of a single point may present some differences for certain si te locations where there is a significant variation in IOP properties fo r the upper water column. The integrated value from the IOP inversion would provide a more accurate determination of the aph() values for the water column under these conditions. For the nonparametric analysis, the Spe caph performed the best under the NF filter while Kdopt had the most problems under th is filter. This problem with Kdopt is possibly due to shallow depths being include d along with cloudiness and low solar zenith angle in clear water. Kdopt also had problems under the bottom only filters. While it did well for the NB filter, it had problem s at shorter wavelengths under the MODNB filter. It appears that clear water wi th cloudiness, high zenith angle, and bottom contributed to problems in inverting aph() from Kd() measurements. However, the other statistics need to be examined before any definitive conclusion can be drawn from this one test. Kdopt performed well under the NB f ilter with the exception being the wavelengths of 650 and 676 nm. The Kdopt doe s not usually fit the modeled curve to these wavelengths because absorption from wa ter is so high that the light is rapidly attenuated near the surface. The rapid attenuation results in few readings collected near the surface with the signal dropping to noise level at a shallower depth. The lower numbers of readings do not provide enough da ta to smooth out the effects of wave focusing. The Rrs() inversions would have more si gnal at the longer wavelengths and not a problem with wavefocusing. Under the KW nonparametric analysis, MODIS has more agreement with consensus values for aph() values under ideal conditions without bottom influence when only the semianalytical model is used. MODIS used a higher ag() coefficient value for the initial inversion to compensate for CDOM fluorescence. Correction for CDOM fluorescence was expected to improve aph() inversions due to the potential for CDOM fluorescence to produce error at the 440 nm peak s. This statistic supports that hypothesis. Rrsopt is best for the BT and BTLCLZ filters under the KW nonparametric analysis for aph(). Kdopt seems to have problems with shorter wavelengths due to wave focusing in shallower water columns but im proves at longer wave lengths. Kdopt method PAGE 99 81 was not statistically similar to the other me thods for wavelengths less than 532 nm, which may have been caused by wave focusing sendi ng longerwavelength light to depth. Since Kdopt relies on fitting a modeled Kd() value to the entire spectrum so the greater Ed() in the longer wavelengths due to wave focu sing could result in a the model slightly overestimating ag() while underestimating aph(). Rrsopt has a longer path length and uses a shape factor derived from regional aph() measurements using the quantitative filter pad technique. The Rrsopt aph() value is close to that of the filterpad method but isn't limited to just one point in the water colu mn. A caveat to this analysis is that the Rrsopt method provides values between the Kdopt and Specaph values therefore, it agrees with two of them while they are too fa r apart to agree with each other. However, since the spectral shape of phytoplankton absorp tion is very different from the albedo of sand bottom, it is very likely that Rrs opt is the better method for determining aph() for shallow waters. 5.4. Comparisons of Idealized Values There are 960 different individual sets based on method, IOP type, wavelength tested, and filter type in this study. In comp arison to the ideal data set, each set generated a regression slope, intercept, co rrelation coefficient, mean pe rcent error, mean absolute percent error, and percent outliers for a total of 5760 different values. Because of the large amount of statistical information, only a general summary of the graphs is presented in this section. The tables of the results ar e presented in the appendix for reference. Only the NB and NF filters will be analyzed in detail as a guide for interpretation of the statistics for each IOP. The rest of the graphics will have generalized observations regarding each set. Each sect ion devoted to an IOP type is followed by discussion of the general results. This section is very long and with a large am ount of statistical analysis. If the reader wishes to know directly which methods are be st under each filter, a table is given in the last chapter summarizing the ove rall performance of each method. There is also a general analysis of each IOP type at the end of their sections. 5.4.1. Unfiltered and No Bottom Filters anw() The unfiltered data (Figure 5.11) exhibits good regression results for all methods except MODIS at wavelengths less than 555 nm. At 650 and 676 nm, Kdopt and KdKirk have the highest and lowest regression slope s, respectively. The slopes at 650 nm have the largest difference from unity. KdKirk and KdLoisel have intercepts furthest from zero at the longer wavelengths. MODI S exhibits intercepts furthe st from 0 at the shortest wavelengths with intercepts closer to zero at the longer wavelengths. Correlations are good for all methods at wavelengths below 650 nm MODIS has the lowest correlation at the shorter wavelengths but it is still above 80%. KdKi rk and KdLoisel have poor correlations at 650 and 676 nm where water dominates the absorption and little light reaches depth. Overall there is good agreem ent at the wavelengths where nonwater absorption is highest. PAGE 100 82 The mean percent errors (Figure 5.12) are closer to 0 at the shorter wavelengths for all methods except for KdKirk, KdLoisel, and the ac9. At the longer wavelengths, Kdopt and Spec have larger errors. MODIS, QAA, and Rrsopt continue with low errors at longer wavelengths. The absolute percen t difference generally follows the same spectral patterns as the percent difference. The Spec is the only method with an ove rall low number of outliers (Figure 5.12C). At 412 nm, the outliers are low (01%) for KdLoisel, Spec, and Rrsopt. At 440 nm the outliers are low for ac9, KdKirk, KdLo isel, and Rrsopt. At 440 the rest of the methods all have outliers between 22% and 26%. At 488 nm, ac9, KdKirk, Spec, and Rrsopt are the lowest. At 510 and 532 nm onl y the ac9, Spec, and Rrsopt are low. At 555 nm only the ac9 and Spec have low outliers At 650 nm only MODIS is low and at 676 only Rrs opt is low. The regression slopes, intercepts, and corre lation coefficients for the NB filter follow similar patterns as under the NF filter (Figure 5.13). The three Rrs() inversions have the lowest error terms (Figure 5.14) unde r both mean and mean absolute value of the percent difference. The Kd() inversions generally have low error for the shorter wavelengths with increasing error at longer wa velengths. KdKirk has higher error above 488 nm. KdLoisel and Kdopt both start to have higher error above 532 nm. Kdopt has the lowest error overall of the Kd() inversions models. The Spec only has low absolute perecent error below 40% at 650 nm and the ac9 only has low error at 412 and 440 nm. Overall the regression results, and percent error are similar to the NF filter. The percent of outliers (Figure 5.14C) has a different pattern from the error terms under the NB filter for anw(). The Spec, which is has one of the highest percent errors, has the lowest percent outliers. The regres sion terms do not indicate a bias for because its intercept is not much highe r than the other methods. Th e only relatively high outliers are found at 440, 650, and 676 nm for the Spec Rrsopt has low outliers from 412 to 532 nm and at 676 nm. The ac9 is next best with low outliers from 440 to 532 nm. KdKirk has low outliers from 440 to 510 nm. KdLo isel has low outliers at 412 and 440 nm. MODIS is the only method that had no outlier s at 650 nm. The low outliers combined with a high mean percent error indicate that a few stations may be responsible for much of the error in the Spec method. There are some general trends noted under th ese filters that continue under several of the anw() filters. The Rrsopt does the best under most conditions at most wavelengths. Outliers seem to cause significant increases in percent error for Spec and ac9. The Rrs() models improve their results as the conditions approach ideal. The more empirical Kd() inversions, KdKirk and KdLoisel, have problems with longer wavelengths of light. The inte rpolated MODIS value at anw(650) nm is better than the models that try to determine that waveleng th. MODIS has an intercept much different form 0 at the shorter wavelengths but moves closer to zero at the longer wavelengths. PAGE 101 83 Figure 5.11. Regression and correlation analysis of anw() versus ideal values using the NF filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression Intercept 0.00 0.02 0.04 0.06 0.08 0.10 Regression Slope 1 0 1 2 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 102 84 Figure 5.12. Percent erro r and outlier analysis of anw() under the NF filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 103 85 Figure 5.13. Regression a nd correlation analysis of anw() versus ideal values using the NB filter. A. Slope of linear regression of each met hod versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Intercept 0.00 0.02 0.04 0.06 0.08 0.10 Regression Slope 2 1 0 1 2 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Correlaton Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 104 86 Figure 5.14. Percent erro r and outlier analysis of anw() under the NB filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 Kdkirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 105 875.4.2. Ideal Conditions anw() The methods exhibit better agreement under the ideal conditions. Except for MODIS all the slopes are close to one for 412 to 555 nm under the NBLCLZ filter (Figure 5.15A). When the methods get to the longer wavelengths, signal to noise for nonwater constituent absorption decreases. The Kd() inversions would especially have trouble in for this filter because their path length s are less than for the Rrs() measurements. Kdopt and MODIS have interc epts at the shorter wavelengths that are different from the other methods (Figure 5.15B ). It may be due to their approach for determining CDOM absorption. MODIS uses a higher slope initially then a lower one to calculate the anw() value and Kdopt allows the slope to iterate. The correlations except for KdKirk and KdLoisel are good at most wavelengths (Figure 5.15C). These two Kd() inversions have trouble at the longer wavelengths through ou t this study because of their empirical approach to modeling combined with shorter path lengths at the longer wavelengths. The percent error generally reflects th e path length and empiricism of the measurements under the NBLCLZ filter (Figure 5.16). Spec has the highest errors at short wavelengths and is followed by the ac9, the empirical Kd inversions, and then Kdopt. The errors then get worse as wavelengths increase. All the Rrs() inversions seem to have low error terms with Rrsopt doi ng the best again for this filter. While the outliers generally reflect the other statistic s, Kdopt is the exception with very few outliers. This would mean that there are a few stations where Kdopt had problems likely due to low solar zenith angles and wave fo cusing. In one of the West Florida Shelf stations included under this f ilter, there was even a problem with amberjack schooling around the slowdrop instrument package shad ing the irradiance sensor. Removing a few stations seems to bring Kdopt closer in agreement to the Rrs() inversions. Under the MODNB filter the higher chlor ophyll waters were removed resulting in lower signal to noise and more divergence from a one to one line for all the methods. MODIS now is using the semianalytical m odel only and has a better regression result (Figure 5.17). Getting rid of the empirical portion of MODIS results in statistics that are similar to the more complex Rrsopt. MODIS and Rrsopt are two very different models but the spectral pattern and magnitude of their statistics are close to the same. MODIS no longer has the largest intercept error and in stead provides one of the closest to zero. The KdLoisel model exhibited improvement under the MODNB filter and was close to Kdopt in slope for regression and correlation at shorter wavelengths (Figure 5.17). This indicates that the empirical a pproach of the KdLoisel model is probably better suited for the clearer waters without bottom. With the rem oval of the band ratio default algorithm for MODIS, the QAA is now the most empirical of the three Rrs() inversions. Path length was the reason for the poor results of the Spec under the MODNB filter. It had the intercept most different from zero (Figure 5.17B). The MODIS algorithm PAGE 106 88 defaults to its empirical band ratio al gorithm when the estimated chlorophyll concentration is high. Genera lly the higher the chlorophyll, the more attenuation there is in the water and the shorter the path length for the AOP inversion. The Rrs() inversions with the longest path lengths performed the best while the Kd inversions were next, followed by the ac9 and Spec. The percent error statistics demonstrate a significant improvement for MODIS in determining anw() under the MODNB filter (Figure 5. 18). While the QAA and Rrsopt have some improvements, MODIS using only the semianalytical algorithm has much lower percent error and absolute percent error, especially in the longer wavelengths. MODIS is better at 650 and 676 nm than any of the other methods. However, MODIS does have an increase in outliers at 488 nm. The Spec and the ac9 have the highest error statistics with numbers similar to those under the NBLCLZ filter. The ac9 does have a low number of outlier at 412 to 488 indicati ng that removing those should improve its error and correlation statisti cs at those wavelengths. PAGE 107 89 Figure 5.15. Regression a nd correlation analysis of anw() versus ideal values using the NBLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Intercept 0.00 0.02 0.04 0.06 0.08 0.10 Regression Slope 2 1 0 1 2 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 108 90 Figure 5.16. Percent erro r and outlier analysis of anw() under the NBLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 109 91 Regression Intercept 0.00 0.02 0.04 0.06 0.08 0.10 Regression Slope 2 1 0 1 2 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. Figure 5.17. Regression and correlation analysis of anw() versus ideal values using the MODNB filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. PAGE 110 92 Figure 5.18. Percent erro r and outlier analysis of anw() under the MODNB filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 111 935.4.3. Bottom Reflectance Only anw() The Kd() inversions and QAA are the only met hods with slopes close to 1 at shorter wavelengths under regressi on slope comparisons for the anw() BT filter. Kdopt does the best under the regression analysis (Figure 5.19). The bottom influence along with some less than ideal conditions results in the Rrs() inversions no longer being the best. Rrsopt and the Spec have similar results for slope and intercept but it may be coincidental. Rrsopt and Spec also had the lowest error terms a nd low outliers (Figure 20). These conditions were the most challenging for all the methods as the correlations were generally below 0.8. The Kd() inversions did best with the ac9 doing the worst in what should have been the be st conditions for the ac9. Under the ideal conditions with bottom (BTLCLZ) Rrsopt fairs much better in determining anw() (Figure 5.21). Generally, Rrsopt and Kdopt proved the best of the inversions. The Spec did bette r than the ac9 for this filter and better than most of the AOP inversions. Many of these stations were collected during the CoBOP cruises where the water had low absorption and the botto m was white sand and the bright bottom degraded the MODIS and QAA Rrs() performances. This means that path length is still a factor for these regions. Kdopt and Rrsopt also used pigment absorption shape factors that were from this region. The phytopla nkton population is much different in the Bahamas from the population on th e West Florida Shelf. Th e more oligotrophic waters of the Bahamas Sound are dominated by small di noflagellates instead of some of larger phytoplankton species found on the West Florida sh elf (Agard et al, 1995). The use of a specific aph() shape factor tailored to this regi on may have given these methods an advantage. The Kd() inversions did not fare as we ll for longer wavelengths under the BTLCLZ filter for anw() (Figure 5.22). Wave focusi ng and signal to noise problems probably cause problems in these shallow wate rs. The irradiance sensor probably could not get deep enough to be out of the influence of wave focusing for many of these casts. The bright bottom sand in the Bahamas sometimes resulted in an increase in irradiance near the bottom due to bottom reflectance. This increase resulted in an odd shape to the depth profile of Ed() and made the curve fit to smoot h wave focusing more difficult and probably resulted in some errors. The Spec method provided accuracies almo st as good as from Rrsopt. Recalling that this is a combination of ag() measured in a spectrophotometer and ap() measured using the filter pad method, th e shortpath (10 cm) of the ag() method appears to be compensated by the longer effective path of the aph() method. Unlike the deeper waters the near shore waters appear to have the right combination of ap() and ag() where the ag() value is not too low and the ap() value is more dominant resulting in better values for the Spec method. PAGE 112 94 Figure 5.19. Regression and correlation analysis of anw() versus ideal values using the BT filter. A. Slope of lin ear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression Intercept 0.00 0.02 0.04 0.06 0.08 Regression Slope 2 1 0 1 2 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 113 95 Figure 5.20. Percent error and outlier analysis of anw() under the BT filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 114 96 Figure 5.21. Regression and correlation analysis of anw() versus ideal values using the BTLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Intercept 0.00 0.02 0.04 0.06 0.08 0.10 Regression Slope 2 1 0 1 2 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 115 97 Figure 5.22. Percent error and outlier analysis of anw() under the BTLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 116 98 5.4.4. Discussion of anw() Comparisons with Ideal Rrsopt was generally the best for most anw() inversions and Kdopt performed well. MODIS did not fare as well until the completely empirical portion of the model and the bottom were filtered out. Howe ver, MODIS performed better than Rrs optimization at 676 nm under many filters. QAA, MODIS, and KdLoisel are further from the ideal under conditions of high bottom reflec tance. The ac9 was not the best or the worst of the methods for determining anw() but did not perform as well as expected under conditions that should have favored it. The algorithm used by MODIS may increa se its accuracy at 676 nm over the other models. MODIS uses an algorithm that tunes the packaging effect to the temperature of the water. This algori thm may blend different packaging effects depending on the nitrate depletion te mperature (Carder et al. 1999). Rrs() optimization attempts to fit the shape of the Rrs() curve by iterating variables and uses a set shape factor for the aph() curve that is applicable to this region. Matching the Rrs() spectra in the longer wavelengths is difficult due to water absorption lowering the signal from aph() at longer wavelengths. The Rrs() optimization algorithm does not attempt to fit in the region around 676 nm since this overlaps th e region of chlorophyll fluorescence. The set shape factor for Rrs() optimization may give MODIS an advantage at 676 nm since it adjusts the shape factor for pigmented partic ulates based on the wate r temperature. One of the goals of the MODIS algorithm is to determine chlorophyll concentrations through using absorption at 676 nm and this study indi cates that it may do th at better than the other algorithms. MODIS does not fare as well as the othe r algorithms when bottom is present for anw() under regression analysis MODIS does not include a bottom albedo model like Rrs() optimization nor does it iterate bbp() like the QAA algorithm. These differences mean that the MODIS algorithm will sometimes decrease the ag() value or increase bbp() to compensate for bottom reflectance In about 41% of the cases where there is any bottom present, MODIS uses the default band ratio algorithm instead of the semianalytical algorithm. The band ratio algorithm is not as accurate as the semianalytical and bottom albedo could easily affect its results. The MODIS algorithm was not parameterized for areas with large bottom refl ectance contributions so it was expected that it wouldn't perform as well under these conditions. MODIS, however, does best for anw(650) when bottom is present. Since MODIS does not output absorption values at this wave length, it was interpolat ed using a 4th order polynomial curve fit in a Matlab routine. This region of the spectrum is very difficult to invert to anw() from Rrs() due to the low signal to noise ratio because of high water absorption and low constituent absorption. From this result it appears that the previously mentioned good aph(676) results from the MODIS algorithm allowed a better fit to interpolate anw(650) and was better than attempting to optimize a curve to this region. MODIS may present a method for other Rrs() inversion models to get better results in PAGE 117 99 the longer wavelengths by using the MODI S algorithm nitrate depletion temperature approach for determining aph(676) and interpolating from anw(555) to anw(676). Overall, Rrs() optimization did the best for anw() under the regression and error statistical analysis. Its slopes were closest to 1, intercepts closest to 0, and error the lowest. The Rrs() optimization algorithm generally had the lowest number of outliers under most conditions. One reason for this is that this method required the most a priori knowledge of the area and had a long effec tive path length. The spectrophotometric method only had a 10 cm path length for ag(), the ac9 has a 25 cm path length, and the Kd() measurements had effective path lengths that were less than that of the Rrs() measurements. If the input parameters for the inversion model are representative of the local conditions then it is expected that Rrs Optimization might be the best for determining IOPs especially in clea r waters without bottom influence. Kdopt was best or second best depending on conditions, however the KdKirk and KdLoisel models had some of the worst resu lts especially at longer wavelengths. These models are more empirical and are not parame terized for a particular region like Kdopt. Optimization doesn't rely on a single wavelengt h and can smooth out the errors through a hyperspectral curve fit. For KdKirk and KdLoisel, the anw() values at longer wavelengths where signal to noise is lo w sometimes had errors over 100%. The optimization model benefited from being able to fit where there was sufficient signal and used extrapolations to the longer wavelengths The algorithm would not attempt a fit if the Kd() values above 600 nm were greater than 10% different from that expected using pure seawater. The Kd() optimization algorithm effectively used an extrapolation to estimate anw() at the longer wavelengths and it pr oved more effective than the other Kd() inversions. The ac9 did fare well for anw() but was limited due to its shorter path length. Unlike the nonparametric analysis, the ac9 wa s not the worst in regression analysis but usually fell among the other methods and belo w the optimization type of inversions. Under several conditions the ac9 had a few outli ers that seemed to skew the error higher and improved the results when removed. Th e ac9 has its own light source instead of relying on the solar irradiance. Changes in downwelling light field due to solar zenith angle, clouds, or waves will not a ffect the ac9 but may affect the Rrs() and Kd() measurements. The ac9 provides a profile of the water column and will not be affected by significant changes in the optical prope rties over depth. The ac9, unlike the optimization inversions, does not require a priori knowledge of the environment to determine absorption. Under certain conditi ons the ac9 did much better than the nonoptimization models so while it was not th e overall best method it is useful when any knowledge of the optical properties of the study area is lacking. The ac9 did not fare as well as expe cted under shallow conditions. The ac9 should do better than the AOP methods when there was a significant amount of bottom reflectance but in those cases there is usually al so a shallow depth. The ac9 is sensitive to bubbles in its flow tubes. If these bubbles are not removed, they can produce highly PAGE 118 100 erroneous readings. Failure to properly clear air bubbles has resulted in absorption values over 25 times the actual value in casts during this study. Usually the instrument is sent to depth and the pressure compresses the bubbles so the pump is able to pull them out. In a shallow 10 m site, the depth might not be great enough to clear the instrument and bubbles can cause problems for the ac9. If there is significant sediment resuspension from the bottom it may cause problems for th e ac9. Sediment suctioned into the instrument can get trapped increasing scat tering. In highatte nuation shallow regions with little resuspension, the ac9 should be better than AOP invers ions for determining IOPs and did better for th e Friday Harbor sites. The spectrophotometric method for anw() had diverging results under the regression and percent error statistics. Under the NB, NF, and NBLCLZ filters, it has a slope close to one, an intercept near 0, and good correlation but high percent errors. Under the BT and BTLCLZ filters, the regressi on results were poor but the percent error was low. For the clear MODNB waters, the Spec did not perform well under all statistical tests. The results under MODNB filter are from th e low signal to noise in the low chlorophyll waters but the others may be the fault of a few large outliers. The spectrophotometric method is the sum of the filter pad ap() measurement and the spectrophotometer ag() measurement and combines the er rors from both techniques. The ag() measurement in the spectrometer has a low accuracy due to a short path length and probably is responsible for some outliers in the lower attenuation waters. If these outliers are in the same direction it can affect the regression statistics but still result in low percent errors. Th e spectrophotometric anw() is usually from a surface or just below surface water sample so it does not capture any changes in the anw() value at depth. The AOP methods produce an integrated anw() based on the amount of light reaching each depth. By integrating the ac9 values over depth and weighting them to the Kd() values, the integrated ac9 value is similar in meas urement to the AOP mode l inversion values. The other methods may produce similar results while the spectrophotometric method will not agree as well under conditions of changing optical propertie s over depth even if it is most accurate. If this results in a few high outliers evenly above and below the ideal value line, the Spec method could have good re gression statistics but high percent error values. 5.5. Comparisons of bbp() to Idealized Values 5.5.1. Unfiltered and No Bottom Filters bbp() Rrsopt has the overall slope closest to one and intercept closest to zero under the NF filter for bbp() (Figure 5.23). The HS6 has the best result at 442 nm with a 1.01 slope but is further from unity than the Rrs() inversions at the rest of the wavelengths. Of the Rrs() inversions, QAA has the best slope followed by Rrsopt, and MODIS. Kdopt has a slope furthest from one for most wavelengths. Rrsopt has the closest intercepts to 0 followed by QAA, HS6, MODI S, and Kdopt. QAA has an intercept of 0 at 589 nm and Rrsopt had an intercept of 0 at 671 nm. While the HS6 has good results at 442 nm, the Rrsopt has the best regression for bbp() under the NF filter PAGE 119 101 The Rrs() inversions have the best correla tion coefficients with the ideal bbp() values under the NF filter (Figure 5.23 C). The HS6 and Kdopt do not have high correlation coefficients. The hi ghest correlation for the HS6 is 0.57 and for Kdopt is 0.26 both at 532 nm. The QAA, which has a correla tion of 1 at 589 nm did the best with a mean correlation of 0.94. Rrsopt is sec ond highest with a mean of 0.93 while MODIS has a mean correlation of 0.81. Rrsopt has th e best correlations at 442 and 488. At 532, 620, and 671, QAA and Rrsopt are with 0.01 of ea ch other with correlations above 0.9. MODIS has its highest correlation at 442 nm but trends lower to 0.69 at 589 then improves to 0.77 for 620 and 671 nm. The Rrs() inversions have the best correlations with Rrsopt and QAA exhibi ting similar spectral tre nds under the NF filter. Rrsopt has the lowest error terms while Kdopt has low mean percent difference but high absolute percent difference for bbp() using the NF filter (Figure 5.24). In mean percent difference, Rrsopt does best but has a large spike in value at 589 nm. Overall, Kdopt has the second lowest pe rcent error and smoothest curv e for mean percent error. The HS6 is third in percent error with negative error terms across the entire spectrum. With the exception of 589 nm where it had a percent error of 0, the QAA had the highest percent error values. The QAA value for bbp(589) was usually the median value so it became the ideal value resulting in no percent er ror for this wavelength. In mean absolute percent difference, Kdopt is the highest overall. QAA is second highest until 589 nm where it is 0 but it quickly rises up in va lue to slightly below MODIS for 620 and 671 nm. Despite the similarities under the re gression analysis, the QAA model has a higher mean absolute percent error for bbp() than the Rrsopt model. MODIS starts off with a low mean absolute percent error but increases in value at the longer wavelengths. Rrsopt is the lowest for absolute percent error but has a large spike in value at 589 nm. The errors for QAA and Rrsopt may be a result of the iterative method of these models compensating for some of the stations with significant bottom reflectance. Kdopt has the overall larg est number of outliers for bbp() under the NF filter (Figure 5.24 C). Kdopt is only exceeded in number of outliers at one wavelength. MODIS for 671 nm at is higher than Kdopt in outliers. The QAA, MODIS, and Rrsopt have 0 outliers at 442 nm and the QAA model has zero outliers throughout the whole spectrum. Rrsopt was second best with ze ro outliers at 488, 620 and 671 nm and low outliers at other wavelengths. MODIS doe s well with 0 outliers at 442 and 532 nm but rapidly increases in outliers at 620 an d 671 nm. Overall the HS6 has outliers of approximately 40% and the Kdopt has outlier s near 80% indicating a lot of deviation from the ideal value. Rrsopt has the best regression results using the NB filter for values of bbp() with QAA closely following it (Figure 5.25). The re gression results usi ng the NB filter are very similar to those under the NF filter. Rrsopt and QAA have the best results followed by MODIS doing pretty good, HS6 having poor numbers, and the Kdopt being the worst. The correlation values follow a simila r trend as under the NF filter. PAGE 120 102 The percent error under the bbp() NB filter has three groupings (5.26). Kdopt has the highest mean absolute percent error, MODIS and HS6 are next and close in value, and Rrsopt and QAA are lowest. The percent error and absolute percent error for MODIS bbp( ) are similar in magnitude under both th e NF and NB filters indicating that MODIS is about 40 to 50% greater than the ideal bbp() value across the spectrum. The more empirical approach of the MODIS algorithm for inverting bbp() appears to result in an overestimate of bbp() under less than ideal conditions and higher chlorophyll waters. Most methods have the best agreement with the ideal at the s hortest and longest wavelengths but tend to have less agreement in the middle of the visible spectrum under the NF and NB filters. The AOP inversions are most influenced by bbp() at the middle wavelengths where absorption is th e lowest. The magnitude of bbp() has the greatest influence on the shape and magnitude of the modeled Rrs() curve at wavelengths approximately from 500 to 600 nm. Envir onmental parameters that influence Rrs() can be masked by the larger absorption values at the longer and shorter wavelengths but can be significant over the middle pa rt of the spectrum. The av erage cosine of downwelling irradiance, ag(), and bottom reflectance all ca n affect the inversion of bbp() from Rrs() in the green region. Sun glint can introduce a bias in the Rrs() values that the inversion method could interpret as an increase in the bbp() reference value. While the Kd() is not greatly affected by sun glint or bottom re flectance, the other factors along with wave focusing can influence its inversion of bbp(). The bbp() value has a much smaller contribution in the Kdopt model than the Rrs() inversions making errors in inverting bbp() due to environmental factors larger. While these other factors may result in some errors for the Rrs() inversions, they can be very significant for a Kd() inversion of bbp(). Some general trends are notable in the bbp() analysis. The three Rrs() inversions may be weighting the ideal value towards th eir values because of the similarity in approaches for determining the bbp() coefficient and using Rrs() as input for determining their bbp() reference value. However, the Rrs() inversions also have the highest signal to noise ratios for bbp() so it could be the case that they are more accurate. Rrsopt and QAA are even more similar in method for determining bbp() than MODIS and may result in the statistics for t hose methods usually be ing close in value. Rrsopt and QAA have the best results under the NF, NB, NBLCLZ, and MODNB filter. For the filters with bottom contribution, HS6 us ually has the best results. MODIS usually has results a little poorer than other two Rrs() inversions for the first four filters because Rrsopt and QAA iterate bbp(550) to determine it while MODIS uses an empirical algorithm. Kdopt is usually the fu rthest from the ideal value for bbp() but shows some promise when outliers are removed. K dopt and the HS6 sometimes have similar statistical results but the similarity between Kdopt and th e HS6 may simply be that they are equally poor in their results si nce their methods for determining bbp() are not similar. PAGE 121 103 Figure 5.23. Regression and correlation analysis of bbp() versus ideal values using the NF filter. A. Slope of linea r regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression intercept 0.002 0.000 0.002 0.004 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 Regression Slope 2 1 0 1 2 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 122 104 Figure 5.24. Percent error and outlier analysis of bbp() under the NF filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 123 105 Figure 5.25. Regression and correlation analysis of bbp() versus ideal values using the NB filter. A. Slope of linear regression of each met hod versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 HS6 Kdopt MODIS QAA Rrsopt Regression intercept 0.002 0.000 0.002 0.004 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 124 106 Figure 5.26. Percent error and outlier analysis of bbp() under the NB filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 125 107 5.5.2. Ideal Conditions bbp() MODIS algorithm has the slope closest to one under ideal c onditions using the NBLCLZ filter (Figure 5.27) but still has hi gh percent error statistics (Figure 5.28). Kdopt and the HS6 both have poor performances under this filter due to their lower path length and sensitivity relative to that of the Rrs() inversions. All of the Rrs() inversions have similar spectral shapes in plots of sl ope and intercept and have high correlations with the ideal value. This indicates that th ey are probably well corre lated with each other spectrally. The intercepts and slopes for Rrsopt and QAA are very close in magnitude adding to the evidence that their simila r approaches give similar values. The error statistics under the NBLCLZ filter again show that the MODIS bbp() value is from 40 to 50% greater than the ideal value just like under the NB and NF filters (Figure 5.28). This indicates that the difference is not due to environmental factors like percent cloud cover, high solar zenith angles, or bo ttom reflectance but due to a difference in method from the QAA and Rrsopt. The HS6 is the opposite of MODIS under this filter and is about 40 to 60% below the ideal value. The error in the HS6 is probably due to it reaching the accuracy of the instrume nt in some of the clear waters. Under the MODNB filter the waters are the clearest and the Rrs() inversions have the best regression results (Figure 5.29). MODIS is using the semianalytical only algorithm and its regression against the ideal value has changed. Under the previous three filters the MODIS values had a slope just below one and a positive intercept. Under the MODNB filter it has a slope above unity and a negative intercept. The three Rrs() inversions have correlations close to 1 while Kdopt and the HS6 are near zero. The results indicate that the longer path le ngths and greater sensitivity of the Rrs() inversion are best for this clear water. The error terms again indicate MODIS ha s an about 40 to 50% greater value for bbp() under the MODNB filter (Figure 5.30). Th e statistics for Rrsopt and QAA indicate that they are very similar to th e ideal value. Whether this is because they are close to the actual value or they give very similar resu lts and weight the ideal value towards their bbp() result is not clear without further study. Its possible th at most of the time MODIS is the higher of the values for bbp() and Kdopt and the HS6 are the lower values. This would leave Rrsopt or QAA as the likely median value. PAGE 126 108 Figure 5.27. Regression and correlation analysis of bbp() versus ideal values using the NBLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 HS6 Kdopt MODIS QAA Rrsopt Regression intercept 0.002 0.000 0.002 0.004 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 127 109 Figure 5.28. Percent error and outlier analysis of bbp() under the NBLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 128 110 Figure 5.29. Regression and correlation analysis of bbp() versus ideal values using the MODNB filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 HS6 Kdopt MODIS QAA Rropt Regression intercept 0.002 0.000 0.002 0.004 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 129 111 Figure 5.30. Percent error and outlier analysis of bbp() under the MODNB filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 130 1125.5.3. Bottom Reflectance Only bbp() Under the filters with sign ificant bottom reflectance only, Rrsopt, Kdopt, and the HS6 were used to determine the ideal bbp() value since MODIS and QAA do not account for bottom reflectance. The results under both all conditions (BT) and the ideal conditions (BTLCLZ) are very similar (Figur es 5.31 and 5.33). QAA and Rrsopt have high slopes near 2, MODIS and Kdopt are close to unity or well below it, and HS6 was near zero in slope. MODIS and QAA have a high positive intercept, with Kdopt and the HS6 in between, and Rrsopt had a negative in tercept. Under correlation analysis, QAA and Rrsopt are near 1, MODI S was near 0.5, and the HS6 and Kdopt were below 0.5. There is no clear statistical best in regre ssion analysis. Based on regression slope and intercept, Kdopt would be best but based on correlation Rrsopt a nd QAA would be best. The percent error and outlier analysis provides gives more information regarding the regression results (Figures 5.32 and 5. 34). The HS6 despite having poor regression results and correlation is the only method with lo w percent and absolute percent error. In addition, it has low outliers relative to the othe r methods. Rrsopt is second best while the percent error for MODIS and QAA are well ab ove 100%. Kdopt is third lowest in error terms but is near or above 100% error. It appears that the HS6 is probably the closest to the actual value but has poorer regression values because of influence by a few outliers. Possibly bottom reflectance is producing an overestimate for the Rrs() inversions by misinterpreting the reflec tance from the bottom as bbp(). Since most of the areas with significant bottom reflectance have a white sand bottom, it would have a similar reflectance for the wavelengths the Rrs() inversions use to determine bbp(). The light reflected off the bottom would be affected by the scattering w ithin the water column as it heads to the surface. The Rrs() inversions are probably dete cting the scattering within the water column but adding some bottom re flectance to it resulting in an overestimate that would still correlat e well with the ideal bbp(). If the ideal value is close to the actual value then Rrsopt and QAA result in double the value for bbp() when the bottom contribution to Rrs() is significant. The HS6 is the best method for measuring bbp() when bottom is present but has some outliers keep it from having a good regre ssion result. Several large outliers in the same direction especially at the minimum or maximum values in the data set can affect the slope of a least squares lin er regression fit. The HS6 oc casionally reached noise level when in the very clear waters off the Bahama s. This was apparent when examining the data because the instrument gave approximate ly the same value for several casts in the clearest waters. While the HS6 has a modulat ed signal from its light sources, it can be affected by bright ambient light To minimize this affect the instrument was pointed downward. In the Bahamas the bottom was ve ry bright white aragonite sand that could have reflected enough sunlight during sha llow casts to interfere with the HS6 measurement. However, when testing the di fferent sources of IO P input for the bottom albedo model (Chapter 7) it wa s found that using the HS6 bbp() data produced results closer to measured values than the ideal value or Rrsopt. PAGE 131 113 Figure 5.31. Regression and correlation analysis of bbp() versus ideal values using the BT filter. A. Slope of lin ear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression intercept 0.002 0.000 0.002 0.004 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 Regression Slope 2 1 0 1 2 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 132 114 Figure 5.32. Percent error and outlier analysis of bbp() under the BT filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 133 115 Figure 5.33. Regression and correlation analysis of bbp() versus ideal values using the BTLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression intercept 0.002 0.000 0.002 0.004 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 Regression Slope 2 1 0 1 2 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 134 116 Figure 5.34. Percent error and outlier analysis of bbp() under the BTLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 HS6 Kdopt MODIS QAA Rrsopt A. B. C. PAGE 135 1175.5.4. Discussion of bbp() Comparisons with Ideal Rrs() optimization had the best performance overall in determining bbp() under most conditions without bottom according to regression and erro r analysis. The QAA model was second best. MODIS was close but didn't perform as well as the QAA model. While all three models use an empirical approa ch to determine the spectral coefficient for bbp(), only MODIS uses an empirical function for the bbp(550) reference value. It appears that even the limited iterations pe rformed by the QAA mode l are all that is necessary for improving the inversion of bbp() from Rrs(). The Hydroscat6 has agreement with the Rrs() inversions for bbp() at 412 nm for the NB filter. Under this f ilter, high zenith values and high cloudiness were not excluded but stations with significant bottom contribution were. As the wavelengths increased the Hydroscat6 did significantly worse in comp arison. This error at longer wavelengths may mean that high solar zeni th angles and high cloudiness affect the empi rical spectral determination by Rrs() inversions producing errors of si milar magnitude and direction. High clouds could create more diffuse downwelling irradiance affecting the average cosine of the downwelling irradiance. Higher solar zenith angles would lower the path length for the Rrs() measurement giving less signal for bbp() in the measurement. The higher solar zenith angle would also affect the average co sine of the upwelling light producing errors due to path length elongati on. Since scattering affects the average cosine too, it would make it more difficult to invert bbp() from Rrs() since most inversion models are parameterized for solar zen ith angles less than 45. In addition to the areas where bottom is pr esent, the HS6 may be the better method for determining bbp() under solar zenith angles greater than 46 and cloudiness greater than 80%. The Hydroscat6 did poorly under the NB LCLZ conditions compared to the Rrs() inversions. Under ideal conditions for Rrs() measurements, the longer path length seemed to be a better method of determining bbp(). According to the manufacturer's specifications, the Hydroscat6 ha s a noise level range of 0.0002 m1 to 0.00002 m1. This lower range is achieved under lo w ambient light levels but at high light levels (bright sun) the noise level increases by an un specified amount. The HS6 determines bbp() based on a p() measurement at 140 by multiplying the result by 2*Pi and 1.08. This conversion gives bb() within 10% of the actual value and in cludes the known backscattering due to water. If the worst er ror of 10% is assumed then the error for bbp() increases as it becomes lower relative to the pure seawater backscattering. Using calculated particulate backscat tering values and the Morel se awater backscattering values (Morel 1974) over a range of bb(525) from 0.05 to 0.0005 m1 demonstrates that a positive 10% error in the backscattering values including seawater can result in an error for bbp(525). This error for bbp() ranges from 10.23% at the bb(525) of 0.05 m1 and increases exponentially to 33.4% at the lower bb() value. Under clearer water conditions, the Hydroscat6 may have more e rror if there is a very different phase function than what was used to calc ulate the factor fo r converting from (140,) to bb(). The Rrs() values will have an increasing signal from bb() under clearer skies, PAGE 136 118 lower attenuation, and lower solar zenith angl es leading to better i nversion results under the NBLCLZ and MODNB filters. Kd() optimization performed the worst for bbp() inversions under most conditions. This result was expected since bbp() makes up about 5% of the Kd() value. Downwelling irradiance measurements also have a lower effective path length than Rrs() measurements resulting in lower signal to noise ratios. Wave focusing, if not completely corrected, would have a large effect on a bbp() result from Kd() inversion since it increases the error in the Kd() value. As error increases due to wave focusing the error in the estimation of the coefficient for bbp() increases since the wave focusing error changes the spectral shape of the Kd() value. Backscattering is a larger portion of the signal at 532 to 555 nm than at other wavele ngths and the iterative fitting process could underestimate backscattering in that region if focusing events are more dominant. If defocusing events dominate the profile then backscattering coul d be overestimated. Changes in cloud cover or solar zenith angle affect the average cosine of downwelling irradiance and affect the Kd() inversions more than from Rrs() inversions. The change in the average cosine can be interpreted as a change in backscattering under the Kd() optimization algorithm. Under pe rfect conditions where the Kd() is not in error due to wave focusing and the average cosines of upwelling and downwelling irradiance are known, the inversion of bbp() from Kd() should be reasonable. The coefficient and intercept can be determined directly from Preisendorfe r's equation with a direct measurement of d. A very slowly descending instru ment package (descent rate of < 0.01 m/sec) that measured both the average co sine and below water irradiance reflectance would be able to determine a more accurate bbp() value. The poor accuracy of the Kd() optimization inversion of bbp() was expected due to the low signal of bbp() in the Kd() values combined with environmental factors that result in errors for Kd(). A problem with this statistical analysis is there needs to be a more independent reliable standard to determine bbp() than any of the methods in this study. The Rrs () methods appeared to vote together. Their ag reement may be due to the higher signal to noise in the Rrs() measurement or due to the similarity of the Rrs() inversion methods. The Kd() method had some problems that made it unreliable due to low signal by bbp(). The Hydroscat6 relies on an empirical rela tionship that may introduce error into the determination of bbp() and has a lower accuracy in very clear waters. There exist methods that require very intensive laboratory procedures to determine bbp() that might improve statistical closure if employed in future research. An approach to better test the backscatte ring of the methods would be select a site that has a water column that is well mixed within one attenuation depth and use proven laboratory equipment to also determine backsc attering. The BricePhoenix was an early device that gave information on particulate scattering at specific angles (Carder 1970). Laser scanning devices using diffraction within a sample can give some information on particle sizes that can be used to determine bbp() (Agrawal and Potsmith 1989). A coulter counter could also provide some info rmation on small particle sizes. With a PAGE 137 119 measured particle size di stribution, Mie theory coul d be used to estimate bbp() based on assumptions about particle shape and i ndex of refraction. Combining several in situ instruments that measure scattering at differe nt angles to better determine the volume scattering function might better approach to determine bbp(). An instrument that was deployed but the data were not used in th is study was the VSF meter. The VSF meter measures backscattering for a single wavelength at several angles ( Moore et al. 2000). Analysis of the VSF output could possibl y yield a better backscattering value for comparison with the other methods. A comb ination of the VSF with the Hydroscat6 may possibly might even give the best results for bbp() (Reynolds et al. 2006). The use of other methods for determining bbp() would improve the stat istical analysis for determining backscattering. An inversion using Hydrolight might al so provide a better estimate of bbp(). Using an accurate anw() as input while incrementing the bbp() levels until the Rrs() and Kd() measurements matched the output of Hydr olight might give a closer value to the actual bbp(). This approach would require very good simulation of the downwelling light field. Using stations wher e above water measurements of Ed() were collected and cloudiness was low might provide a better irradiance inpu t into Hydrolight. The biggest problem with this approach would be that it would require a large amount of computer time and setup time. The benefit is th at it could provide closure to the bbp() methods using the existing data set. 5.6. Comparisons of ag() to Idealized Values 5.6.1. Unfiltered and No Bottom Filters ag() Path length and the method of determining the coefficient for ag() are the big factors for this IOP. MODIS has the result clos est to 1, the intercept closest to 0, and the highest correlations under the ag() NF filter (Figure 5.35). The ac9 only does well for the 412 and 440 nm wavelengths then rapidly drops off in value as the wavelengths increase. The signal to noise ratio decreases rapidly with ag() measurements and the 25 cm path of the ac9 does not provide the sensi tivity of the AOP measurements. Rrsopt is the only technique with a negative intercept. Rrsopt is assumes a set spectral coefficient for ag() and could have influe nce from CDOM fluorescence. Kdopt iterates the coefficient and would have less influenc e from CDOM fluorescence than the Rrs() inversions but could have errors associated with iteration of the slope coefficient. Spectral errors in the Kd() values due wave focusing or incorrect estimates of d could result in an incorrect ag() coefficient. MODIS uses a higher coefficient for an initial determination of ag() and a lower coefficient for calculated ag() at longer wavelengths. Kdopt does well for the regressi on analysis but has a poor correlation. Specag with the shortest path leng th does somewhere in between the Rrs() inversions and the other methods. PAGE 138 120 The percent error under all the filters for ag( ) exhibit logarithmically increasing values with increasing wavelength (Figure 3.36) The error at the l ongest wavelengths is usually above 100%. Almost all oceanic ag( ) values logarithmically decrease as a function of wavelength. The result is that for wavelengths of 555 nm or longer, the ag( ) may be below the accuracy of the instrument for the direct measurements or masked by other IOP values in the AOP inversions. The ag( ) values were so low during the CoBOP cruise that even some measurements at 400 nm were not above the noi se level for the ac9 and Specag. The median ag() values of each method for the en tire data set are very different from each other. The ac9 has the highest value at 0.011 m1, which is right at the instrument's accuracy of 0.01 m1, and the Specag has a median of 0.004 m1, which is below its accuracy. For comparison, the median for Rrsopt is 0.004 m1, for MODIS is 0.006 m1, and for Kdopt is 0.006 m1. The inversion algorithms have an advantage because they are only estimating ag() at 400 or 440 nm and us ing a decaying log slope equation (Equation 3.1) to extrapolate it to other wavelengths. Using this equation guarantees that that they will never have nega tive values at the longer wavelengths. The ac9 and Specag both had over 9% of their ag() values below zero at 555 nm and had to have them filtered out before statistical an alysis. As the wavelengths increase, the differences between the methods become gr eater due to lower accuracy for ac9 and Specag along with spectral coefficient differenc es in the inversion algorithms. The best wavelength range to compare these methods is from 412 to 510 nm because above that the signal to noise ratio is too lo w for any method to be trusted. The method used to determine the spectr al coefficient for Kdopt resulted in improved values under the NF filter but pr obably contributed to outliers in some instances. The method of iterating the ag() coefficient probably re sult in Kdopt having a higher number of outliers that increased in pe rcentage with wavelengt h due to errors in estimating the slope coefficient. The itera tion of the slope coe fficient was performed separately from the iteration to determine th e other unknowns to minimize errors but it may not have done enough. Under the unfiltered data set, some of the high solar zenith angles, wave focusing in shallow waters, a nd cloudiness may have been interpreted as a change in the ag() slope coefficient by the model. The other methods only had a few outliers at the shorter wavelengths. The removal of a few outliers might bri ng the ac9 regression slopes much closer to one under the NF filter for ag() (Figure 3.36). A few stations may have some errors due to bubbles in the ac9 flow tube or clogge d filters bringing the values for the ac9 down. While the ac9 lacks the sensitivity of the other methods it makes separate measurements at the longer wavelengths. The Rrs() inversions are limited to determining the value at one shorter wave length then extrapolating it to longer wavelengths. The Rrsopt method can have problems due to an error at one wavelength affecting all the other wavelengths. The ac9 has less depe ndence between the measurements at each wavelength and an error at one wavelengt h won't necessarily affect the other wavelengths. If the error is due to bubbles in the ac9 it will affect all wavelengths but if PAGE 139 121 the error is due to a film on one or its nine filters, it will only affect that particular wavelength. Despite the poorer performance of the ac9 relative to the other methods, its values at the shorter wavelengths are may be good if a few outliers are removed. MODIS again has the best regression results for ag() under the NB filter (Figure 5.37). MODIS has the best correlation results and the numbers are si milar to those under the NF filter. The removal of the stations with a significant bottom contribution resulted in a greater amount of divergence from zero at shorter wavelengths for intercept by all methods. Only MODIS remained close to zero The intercepts loga rithmically approach zero as the wavelengths increase. This dive rgence is probably th e result of different approaches for estimating the spectral coefficient of ag(). Different spectral coefficients would result in intercepts further from ze ro that approach zero as the wavelengths became longer and ag() became smaller. Rrsopt has low error terms for ag() under the NB filter and based on its low number of outliers it probably would have done better under the regressi on analysis if the outlier values were excluded (Figure 5.38). The error terms reflect the path length of the measurement. Rrsopt, MODIS, and Kdopt are lo west in error terms in that order. The ac9 had few outliers from 412 to 510 nm indi cating that a few bad stations probably increased its percent error and removing those values may result in significant improvement for the ac9 over the shorter wavelengths. MODIS has low outliers for 412 and 440 nm und er the NB filter but spikes up to greater than 50% outliers for wavelengths greater than 440 nm (Figure 5.38). While the regression, correlation, and error results fo r MODIS are good, the outliers at the longer wavelengths indicate a potential problem due to selection of the second slope. MODIS ag() values are close to unity in slope versus the ideal value but are just far enough off that the slopes are not within the 10% range. This indicates that despite being within the range the values at the longer wavelengths are off by a small but consistent factor. The coefficient selected for the calculation of the ag() values is probably slightly too low under the conditions of the NB filter resul ting in good agreement at 412 and 440 nm but less at longer wavelengths. CDOM fluoresce nce may not be as big a factor under some of the less than ideal conditions due to lo wer direct sunlight. Th e compensation for it by the higher coefficient under MODIS may in troduce some errors under those conditions. The ag() coefficient used for first calculating the aph() and ag(400) value was 0.018 and the value for calculating anw() and ag() was 0.16. A slight increase in value to 0.017 or 0.0165 may result in improving the MODIS valu es at longer wavelengths. However, the outlier method is just one of the statistics. Another possibility is the inclusion of higher cloudiness and solar zenith angles are affected the ag() inversions using MODIS by affecting the average cosine. The less dire ct and more diffuse li ght could change the spectral values of and may cause a slight multiplicative error in ag(400). While MODIS has a consistent factor that keeps it from having a slope within the 10% range of the ideal, the difference in slope is not large and MODIS still has the best results for ag() under the NB filter. PAGE 140 122 Figure 5.35. Regression and correlation analysis of ag() versus ideal va lues using the NF filter. A. Slope of lin ear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 ac9 Kdopt MODIS Rrsopt Specag Regression intercept 0.04 0.02 0.00 0.02 0.04 0.06 0.08 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 141 123 Figure 5.36. Percent error and outlier analysis of ag() under the NF filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 Kdopt MODIS Rrsopt Specag A. B. C. PAGE 142 124 Figure 5.37. Regression and correlation analysis of ag() versus ideal values using the NB filter. A. Slope of linear regression of each met hod versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 ac9 Kdopt MODIS Rrsopt Specag Regression intercept 0.04 0.02 0.00 0.02 0.04 0.06 0.08 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 143 125 Figure 5.38. Percent error and outlier analysis of ag() under the NB filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 ac9 Kdopt MODIS Rrsopt Specag Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 144 1265.6.2. Ideal Conditions ag() MODIS has the best statistics under the ideal conditions for AOP measurements for ag() values under the NBLCLZ filter (Figur e 5.39). Rrsopt has a much higher regression slope and its difference in intercept from zero is more pronounced. The poorer performance of Rrsopt may be due to in creased CDOM fluorescence. Under these conditions there is more direct sunlight reac hing depth stimulating more fluorescence that would show up in the water leaving radiance. Despite its smaller path length, Specag was second best for regression under this filter followed by Kdopt. The Specag only exhibited poor regression results at 676 nm where possibly some ba d filtering techniques allowed some chlorophyll to contaminate the sample. Chlorophyll ab sorbs strongly at 676 nm and using a high vacuum pressure dur ing filtering can result in rupture of phytoplankton cells releasing some chlo rophyll into the di ssolved sample. The percent error results using the NBLC LZ filter are similar to the results under the NB filter but the outliers exhibit larger differences from the previous two filters (Figure 5.40). MODIS has zero outliers for all wavelengths while the other methods have high outliers. Comparing this to the outlier s using NB filter provides evidence that the reason for the high outliers for MODIS under the NB filter is a problem with high zenith angles and cloudiness. MODIS is an algorithm for inverting Rrs() from satellite imagery (like the MODIS satellite). Satellite im agery is masked by clouds and usually not collected at high zenith angl es so the MODIS algorithm normally does not have to deal with them in its inversions. This results demonstrates that the MODIS algorithm using the higher ag() coefficient to calculate the initial ag(400) and aph() works well under the conditions where MODIS wa s designed to work. MODIS and Rrsopt have almost identical regression and correlation values under the MODNB filter for ag() (Figure 5.41). Kdopt has good regression results under this filter. Path length is the domina nt factor under this filter si nce it represents the clearest waters. Both the ac9 and Specag perform poorly for regression and correlation under this filter. The error terms are similar to the other filters but the outliers are different under the MODNB filter for ag() (Figure 5.42). Rrsopt has the lowest percent error followed by MODIS and Kdopt. Only MODIS and Rrsopt have low outliers at for 412 and 440 nm. Rrsopt rapidly increases in va lue to some of the highest outlier values for 488 nm and longer. This indicates that while Rrsopt is close to the ideal value at 412 and 440 nm, its coefficient for ag() is wrong. The coefficient used for Rrsopt was 0.018 and probably was too high for most of these waters since Rrsopt has a slight ly negative percent error. Kdopt has low outliers at 532 nm and longer. Kdopt probably has the opposite case from Rrsopt, the coefficient is right but the ag(440) values used to calculate ag() were too high. MODIS may also high coefficient for ag() and it might have problems with the high solar zenith angle and cloudiness that was included under this filter. PAGE 145 127 5.39. Regression and correlation analysis of ag() versus ideal values using the NBLCLZ filter. A. Slope of linear regression of e ach method versus ideal value. B. Intercept of linear regression of each met hod versus ideal value. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 ac9 Kdopt MODIS Rrsopt Specag Regression intercept 0.04 0.02 0.00 0.02 0.04 0.06 0.08 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 146 128 Figure 5.40. Percent error and outlier analysis of ag() under the NBLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 ac9 Kdopt MODIS Rrsopt Specag Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 147 129 Figure 5.41. Regression and correlation analysis of ag() versus ideal va lues using the MODNB filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 ac9 Kdopt MODIS Rrsopt Specag Regression intercept 0.04 0.02 0.00 0.02 0.04 0.06 0.08 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B, C. PAGE 148 130 Figure 5.42. Percent error and outlier analysis of ag() under the MODNB filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 ac9 Kdopt MODIS Rrsopt Specag Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 149 1315.6.3. Bottom Reflectance Only ag() With bottom reflectance included under the BT filter for ag(), the ac9 and Specag have the best regressions (Figure 5.43). Th e problems with the AOP methods are similar as under the BT filter for bbp(). Increased bottom influenc e can be interpreted by the model as decreased ag(). Even though Rrsopt takes in to account bottom albedo, it can still affect inversions of IOPs that have spectrally increasing or declining values. MODIS was not designed to work with significant bottom reflectance so its performance is no surprise. Kdopt was expect ed to perform better but ha s the poorest regression and correlation results. Kdopt ag() inversions were probably affected by wave focusing, higher cloudiness and higher solar ze nith angles under this filter. Rrsopt and Specag have the lowest pe rcent error terms under the BT filter for ag() but Rrsopt has some of the largest outlie rs for 488 and higher (Figure 5.44). Specag has the lowest percent outliers but the ac9 is close indicating a few outlier cause problems for the ac9. The filtered ac9 can have some problems in shallow waters since it is more difficult to clear bubbles from the flow tube. Shallower waters, especially along the West Florida Shelf, have much more particles that co uld fill the pores of the filter used with the ac9. These two factors may be respons ible for the errors in the ac9 ag() values. The regression results under the BTLCLZ filter for ag() are show that ac9 and Specag have the best results (Figure 5.45). Both Rrsopt and Kdopt have good results for 412 nm but decrease in slope at longer waveleng ths but have intercepts that are spectrally flat. Kdopt and Rrsopt are getti ng the right refere nce value for ag() but are not using the right coefficient. The presence of the botto m limits the path length advantage of the AOP methods and the higher signal to noise ratios usually found in shallow waters helps the ac9 and Specag in obtaining better measurements for ag(). The percent error statistics have Specag and Rrsopt performing the best for the BTLCLZ filter for ag() (Figure 5.46). Kdopt has a lo w percent error at 412 and 440 nm but is above 60% error for abso lute percent error at those wavelengths. This indicates that while it is around the idea l value, it is evenly under a nd over the value for all the stations. Using the iterative approach to determining the coefficient for ag() may not be a good method for Kdopt in shallow regions. It may be best to use a set coefficient when the irradiance sensor cannot get below th e depths of severe wave focusing. The ac9 and Specag have low outliers ove rall and the AOP inversions have high outliers under the NBLCLZ filter for ag() (figure 5.46). There is a spike in outliers at 488 nm by the ac9 while MODIS dips to almo st zero outliers. MODIS initially has a regression slope much larger than unity but declines to near unity at 488 and then is below unity indicating a spectral slope problem (Figure 5.45). About half the ac9 outliers at 488 nm were from the first CoBOP crui se to the Bahamas. The ac9 used for ag() during that cruise had problems with degradation of its optical filters and had to be repaired after the cruise. Th e 488 nm filter was one of those replaced. This demonstrates PAGE 150 132 that intercomparisons between these methods are a way to determine problems with instruments. Figure 5.43. Regression and correlation analysis of ag() versus ideal va lues using the BT filter. A. Slope of lin ear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression intercept 0.04 0.02 0.00 0.02 0.04 0.06 0.08 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 Regression Slope 2 1 0 1 2 ac9 Kdopt MODIS Rrsopt Specag A. B. C. PAGE 151 133 Figure 5.44. Percent error and outlier analysis of ag() under the BT filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 ac9 Kdopt MODIS Rrsopt Specag Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 152 134 Figure 5.45. Regression and correlation analysis of ag() versus ideal va lues using the BTLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression intercept 0.04 0.02 0.00 0.02 0.04 0.06 0.08 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 Regression Slope 2 1 0 1 2 ac9 Kdopt MODIS Rsopt Specag A. B. C. PAGE 153 135 Figure 5.46. Percent error and outlier analysis of ag() under the BTLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 ac9 Kdopt MODIS Rrsopt Specag Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 154 1365.6.4. Discussion of ag() Comparisons with Ideal MODIS has the best inversion for the unfiltered data. This is surprising in one respect because the MODIS algorithm does not compensate for some of the external environmental variables. The change to the MODIS algorithm using the higher estimated CDOM coefficient for initial inversion and th en a lower value for the output IOPs seems to give this algorithm an advantage in determining ag() over the Rrs optimization and QAA models. MODIS continued to have the best inversion re sults for all filters except those where only bottom was present. Unde r conditions where bottom reflectance was significant, MODIS had regres sion slopes approaching two at shorter wavelengths then declining to below one at longer wavele ngths. Without corr ecting for the bottom contribution, the bottom influence was calculated as lower ag() and or higher bbp() resulting in errors in ag() for MODIS. MODIS did the be st under the unfiltered data and performed better that Rrs() optimization for ag() inversions except where bottom was present. The higher ag() coefficient used in the M ODIS algorithm compensates for increased upwelling radiance associated with CDOM fluorescence and improves aph() values for Rrs() inversions. Using a fulvic acid dominated fluorescence efficiency equation in Hydrolight and an ag() coefficient of 0.016 results in an increase in Rrs() that has a peak around 450 to 500 nm near th e Soret peak for chlo rophyll a absorption (Hawes 1992). Without correction, this p eak would produce an e rror under estimating the phytoplankton absorption coefficient. This increase in fluorescence will also affect bbp() inversions MODIS is possibly less affected for bbp() than the Rrs optimization model since the MODIS algorithm uses an empirical approach for bbp() while Rrs optimization iterates bbp(400). Rrs optimization still returns good inversions for aph() without taking into account CDOM fluor escence because it compensates for the fluorescence by increasing bbp() and decreasing ag() instead of decreasing aph(). The MODIS approach is best for high CDOM waters where fluorescence is a problem. Kdopt performed well under the MO DNB and NBLCLZ filters for ag() but did poorly under the other filters. Higher cl ouds and zenith angle affected the ag() inversion from Kd() values. The initial testing where anw() was intercompared under varying degrees of cloudiness and zenith angles using the KW statisti c indicated that Kd() was more affected than Rrs() by these parameters. Changes in the average cosine would affect the spectral shape of the ag() values under the iteration method used for the ag() coefficient. The iteration of the ag() coefficient seems to work well for ideal conditions but had problems under other conditions due to increased cloudine ss and higher solar zenith. Under the regression analysis, the Kd() optimization performed poorly for bottom conditions. While it performed well unde r the nonparametric analysis, it appears that it has a significant number of outliers that increase in number with increasing wavelength. Correction for wave focusing is more difficult in shallow environments PAGE 155 137 since the depth may be too shallow to get below the depths where wave focusing is a significant effect. The result can be a spectral shift in the valu es. Since outliers affect the nonparametric technique less than the regres sion analysis, it seems that adjusting the model for the conditions may improv e it. In shallow regions, the ag() coefficient should be set to an estimated value instead of iterated. The ac9 is only reliable from 412 to 510 nm for ag() measurements. The accuracy of the ac9 is 0.01 m1 for a wellcalibrated instrument. The values at wavelengths beyond 510 nm were usually below th e level of accuracy. A solution to this error is fit the logarithmic spectral curve for ag() though the first 3 to 4 wavelengths of the ac9. However, the ac9 was one of th e best methods under th e regression analysis for determining ag() when bottom was present. Despite its lower optical path compared to the AOP inversions, the ac9 has no interf erence with the bottom due to changes in the geometric light field. The more direct measurement is sometimes better under these conditions. The high error for ac9 ag() under most filters is due to outliers. Problems with bubbles and flow rate can result in data from and ac9 that is very different from the actual value. Removing the outliers does improve the statistical agreement to the idealized data. The presence of the outlier s indicates the complexity of deployment of this type of instrument especially with a 0. 2 m filter inline. Late r improvements to the method resulted in a lower number of outliers. Th e higher error for the ac9 appears to be function of some really bad outliers from earlier deployments that if removed will significantly lower the error. The spectrophotometric technique for ag() has high error unde r conditions with low bottom contribution to Rrs(). There are three reasons for this error, low path length, bad technique, and variations in ag() over depth. The spectrophotometer has only a 10 cm path cell giving it the shortest path length of any of the instruments. This results in a lower signal to noise for the instrument. During one of the main cruises used in this study, a student that was just learning the technique may have not performed it properly. The samples were improperly filtered resulti ng in some contamination by particles. The spectrophotometric measurements use seawater collected from a sp ecific depth at a specific point in time. If there exists a change in ag(), either in magnitude or spectrally, over depth then the value would not be similar to the other methods, which are integrated over depth. All or some of these problems could result in the hi gh error and outliers for the deeper waters. Changing IOPs over depth can be a signifi cant problem for AOP inversions in coastal environments. The outflow from a ri ver can have high CDOM concentrations with a lower ag() coefficient and can form at layer over the top of mo re saline oceanic waters that typically have lower ag() coefficients. During the formation of a seasonal thermocline higher CDOM concentrations usually occur in the deeper cooler waters with lower concentrations at the surface. Hypers aline bays like Florida Bay can have outflows on the shelf waters that are high in CDOM with low ag() coefficients that will sink PAGE 156 138 below the more oceanic waters. All of these environmental conditions will present problems for AOP inversion models that can lead to errors in their IOP results. 5.7. Comparisons of aph() to Idealized Values 5.7.1. Unfiltered and No Bottom Filters aph() The Specaph method has the best regression results for aph() values under the NF filter but has low correlation at 555 nm (Figure 5.47). While the ac9, HS6, and Specag have much shorter path lengths, the Speca ph method has a fairly long effective path length. By taking samples from a particul ar depth and concentrating them on a glass fiber filter, the aph() measurements using the Specaph approach have an effective path length of meters to tens of meters long The Specaph method does not have problems with other absorbing components masking the measurement value or environmental conditions affecting the measurement. The Specaph measurement does have problems in that it represents only a point in the water column. If aph() values change with depth then this technique may not represent the water column value. The Specaph requires an empirical correction for scattering within the filter pad that results in increased path length for the measurement. This correction ca n result in errors for the value that could be the reason for the poor correlations for Specaph at 550 nm. Another factor for the poor correlations is that the absorbance values at 550 nm ar e very low and may be near the accuracy limit of the spec trophotometer used for these measurements resulting in more noise at the middle wavelengths. Rrsopt, Kdopt, and MODIS have poor regres sion results under the NF filter for aph() but correlations above 90% (Figure 5.47) Kdopt and Rrsopt track closely in magnitude and spectral shape for both slope and intercept. This agreement between Rrsopt and Kdopt is due to both techniques using a similar approach to determining aph() by iterating a shape factor. Both algorithms used the same values for the shape factors that were based on filter pad meas urements from the three study areas. MODIS has a different approach using generaliz ed values that correspond to different phytoplankton pigment packaging. The MODIS e quations were based on the analysis of an extensive library of aph() filter pad measurements from around the globe. The use of the aph() filter pad measurements to parameteri ze the AOP inversion algorithms means that there is more dependence between th e methods than in previous statistical comparisons. Rrsopt and Kdopt will have more dependence on the filter pad method than the MODIS algorithm because they are using so me of the actual measurements in this study to determine the shape factor for aph(). None of the techniques has low pe rcent error terms or outliers for aph() under the NF filter except for MODIS at 510 nm (Fi gure 5.48). The only good regression results for MODIS were at 510 nm where it was near uni ty in slope and zero in intercept. The percent error for Specaph and Kdopt are especially high at 532 to 555 nm. MODIS takes into account pigment packaging by using different factors for aph() based on nitrate PAGE 157 139 depletion temperatures. This approach may serve to better estimate the aph(510) values instead of using the shape fa ctors like Kdopt and Rrsopt. Under the NB filter for aph(), Specaph again has the be st regression results but low correlation at 532 to 555 nm (Figure 5.49). Rrsopt and Kdopt are further apart in value but have similar spectral shapes. Kdopt does not perform as well as Rrsopt since Rrsopt has a longer effective path length MODIS has a slope well below one and probably has problems due to the less than id eal conditions and inclusion of the default algorithm. With the removal of the stations with signifi cant bottom contribution, Kdopt and Rrsopt no longer have the spike up in slope at 532 and 555 nm observed under the NF filter nor does MODIS have the spike in slope value at 532 nm. This indicates that the bottom contribution, which would be signi ficant at 532 nm, may have affected these values under the NF filter. The Specaph and Kdopt both have spikes in value at 532 to 555 nm for absolute percent error using the NB filter (Figure 5.50). Rrs() measurements would have the longest path length in this region and Kdopt and Specaph may be affected by a low signal to noise over the green wavelengths. K dopt generally has the highest error and this probably due to the low path length compared to the Rrs() inversions and greater path length and signal to noise of the Specaph. The outliers are lower for Kdopt than under the NF filter and all methods have around 40% outliers. The Rrs() values exhibit a spike in outliers at 650 nm. The MODIS value at this wavelength is an extr apolation so higher error is expected for it. The Rrsopt outlier values are up near 80% at 650 nm and the percent error indicates an overestimate by Rrsopt for aph(650). Since Rrsopt did not exhibit the same spike for ag() or bbp() it may be due to spectr al factors related to sun glint. PAGE 158 140 Figure 5.47. Regression and correlation analysis of aph() versus ideal values using the NF filter. A. Slope of lin ear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 Kdopt MODIS Specaph Rrsopt Regression Intercept 0.03 0.02 0.01 0.00 0.01 0.02 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 159 141 Figure 5.48. Percent error and outlier analysis of aph() under the NF filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 Kdopt MODIS Specaph Rrsopt A. B. C. PAGE 160 142 Figure 5.49. Regression and correlation analysis of aph() versus ideal values using the NB filter. A. Slope of linea r regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 Kdopt MODIS Specaph Rrsopt Regression Intercept 0.03 0.02 0.01 0.00 0.01 0.02 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 161 143 Figure 5.50. Percent error and outlier analysis of aph() under the NB filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 Kdopt MODIS Specaph Rrsopt Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 162 1445.7.2. Ideal Conditions aph() Rrsopt and Specaph have the best regre ssion results but Kdopt is greatly improved over the previous filters under the NBLCLZ filter for aph() (Figure 5.51). The improvement in Rrsopt and Kdopt regression values under the ideal conditions indicates that high solar zenith angle and cloudiness do have some effect on the inversion of aph() by the iterative models. MODIS has the slope furthest from one and it is probably due to the errors from its default empirical algorithm. Kdopt has the highest percen t error terms because the Rrs() methods have the longest path lengths under the ideal conditi ons (Figure 5.52). Both Specaph and Kdopt exhibit spikes in percent erro r at 532 to 650 nm probably due to low signal to noise for Kdopt and packaging effects for the Specaph surface measurements. The high outliers for Specaph may be due to it being a measurem ent at a single depth. The integration of the water column aph() values by the AOP inversions may produce difference from the ideal value for the Specaph values. Rrsopt has a high number of outliers and approaches 100% for 555 to 650 nm wavelengths. The co rrelation between erro r and environmental factors presented later in this section indica tes a negative correlation between solar zenith angle and absolute percent error at the longer wavelengths for Rrsopt aph(). By using the different filters and statistics, a conclusion can be reached, the main cause of Rrsopt's aph(650) outliers is probably sun glint which occu rs at lower solar zenith angles. MODIS and Kdopt have relatively low outliers fr om 412 to 555 nm indicating that a removing less than 20% of the stations woul d improve their regression results. Under the MODNB filter for aph() the water is the clearest and Rrsopt has the best results (Figure 5.53). Specaph and M ODIS are close seconds. MODIS now is only using the semianalytical portion of the mode l and has much better regression results. Kdopt is has the poorest regres sion results due to a shorter path length than the other methods. Kdopt even has much worse results at the longer wavelengths. The absolute and signed percent error terms indicate that MODIS slightly underestimates the ideal aph() value for 412 to 532 nm but ge nerally has the lowest error terms for all except the extrapolated va lues under the MODNB filter (Figure 5.54). Kdopt and Specaph have very high error at 532 nm. This error may be due to packaging effects not captured by the single near surf ace Specaph measurement and low signal to noise for the Kdopt aph(532). The ideal value could also be biased due to errors in the same direction for the Rrs() inversions. Rrsopt again e xhibits high number outliers at 555 and 650 nm that are likely due to sun glin t. MODIS has a high number of outliers at the extrapolated value of 555 nm but this is an extrapolated value. Excluding the two wavelengths where there are extrapolated values and MODIS has the lowest mean number of outliers. PAGE 163 145 Figure 5.51. Regression and correlation analysis of aph() versus ideal values using the NBLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 Kdopt MODIS Specaph Rrsopt Regression Intercept 0.03 0.02 0.01 0.00 0.01 0.02 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 164 146 Figure 5.52. Percent error and outlier analysis of aph() under the NBLCLZ filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 Kdopt MODIS Specaph Rrsopt Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 165 147 Figure 5.53. Regression and correlation analysis of aph() versus ideal values using the MODNB filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 Kdopt MODIS Specaph Rrsopt Regression Intercept 0.03 0.02 0.01 0.00 0.01 0.02 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 166 148 Figure 5.54. Percent error and outlier analysis of aph() under the MODNB filter. A. Mean of the percent difference fr om the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Percent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Percent Difference 100 50 0 50 100 Kdopt MODIS Specaph Rrsopt Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 A. B. C. PAGE 167 1495.7.3. Bottom Reflectance Only aph() Specaph and Rrsopt have the be st regression results for aph() under the BT filter (Figure 5.55). MODIS has very poor regres sion results with slopes near zero, high intercepts, and low correlations. The perfor mance of MODIS is not unexpected since it was not set to work with significant bottom reflectance. Unlike bbp() and ag() when bottom is present, Rrsopt has good results for aph(). The spectral shape of the aph() curve is different enough from the spectral albedo of the bottom that its signal is unique for the iterative Rrsopt method. Kdopt suffers from wave focusing due to the shallower depth but does improve its regressi on results at longer wavelengths. Kdopt has a low percent error but high absolute percent er ror indicating that it is around the ideal value but there is a lo t of noise in the inversion for aph() under the BT filter (Figure 5.56). Rrsopt and Specaph are th e lowest in error. Rropt has zero outliers from 412 to 510 nm indicating that is was the median value for most stations at those wavelengths. Kdopt has high outliers of near 80% for 412 to 510 nm but rapidly drops to near 20% for the longer wavelengths. This i ndicates that the spectral affects of wave focusing are affecting the aph() inversions from Kd() in the shorter wavelengths. Rrsopt has the best results for regr ession and correlation analysis for aph() under the ideal conditions with significant botto m contribution (Figure 5.57). Specaph is second best in regression results but has hi gher percent error terms (Figure 5.58). Kdopt has higher percent error terms under this filt er than under the less than ideal conditions providing further evidence for wave fo cusing problems interfering with aph() inversions from Kd(). Under the ideal conditions the sun w ould be closer to zenith and the light would enter the water closest to the vertical. The water column is shallow and the irradiance sensor cannot go to the depth wh ere the focused rays becomes scattered and mixed. The effects of wave focusing would be greatest under these conditions. Rrsopt has high outliers at 650 nm possibly due to s un glint. It appears that wave focusing affects Kd() inversions for aph() in the short wavelengths while Rrsopt has affects from sun glint on its inversions at the long wavelengths. PAGE 168 150 Figure 5.55. Regression and correlation analysis of aph() versus ideal values using the BT filter. A. Slope of lin ear regression of each method versus ideal value. B. Intercept of linear regression of each method versus id eal value. C. Correlation between ideal value and each method. Regression Slope 2 1 0 1 2 Kdopt MODIS Specaph Rrsopt Regression Intercept 0.03 0.02 0.01 0.00 0.01 0.02 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 169 151 Figure 5.56. Percent error and outlier analysis of aph() under the BT filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 Kdopt MODIS Specaph Rrsopt A. B. C. PAGE 170 152 Figure 5.57. Regression and correlation analysis of aph() versus ideal values using the BTLCLZ filter. A. Slope of linear regression of each method versus ideal value. B. Intercept of linear regression of each method versus ideal va lue. C. Correlation between ideal value and each method. Regression Slote 2 1 0 1 2 Kdopt MODIS Specaph Rrsopt Regression Intercept 0.03 0.02 0.01 0.00 0.01 0.02 Wavelength (nm) 400450500550600650700 Correlation Coefficient 1.0 0.5 0.0 0.5 1.0 A. B. C. PAGE 171 153 5.58. Percent error and outlier analysis of aph() under the BTLCLZ filter. A. Mean of the percent difference from the ideal value. B. Mean of the absolute value of the percent difference from the ideal value. C. Perc ent outliers determined by removing high error values until the regression slope versus the ideal value was near unity. Mean Abs Percent Difference 0 20 40 60 80 100 Wavelength (nm) 400450500550600650700 Percent Outliers 0 20 40 60 80 100 Mean Percent Difference 100 50 0 50 100 Kdopt MODIS Specaph Rrsopt A. B. C. PAGE 172 1545.7.4. Discussion of aph() Comparisons with Ideal Under Regression analysis, the filter pad me thod performs the best overall for the NF and NB filters. The regression results e xhibit a large spread in values under the less than ideal conditions with the filter pad met hod being the closest to 1 for slope. There is the possibility of the two iterative models voting together. Kdopt and Rrsopt use the same shape factors for aph() and their slopes and intercepts under the regression analysis followed the same spectral pattern for the unf iltered data. However, Kdopt and Rrsopt did not have similar spectral patterns for the regression analysis under th e other filters. It is not clear if they coincidently followed the same pattern under these two filters or they match in regression results because of th e similar approaches and model factors. The good results for the Specaph method we re not surprising since it has the longest effective path length of the met hods not based on AOPs. To determine the effective path of the measurement, the volume filtered in cubic meters is divided by the area of coverage of the particles on the filter pad. The measurement is then multiplied by a Beta factor that takes in to account the scattering thr ough the glass fiber filter pad increasing its path length (Mitchell and Kiefer 1988). The Beta factor is typically around 2 in value indicating that it the path of the light through th e filter pad is double the length of the straight path through the pad. These values combine to give an effective path length for the filter pad method from above 1 to over 20 meters for the areas in this study. Like AOP values, the filter pad method usually increases its path le ngth as attenuation decreases. Generally, in clearer waters, more water has to be filtered to achieve optimum optical density on the filter pad for a measurem ent resulting in an increase in effective path length (Fig. 5.60). This longer path resu lts in a high signal to noise ratios without masking of the signal by other substances or influences from external environmental factors. PAGE 173 155 Figure 5.59. Effective path length for the quantitative filter pad me thod as a function of the volume filtered and assuming a beta factor of 2. With the exception of the two bottom only filters, there are a low correlation values for Specaph from 532 to 555 nm. One poss ibility is that the Be ta factor that is used to empirically determine the path le ngth elongation in the filter pad method is wrong. The 532 to 555 nm region is an area of low optical density in a filter pad absorbance spectrum. The Beta factor is empirically fit over a range of absorbance values. If the optical density is below the range of the fit, then the filter pad aph() measurements may be inaccurate at that wavelength. The filter pads for aph() under the CoBOP project had problems with achieving ideal optical density in the 532 to 555 nm region. The pores in the filters tended to stop up before the pad had reached the ideal optical density. During the 1999 CoBOP cruise 25 out of 49 pads had absorbance values below 0.04 at this wavelength. CoBOP al so may have had different species of phytoplankton than used in the original calcul ation of the equation for the Beta factor. The Bahamas Banks are dominated by small di noflagellates according to some surveys of that area (Agard et al. 1995) These organisms may have di fferent optical properties from the phytoplankton used to parameterize the beta factor in this study and require a different beta factor. The Beta factor or filtering technique may have produced errors around 555 nm for aph(). The AOP aph() inversions could have errors in the 532 to 555 nm region that bias their values in the same direction. Th e 532 to 555 nm wavelength is affected by scattering or bottom reflectance in the AOP inversions. The aph() values selected for calculating the aph() curves under Rrsopt and Kdopt may not be representative of the phytoplankton species for the study and could re sult in errors. The actual absorption spectrum may have packaging effects that lead to a different absorption than the Volume Filtered (l) 0.250.51234 Path Length (m) 0 5 10 15 20 25 PAGE 174 156 parameters used in the model at the 532 to 555 nm wavelength. The error due to packaging can also be applied to the filter pad aph() since the samples were usually collected near the surface. However, si nce MODIS used a set of parameters for aph() that was different from the Kd() and Rrs() optimization, the filter pad method may be the source of the error in this wavelength region. MODIS aph() values did improve to second best under the MODNB filter under regression analysis for aph(). Only the SemiAnalytical method for MODIS was included under this filter resu lting in a less empirical approach. However, none of the methods were very good at aph(555) under the MODNB filter. The filter pad method had a regression slope of near 2 wh ile the AOP inversions were ne ar 0. This may be further evidence that the change in aph(555) with changes in packag ing or pigments over depth results in problems with comparison to the filter pad method. Comparing the filter pad results for the FSLE4 cruise where there was a bottle sample taken at three different depths illustrates the changes in aph(555) versus aph(440) at different depths. A change in depth from about 1.5 m below the surface to 25.3 m below the surface resulted in a 39.04% change in the aph(555) to aph(440) ratio and a 52.11% change in aph(555) value. The AOP measuremen t may reflect the increased relative value of aph(555) at depth if that depth is opt ically shallow enough to influence Rrs() but the surface filter pad may not. A caveat to the change in aph(440) relative to aph(555) is the amount of CDOM fluorescence. CDOM fluorescence at this re gion would act in an opposite affect on Rrs() and to a lesser extent Kd() as an increase in the aph(440) to aph(555) ratio. To resolve the issue, known values of CDOM fluorescence at individual sites would have to be compared to known values of aph() over depth using an exact model like Hydrolight to determine the extent of the factors. E ither packaging effects or CDOM fluorescence could produce errors in all the IOPs in this wavelength region. It seems likely that the errors at 555 nm for aph() are due to a combination of sources of error and further research is needed to determine the significance of each source of error. The filter pad did best under most filters for aph(676). Since water absorption at 676 nm is not a factor for the filter pad method, it has the best signal to noise ratio of any method at this wavelength for aph(). Rrs() optimization and MODIS both do well for the filters that are not bottom only at 676 nm. Both methods have slopes close to the filter pad method. Under bottom conditions the Rrs() inversions have more difficulty at 676 nm and the Kd() optimization method does better. This difference for the Rrs() inversions is possibly an arti fact of the bottom reflectance es pecially in shallow bright bottom. It may cause the Rrs() inversions to sligh tly decrease their aph() reference value to compensate for increased reflectan ce resulting in errors at 555 nm.. The Kd() optimization method is usually not able to fit its model curve fo r wavelengths greater than 600 nm and it is relying on the values at shorter wavelengths to determine 676 nm based on the aph() shape factor so it is surprising that it does much better. Since the PAGE 175 157 filter pad value at 676 nm is better, it underscores the need for multiple techniques when working under less than ideal conditions such as those with a significant bottom contribution. One of the difficulties with the Kd() optimization method was determining the average cosine of down welling irradiance and errors in estimating this term could result in errors in separation of aph() and ag() from anw(). Both scattering ratios and cloudiness had significant spectral correlati on with absolute pe rcent error in aph(). The main effect of these errors would be in de termination of average cosine. Backscattering is more difficult to estimate from Kd() since it only makes up 5% of the signal. The average cosine across the air water interface can be estimate d based on Snell's law but it is more difficult at depth without a priori knowledge of scattering or a direct measurement. Wave focusing has a spectral effect resulting in errors in average cosine. The magnitude of ag(), under less than ideal conditions can be in error resulting in errors in aph(). If there is a tradeoff in value between ag() and aph() in the blue wavelengths then anw() can be close to right but both ag() and aph() can have errors. 5.8. Absolute Percent Error Correlations with Parameters 5.8.1. Correlations with anw() Under the NF filter and several other filters, there was a negative correlation between the solar zenith angl e and the AOP inversion models (Figures 5.61, 5.62, 5.65, and 5.71). As the solar zenith angle decreased the error increa sed. Solar zenith angles of 45 or less are generally considered the best for low sun glint, surface reflectance, and sufficient water leaving radiance, but that ma y have to be reconsid ered with the higher errors due to sun glint at lower zenith angles. A lower range limit may need to be set. Kd() has increased wave focusing at lower angles and also exhibited a negative correlation with solar zenith angle under several filters. The sun being closer to nadir will result in greater penetration of the lig ht under wave focusing conditions. Kdopt and Rrsopt have less of a problem with nega tive correlations with zenith angle for anw() as compared to the more empirical models. Th e problems experienced with low solar zenith angle under anw() seem to occur more in conjuncti on with increased cloudiness and not under the ideal condition filters. The ac9 had some correlations with envi ronmental factors that should not have any influence on it but may be related to othe r factors. The ac9 ha s a negative correlation with solar zenith angle under the NB f ilter and the NBLCLZ filter (Figures 5.66 and 5.69). The ideal value may be biased because of the affects on the AOPs resulting in similar errors in the same direction. The ac9 has some positive correlations with increases in bottom reflectance contributi ons under the NF, BT, and BTLCLZ filter usually at or between 488 to 555 nm (Figures 5.63, 5.75, and 5.78). The Spec does not have correlations with bottom reflectance contribution except at 412 nm under the BT filter. While this correlati on could be a bias in all the AOP methods affecting the ideal value for the ac9 but the correlation is likely because bottom contribution to Rrs() PAGE 176 158 generally increases with shallower waters. The ac9 has troubles with the clearance of bubbles from its flow tubes and one method of clearance is to send the instrument deeper to about 30 m to where the bubbles are compre ssed and can be forced from the tubes. The shallower waters with significant botto m reflectance may not be deep enough to clear the flow tubes in the ac9. The correlati on is really between the ac9 and depths less than 30 m and is especially problematic in clear waters. The Spec has of correlations with anw() absolute percent error and various parameters at 650 nm for the all the filte rs but only a few correlations at other wavelengths. The main correlations at 650 nm for the spec were with negative with anw(440), cnw(440), and bp/cnw(440) and positive for bbp/anw(440) and bbp/bp(440) (Figures 5.63, 5.66, 5.69, 5.72, 5.75, and 5.78) The negative correlations indicate that the Spec increases in error at 650 nm as the attenua tion and absorption b ecome lower and the particulate scattering relative to atte nuation becomes lower. The lowest anw() values generally occur at 650 nm. At this wavelength the optical density of the filter pad is may be below the minimum value for the Beta correction and the spectrophotometric ag(650) values are well below the accuracy of the inst rument. Lower particulate scattering to attenuation may mean that ag(650) is a greater c ontribution to the anw(650) value than ap(650) resulting in higher error due to th e lower accuracy of the spectrophotometric ag() measurement. The backscattering ratios could also indicate pr oblems with the beta factor in clear waters. The lowest atte nuation waters in this study were around the Bahamas where the phytoplankton species popu lation was composed primarily of small dinoflagellates. The fine aragonite sand in the Bahamas could be resuspended and clog the filter pores before a large enough quantit y of water could be filtered to achieve the required absorbance on the filter pad. These aragonitic particles also have a higher bbp/anw(440) and bbp/bp(440) explaining the positive corr elation between error and those ratios. If the beta factor was not sufficient to account for the scattering in the filter by the different phytoplankton sp ecies or the aragonite particles, then it could cause the error at 650 nm. While the absolute percent error correlations for the Spec at 650 nm could simply be that it is the only method that is correct, it appears po ssible that this is a wavelength where it has errors due to environmental factors. MODIS has positive correlations with significant bottom reflectance but negative correlations with bp/cnw(440) under filters, NF, BT a nd BTLCLZ (Figures 5.61, 5.73, 5.76). As scattering decreases relative to attenuation, mo re of the bottom reflectance might increase due to a lower return path to the surface for the light. For this study percent bottom contribution is slightly correlated (r2 = 0.56) with bp/cnw(440). The stations with the highest bottom reflectance we re in the Bahamas and these stations also had the lowest bp/cnw(440). It is likely the correlation is simply with the increased bottom reflectance and not the bp/cnw(440) ratio. The absorption b ecomes a larger portion of the attenuation due to the observed high ag() relative to anw() in the waters around Lee Stocking Island, Bahamas decreasing the bp/cnw(440) ratio by increasing the attenuation. This correlation is more bp/cnw(440) correlating with shallower waters in this study that it is correlating with absolute percent error for MODIS. PAGE 177 159 MODIS also has positive correlations with bbp/anw(440) and bbp/bp(440) but negative with bp/cnw(440) for several wavelengths under the NB, and NBLCLZ filters but not for MODNB (Figures 5.64, 5.67, and 5.70) Unlike the correlation with percentage of bottom contribution and bp/cnw(440), this appears to be a correlation based on the use of the empirical portion of the MODIS algorithm instead of the semianalytical portion. The empirical portion is for waters with hi gher chlorophyll concen trations that were removed using the MODNB filter. Based on th is correlation, the empirical portion of the MODIS algorithm does have problems in waters that are probably Case II waters. As backscattering increases as a proportion of the component absorption or particulate scattering, the absolute percent error increases As particulate sca ttering decreases as a proportion of the component attenuation, the abso lute percent e rror increases. This water probably has high CDOM and high backsc attering but overall lower particulate scattering. The area with high backscattering ratios but low bp/cnw(440) was in the Bahmas. These optical characteristics were water close enough to shore to receive the higher CDOM but far enough offshore that they are more dominated by smaller phytoplankton species with higher backscattering efficiencies. The Kd() inversions have correlations between percent error for several wavelengths and parameters that repres ent water clarity and cloudiness. The Kd() inversions have some correlations with bo ttom reflectance but this more a correlation with the increased wate r clarity and shallower bottoms. Under these cases the irradiance sensor may not get deep enough below the areas of high wave focusing so that a polynomial fit can correct the wave focus valu es. This correlati on is higher than a correlation with depth because it also factors in the water clarity. KdKirk has negative correlations with anw(440) for the longer wavelengths especially under the NF, NB, and MODNB filters (Figures 5.62, 5.65, and 5.71). KdKirk is the most empirical of the Kd() inversions and will have more problems under co nditions that are not ideal, waters that do not match the estimated bbp/anw() ratios, and waters that do not have phase functions close to the Petzold phase f unction. Cloudiness also shows up more as a percent error correlation more under the Kd() inversions than under the Rrs() inversions. The problems with Kd() and cloudiness were observed unde r the KW nonparametric tests. KdOpt has several percent e rror correlations with diffe rent parameters at 412 nm including the bbp/anw(440) and bbp/bp(440) ratios (Figures 5.62, 5.65, 5.68, and 5.71). While it is not exactly clear why it has so many different error correlations at this wavelength under several of the filters, it may be because of the method of iterating the ag() coefficient. While both Kdopt and Rr sopt determine the a reference value ag(), Kdopt iterates over a set range to determine the best ag() coefficient. Because the iterative models focus on minimizing the differences between th e two measured and modeled curves over most of the spectrum, th ey are not just determining the reference value based on one wavelength. Since the ag() is higher with decreasing wavelength, combining the iteration of the coefficient and reference may result in errors that will affect the 412 nm region more under Kdopt. Conditions where the scattering ratios are distinctly different or cloudiness is high may exacerbate the errors in estimating both the reference and coefficient for ag(). While bbp() is not a large factor in the Kd() PAGE 178 160 inversion equation, the bbp/anw(440) and bbp/bp(440) ratios could be indicators of changes in the average cosine of downwelling irradian ce because of changes in scattering. The combined effects of bbp() attenuating downwelling irradi ance and the effect of bbp() on the average cosine could possibly make bbp() a bigger factor in inversions from Kd() but will require much more research to determine whether this valid. Other correlations have explana tions that are more obvious. Kd() inversions, MODIS (under the BT and BTLCLZ filters), and the ac9 sometimes have negative percent absolute error correlations with anw(440), cnw(440), and chlorophyll concentrations (Figures 5.68 and 5.72). Ch lorophyll was found under many of these tests to have similar correlation values as anw(440) so it is acting as a proxy for absorption at 440 nm (Figures 5.64 and 5.72). Chlorophyll con centrations could act as an indicator for aph(440) when it is by itself in co rrelation with a method. The Kd() and ac9 values have more error as absorption and attenuation decreas e because the signal to noise ratio is also declining and the l onger path length Rrs() inversions are better. QAA, KdLoisel, and MODIS were not designed to take into account the bottom contributions to Rrs() and have errors when it is significant (Figures 5.61 and 5.62). Even the less than 10% bottom contribution under the nonbottom filters can contribute to some error. Rrsopt and MODIS under the NB and NBLCLZ filters exhibit error correlations with bottom contribution even though the bottom contributio n is less than 10% (Figures 6.64 MODIS and 5.76 Rrsopt). PAGE 179 161 Figure 5.61. Percent error correlations with environmental parameters under the NF filter for anw() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 180 162 Figure 5.62. Percent error correlations with environmental parameters under the NF filter for anw() inversion from Kd(). Kd Loisel Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd KirkWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 181 163 Figure 5.63. Percent error corr elations with environmental parameters under the NF filter for anw() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotometric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 182 164 Figure 5.64. Percent error correlations w ith environmental parameters under the NB filter for anw() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 183 165 Figure 5.65. Percent error correlations w ith environmental parameters under the NB filter for anw() inversion from Kd(). Kd Loisel Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd KirkWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 184 166 Figure 5.66. Percent error correlations w ith environmental parameters under the NB filter for anw() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotometric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 185 167 Figure 5.67. Percent error correlations with environmental parameters under the NBLCLZ filter for anw() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 186 168 Figure 5.68. Percent error correlations with environmental parameters under the NBLCLZ filter for anw() inversion from Kd(). Kd Loisel Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd KirkWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 187 169 Figure 5.69. Percent error correlations with environm ental parameters under the NBLCLZ filter for anw() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotometric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 188 170 Figure 5.70. Percent error correlations with environmental parameters under the MODNB filter for anw() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 189 171 Figure 5.71. Percent error correlations with environmental parameters under the MODNB filter for anw() inversion from Kd(). Kd Loisel Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd KirkWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 190 172 Figure 5.72. Percent error correlations with environmental parameters under the MODNB filter for anw() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotometric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 191 173 Figure 5.73. Percent error corr elations with environmental parameters under the BT filter for anw() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 192 174 Figure 5.74. Percent error corr elations with environmental parameters under the BT filter for anw() inversion from Kd(). Kd Loisel Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd KirkWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 193 175 Figure 5.75. Percent error corr elations with environmental parameters under the BT filter for anw() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotometric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 194 176 Figure 5.76. Percent error correlations with environmental parameters under the BTLCLZ filter for anw() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 195 177 Figure 5.77. Percent error correlations with environm ental parameters under the BTLCLZ filter for anw() inversion from Kd(). Kd Loisel Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd KirkWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 196 178 Figure 5.78. Percent error correlations with environmental parameters under the BTLCLZ filter for anw() direct measurements. 5.8.2. Correlations with bbp() The bottom contribution correlates with ab solute percent error under most filters for bbp(). Even the less than 10% contributio n has an effect on the determination of bbp() from Rrsopt (Figure 5.81). QAA seems to be affected the most when bottom was above 10% (Figures 5.76, 5.87, and 5.88). The bottom is most visible in the middle wavelengths where the attenuation is lowest and most models use that to fit the bottom contribution. By iterating the bbp(555) value QAA and Rrsopt may be more likely to include the bottom contribution as bbp() under conditions where the contribution is small. By using an empirical approach, MODIS may not have the same errors in bbp(). MODIS Max bottom b/c(440) bb/b(440) Spectrophotometric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 197 179 This does not mean that MODIS has the best approach for determining bbp() from Rrs() when bottom is present but it di d have regression results that were closer to unity as compared to the QAA and Rrsopt inversions when bottom contribution to Rrs() was significant. QAA has a positive correlation between absolute percen t error for bbp() and anw(440) under the NB filter but a negative correlation unde r the MODNB filter (Figures 5.81 and 5.85) and a negative spectral correl ation with chlorophyll under the BT filter (Figure 5.87). The QAA model appears have problems with absorption under conditions where solar zenith angle or cloudines s is high resulting in errors in bbp() with increasing absorption. The MODNB filter results in lo wchlorophyll lowattenuation waters and as the absorption value decreases the QAA has mo re error under this fi lter (Figure 5.85). Under the NBLCLZ filter and unde r the NB filter, QAA has po sitive correlations with bbp/anw(440) and bbp/bp(440) but negative with bp/cnw(440) for several wavelengths (Figures 5.81 and 5.83). Like MODIS, th e QAA model may not be able to compensate for changes in parameters like the Q factor under coastal water that are high back scattering but have low particulate scatteri ng. Even though Rrsopt and QAA have similar approaches to inverting Rrs() for bbp(), the QAA model has a more empirical approach to determination of the "g" coefficient and does not do as many iterations for determining the reference values for bbp(). This more empirical appr oach makes it computationally faster but makes it more sensitiv e to conditions th at are not ideal. Kdopt has a positive spectral correlation with anw(440) and chlorophyll but a negative correlation with bp/cnw(440) under the NB filter for bbp() (Figure 5.82). This correlation gives information that was al ready suspected, that Kdopt has problems determining bbp() when its signal is small relative to absorption. The percentage of bbp() contributing to the Kd() signal is only about 5%. As absorption increases in value relative to scattering, the pe rcent error for the inversion using Kdopt increases. The HS6 has several positive correlations with bbp/anw(440) and bbp/bp(440) (Figures 5.80, 5.82, 5.86, 5.87, and 5.88). This increase in absolute percent error could be due to problems with the AOP inversions under these environments biasing the ideal values in the same direction. However, it may be a problem with the assumption that total backscattering is 1. 08 *Pi*bb(140). The HS6 actually only measures backscattering at a 140 but extrapolates it all backscattering angles based on an empirical assumption that usually can estimate backscattering to within 10%. The higher backscattering ratios are often indicative of smaller particles. These particles may not fit the relationship used by the HS6 for the estimating total backscattering. The result is that under these conditions, the HS6 may need a different empirical function to more accurately estimate bbp(). PAGE 198 180 Figure 5.79. Percent error corr elations with environmental parameters under the NF filter for bbp() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 199 181 Figure 5.80. Percent error corr elations with environmental parameters under the NF filter for bbp() from HS6 and Kdopt. MODIS Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Hydroscat6Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 200 182 Figure 5.81. Percent error correlations w ith environmental parameters under the NB filter for bbp() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 201 183 Figure 5.82. Percent error correlations w ith environmental parameters under the NB filter for bbp() from HS6 and Kdopt. MODIS Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Hydroscat6Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 202 184 Figure 5.83. Percent error correlations with environmental parameters under the NBLCLZ filter for bbp() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 203 185 Figure 5.84. Percent error correlations with environm ental parameters under the NBLCLZ filter for bbp()from HS6 and Kdopt. MODIS Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Hydroscat6Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 204 186 Figure 5.85. Percent error correlations with environmental parameters under the MODNB filter for bbp() inversion from Rrs(). MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith QAAWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 205 187 Figure 5.86. Percent error correlations with environmental parameters under the MODNB filter for bbp() from HS6 and Kdopt. MODIS Max bottom b/c(440) bb/b(440) Kd Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Hydroscat6Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 206 188 Figure 5.87. Percent error corr elations with environmental parameters under the BT filter for bbp() for QAA and HS6. MODIS Max bottom b/c(440) bb/b(440) QAA Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Hydroscat6Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 207 189 Figure 5.88. Percent error correlations with environmental parameters under the BTLCLZ filter for bbp() Rrsopt, QAA, and HS6. QAA Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Hydroscat6Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 208 1905.8.3. Correlations with ag() Kdopt absolute percent error for ag() had positive correlations with cnw(440) and cloudiness under all the filters with no si gnificant bottom contribut ion to reflectance (Figures 5.89, 5.92, 5.93, and 5.95). The co rrelations either starte d lower at 440 or 488 nm and increased slightly with wavelength. Under MODNB there were also similar magnitude correlations with Ch lorophyll concentrations and anw(440). While the NBLCLZ filter was considered low cloudiness, it used at 80% or greater cloudiness as its filter point. This correlation may be the reason for the lower agreement for the Kd() inversions with increasing cloudiness using the KW nonparame tric statistics. Since there is no correlation with these parameters at 412 nm, they are not affecting the reference value for ag(). This error correlation is po ssibly an effect from the Gordon Normalization (Gordon 1989). Even though the di ffuse light values used in the Gordon Normalization were calculated using the cloud iness correction in Hydrolight, it may not have properly modeled it. As cloudiness incr eases the light becomes more diffuse. As attenuation increases the light becomes less at depth. Kdopt ag() does not have a similar correlation when the bottom contribution is sign ificant indicating that this is probably a effect on the geometric light field at dept h. Kdopt method cannot compensate for the longer path length of light in conjunction w ith greater attenuation. While the problem with the model is not clear without further testing, the average cosine of downwelling irradiance is probably competing with the spectral slope coefficient of ag(). MODIS and Rrsopt both had negative corr elation at the longe r wavelengths with solar zenith angles using the NB, NF, NBLCLZ, and MODNB filters (Figures 5.89, 5.92, and 5.95). In addition, MODIS had negative correlations with sola r zenith angles at 412 and 440 nm using the BT filter (Figure 5.97) and Rrsopt had negative correlations under the BTLCLZ filter. MODIS always correlate d with 412 and 440 nm but continued out to 555 nm under the NF and NB filters. Rrsopt never had correlations at 412 nm but had correlations from either 440 or 488 to 532 or 555 nm. This error is lik ely due to sun glint but affects each Rrs() inversion model in different wa ys because of their different ag() slope coefficients. Solar zenith angle was a significant affect on ag() as all AOP methods had correlation with it and ag() under some filters. Even Specag had correlations under every filter except for BTLCLZ. This correla tion indicates that the solar zenith angle affected all the AOP methods introducing an e rror in the ideal value. This error in ag() usually occurred at a wavele ngth greater than 412 nm. While MODIS had several positive correlations with ag() absolute percent error and bottom contribution to reflectance unde r the NF, BT, and BTLC LZ filters (figures 5.89, 5.97 and 5.99) Rrsopt only had correlations at 412 to 488 nm under the NB filter (Figure 5.92). Rrsopt had co rrelation with bottom contribution and absolute percent error using the NB filter for anw() and bbp() despite the contributi on being less than 10% (Figures 5.64 and 5.81). A low bottom contribu tion to reflectance is detectable under the PAGE 209 191 Rrsopt model but it does seem to produce erro rs in the IOP values when conditions are not ideal or the water has a highe r chlorophyll concentration. MODIS had positive ag() error correlations with bbp/bp(440), bbp/anw(440) and chlorophyll concentrations under the NB and NBLCLZ filter at 412 and 440 nm (Figures 5.92 and 5.93). This looks similar to the correlations under for anw() the backscattering ratios. This correlation appears under th e filters where bottom contribution to Rrs() is not significant and MODIS includes the defau lt algorithm in the mix. These correlations appear to indicate a path length problem with the default algorithm because of the error associated with the scattering ratios. Specag and filtered ac9 had negative correlations with anw(440) and ag() absolute percent error. Specag was spectra l for MODNB while the ac9 was at 412 and 440 nm (Figure 5.96). This was probably due to low signal to noise from the lower path length instruments. MODIS ha d a negative correlation with anw() for the entire spectrum under the MODNB filter and Rrsopt had negative ag() error correlations with anw() for 532 to 650 (Figure 5.95). Kdopt had positive error correlations for 488 to 676 with anw() under the MODNB filter. Except for K dopt, all the methods had some signal to noise problems for ag() in the clearest waters. Kdopt had problems with too high of an absorption producing errors in ag(). PAGE 210 192 Figure 5.89. Percent error corr elations with environmental parameters under the NF filter for ag() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 211 193 Figure 5.90. Percent error corr elations with environmental parameters under the NF filter for ag() from Specag. Figure 5.91. Percent error correlations w ith environmental parameters under the NB filter for ag() from Specag. ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith PAGE 212 194 Figure 5.92. Percent error correlations w ith environmental parameters under the NB filter for ag() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 213 195 Figure 5.93. Percent error correlations with environmental parameters under the NBLCLZ filter for ag() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 214 196 Figure 5.94. Percent error correlations with environmental parameters under the NBLCLZ filter for ag() from Specag. ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith PAGE 215 197 Figure 5.95. Percent error correlations with environmental parameters under the MODNB filter for ag() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 216 198 Figure 5.96. Percent error correlations with environmental parameters under the MODNB filter for ag() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 217 199 Figure 5.97. Percent error corr elations with environmental parameters under the BT filter for ag() from AOP inversions. Rrs Optimization Chl Clouds Zenith MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 218 200 Figure 5.98. Percent error corr elations with environmental parameters under the BT filter for ag() direct measurements. MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 219 201 Figure 5.99. Percent error correlations with environmental parameters under the BTLCLZ filter for ag() from AOP inversions Rrs Optimization Chl Clouds Zenith MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 220 202 Figure 5.100. Percent error correlations with environmental parameters under the BTLCLZ filter for ag() from Specag. 5.8.4. Correlations with aph() For aph() MODIS has positive correlations between absolute percent error and bbp/anw(440) and bbp/bp(440) but negative with bp/cnw(440) for most wavelengths under the all filters but except for MODNB. These correlations are similar to those for anw() and ag() percent error. Because the semiana lytical MODIS exhibits few correlations with the scattering ratios, it is the default band ratio algorithm that is having the most difficulty with aph(). This error seems to occur when optical properties are very different from Case 1 waters. At 650 nm, MODIS has fewer correlations with the scattering ratios but this is an extrapolated value. MODIS is at a disadvantage in this comparison, though. Kdopt and Rrsopt use known shape factors for aph() based on the filter pad measurements from each of the 3 locations leading to dependencies among their results. MODIS requires no a priori knowledge of the area and is designed for large pixel satellite images collected around the globe. The empirical portion of MODIS will only be used for high chlorophyll regions so this does not indicate an error for most of the regions where the MODIS algorithm is used for Rrs() inversions from satellite data. Kdopt has more correlations betw een absolute percent error for aph() and factors that affect the light field above the surface. Under the NF filter, Kdopt has correlations with solar zenith angle fo r 412 to 488 nm and cloudiness for 532 to 676 nm. Under the NB and MODNB filter there were also correlation with both, but only negative ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith PAGE 221 203 correlation with solar zenith angle unde r the NBLCLZ filter. Kdopt for the aph() inversion appears more susceptible to the diffuse light from increase cloud cover and spectral shifts from wave focusing at lowe r zenith angles. Kdopt percent error had a spectral correlation with bottom contribution to reflectance under the BT filter and for the short wavelengths under the BTLCLZ filter. Part of this may be that the aph() methods from the Rrs() inversions are much bette r since Kdopt has the shorte st path length of the AOP inversions. As presented earlier, the quantitative filter pad method for aph() has a very long effective path le ngth and it may even exceed the path length for the Kd() measurement if a shallow bottom limits the depth for the profile of Ed() to determine Kd(). Even though cloudiness did seem to cause problems for the Kdopt inversion for aph(), this may not a factor where the K dopt model failed but a case where the Rrs() inversions and the Specaph methods were ju st that much better under those conditions. While the bp/cnw(440) values do correlate with bo ttom contribution to reflectance, there were some correlations with absolute percent error for aph() under conditions with little bottom influence for the AOP invers ions. For total scattering divided by attenuation, this term is cal led single scattering albedo or probability of photon survival. If the ratio is close to one, then the photon is more likely to be scattered while if the ratio is lower the photon is more likely to be absorbed. For the inversion of aph(), it appears that under most filters there is a negative co rrelation between the bp/cnw(440) ratio and percent error for AOP based models. As the chance for survival of the photon goes down, the effective path length of the AOP valu e decreases. This results in a lower signal to noise for the AOP inversion. For waters th at are high in CDOM or have particles that are low in scattering, the AOP inversions for aph() experience more error. PAGE 222 204 Figure 5.101. Percent error co rrelations with environmenta l parameters under the NF filter for aph() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 223 205 Figure 5.102. Percent error correlations w ith environmental parameters under the NF filter for aph() filter pad method. Figure 5.103. Percent error correlations w ith environmental parameters under the NB filter for aph() filter pad method. ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith PAGE 224 206 Figure 5.104. Percent error correlations w ith environmental parameters under the NB filter for aph() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 225 207 Figure 5.105. Percent error correlations with environmental parameters under the NBLCLZ filter for aph() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 226 208 Figure 5.106. Percent error correlations with environmental parameters under the MODNB filter for aph() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 227 209 Figure 5.107. Percent error correlations with environmental parameters under the MODNB filter for aph() filter pad method. ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Figure 5.108. Percent error correlations w ith environmental parameters under the BT filter for aph() filter pad method. ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith PAGE 228 210 Figure 5.109. Percent error correlations w ith environmental parameters under the BT filter for aph() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 229 211 Figure 5.110. Percent error correlations with environmental parameters under the BTLCLZ filter for aph() from AOP inversions. MODIS Correlation Error 1.0 0.5 0.0 0.5 1.0 Max bottom b/c(440) bb/b(440) Rrs Optimization Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith Kd OptimizationWavelength (nm) 400450500550600650700 Correlation Error 1.0 0.5 0.0 0.5 1.0 bb/a(440) cnw(440) anw(440) PAGE 230 212 Figure 5.111. Percent error correlations with environmental parameters under the BTLCLZ filter for aph() filter pad method. 5.9. Problems with Making Comparisons Between Methods The comparisons in this study may not be fair to all the AOP inversion models since some were better designed for these en vironmental conditions in this study. Some of the AOP inversions models tested in this study were at a disa dvantage to the other inversion models due to data not collected. Bottom reflectan ce was possibly an influence at 46 of the 126 stations in this study and the only Rrs() inversion model that took it into account was the Lee et al. Rrs() optimization algorithm (Lee et al. 1998, Lee et al. 1999). The geometric underwater light field may be influenced by cloud cover and zenith angle affecting all AOPs in a similar manner biasing the ideal IOP values. Some of the models were created to work with the limited wave bands available from satellites and are being compared to models that use hyperspectral data putting them at a disadvantage. The limitations of the some of these models were expected and were factored into the comparisons. The inversion model by Loisel et al. re quired below water irradiance reflectance (rrs()0), as an input (Loisel et al. 2001). Only downwelling irradiance was collected below water not upwelling radiance. To substitute for the rrs()0, Rrs() with an empirical function (Carder et al 1999) to correct for the air water interface and irradiance to radiance ratio (Q factor) was substituted. This substitution introduced errors into the algorithm since they use rrs()0in a function to determin e scattering and the average cosine of scattering. The porti on of the model to determine bbp() wasn't even used since ac9Wavelength (nm) 400450500550600650700 bb/a(440) cnw(440) anw(440) MODIS Max bottom b/c(440) bb/b(440) Spectrophotmetric Methods Correlation Error 1.0 0.5 0.0 0.5 1.0 Chl Clouds Zenith PAGE 231 213 it would have resulted in very large errors without including a measured rrs()0. The Loisel et al. model is not expected to f unction as well as the Kd optimization model because of this missing input. The Rrs() inversion models had difficulties in estimating bbp() when bottom contributions to Rrs() were significant. The QAA and MODIS algorithm were not parameterized to take into account the bottom albedo. The Rrs() optimization algorithm took into account the bottom but like the other Rrs inversions it used an empirical model to determine the spectral slope of bbp(). The bbp() value generally affects the spectral shape of the Rrs() curve in the areas of lowest absorp tion. This usually falls into the green area of the spectrum around 532 to 555 nm. The combined affects of bottom reflectance and backscattering are hard to separate resulting in errors in bbp() from Rrs() inversion algorithms even if they take into account the bottom contri bution. The Rrsopt method has a set spectral shape for the bottom albedo that is only cont rolled by a factor. The albedo is based on pure sand and increases almost linearly with wavelength. Actual measurements of bottom albedo can have variat ions in shape spectra lly that are non linear or have a different intercept if linear. These variations can result in further errors in bbp() values from the Rrs optimization model. The in situ bbp() measurements from the HS6 had to be used to achieve reasonable results for the bottom al bedo inversion instead of the Rrsopt bbp() values due to probl ems with inverting bbp() from Rrs() in areas where there is significant bottom reflect ance. The presence of significant bottom reflectance in the Rrs() signal results in lower accuracy for the inverted bbp() values. The Kd() measurements had the most noticeab le effects from zenith angle. A lower solar zenith angle resulted in errors in Kd() that increased with wavelength. The higher the sun was in the sky the greater magn itude of the wave focusing. Wave focusing affects the Kd() primarily in the longer wavelengths since these are normally attenuated by water absorption, the sudden focusing al lows them to penetrate deeper. Ed() drops off rapidly at the wavelengths greater than 600 nm due to water absorption and there are fewer readings to fit a curve th rough resulting more noise in Kd() values. For Kdopt this error can show up at other wavelengths th an those most affected by wave focusing because it does an iterative fit to most of th e visible spectrum. This zenith angle effect on wave focusing especially hurts the Kd() inversion models that rely more on empiricism. The Rrs() error sometimes increases with lo wer solar zenith angles. When the sun is higher there is a greater amount of sp ecular reflection (sun glint) on the surface of the water. This results in a bias to the Rrs() spectra making it appear higher than normal. The Rrsopt algorithm can correct some for errors due to sun glint by subtracting off a bias that is determined thr ough iteration but the other Rrs() inversion models do not do this. If the reflectance is too much it can increase the whole spect ra but especially affect the red end and none of the models can correct for this. The incl usion of sun glint will most affect the inversion for bbp() resulting in an underestimate since it's spectral shape is flatter than aph() or ag(). Both high and low solar zenith angles can affect Rrs() PAGE 232 214 inversion accuracy but the lower solar zenith angl es appear to be a bi gger factor than first thought. Sometimes sun glint can be minimized by use of a different technique or processing method for collecting the Rrs() data. One alternative is to try to collect the Rrs() at an angle different from the usual 30 Sometimes a 40 to 45 angle for view angle of the radiance spectrometer can result in less sun glint. In some cases, sun glint results in a saturation of th e reading by the spectrometer. The spectrometer takes an initial scan to determine how long to integrate the reading. If the movement of the water from waves or swells results in a change in the amount of sun glint du ring the actual scan the result can be a reading that is the maximum allowed due to saturation of the detector. The standard procedure us ed in collecting the Rrs() was for 3 sets of one scan of the grey card, three scans of water radiances, and one sc an of sky radiance. The saturated scan is then excluded. However, if the scan is highe r in value but not saturated, it introduces a bias to the Rrs() values if it is not noti ced during processing. Th is bias can affect all Rrs() inversion techniques. While attempts are made to minimize sun glint in Rrs() measurements, it can still have some effects. Cloudiness had a minimal effect on Rrs() but had a noticeable effect on Kd(). A Rrs() scan collected under partly cloudy skies ca n exhibit a lot of noise with small spikes in value over the spectrum but can still have an overall shape that can be inverted if smoothed or used in a hyperspectral algorit hm. The only affect is minimally on the bbp() and not the anw(). The effect on Kd() was more pronounced. The change in the average cosine of downwelli ng irradiance affects the Kd() inversions resulting in an overestimate of absorption. The Ed() is lower due the longer path and lower surface irradiance. The lower subsurface irradiance re sults in fewer depths for curve fitting to determine Kd() resulting in a less accurate value due to cloudiness. The Kd() optimization algorithm was able to compensate somewhat for cloud cover by using Gordon's normalization for Kd() (Gordon 1989). Hydrolight has a simple algorithm that takes the input from Radtran (Gregg and Carder 1990, Mobley 1994) and adjusts the direct and diffuse ratios for cloudiness. These direct and diffuse irradiance ratios are used in Gordon's norma lization algorithm to re move the effects of the average cosine due to solar zenith angl e and diffuse sky irradiance leaving only the average cosine due to scattering. While this technique cannot accurately compensate completely for partly cloudy skies, it did improve the results for the Kd() optimization method. Further improvement in model re sults was made under cloudy conditions by having the average cosine of downwelling irradiance spectrally vary under the Kd() optimization algorithm. This allowed the mode l to compensate for changes in spectral average cosine due to cloudiness with an itera ted value for the magnitude to compensate for the increase in diffuse downwelling irradiance. The Kd() optimization algorithm was able to compensate some for the effects of cloudiness while the other Kd() inversion algorithms were more limited. PAGE 233 215 Several of the models were originally parameterized to use only specific wavelengths. These models are at a disadva ntage when compared to models that use hyperspectral input data. This is most notable in the red end of the spectrum where there is low signal. The KdKirk and the KdLoisel Models do not take into account spectral variations in bb() or a() that are outside expected levels. The MODIS Rrs() inversion algorithm is parameterized to function at the MODIS satellite wavelengths. The QAA model is parameterized to use only 440 and 550 nm wavelengths in the version used in this study. One advantage to these models us ing these wavelengths is that satellites and some oceanographic instruments only collect data at specific optical wavelengths. However, when there is hyperspectral data av ailable, the models that use a fitting method to the spectral curve are expected to outpe rform the others. In the case of the Kd() inversions, there is a much lower sign al at the longer wa velengths, but the Kd() optimization algorithm uses a fit at all wavelengths and filters out the longer wavelengths that are obvious errors. The use of a hyperspectral fit means that the Kd() optimization method performs better than either of the ot her models at the longer wavelengths. The models that are designed to use hyperspectral data were able to compensate for spectral changes in in situ values while the others are more limited. Field comparisons introduce more errors th an laboratory or artificial data when comparing AOP inversions to more direct IO P measurements so the best closure to the ideal value is around 20% for this study. Th e artificial data used for other closure experiments for AOP models does not contain possible operator error, instrument failure, or instrument accuracy limitations. The surface waves are ideal structures in data from the Hydrolight model and do not contain sea fo am or floating debris like field conditions. The input data under idealized modeled conditio ns usually doesn't in clude partial cloud cover, low solar zenith angles, or sun glint. Hydrolight does not even simulate fish schools swimming over the submersible downwe lling irradiance sensor or doing profiles in schools of thimble jellyfish. Since the condi tions are rarely absolu tely perfect in the field and this study assumes that no model or method is the absolute truth under any conditions, it is not surprising that the best closure achieve d by any model or method was 20%. Most closure experiments premise one me thod as most accurate and then compare the other measurements to it. While this a pproach can achieve much greater closure than 20%, it does present some problems. Usi ng a single method assumes that it is independent from the other methods and is cl ose to the actual value. Dependence can vary between the measurements and mode ls depending on how and where the models were parameterized and the data collected. The Rrs() and Kd() optimization models might have dependencies based on how close the aph() measurements are to the filter pad values that were used to cal culate the shape factors. The ag() inversions might have more dependencies if they are adjusted base d on measurements from the same area. The measurements from a surface water sample when there is a change in optical properties over depth will not have the same result as a profile over depth. Most closure experiments examine areas with less optical variability than those in this study and consider a single measurement to be the truth. PAGE 234 2165.10. Best Methods Overall the best method for determining IOPs under most conditions was the Rrs() optimization algorithm. Rrs() measurements provide the longest path length of light to determine signal. The inversi on models and techniques for measuring Rrs() have progressed to the point where they are good alternatives for in situ measurements. In optically clear waters, the Rrs() inversions have better signal to noise ratios than any of the more direct IOP measurements except for the quantitative filter pad technique. However, under certain conditions the other techniques are be tter. The Hydroscat6 is better for determining bbp() in waters where the bottom re flectance is greater than 10% of the Rrs() signal. For anw() in areas with greater than 10% bottom reflectance, the Kd() optimization method was the best when doing inversions to determine albedo. Overall Rrs() optimization was the best method but under certain conditions, wavelengths, and IOP types ot her methods proved better. The mean absolute percent error as aver aged over the first six wavelengths are listed at the end of this chapter. They can give a little idea about which method did best under each filter but should be viewed with caution. For example under the anw() bottom filters KdKirk and KdLoisel appear to be some of the best inversions. Because these tables are for the first three wavelengths it does not show that they sharply increase in error immediately at the ne xt one or two wavelengths. Th ese tables do not show that while Specag appears to have low absolute pe rcent error when the bottom contribution is significant that it also has poor regression results under those filters. So while this can provide a little insight into which model pe rformed best it would be best to check the other statistics before using that method fo r analysis of an environmental problem. PAGE 235 217 Table 5.2. Mean absolute percent error for anw() from 412 to 555 nm. *QAA is a mean of 440 and 555 nm not a mean over six wavelengths like the other values. Filter type ac9 KdKirk KdLoisel Kdopt MODIS Spec QAA Rrsopt N F 90.28 164.88 69.09 38 .34 35.36 60.25 21.24 19.39 N B 76.36 132.61 48.22 29.79 22.02 74.71 16.03 16.36 N BLCLZ 88.88 205.92 56.59 32.70 19.71 85.81 15.37 14.24 MODNB 91.08 176.91 59.68 33.46 15.38 81.38 16.02 15.33 BT 108.37 226.31 107.49 52.63 57.41 28.81 28.05 23.71 BTLCLZ 104.56 214.94 83.62 57.44 72.26 32.05 35.10 21.15 Table 5.3. Mean absolute percent error for bbp() from 442 to 589 nm. Filter type HS6 Kdop t MODIS QAA Rrsopt N F 44.82 82.58 40.02 56.60 36.25 N B 47.34 65.96 39.17 11.53 9.30 N BLCLZ 48.13 67.74 47.26 12.43 10.81 MODNB 50.80 62.33 37.40 7.89 4.93 BT 27.70 106.11 455.65 695.07 74.88 BTLCLZ 30.64 134.35 694.67 1031.38 67.58 Table 5.4. Mean absolute percent error for ag() from 412 to 555 nm. Filter type ac9 Kdopt MODIS Rrsopt Specag N F 378.51 79.18 47.54 34.85 70.70 N B 504.96 66.93 34.25 34.20 89.98 N BLCLZ 933.03 71.67 40.74 34.63 93.49 MODNB 687.26 72.06 39.55 32.44 101.11 BT 94.65 104.07 95.13 42.65 34.04 BTLCLZ 108.69 93.39 123.51 45.73 41.92 Table 5.5. Mean absolute percent error for aph() from 412 to 555 nm. Filter type Kdopt MODIS Specaph Rrsopt N F 92.08 37.62 86.87 36.33 N B 78.30 37.63 120.62 34.02 N BLCLZ 77.91 40.68 198.47 35.03 MODNB 67.18 34.06 46.24 63.14 BT 75.93 105.33 24.40 28.07 BTLCLZ 93.78 136.41 26.45 33.80 PAGE 236 218 6. Improvements to Instruments and Methods 6.1. Analytical Versus Empirical Models The more analytical models were hypothe sized to produce bett er results and the statistical comparisons suppor t that hypothesis, with a few exceptions, was supported. The analytical models do have disadvantages when compared to the more empirical models since they require more a priori knowledge of a study region. There is some empiricism required even for the methods that are more direct. All of the direct IOP measurements require corrections for path length elongation, a ttenuation, or scattering. The inversion models varied as to their degree of empiricism. For the Kd() inversions, the Kd() optimization model was the least empirical followed by the Kd Loisel Model, and the Kd Kirk model. The ranking from l east to most empirical for the Rrs inversions are Rrs() optimization, MODIS semianalytica l, QAA, and the MODIS default band ratio model. The inclusion of empiricism in all methods is one of the reasons why it is difficult to determine absolute truth in the value of the IOPs. The best illustration of the degree of empiricism as a contribution to error are the regression statistics for anw() under the filters MODNB and NBLCLZ. Under the NBLCLZ filter, the Kd() models exhibit a larger divers ion from a regression slope of one at the longer wavelengths due to less signa l but have median valu es overall that are close to one. However, the Kd() optimization method is the only Kd() inversion method that comes close to zero inte rcept at the longer wavelengths. Rrs() optimization has the median slope closest to one u nder the NBLCLZ method while MODIS and the QAA model have median slopes much differe nt from one. Under the MODNB filter, where only the semianalytical model for MODIS is used, MODIS improves its regression results and track s closer to the values for the less empirical Rrs() optimization algorithm. The degree of empiricism of thes e methods corresponds almost directly to the regression results under the ideal conditions. The ac9 uses four different empirical or estimated corrections to correct absorption values. It uses the ratio of the initial estimate of scattering at a given wavelength to scattering at 715 nm times th e absorption value at 715 nm to estimate a correction for internal losses of signal. In addi tion to that correction, there is an empirical correction for internal temperature shifts in the ac9 that would a ffect its photocells. The ac9 also uses an empirical relationship to correct for the difference between the temperature and salinity of the pur e water used for calibration and the in situ values. Even the direct ac9 IOP meas urements rely on some empiricism to correct for errors and path length elongation. PAGE 237 219 Each of the spectrophotometric methods uses an empirical or estimated correction. The filter pad method uses an em pirical equation called the beta factor to correct for path length elongation. The beta factor is based on the expected types and sizes of particulate matter present in the sa mple. The correction is limited to a minimum and maximum value of absorbance based on the range of its empirical fit. Even the spectrophototmetric CDOM absorption measuremen ts assume that the 750 nm value is all scattering and that scattering is spectrally flat to correct for internal scattering within the cuvette. Even the laboratory direct IOP measurements require empiricism. The Hydroscat6 uses three empirical equa tions in processing the output. During calibration, an empirical relationship is es tablished at each wave length to correct for attenuation along the path of the signal. Th e Hydroscat6 uses an empirical equation for the backscattering due to seaw ater that is about half th e value determined by Morel's research. The instrument measures backscatte ring at an angle of 140 but estimated total backscattering through an empirical relationshi p. Total backscattering is estimated by multiplying the bb( 140) by pi and 1.08. The assumption is that the total backscattering is equal to 8% more than if integrated over a hemisphere. The three empirical corrections for the Hydroscat6 can have a significant affect on its bb() value if any of those assumptions are not met. The Kd() optimization algorithm is the least empirical of the Kd() inversions algorithms. The Kd() optimization model is based on Pr eisendorfer's formulation of the relations between Kd() and IOP values (Preisendorfer 1961) If the average cosines are known and the Kd() values are perfect, then the mode l should give the cl ose to the exact value for anw() and bbp(). The empiricism in this model arises from determining the average cosines of upwelling and downwelling light. The Kd() Loisel model uses the below water irradiance reflectance and a bove water average cosine of downwelling irradiance to empirically estimate the average cosine and then determines a() empirically. The Kirk Kd() inversion is most empirical and requires an estimate of the b() to a() ratio along with the average cosine of above surface solar zenith angle to determine a() from Kd(). Both the Kirk and Loisel Kd() inversions perform well at shorter wavelengths from 400 to about 500 nm However, they have problems at the longer wavelengths due to lower signal and the lack of spectral variations in their parameters. The Kirk Kd() inversion performs well enough at 440 nm that it was used to initialize the absorption values for the iteration process in the Kd() inversion algorithm. The Kd() optimization algorithm is the least empirical of the three Kd() inversion algorithms and provided th e best inversion results for Kd() under the most conditions and wavelengths. The Rrs() inversions consist of ac tually 4 models. The Rrs() optimization model is the least empirical followed by the M ODIS semianalytical, the QAA, and the MODIS default algorithm. The Rrs() inversion algorithm breaks the path of the light into two components, rrs() due to the water column and the rrs() due to the bottom albedo. Empirical relationships with ab sorption and backscattering are then used to determine the PAGE 238 220 light field geometry while the rest of the va lues are determined through iteration. The MODIS semianalytical algorithm uses an iterative process to determine a() but relies on an empirical algorithm for bbp() at the reference wavelength. The QAA model uses only three iterations to solve for anw(440, 550) and bbp(440, 550). All three models use an empirical relationship to determine the coefficient for bbp(). MODIS has a default algorithm for high chlorophyll areas that uses ratios of Rrs() at specific wavelengths to empirically determine a(). The MODIS default algorithm is the most empirical of the Rrs() inversion algorithms. The use of empiricism and the accuracy of the methods make it difficult to determine the real value of the IOPs. The AOP inversions have greater accuracy at most wavelengths in optically clear waters due to the longer path length the light travels. However, the empiricism in some of these models may cause spectral inaccuracies at longer wavelengths where path length is reduc ed as observed for the Kirk and Loisel Kd() inversion models. While the direct me thods have fewer empirical assumptions, most have lower accuracy when the signal to noise ratio is lower due their shorter path length. The use of empirical methods in the direct measurements means that it is difficult to get an absolute measure of the IOPs. If it were possible to provi de these corrections from first principles, then the limitation woul d be simply the accuracy of the instrument. As it stands, most of these corrections are small but some of them can have a large influence on smaller values. The ac9 anw(650) measurement can be in error by over 50% due to a 5% error in the anw(715) value used in the correction algorithm. This error is part of the reason why the ac9 performs best in areas of higher absorption. The anw(715) value is usually very low and may be below the accuracy limit of th e ac9. Because of this low value, the magnitude of the anw(715) from the ac9 may be more a function of instrument noise than scattering in low attenuation waters. While AOP methods perform best at the shorter wavelengths (412 and 440 nm), there are assumptions in these models that can affect their accuracy at the longer wavelengths. If the phytoplankton absorption sp ectra in the optimization models are not representative of the study area, then there could be spectral differences at the longer wavelengths. Since the Kd() optimization and Rrs() optimization use the same phytoplankton shape factors, it co uld mean that they might be biased in a similar manner. This would bias the median ideal value used to compare against the other models. If the spectral coefficient for bbp(), if wrong, its could affect th e AOP inversions spectrally. Its effect is smaller than that for aph() but it can have an effect in the 530 to 555 nm range where a() is low. The slope coefficient for CDOM is assumed to be constant in all inversion algorithms except for Kd() optimization. If this co efficient is wrong then it can affect the spectral inversion results especi ally at green wavelengths in the 500 to 555 nm range. Despite higher signa ltonoise ratio at longer wave lengths it would be an error to assume that the AOP inversions are al ways the most accurate under every condition. PAGE 239 221 None of these methods achieves the perfec tion of a pure first principle approach to measuring IOPs. The common assumption that the more direct methods are always the most accurate was disproven by the statistical results. The Rrs() optimization method was best under most of the tested cond itions in determining the IOP values. The statistical results indicate ar eas of weakness in all the me thods under certain conditions. By examining the statistical results, it is possible to determine some approaches that might improve these methods and lessen inac curacies due to empi rical assumptions or environmental parameters. 6.2. Improvements to Kd() optimization The Kd() optimization model was developed duri ng the course of this study. It proved to be the best of the Kd() inversions but not as reliable under all conditions for some IOP inversion results as the Rrs() inversions. The best results were for anw() inversions under ideal conditions. Some improv ements in future versions of this model may increase its accuracy. These improvement s can be divided into two categories, better Ed() measurement techniques and making th e algorithm more analytical. Wave focusing is one problem that c onfounds the measurement of downwelling irradiance below the sea surface. The correction for wave focusing does have some flaws. When using a modeled value for the n ear surface value it relies on the accuracy of the input values to the Hydrolight model. Unless there is an above water measurement that can be properly used as a reference to match the above water downwelling irradiance in the model, there may be errors in the Hydrolight model result. Since the determination of large increases in value using a depth versus Ed graph is slightly subjective, there can also be errors introduced. The smaller wave focusing events could still be biased towards a focus or defocus, since it depends on when the irradiance meter is sampling relative to focus or defocus events. If there are not enough measurements at the surface to average the focusing out, it could have a bias one way or another. The Kd() optimization method had negative co rrelations between solar zenith and absolute percent error for many IOP inversions. The closer the sun is to zenith, the more direct becomes the lens effect of the wa ve. Alternatively, the closer the sun to the horizon, the less light is avai lable at depth due to a longe r path length of the solar irradiance. The best conditions for Ed() were when the sun was approximately between 15 and 45 zenith. Since wave focusing a ffects the spectral nature of the light by sending more light at longer wavelengths to depth, this in turn affects the separation of ag() and aph() from anw() by over or under estimati ng the magnitude of ag(440), the ag() coefficient, and the magnitude of aph(440). The correction for wave focusing is more critical with the sun at a low zenith angle than when it is closer to the horizon. Several IOP results from Kd() inversions had a strong correlation with bottom reflectance and absolute pe rcent error using the Kd() optimization method. At first it was suspected that this might be due to in ternal reflectance from upwelling irradiance PAGE 240 222 reflected off the bottom. Hydr olight model results demonstr ated that this was not the case but that a greater percentage of upwe lled light was actually transmitted through the air water interface with a greater bottom albedo. This increase in transmittance demonstrates that there is less internal re flectance at the surface with a Lambertian bidirectional reflectance (BDRF) for the bottom than for water column where the bottom is well below the 1% light level. Near the bottom there can be some increase in light resulting in a "C shape to the Ed() profile due to reflectance by a bright bottom. The increase in light near the bo ttom is due to scattering forcing the light reflected off the bottom back in the downward direction. Ho wever the bright bottom does not seem to affect the inversions since the th ird order polynomial fit for the Ed() over depth compensated for this increase near the bo ttom. The increased fraction of bottom reflectance in the total reflectance value is corr elated with the optical depth of the water column. Generally, the greater the bottom contribution to below surface reflectance, the shallower and clearer the water column. The main factor is that, for a shallow water column, the instrument cannot descend below th e level of high wave focusing. Once the light becomes diffuse enough due to scattering ov er depth, wave focusing ceases to be a significant factor and the pol ynomial fit through the unfocused deeper layer smoothes the focusing in the upper water colu mn. The correlation between Kd() optimization error and percentage of bottom reflectance for se veral IOP values actually represents a correlation with increased wave focusing errors. A byproduct of wave focusing is saturation of the downwelling irradiance measurement when the integration time is too long. The Spectrix downwelling irradiance sensor takes an initial scan and the magnitude of this initial measurement determines how long the shutter will stay open to achieve an adeq uate signal. If this initial scan occurs during a defocus event and the actual sample occurs during a focus event, the result may be an over exposure leading to saturation of the spectrometer. These saturated scans are taken as indications of the po ssibility of wave focusing. If only a few wavelengths are saturated, it can be corrected by interpolati ng the saturated values using an unsaturated scan at the nearest depth but if the numbers of saturated wavelengths are greater than 75 out of 512 total then the scan is not used. The number of discarded scans is used as a proxy for severity of wave focusing. To force the curve fit th rough the modeled subsurface value, the number of modeled subsurf ace values added are equal to the number of discarded saturated scans. While this does improve the quality of the data especially in the longer wavelengths, it is not as good as collecting real data near the surface. The greatest improvement in accuracy for Kd() measurement is greater Ed() sampling near the surface. This would require an active contro l of the rate of descent for the instrument package so that it would stay just below the surface longer. While the rate of decent can be controlled by attachment to a winch, this approach requires the instrument package to be located close to a vessel and would result in the vessel shadowing the instrument. If the seas are si gnificant, a hard wire attachment to a vessel can result in rapid changes in depth, both up and down, for the instrument during a measurement. Under extreme cases the change s in depth can be seve ral meters resulting in a smearing of Ed() over depth and less accuracy in Kd(). Active control of the PAGE 241 223 descent rate coupled with isol ation from the movement of the platform would provide the best method of increas ing near surface Ed() measurements. The best method is to place the downwe lling irradiance meter on a ROV, move the vehicle away from the vessel, and then slowly lower it through the water column. The problem with this method is that a ROV is very expensive to purchase and operate. A ROV requires several knowledgeable personn el to deploy and maintain it. ROVs require a much longer time to prepare and de ploy than a vertical profiling package. These platforms are usually more limited in their payload capacity and can carry fewer instruments than a profiling package. They require adjustment to trim the vehicle any time the payload weight is changed so that it is balanced in the water column. This limits changes in instrumentation duri ng a research cruise. Though they are the ideal platform, they are not ideal in ease and cost of deployment. A slow descent, free falling profiling p ackage that is near neutral buoyancy is a good compromise between a ROV and attaching a profiling package to the ship wire. It has some drawbacks. If the buoyancy is ad justed properly a free falling package can collect data with a very high resolution over depth. The pack age can also drift away from the ship minimizing ship shadow. Since its at tachment to the vessel is loose, it is not pulled up and down in the water colu mn smearing the depth of the Ed() measurement. However, it does not allow for slowing descen t near the surface to collect a greater number of measurements to better resolve wa ve focusing and improve signal to noise at the longer wavelengths. A more active me thod of controlling descent is needed. A vertical profiling package with an active control for buoyancy would be the ideal setup. An extremely slow descent (< 0.01 m/s) near the surface would give enough measurements to aid in removing the effect s of wave focusing. The BSOP profiler (Langebrake et al. 2002) uses a method of active buoyancy control by pumping a fluid from one reservoir to another. This met hod would be better than other methods using compressed air and a bladder. The bubbles fr om the release of the air could possibly interfere with down welling irradiance meas urements by scattering light. The control would not have to be large and would only re quire a fine adjustment in the buoyancy. The active buoyancy control coul d be autonomous, receiving de pth input from a pressure sensor and slowly descending for the first 10 me ters then descending at a greater rate to depth. The cost of such a system would be moderate comp ared to the instrumentation and would greatly improve the Ed() measurements. Measurements from a scalar down welli ng irradiance sensor would improve the Kd() optimization accuracy. The ratio of s calar downwelling irradiance to planar downwelling irradiance (E0d()/Ed()) is defined as the average cosine of the angle of downwelling light. Knowing the average cosine of downwelling irradiance at a single wavelength or PAR would impr ove the inversion from Kd() by removing one unknown. While there is some spectral variation to the average cosine, it is small compared to the spectral variation of the IOPs. A simple m odel could estimate the slope of the spectral change in the average cosine of downwelli ng irradiance using the measurement as an PAGE 242 224 intercept if E0d() was only collected at a single wa velength. This measurement would eliminate the need for Gordon's normalizati on to remove the average cosine due to skylight and solar zenith angle. The aver age cosine under cloudy c onditions is difficult to model but would be directly m easured using this approach. The scalar E0d() sensor data could be compared to the planar sensor data to determine the extent of wave focusing. A s calar measurement is less affected by a wavefocusing event since it collects light evenly fr om all directions over a hemisphere while a planar collector collects light as a function of the cosine of the downwelling irradiance. Knowledge of a wave focus or defocus event ca n aid in filtering the near surface data so that it is not biased towards fo cusing or defocusing. It woul d then provide a truer balance to improve a curve fit through the data. Tes ting this configuration just below the surface would lead to an idea of how to determine when wave focusing is occurring. Shadowing of the irradiance sensor is a nother problem with the measurement of Ed(). While ship shadows can be avoided with proper deployment, some shadowing cannot be avoided. During one cast a large school of amberjack was observed swimming over the sensor. During another cruise, a school of dolphins became curious about the instrument package and swam around it sh ading the instrument. Problems with swimming creatures or floating algae are difficult to contro l and can only be noticed if there is someone observing the package descent or there is a camera on board the package recording the descent. A method propo sed to further prevent ship shadow was a float attached to the package allowing it to dr ift away from the ship Once away from the ship, a release is triggered allowing the in strument package to sink thus avoiding any chance of shadowing by the vessel. An alternative to the direct measurem ent of the average cosine is a more analytical approach to modeling it. Th e HeneyGreenstein phase function uses the average cosine of scatteri ng as input to the function (Henyey and Greenstein 1941). Using bb() to b() ratios, it is possible to invert the HenyeyGreenstein function and determine the average cosine due to scattering. This result can possibly be used to estimate the average cosine of downwelling irradi ance for the Kd() optimization model making it more analytical. While this approa ch does require additional instrumentation, the ac9 and the Hydroscat 6 provide this info rmation within the instrument package used in this study. The Gordon normalization r outine removes the average cosine of downwelling irradiance due to above surface condi tions and the HenyeyGreenstein equation could provide the average cosine due to scattering. Using the change in Ed() value across two depths wh ere IOPs remain constant may also give some information on the aver age cosine of down we lling irradiance. Once the loss due to absorp tion and backscattering is account ed for, the change should be primarily due to changes in the path elongati on of the downwelling irradiance. It may be possible to model this resulting in an estim ate of the average cosine. Another optical sensor such as a beam attenuation meter coul d provide information on whether there is a significant change in optical properties between the two depths. If the optical properties PAGE 243 225 are constant then solving the Preisendorfer equations for Kd() between two depths could give the change in the average cosine of downwelling irradian ce. This approach requires further study but may be able to create a more analytical approach to modeling the average cosine and inverting the Kd() for IOPs by examining the changes in Ed() over an area of constant IOPs. Another approach that could increase accuracy is to use the inversion algorithm at several depths. The Kd() value used in the model is the result of a fit to the depth where the instrument reached its accuracy limit for th at particular wavelength While using the watercolumn total Kd() values seems to minimize noise and provide an average value comparable to the Rrs() inversions, the average cosines ar e different at each wavelength due to shallower depths of penetration of li ght, resulting in greater spectral differences in value. If the fit to determine Kd() through the Ed() values was done for the same depth, the fit would have to occur at a shallow depth due to water absorption limiting the penetration of light at longe r wavelengths. Using a shallo w depth would limit the curve fit for Kd() to the region most in fluenced by wavefocusing and would miss changes in inherent optical properties deeper in the water column. A 10 m Kd() value was tested and found to result in less accurate inversions compared to the fit to depth. The average cosine was iteratively solved in the Kd() optimization method and an empirically determined spectral slope spectral slope was used to extrapolate that value to other wavelengths. However, it may be better to r un the algorithm at seve ral depths where the average cosine of downwelli ng irradiance is more consta nt spectrally. Instead of determining Kd() for the water column, Kd() would be determined by changes between two individual depths over a smoothed Ed() profile. The Kd() optimization routine could then be run at several depths to obtain an IOP profile that c ould be integrated to compare to the Rrs() inversions. The model would have to limit the fit to just the wavelengths at that depth where the Ed() measurement is above noise level. This change in method is computationally more intensive but has th e added benefit of providing changes in absorption a nd backscattering at each depth. The Gordon normalization portion of the Kd optimization algorithm can be made more analytical. Instead of modeling the direct and diffuse above surface downwelling irradiance, it could be directly measured by shading the direct sunlight from the irradiance meter during a surface measurement. This shading would provide a more accurate diffuse irradiance estimate especially during cloudy periods. When using Gordon's normalization, Gordon's original algorithm called for including waves using a formulation by Cox and Monk but that was not used in this correction (Gordon 1989). It should be tested to observe if it improves th e algorithm. Another improvement would be to use the results from a Hydr olight run instead of Gordon's empirical approach. In the absence of a scalar irradiance sensor, the subsurface water average cosine from Hydrolight would be a more accurate norma lization than Gordon's especially with a measurement of direct and diffuse solar irradiance as input. While the iteration of the ag() coefficient improved the model results under most conditions it was possibly a source of error under other conditions. When there was a PAGE 244 226 large amount of wave focusing, the iterati on possibly introduced a dditional errors. Under conditions of high wave focusing, such as a shallow cast or sun near zenith, the model may be improved by locking the ag() coefficient to a set value that is representative of the ag() for the study area. The Kd() optimization exhibited significant error correlation between IOP values and cloudiness. This error in the IOP values is probably the result of the downwelling ir radiance being more diffused and the average cosine of downwelling irradiance not being estimated pr operly. Under these conditions some of the error in the average cosine may affect the iteration of ag() and the coefficient may need to be locked to one value. A more de tailed analysis under different conditions is needed to develop a criteria for locking the ag() coefficient. 6.3. Improvements to Loisel Kd() inversion The Kd() optimization method compensated for the downwelling direct and diffuse light by using Gordon' s normalization method. This method should normalize the Kd() values to a black sky and sun at zenith. Using this method for input into both the Loisel and Kirk Kd() inversion models should improve them slightly. Currently the Loisel model relies on an empirical relati onship with below water remote sensing reflectance to estimate the average cosine. Th e Kirk model uses the solar zenith angle as input to estimate the average cosine. If Gordon's normalization functions properly then these models would only have to compensa te for the change in downwelling average cosine due to scattering. The Loisel Kd() inversion model in this study was hampered by using an above water remote sensing reflectance instead of the below water value. The above water value was empirically converted to a below wa ter value based on the method of Carder et al. (1999). However, it still would not be as exact as having an actual below water measurement. The Loisel model does offer a method for separating the aph() and ag() values from anw() in addition to calculat ed scattering. Since it performed poorly for the anw() inversion, the other values were not ca lculated. The model results probably would have been better with the below water reflec tance but that data was not collected during this study. 6.4. Improvements to Hydroscat6 One major problem with the Hydroscat6 is that the processing of the data uses a different backscattering from seawater than the Hydrolight model. The Hydroscat6 processing method results in tota l backscattering as estimated from the backscattering at a single angle of 140 using an em pirical factor. When Hydroli ght takes this data in for modeling it separates it into co mponent of particulate and wa ter backscattering. While running the model it was noticed that some of the Hydroscat data was creating errors in some of the lower attenuation waters. The Hydrolight model uses seawater backscattering values based on a model by Andre Morel (Morel 1974). These bbsw() were sometimes higher than the total backsc attering from the Hydr oscat6 processing. Using the Hydroscat6 values resulted in a ne gative particulate back scattering causing an PAGE 245 227 error in the Hydrolight model. To correct for this, the backscattering due to sea water used by the Hydroscat processing program had to be subtracted from the Hydroscat6 bb() values and the Morel values added to it. This correction resulted in no errors and produced the best results for the albedo inversions. This correction to the Hydroscat6 pr ocessing also calls into question the approach by the manufacturer that suggests th at Morel's seminal wo rk on backscattering for pure seawater was too high. It indicates that a spectra l parameter in the HOBI Labs processing method is slightly off by the ma gnitude of the difference between Morel's bbsw() values and those used by HOBI Labs. Th is may be a factor related to their 1.08*2*Pi value for converting the () at 140 to total bb(). The relationship of (,140) to bb() may also have a bias that varies spectrally instead of just a factor. 6.5. Improvements to MODIS Algorithm The change in the way the MODIS algorithm deconvolves anw() into ag() and aph() was demonstrated to be an improvement on the algorithm. For the initial process, the ag() coefficient was set at 0.018. The aph() result is then added to an ag() value calculated using the resulting ag(400) and a lower ag() coefficient of 0.016 to give an anw() value. This change resulted in better agreement with the ideal value for anw(). This change in the algorithm also improved the aph() inversion and the ag() inversion results. The higher coefficient compen sated for CDOM fluorescence by lowering ag() absorption at the affected wavelengths. A correc tion like this needs to be made a part of the MODIS algorithm. The initial coefficient and second coeffi cient were determined by statistical analysis of the MODIS results for several co mbinations of CDOM coefficients. Further research is need to determine the magnitude of difference between the two coefficients for ag(). Measurements need to be examined to determine how much is needed to compensate for CDOM fluorescence and unde r what conditions. Questions like the effect of solar zenith angle on the magn itude of CDOM fluorescence need to be addressed. The correlation of CDOM fluores cence with CDOM concentration is another question. The effect of photobleaching need s to be included t oo (Kramer 1979). Since most of these casts were on the continental shelf, the CDOM was expected to be less photobleached than CDOM found in offshore wa ters. The magnitude of the correction may need to be tied to the expected CDOM co efficient. A higher coefficient like those found in offshore waters might only require a correction of 0.001. During several of the research cruises in this study, another rese archer was measuring spectral fluorescence. Combining the Rrs() data, IOP data, and this fluorescence data will an aid in determining how best to make the corre ction for CDOM fluorescence. The bbp() intercept is locked at an empiri cally determined value for MODIS, while the other methods use an iterative pr ocess. Under several conditions MODIS did not produce results as close to the other methods for bbp(). Further analysis is needed PAGE 246 228 but it does appear that, u nder the filters without si gnificant bottom reflectance contributions to Rrs(), the iterative approach to bbp() is more accurate. MODIS has a factor offset from the ideal value for anw() and is about 40% higher for bbp(). The offset to the anw() value might be corrected by a better method of determining bbp(). The QAA model only uses a couple of iterations to determine bbp() and does not require an increase in computational requirements. An improvement to MODIS may be to use a similar approach for bbp() as found in the QAA model. MODIS has significant spectral correlations with scattering ratios when the default algorithm is included for aph() and anw(). The MODIS algorithm has a negative correlation with bp(440)/cnw(440) but positive co rrelations with bbp(440)/bp(440) and bbp(440)/anw(440). Under the MODNB filte r, that only uses the se mianalytical data from MODIS, there are very few correlations with any of the parameters. This difference in correlation indicates that the empirical defau lt MODIS algorithm can lead to errors when backscattering is a higher porti on of the IOPs but total scatte ring is a lower percentage of attenuation. One possibility is that the algorithm is switching to the default when it would be better using the more accurate se mianalytical approach. Many of the study sites have high ag() values relative to anw(). This high CDOM to absorption ratio could cause the algorithm to categorize these sites as high chlorophyll and sw itch to the default algorithm. Further review of the data is necessary to dete rmine exactly the affect of this on the MODIS algorithm and how it could be corrected. 6.6. Improvement to the ac9 The ac9 is currently the most popular in strument for high resolution sampling of anw() over depth. A new instrument using an integrating sphere may change this but it needs to go through the rigorous testing that the ac9 has been through. The ac9 could be improved in ways that increases its accura cy and stability. The method for deploying this instrument has changed to compensate for some of the problems with using this instrument but some additional equipment a nd procedures could improve the deployment of this instrument. One of the biggest weaknesses in the ac9 is the use of a quartzhalogen light source. The ac9 works by projecting light thro ugh a rotating filter wheel and into a flow tube where change in radiance at a given wave length is then determined by a photocell at the other end of the tube. The lamp takes a few minutes to warm up and stabilize before any measurements can occur. The lamp produces a lot of heat resulting in a large temperature correction for the internal electronics. The heat possibly contributes to degradation of the filters over time. If the ac9 is not placed in a water bath when operating on bench top for an extended length of time the internal temperature can easily rise above 40 C. The lamp has a lower output at shorter wavelengt hs. The output at 412 nm is about half that at 555 nm but the ab sorption at 412 nm is usually many times that that at 555 nm. The output is lowest where absorption is the highest resulting in lower signal to noise at those wavelengths. The la mps age requiring regular calibration as the PAGE 247 229 output shifts spectrally. Mode rn high output LEDs would make a better source light than the quartzhalogen lamp. LED lamps are now capable of white light output due to phos phorescent coatings and would make a good replacement for the qua rtzhalogen lamp in the ac9. The LED lamps are more stable than a quartz hal ogen lamp and power up to a maximum output rapidly. The LED lamps would generate less heat allowing bench top operation for an extended period of time without a bath to cool the instrument. The internal temperature correction wouldn't have to be applied over as wide of a range. LEDs use less power resulting in longer battery life for mooring deployments. A combination of LEDs could provide light output at wavelengths centered around the filters in the rotating filter wheel giving more output at the measured wavele ngths instead of focusing on a white light source. LED lamps would make the instrument a more stable, energy efficient, and give it a lower operating temperature. The filters in the ac9 are on a rapidly rotating wheel that operates at about 6 hz. The filters degrade over time due to a film that slowly forms over them. The manufacturer is not clear on what causes this film. The degradation of the filters is one reason that the instrument requires a daily calibration and regular f actory maintenance. The wheel itself is a mechanical part that may eventually fail. Vibrations to the instrument can cause tiny movements in the filte r wheel resulting in noise in the data. The instrument is so sensitive to vibration that stomping hard on a floor near the instrument can cause a jump in its output values. The filters wheel is a weak point in the ac9. The wheel could be replaced by a series of LEDs at wavelengths centered at the measurement wavelengths. It would require a more complex optical setup but they would provide an interface with lower mechanical parts for failure. Another possibility would be for the manufacturer to find a better quality filter. There are literally hundreds of manufacturers of opti cal filters for every sort of appli cation or condition. If the cause of the filter failure resides in the filters th emselves, then there should be a manufacturer that has addressed this probl em. Alternatively a cooler light source may minimize the filter problems. A vexing problem with the ac9 is the clearance of small bubbles from the instrument. Air bubbles tra pped in the flow tubes can result in a la rge amount of scattering rendering the data useless. As the bubbles bounce around in the tube, the values often reach the maximum possible for the instrument. To clear out bubbles, great care is made during the plumbing of the in take and exhaust path for water pumped through the instrument. The data output is mon itored to determine if there are spikes in the values that are indi cative of bubbles before the data from the instrument is logged. If there is a difficulty clearing the ac9 near the surface, it can be sent to depths of around 20 to 30 m to compress the gas bubbles aid in clearing them from the instrument. Some design or deployment changes may make it easie r to purge bubbles from the instrument. PAGE 248 230 Filling the ac9 flow tubes with water be fore deployment might make it easier to clear bubbles once it is deployed. It would require a device to close the intake tubes for the ac9 and open it once it is deployed. The caps on the inlet tubes would protect against air being forced into the instru ment's flow path as it is being lowered into the water. The flow path could be filled from the bottom in lets using a pressurized reservoir forcing out the bubbles. The orings on the flow tubes woul d need regular maintena nce to insure that water doesn't leak from them while the instru ment is sitting on deck and a more secure system would be needed for attaching the fl ow tubes. The caps on the inlets wouldn't require an electronic release mechanism. Th e release could be a float well above the instrument package that pulls a release pin or a tag line that pulls the pin. A similar device could be developed for the filtered ac9 that releases a reservoir full of deionized water that the filter is stored in. This w ould provide a simple and inexpensive method of purging the bubbles from the ac9. A high volume pump for purging bubbles from the ac9 followed by a low volume pump for sampling could reduce air bubble scattering. Either a twospeed pump or a valve with a separate high volume pump co uld be used to purge the instrument. The highspeed pump would create enough force to pull the bubbles through the instrument but could not be used during regular deployment due to turbulence related density shifts in the incoming water that can increase scat tering. The filtered ac9 would require a valve on the inlet to bypass the filter during a purge by a highspeed pump because pulling a large amount of seawat er through the filter could ca use it to prematurely clog. This setup would require additional plum bing and electronics but would be more convenient than priming with water before deployment. The path of the water through the flow tubes could be improved to aid in removing bubbles. It might be a better design to bevel the outlet at the top of the flow tube to allow the bubbles to flow up and out of the instrument. The current design has a flat surface with the outlet near level to the plane of the window covering the detector at the top of the tube. If the window was a little further down in the tube, then a sloped area leading up to the outlet could be used to al low bubbles to flow outward. Several designs could be tested with a clear glass tube to determine the best design for clearance while retaining the maximum reflective surface of the absorption tube. The original ac9 design was modified by the addition of larger diameter exit tubes fo r the flow and resulted in fewer problems with bubbles. A new design fo r the flow tubes might improve purging of air bubbles without ex tra procedures or new equipment. The output from the filtered ac9 may be improved by calibrating the instrument with a filter in place. The filter restricts the flow through the instrument and changes in the flow rate do affect the calibration and clea rance rate. The ac9 is found to produce its best results with a flow rate of greater than one liter per minute. At a higher rate there may be turbulence related scat tering. At a lower rate, th ere may be problems with clearance of bubbles and aliasi ng of the values versus depth. The calibration is most effective when a similar flow rate is used for both calibration and deployment. Some of the differences due to scattering by turbulence will be compensated for by the calibration PAGE 249 231 if the rates are similar. Using a setup with the filter in place in a sealed polycarbonate container that has a valve for degassing th e container would better match the flow conditions the instrument will experience during deployment. An inline flow meter on the outflow ac9 can determine the clear ance rate of the instrument and compensate for aliasing. An inline flow meter will allow knowledge of the clearance rate and how it might change during the deployment. The depth for the sample can be adjusted based on the cleara nce rate and a more accurate profile of absorption or attenuation can be obtained. The flow meter can aid in determining the ideal flow rate for a particular setup. The meter can be cal ibrated under a variety of flow conditions and a calibration adjustment for each rate determined. The calibration under different rates would especially benefit the filt ered ac9 since the flow rate will change as particles fill up the filter por es. Monitoring the flow rate would reduce aliasing and improve calibration values. The post processing of the ac9 uses a co rrection for the scat tered light in the absorption tube that might be improved by using data from other instruments. Backscattered and some forward scattered light is lost by the ac9 on the absorption tube. Using backscattering measurements from the Hydroscat6 may assist in some of the correction for the absorption tube by providing a more exact measurement of the loss due to backscattering. The remaining scattering lo ss in the absorption tube is primarily due to forward scattering at angles that are refracted by the glass window pr otecting the detector in the absorption tube and could be corrected in using the ratio method of Zaneveld 1994. The post processing for the attenuation tube could take into account the near forward scattering. The acceptance angle of a ny attenuation meter is not limited to only light scattered in the same direction as th e source. A limited acceptance angle like that would be almost impossibly tiny to build, requi re precise alignment with the source, and need a sensitive detector. Therefore, most ma nufacturers use an apertu re that allows light at more angles than absolute 0. The acceptance angle for the ac9 is 0.93 0.07. A model could estimate the amount of forward scattering not counted as attenuation to improve the attenuation results The error can range from 5% to 20% underestimate for the ac9. One method for estimating the near forw ard scattering would be to use the bbp() to bp() ratio to model the phase function using the HeneyGreenstein (1941) method. It might still slightly underestimate the forward scattering but it would probably be by such a small amount that it would not make a major difference in the values. Another approach would be to use a multiple angle scattering meter like the VSF to estimate the phase function and determine forward scattering. The attenuation tube of the ac9 could be calibrated using a known sca ttering standard such as polysty rene beads. An empirical correction for the losses by forward scattering could be determined and applied for the ac9. This correction combined with a corr ection for backscattering for the absorption tube should improve the results from the ac9. PAGE 250 2326.7. Improvements to Quan titative Filter Pad Method One of the biggest problems with the filter pad method during this study was obtaining sufficient optical density on the filter s to make the beta correction valid. Most beta corrections are fit for values within a sp ecific range of optical densities (Bricaud and Stramski 1990). However, in waters, such as those in the Bahamas, the filter pads would stop up before they achieved the lower limit for optical density. Transparent material such as small zooplankton or transparent e xopolymers (TEP) might be responsible for clogging the pores of the filter (Alldredge et al. 1993). Another possibility could be precipitation of calcium carbonate particles. A way to determine the source of the clogs in the filters would be to examine the filter pads after they become clogged under a highpowered microscope. If the problem is due to transparent zooplankton or TEP then a fine zooplankton mesh screen may remove them from the sample. Since they ab sorb little to no visibl e light, removal would not significantly affect the absorp tion result from the filter pad. If the problem is due fine calcium carbonate particles, then maybe adju sting the pH of the sample a little lower might keep more in solution. Adjusting the pH would have to be carefully tested under controlled laboratory conditions to assure that it would not di ssolve absorbing particles. These changes might allow for a greater optical density under conditions of nonabsorbing material clogg ing the filter pores. The beta factor is usually based on the dominant species assemblage of phytoplankton. The common method for determ ining a Beta factors is to take a concentrated monoculture of phytoplankton a nd measure the absorption within a cuvette in very accurate bench top spectrophotomet er (Bricaud and Stramski 1990, Cleveland and Weidemann 1993). The same culture is then fi ltered onto a glass fiber filter and the path length elongation due to light scattered by pa rticles through the filter pad and the optical density measured. The measurements are repeated for up to hundreds of different phytoplankton species. The equation for this correction is dete rmined through an empirical fit of optical density to actual absorption measured from the concentrated sample for all the species. Some Beta factors are more appropriat e for estuaries where there are large diatoms while others are designed for ope n ocean waters where there are smaller chlorophytes and cyanobacteria. Other phytoplankton can have unusual indices of refraction due to their physical composition. Trichodesmium and coccolithophores can scatter light more than some of the ot her phytoplankton (Subramanian et al. 1999, Ackleson et al. 1994). Usually a beta factor is used that re presents a diverse assemblage of phytoplankton species unless the composition is known. Under certain conditions these may not be representative of the phytoplankt on species and could produce some errors in the filter pad measurement. Ideally the researcher would de termine the dominant types of phytoplankton and then select a beta factor sp ecific for those species. Determination of species composition could be either through direct counts under a microscope or by examining the pigment composition of the samp le. Alternatively, a review of data PAGE 251 233 collected by researchers that examined speci es or pigment composition for the study site could provide some information about the phytoplankton species assemblage. The filter pad data in this study used a generalpurpos e beta factor (Carde r et al. 1999). The statistical agreement especially at some of the lower absorption values might have been improved with a beta factor more repr esentative of the phytoplankton species composition. A surface measurement was used for comparing the results from the filter pad method to the results from AOP models in this study and it may not give the same result. While the absorption value from the surface is the most dominant influence on the AOP values, it may not be representative of lower depths if there is a change in packaging, species composition, or detritus particles. The AOP measurement represents an integrated value over depth and the discrete samples represent a single point. The filter pad measurement may represent a closer valu e to the AOP inversion results if multiple depths are collected and then the depths in terpolated and integrated to give a value comparable to the AOP inversions. A chlor ophyll and backscattering profile can be used to indicate the best sample depths for both pi gmented and detrital particles. The profiles could aid in interpolation of the filter pad method. If the signal to noise ratio is high enough, an ac9 profile could be used to inte rpolate the filter pad method resulting in a hyperspectral profile for absorption. 6.8. Improvements to Spectrophotometric ag() The spectrophotometric dissolved organic absorption measurements could benefit from an instrument with a longer path lengt h. A path length longer than the 10 cm cuvette would increase signal to noise providing more signal for sample collected from waters with very low absorptions. A spectr ophotometer with a folded path was proposed by Peacock (1992) and would have made thes e measurements more accurate. A recent innovation is the submersible integrating sphe re by HOBI Labs. It uses multiple bounces of the light within a sphere that has a Lambertian reflective surface to increase path length while reducing scattering errors (Kirk 199 5). It could be a be tter instrument for determining absorption by dissolved substa nces with higher accura cy. Some of the spectrophotometric measurements have incr easing noise at longer wavelengths due to low signal. A long path instru ment would have more signaltonoise especially at the longer wavelengths. Like the filter pad measurements, the ag() measurements could be improved by more samples at depth. Unless the water column is well mixed, ag() will vary some over depth. The changes can be both in magnit ude and spectral slope. Photobleaching near the surface results in a higher coefficient for the logarithmic spectral equation for ag() (Twardoski and Donaghay 2002). The deeper wa ters may also have a higher coefficient due to decomposition of the dissolved organi c matter. Any near shore measurements could have more terrestrial humic substan ces making up the CDOM, which typically has a lower coefficient than the fulvic CDOM of fshore (Carder et al. 1989). As estuarine waters mix with offshore waters they are us ually less saline and stay at the surface. PAGE 252 234 However, an inversion was noticed at the Bahamas sites where higher salinity warmer high CDOM waters from the banks were dens er than the offshore waters and formed a bottom layer (Otis et al. 2004). All these c onditions may result in a surface sample not being comparable to an AOP inversion result that represents and integral of the values over depth. A CDOM fluorescence meter woul d indicate the depths necessary for sampling to interpolate the bench top spectral measurements over depth. It would indicate changes in CDOM concentration or compositi on where sampling could take place. As with other single depth measur ements, the lack of samples at deeper depths limits the comparison to Rrs() inversions for ag(). 6.9 Improvements to Rrs() Optimization Algorithm Rrs() optimization could benefit from si milar changes made to the MODIS algorithm. A compensation for C DOM fluorescence would improve ag() values. Rrs() optimization optimizes both ag() and bbp() and may need to empirically set bbp() under certain conditions. The bottom albedo model used in Rrs() optimization may need an additional parameter to reflect actual albedo measurements. The aph() shape factors could benefit from a model that ties them to nitrate depletion temperatures like MODIS. However, despite a few possible changes, this algorithm proved to be the most robust of the AOP inversion algorithms. A problem with the Rrs() optimization method is that the ag() and bbp() values can have similar effects on the shape of the modeled Rrs curve. An increase in ag() gives a similar result spectrally as a decrease in bbp(). Normally this doesn't result in a large error but under some conditions it can create problems. When there is significant bottom contribution, bbp() and ag() appear to be less accurate for Rrs() optimization because there is a trade off for bottom albedo and bbp() or ag(). Solar zenith angle and cloudiness can also affect the inversion for bbp() and ag(). Under conditions where these effects could be significant, it may be better to determine bbp() empirically instead of iterating it's value to prevent interference with the ag() inversion. CDOM fluorescence appears to affect the Rrs() optimization algorithm in a different manner than the MODIS algorithm. Because Rrs() optimization iterates bbp(), it appears to compensate for CDOM fluorescence by increasing bbp(). Instead of using the two ag() coefficients like used for MODIS, it may be better under Rrs() optimization to either adjust bbp() or come up with an spectr al CDOM fluorescence term tied to ag() values. The bbp() values could use a lower slope followed by a higher slope for the actual calculation in a manner similar to what was used for MODIS. Another method that could be explored for all Rrs() inversions is to tie the magnitude of the CDOM absorption and down welling irradiance to a value for spectral CDOM fluorescence. Directly correcting for CDOM fluorescence would be the most analytical method for correcting Rrs() inversions. Either of the approaches could correct for CDOM fluorescence in the Rrs() optimization inversions. PAGE 253 235 CDOM fluorescence could produce errors to the empirical relationship for the spectral coefficient for bbp(). All the Rrs inversions us e an empirical relationship at wavelengths that would be affected by signi ficant CDOM fluorescence. Rrs optimization uses the ratio of Rrs(440) to Rrs(490). QAA uses the ratio of Rrs(440) to Rrs(555). Further study is needed but under high CDOM conditi ons, the relationship may not be the same as for low CDOM conditions. Either the sl ope needs to be adju sted based on a CDOM fluorescence compensated Rrs() or different wavelengths need to be selected for the bbp() coefficient. Another improvement for the Rrs() optimization method might be to vary the aph() shape factor as a function of temperature similar to the method used by MODIS. Packaging usually varies from onshore to deeper waters. The temperature factor, a distance from shore, or anw() might serve as a method to shift the shape factor from larger more estuarine phytoplankton to sma ller more open ocean phytoplankton. Ideally, one would have direct measurements of aph() to use if the Rrs() measurements are collected aboard a ship. The direct measuremen t could then be used for the shape factor. When using satellite data it is not always possible to have a ship taking direct measurements. The aph(440) to aph(676) ratios are usually more affected by changes in packaging (Kirk 1975). A scaling factor could shift the spectra l ratios to better match the changes in packaging. MODIS uses the ni trate depletion temperature with its more empirical approach but has better results at aph(676) under the semianalytical algorithm. Rrs() optimization could benef it from this approach. Rrs() optimization, like all the AOP inve rsions, had problems at sites where bottom reflectance was a signi ficant proportion of the Rrs() signal. Actual albedo measurements demonstrate that not only is a fa ctor needed but a bias is required too. The spectral measurements show that most albedo ov er sand is close to linear with a positive slope under the visible wavelengths (next chap ter). A linear fit th rough this measurement shows not only a change in slope but also a ch ange in intercept is needed for different sand bottoms with similar slopes. This cha nge may be due to the different amounts of organic material on the bottom absorbing more at shorter wavelength. Differences in mineragenic composition of the bottom cannot be ruled out without some testing. The Rrs() optimization model could be parameterize d to include an iterated bias over a limited range along with a slope for the bo ttom. Further measurements along with analysis of bottom composition could lead to a relationship between the magnitude of the albedo at a specific wavelength and the slope of the spectra l albedo. Using a better albedo both spectrally and in magnitude would improve the IOP inversions especially for ag() and bbp(). 6.10. Improvements to Kirk and QAA models The QAA and Kirk models were not critici zed as much as the other models since they represent mostly empirical algorith ms. These algorithms are useful when computational resources need to be conserve d or a simple estimate is needed. Both models could benefit from some of the sugge sted changes in similar algorithms but it PAGE 254 236 would result in increasing their complexity and computational requirements. The Kirk Kd() and QAA Rrs() models can be used to improve the more analytical optimization models by giving initial input values. The Kd() Kirk model was used to estimate the initial absorption value for the Kd() optimization model and improved the algorithm results. The approach fro m QAA model can be used to better estimate the bbp() values for the MODIS algorithm with little additional computational requirements. Small changes like using the Gordon nor malization for input into the Kd() inversion and not iterating the bbp() reference value when bottom is present for the QAA model would give some improvement to these algorithms. PAGE 255 237 7. Bottom Albedo 7.1. Introduction Now that closure has been achieved, it is possible to utilize combinations of the different measurements and methods to gather more detailed optical information. One way to do this is to use the IOP values and combine them in a numeric model that can relate them to the AOP values. With these relationships other AOP values that were not directly measured can be determined. Hydroli ght is a unique model in that its solution to the radiative transfer equation is exact if th e input data to the m odel is accurate (Mobley 1994). The inputs to the Hydrolight model ar e the IOP values and the downwelling solar irradiance. The outputs are the AOPs such as Rrs() and Kd(). By comparing the output AOPs from Hydrolight to the measured valu es, the quality of th e input IOPs can be tested. The Ed() measurements can also be used to assure that the parameters for solar input for Hydrolight are correct. Unde r the conditions with significant bottom contribution to the reflectance value, Kdopt is best for anw( ) and the HS6 is best for bbp( ). With input of these values into Hydr olight, it is possible to extrapolate other optical properties such as average cosines and bottom albedo. The Rrs() optimization method provided an in teresting formula for determining albedo. Spectral albedo inversions using the Rrs() optimization algorithm did not produce useful results because the reflectance from the bottom was so small relative to the model uncertainties that the result was noise. However, the formulation of the Rrs() optimization model did give a example of how to invert Rrs() values to obtain bottom albedo. The optimization method separates subsurface irradiance re flectance into two components. One component is due to the wate r column and the other is that due to the light reflected off the bottom. Each has a di ffuse attenuation factor empirically set to estimate the change in averag e cosine and attenuation along the path. The bottom path diffuse attenuation factor is a function of depth and the iterated IOP values. This factor is multiplied by the albedo at each wavelength. Therefore, a black bottom (albedo = 0) should represent the water column only and a white bottom (albedo = 1) would give the bottom component with 100% refl ectance. If it is assumed that the factors determining the transmittance across the ai r water interface are close to the same with the black bottom and white bottom, then a measurement of Rrs() can be used instead of the subsurface remote sensing reflectance values. This approach does make another big assumption. It assumes the bottom has a Lambertian reflectance. Albedo is the planar irradiance leaving a flat surface divided by the planar irradiance impacting that surface. Rrs( ) is radiance leaving the water divided by the irradiance entering the water. This means that Rrs( ) is only looking at one angle PAGE 256 238 while a true albedo measurement would coll ect radiance from all the angles. This approach is actually measuring part of the Bidirection Reflectan ce Distribution Function (BRDF, Nicodemous et al, 1977). The BRDF is the radiance reflectan ce of all angles of light leaving a surface over a unit hemisphere at all possible angl es of radiant light striking the surface. This is an extremel y difficult measurement because it requires precise knowledge of the source and reflected light for a given surf ace at several angles that can be interpolated to determine this function. A Lambertian reflector appears to reflect light evenly to the obser ver from all angles as function of the average cosine of the radiance striking the surface. While the assu mption of a Lambertian reflector greatly simplifies the inversion, it may result in inaccuracies if the bottom is not close to Lambertian in BRDF. The Rrsopt model assumes a Lambertian BRDF as it divides the albedo by Pi in equation 7.1. A recent study ha s pointed out that for a fairly flat uniform bottom assumption of a Lambertian BRDF will only introduce about 10% error under most angles of source and reflect ed light (Mobley et al. 2003). There are several benefits of this appro ach for deriving albedo values from Rrs() and IOP measurements. The algorithm doe sn't require expensive or complicated equipment. With an aircraft or towed ra diometer; the method can provide albedo values for a large area. The method can provid e output over many wavelengths. Many models start out assuming an estimate of the albedo a nd then attempt to match the values to that. This method doesn't require an a priori estimate of the albedo value. This model, if the assumptions are correct, will give a close estimate of the albedo for any bottom type. The measurements required for the albedo inversion are absorption, attenuation, and backscattering along with an above water Rrs(). The depth of the water column should also be known. If the water colu mn is well mixed optically, then surface measurements will suffice for the IOPs. The equipment can be as simple as a pair of attenuation meters, a 2 channel backscatteri ng meter, and a radiometer along with surface samples collected for spectrophotometric absorp tion values. The best results would come from a profile of reflectance using a radiometrically calibrated downwelling irradiance meter in conjunction with a radiometrically ca librated upwelling radiance meter, an ac9, Hydroscat6, and acoustic bottom sounder. A profiling package would be required at locations where there are significant changes in optical properties over depth. A flow through optical system would complement the profiling. When changes in optical properties are noticed in the flow through, an optical profile c ould be collected. Either of these approaches is simpler than anchoring the ship for hours while divers measure small areas of the bottom with hand held radiance me ters or a team of technicians deploy an ROV. One of the more intriguing approaches is to use this method is in conjunction with an aircraft mounted radiometer to measure reflectance over a large region This approach would allow the mapping of the bottom albedo for a large area of interest (Dierrson et al. 2003). Alternatively, the radi ometer could be towed behind the vessel or deployed on an AUV (English et al. 2006). The towed or AUV method would give a much smaller view of the bottom but would give a much greater resolution and eliminate the atmospheric PAGE 257 239 attenuation correction associated with air borne sensors. Eith er of these approaches could provide the baseline for environmental monito ring of a region with a shallow benthic community. 7.2. Bottom Albedo Inversion Method The path of light to the bottom and back to the surface can be broken up into the path due to interaction with the water column only and the light that reaches the bottom and returns to the surface. The Rrs() optimization algorithm uses a method that sums both components of rrs(). The equation can be simplified to equation 7.1. rrs() = rrs() (water column) + / *rrs()(bottom) Equation 7.1 The Greek letter, represents the bottom albedo. If the bottom absorbed all light, only the water column rrs() to that depth would be meas ured and the bottom would have an albedo of zero. If the bottom reflected li ght, then it would have both the water column rrs() and the rrs() from the bottom. If closure is achieved between the AOPS and IOPs based upon the previous statistics, then the IOPs can be used as input into the analytical forward model, Hydrolight, to determine the bottom albedo. If the difference in transmittance across the air water interfaces is insignificant for different bottom albedo values, it can be assumed to be a constant and the above water Rrs() can be used. A Hydrolight model gives us the water column only Rrs() using a black bottom (albedo of 0). A second run using a white bottom (an al bedo of 1) gives us both water column and bottom reflectance Rrs(). Subtracting the Rrs(,black) from both the measured Rrs() and the Rrs(,white) leaves us with only the bottom contribution. Taking a ratio of the two factors of Rrs() provides the albedo. ) ( ) ( ) ( ) (black R white R black R measured R albedors rs rs rs Equation 7.2 The IOP value from all 126 stations used in this study were divided into five groups based on attenuation at 440 nm. The me an IOP values at 440 nm from each of these groups were used with different bottom al bedos and solar zenith angles as input in to the Hydrolight model to test the albe do inversion (Table 7.1). The resulting Hydrolight data use IOP values that were similar in relationship to each other as actual field data but without the accuracy limits of the instruments or techniques. The 5 sets of IOP values were run through Hydrolight simula tions with bottom albedo values of 0, 10, 20, 30, 40, 50, 60, 80, and 100. Three differe nt solar zenith angles of 15, 45, and 60 were used in the simulations. This sunthetic data set was used to test the effectives of the model and the limits under which it was applicab le if all the input da ta were perfect. The limits of diffuse attenuation, beam attenuation, solar zenith angle, and depth were tested to determine where the model functioned correctly and where it had errors. The resulting limits were then compared to the albedo inversions based on measured values to determine if they were applicable. PAGE 258 240 Table 7.1. Mean values of i nherent optical properties from study locations. The IOP data from all stations were ranked and split into 5 groups according to attenuation values. The high bb(440)/b(440) ratio from th e 2nd quintile is due to re suspended or precipitating aragonite particles at the CoBOP near shore stations. Quintile b b (440)/b(440) cnw(440) anw(440) b(440) m1 m1 m1 1st 0.0270.0760.0220.054 2nd 0.0600.1240.0370.087 3rd 0.0270.1850.0420.143 4th 0.0210.2640.0500.214 5th 0.0230.7640.1890.575 The albedo inversion results were compared to known bottom albedo measurements. These measurements included the sand, sea grass, green algae, brown algae, and red algae albedo values provided w ith the Hydrolight m odel (Figure 7.1 A). Nine direct measurements ta ken of albedos of sand bottoms near the 10 m isobath off Sarasota, FL were also compared (Mazel 1997, McIntyre 2003) to the inversion results (Figure 7.1B). The measured albedos were collected at close to the same time and area as the FSLE 3 cruise data used in this study (See Table 2.3 in Chapter 2). The closest match was determined by the lowest total absolute percent error of the modeled albedo values from a measured albedo values. The matched albedos were adjusted over the spectrum using a factor and a bias if the correlation w ith one of the measured albedos was greater than 0.5 but the percent error was greater than 20%. The scaling wa s limited to the range of slope and intercepts of albedo value versus wavelength calculated for the 9 measured sand bottoms in Figure 7.1 B. PAGE 259 241 Figure 7.1. Measured albedo values compared to albedo inversion results. A. Measured values used in the Hydrolight model. B. Measurements made us ing a submersible handheld radiometer off the West Florida Shelf. Albedo 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Brown Algae Green Algae Sea Grass Red Algae Sand Wavelength (nm) 400450500550600650700 Albedo 0.0 0.1 0.2 0.3 0.4 St 2 St 3 St 4a St 4b St 5a St 5b St 7a St 7b St 9 A. B. PAGE 260 2427.3. Inversion Results There were errors associated with the bottom albedo inversion using Equation 7.2 that increased in shallower environments with higher albedo values (Figure 7.2). Analysis of Hydrolight runs with varying bo ttom albedos revealed th at the light reflected off a bottom with a Lambertian BRDF and a shallow water column resulted in a higher average cosine of upwelling irra diance than for an infinitely deep bottom (Maritorena et al. 1994). This produced a nonlinear function for Rrs() versus bottom albedo. Holding all conditions constant except for bottom albedo, it was observed that bottom albedo correlated with a Rrs() fit using a second order polynomial function (r2 > 0.99 n = 8, Equation 7.3). Using a third Hydrolight modeling run with an albedo of 50% (Rrs(,grey)) was enough to obtain a correlation of 0.98 which compensated for the nonlinearity resulting from lower internal reflectance. While it may be possible to come up with a function to compensate for the change in average cosine, it was less complex to use the polynomial fit with a third model run. C Meas R X Meas R X albedors rs ) ( ) (0 2 1 Equation 7.3 The measured albedo values from the We st Florida Shelf were mostly linearly increasing values with wavelength for < 600 nm. Normalizing these values at 550 revealed that they not only had different slop es but different intercepts (Figure 7.3). The differences are possibly a functi on of the coverage of the sand with biological material such as detritus, bacteria, or algae. A pur e sand albedo is approximately linear in the same manner as these measurements but has a much large magnitude. The absorption by detritus has a decaying log slope that is much higher in shorter wavelengths than longer ones. A covering of detritus across the bottom could serve to lower the albedo values at shorter wavelengths resulting in a nearly lin ear spectral shape with a much lower slope and different intercept. This change in slope and intercept means that Rrs() inversions that take into account the bottom albedo need both a bias and multiplicative factor to adjust the albedo values. This spectral lin ear relationship means th at it is not easy to compare measurements from different locations and times with the model results. The scaling of these sand albedo values was limite d to the range of sl opes and intercepts observed in the measured albedo values. PAGE 261 243 Figure 7.2. Comparison of ratio method to polynomial method using Hydrolight generated data. The ra tio method averages 7.1% less than the input green algae albedo while the polynomial fit average 7.5% higher over 400 to 625 nm. Figure 7.3. Measured West Florida Shelf albedos and Hydr olight sand albedo normalized to their 550 nm values. wavelength (nm) 400450500550600650700 Normalized Albedo 0.4 0.6 0.8 1.0 1.2 1.4 Mazel St 2 Mazel St 3 Mazel St 4a Mazel St 4b Mazel St 5a Mazel St 7a Mazel St 7b Mazel St 9 Hydrolight sand Wavelength (nm) 400450500550600650 albedo value 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Polynomial albedo Ratio albedo Input albedo PAGE 262 244 Of the 126 stations, 86 are shallow enough that some reflectance from the bottom could be a part of the Rrs() measurement. All were processed using the albedo inversion. Only 46 of the 86 stations have sufficient bottom reflectance in the Rrs() measurement for depth analysis using the Rrsopt algorithm. Only 23 of the stations have Rrsopt inversion results for depth that were within 20% of the actual depth and only 13 stations within 10% of the actua l depth. The IOP data and Rrs() from the 86 stations were input into Hydrolight to determine if they could provide a realistic bottom albedo value. The modeled data were run at 10 nm increments from 400 to 700 nm at albedos of 0, 0.5 and 1. The albedo inversion had matches within 20% for at minimum 3 wavelengths (10 nm increments) for 30 stations. There are seven stations where the Rrs() inversion algorithm did not find the bottom but the albedo inversion was able to provide an albedo result (ECO2, F3005, F3014, F4006, F4012, LK204, and LK205). The best matches were in the optically clear waters in the Ba hamas with the poorest matches in the more turbid waters off the West Florida Shelf (F igures 7.4 and 7.5). The bottom contribution was not significant in the Puge t Sound stations. Sixteen stations had matches to an albedo that did not require scaling. Fourteen of those stations we re off the West Florida shelf near the location where some of the bottom al bedo measurements were collected (Figures 7.6 to 7.8). Of the 86 stations put thr ough the model, 30 produced albedo inversion results that are within 20% of measured albe do values from other studies at 3 or more wavelengths. PAGE 263 245 Figure 7.4. Albedo invers ion results and similar measured albedos: 1998 Bahamas stations. Any values to the ri ght of the solid blue line and to the left of the dashed blue line are greater than 2 optical depths. Values less than or equal to zero were not plotted since they were not considered a real result. St 304bWavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 5a St 108Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 5a St 208Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 5a St 109Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 9 St 304aWavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 5a St 103Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 PAGE 264 246 Figure 7.5. Albedo inversi on results and similar measur ed albedos: 19981999 Bahamas stations. Any values to the ri ght of the solid blue line and to the left of the dashed blue line are greater than 2 optical depths. Values less than or equal to zero were not plotted since they were not considered a real result. St 117Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 5a St LSC27002Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 4a St LSC28002Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 7a St LSD521001Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Green Algae St 111Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 4a St 110Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Red Algae PAGE 265 247 Figure 7.6. Albedo inversion results and similar measured albedos: 11/99 to 07/00 West Florida Shelf stations. Any valu es to the right of the solid blue line and to the left of the dashed blue line are greater than 2 optical depths. Values less than or equal to zero were not plotted since they were not considered a real result. St ECO2Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 St F3005Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Green Algae St F3008Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 St F3010Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 3 St ECO03004Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Green Algae St ECO3002Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 3 PAGE 266 248 Figure 7.7. Albedo inversion results and similar measured albedos: 07/00 to 11/00 West Florida Shelf Stations. Any valu es to the right of the solid blue line and to the left of the dashed blue line are greater than 2 optical depths. Values less than or equal to zero were not plotted since they were not considered a real result. St F3022Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 St F3026Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 4a St F4006Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 7b St F4012Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Green Algae St F3018Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 St F3014Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 PAGE 267 249 Figure 7.8. Albedo inversi on results and similar measur ed albedos: 2001 West Florida Shelf Stations. Any values to the right of the solid blue line and to the left of the dashed blue line are greater than 2 optical depths. Values less than or equal to zero were not plotted since they were not considered a real result. St LK205Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Sand St LK305Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 7b St LK306Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 2 St LK207Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel ST 7a St LK304Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Mazel St 4a St LK204Wavelength (nm) 400425450475500525550575600 Albedo fraction 0.0 0.1 0.2 0.3 0.4 0.5 0.6 Modeled Sand PAGE 268 2507.4. Accuracy of the Albedo Inversion Algorithm Hydrolight is an exact numerical mode l but has a limit due to the number of significant digits it can calculate and still be able to complete the calculation in a reasonable time. For certain combinations of input factors, the model would not produce a result for albedo. In these cases the surface Rrs() signal from the backscattered irradiance just above the bottom was lowe r than the noise in the model due to the rounding of very small numbers. While this a ccuracy is not the same as accuracy using actual data, it does provide an upper limit to determine the conditions under which the Hydrolight model is limited in calculating a bottom albedo. To determine the environmental conditions at which this model is applicable, the synthetic data set created us ing Hydrolight was compared to various combinations of AOPs, IOPs, depths, and bottom albedo values The magnitude of the albedo did not have an influence on whether the albedo can be modeled. The factor that indicated the noise level was the optical depth as calculated by Kd() multiplied by the depth of the water column resulting in a unitless number indicating the penetrati on of light to depth (Kirk 1994). There are some differences in th e literature over the term optical depth. Kirk (1994) defines it as used in this study but Mobley ( 1994) defines it as the beam attenuation times the depth. Kd() times depth is more useful for determining the limits for albedo inversions since it combin es absorption, backscattering, and d into one term. The optical depth is useful becaus e it can give both maximum depth if the Kd() value is known and can give maximum Kd() if the depth is known. An optical depth of 3.2 appears to be the cutoff point using the artificial data set (Figure 7.10). If the Kd() value for an area is 0.1 m1 then dividing the 3.2 limit by it would give a maximum depth of 32 meters. Likewise if the depth is 10 me ters, dividing the optical depth of 3.2 by 10 m would give a maximum Kd() value of 0.32 m1. By raising the base of the natural logarithm (e) to negative of the maximum op tical depth then multiplying by 100 gives the minimum percent of downwelling irradiance r eaching the bottom nece ssary to determine albedo as 4.1%. Field data are rarely as accurate as the Hydrolight modeled values so 3.2 optical depths should be considered the theoretical limit. PAGE 269 251 Figure 7.9. Absolute percen t error for albedo at 440 nm us ing the Hydrolight generated data set. All quintiles of IOPs, solar zenith angles, and bottom albedos are included in this graph. When using actual field data the maxi mum optical depth at which the bottom albedo could be reasonably determined wa s 1.5 to 2.0 (Figure 7.11). The percent difference from the input albedo noticeably in creased above 3.2 optical depths. A value of 3.2 to 3.0 might be the highest usef ul optical depth under ideal environmental conditions with very precise in strument data but an optical depth of 2 is probably the most practical limit. At an optical depth of 2 only 1.8% of the light reaching a bottom with 100% reflectance would make it back to the surface. Based on the comparison of environmental parameters, the accuracy of the IOP input into Hydrolight and Rrs() measurements limits the accuracy of the m odel to about 2 optical depths. Albedo inversions using actual data were achieved for optical depths as high as 4 but the agreement between the measurements and the modeled values became significantly noisier above 2 optical depths. Plotting th e cumulative percentage of values with agreement of 20% or less revealed that there is an inflection point at 2 optical depths after which the fraction with good agreement signifi cantly declines (Figur e 7.12). There is another inflection point at 1.2 opt ical depths but it reflects a leveling of the change in the percentage of good agreement. Until testing with a larger data set is available, 2 optical depths is probably the practical limit. Optical Depth (Kd(440)*depth(m)) 0.00.51.01.52.02.53.03.54.04.55.05.56.06.57.0 Absolute Percent Error 0 2 4 6 8 10 PAGE 270 252 Figure 7.10. Plot of absolu te percent difference from best match measured albedos versus albedo inversion results at 440 nm. This is based on actual field data. Figure 7.11. Cumulative percen tage of matches that are 20% or less than the given optical depth at 440 nm. This data set is based on the actual field data. The percent difference is based on the best match to m easured values where the albedo result was greater than zero. Optical Depth 012345 Percent with <=20% error 0 10 20 30 40 50 60 Optical Depth 012345 Absolute Percent Difference 0 100 200 300 400 500 PAGE 271 253 Based on the Hydrolight modeled data set, an optical depth based on beam attenuation (Mobley 1994) at 440 nm could also function as a limit. The correlation between error and a diffuse attenuation optical depth or beam attenuation optical depth is 0.86 for both. The upper limit for the model da ta using beam attenuation based optical depth is 15.28 and noise starts to occur at 6. 20 (Figure 7.13). This information could be useful for field exercises where a submer sible downwelling irradiance meter is not available. As with the other modeled results this represents a theoretical limit not the practical limit as determined from field measurements. Figure 7.12. Absolute percent error versus opt ical depth as calculat ed using attenuation for Hydrolight generated data set. This method of calculating optical depth is also referred to as attenuation lengt h. All quintiles of IOPs, solar zenith angles, and bottom albedos are included in this graph. The change in average cosine is a mu ch more significant effect than the magnitude of the albedo value. Instead of light continuing to depth and being backscattered, the light is cut off at a certain depth and either reflected back towards the surface or absorbed. If the bottom is close to Lambertian in reflectance, then the average cosine of the light reflected off the bottom is 0.5. This means that the downwelling irradiance, as a function of the attenuation by the bottom, is returned less diffusely than if there were no bottom. This results in a greater percentage of light being transmitted across the air water interface (M aritorena et al. 1994) instead of lost to internal reflectance. Even a black bottom affects th e average cosine if it is shallow enough. A dark bottom cuts off the light before it re aches depth and undergoe s multiple scattering events. The average cosine is a functi on of a shallower water column where u is Optical Depth (attenuation depth) 01234567891011121314151617181920 AbsolutePercent Error 0 2 4 6 8 10 PAGE 272 254 greater due to a shorter path to the surface. The limit to this albedo inversion is independent of the actual albe do but relies on whether there is sufficient signal from the water column at a depth just above the bottom. The Q factor is the ratio of subsur face upwelling irradiance to subsurface upwelling radiance at depth and varies as a f unction of the bottom albedo (Figure 7.14). The Q factor exhibits significant variati on as a function of albedo resulting in a hyperbolic curve. As the albedo value incr ease, the ratio of radiance to irradiance increases. This increase in the Q factor is due to two factors: the increased amount of downwelling irradiance that is reflected up due to the bottom, and the change in angle of the upwelled radiance to a more direct path to the surface. The more direct path will result in lower attenuation and less chance of internal reflection at the surface. Figure 7.13. Rrs(440) and belowsurface Q factor at 440 nm versus albedo values for middle quintile IOPs and 10 m bottom depth. A ratio equation using modeled Rrs() values with albedos of 0 and 1 is a close approximation but results in a slight error depending on th e change in Q factor for different albedo values. The fit for the Rrs(440) values to albedo for the median values in this study, had r2 values of over 99% for both a linear and second order polynomial fit. However, the differences between the measured and modeled values can be large for the linear fit especially at smaller albedo values. Because of a bias in the regression line, the middle quintile of IOP values the linear fit had a 170% error predicting an albedo of 0.5% while a second order polynomial had a 4% erro r. The ratio method is not good for small albedo values due to the nonlinear relationship between albedo and Rrs(). Rrs(440) (sr1) 0.000.020.040.060.08 Percent Albedo 0 20 40 60 80 100 Q Factor 2345678 Rrs(440) Regresion line Q Factor PAGE 273 255 Due to the possibility of problems with the fit of the second order polynomial curve to albedo values below 10%, a second se t of modeled data was created with 12 total values by adding four values between the albedo values of 0 and 10. Additional albedo values of 0.5, 1.7, 2.8, and 5 were in cluded with the origin al group using the 3rd quintile of IOP values, a 15 solar zenith an gle, and 10 m depth. Us ing 12 albedo values resulted in similar statistics but higher perc ent differences at some lower albedo values. At an albedo value of 0.5, the fit through 12 albedo values had a percent e rror of 4.14% while the fit through three albe do values had a percent error of 0.81%. The extra values probably would have better results with a higher order polynomial equation but that was not necessary since using the three values provides an error of less than 1%. The three point albedo value fit was used instead of a larger number of computationally intensive Hydrolight runs at more albedo values since the greater number of values did not improve the results when using a second order polynomial fit. The optical depth limit of 2 was not always a perfect predictor of when the albedo inversion could be achieve d. With values at greater than two optical depths removed, the CoBOP stations had about 68% of the possibl e wavelengths within 20% of the reference albedo values. The West Florida Shelf stat ions had 50% within 20% of the reference albedo values. Station F4006 on the West Fl orida Shelf has matches within 20% at 5 wavelengths from 460 to 510 nm but the whole spectrum is outside the optical depth limit of 2. The optical depth limit was not a perf ect predictor of mode l success but only one station had realistic inversion values that were seriously outside it. 7.5.Sources of Error There are some liabilities to this approach. The data collected must be of very high quality. The use of several different instruments can compound the error from each. The method assumes that the bottom is Lamb ertian in reflectance and may have some errors if the BRDF for the bottom substrate differs much from a Lambertian BDRF (Voss et al. 2003, Mobley et al. 2003). In additi on to very good IOP input, the model requires very good meteorological data so that the input solar radia tion is a close match to the actual down welling irradiance for determining tr ansitions across the ai r water interface. Accurate data are crucial for the succe ss of the polynomial approach to bottom albedo modeling. Most instruments are accurate to within 10% of the actual value at best. Since the method requires the use of Rrs(), anw(), cnw(), and bbp(), there are four instruments that can contribute to errors in th e resulting albedo if they are too far from the actual value. The error in instrument accuracy is most likely the reason why the technique is limited to 2 optical depths using real data but is usable up to 3.2 optical depths for the Hydrolight simulated data. This also is the most likely reason for some high error values at optical depths be low 2 when using the real data. Some of the inversions clearly have inaccura te data as inputs. The inversion from station ST103 has a deviation from the meas ured value from 400 to 475 nm that has a decaying slope logarithmic shape (Figure 7.4). The error could be due to a low ag() PAGE 274 256 value, too high bbp() value, or too much skylight in the Rrs() signal. Adjusting the values or trying different inst ruments might improve this inve rsion. However, without an absolute measurement of this bottom, it can't definitely be defined as any one cause. Adjusting the anw() up by 30% and the bbp() value down by 20% brought the values closer to one another in the longer wavelength range but did not signi ficantly effect the area that was already matched. This test at one station i ndicates that the inversion is pretty robust in the region s of strongest signal. The meteorological data could introduce er rors if there is a problem with the estimate. Hydrolight can use di rect measurements also as input if the separation of direct and diffuse light is first determined by sh ading the sun from the above water radiance meter. Without knowledge of the direct and diffuse irradiance values, the best way to input the down welling solar irradiance into H ydrolight is to first match the above water values to a direct measurement that is synchronous with the Rrs() measurement. Hydrolight uses the Radtran so lar irradiance model as one of its inputs (Gregg and Carder 1990). The Radtran algorithm can be coded in ei ther Matlab or Excel in such a way as to allow the values to be iterated until a match is achieved with a direct measurement. This match would minimize one source of error for the inversion. Actual measurements of radiance from different zenith and azimuthal angles indicate that most botto ms are not purely Lambertian in re flectance (Voss et al. 2003). In one particular direction there is usually a "hot spot" where more radiance is emitted. However, most bottom albedos do come close to Lambertian especially after attenuation through the water column. Mobley et al. (2003) estimate that assuming a Lambertian bottom albedo will only introduce errors of 10% in modeled Rrs() values. This is an area where further research is needed. After compiling how different bottom types respond to light, it may be possible to estimate the bid irectional reflectance distribution function based on the bottom type. Another method that might help in determining the BDRF is through using this albedo invers ion method but taking several Rrs() measurements at different angles. The BRDF could be calcula ted by looking at the differences in albedo from several different points. The albedo valu e from this albedo inversion is valid for the solar zenith angle, solar azimuth angle, and view angle of the radiance sensor for this Rrs() measurement. It just may not be as accu rate under different angles if the bottom is assumed to be Lambertian in reflectance. Since the Rrs() value collected in the field represents the effects from a three dimensional bottom it could influence the overall albedo inversion. Most models assume that bottoms have one set albedo and BRDF but in reality, they can vary widely over a short range. Sand waves trap detritus resulti ng in darker patches in troughs while there are light areas at the peaks (Car der et al. 2003). The slope of the bottom especially for a rapidly changing bottom can resu lt in different albedo values even if Lambertian (Mobley and Sundman 2003). Adjacency effects can cause errors. These occur where the reflectance from two different bottom types me rge together in the water column due to scattering. This smearing of the two albedos can make it difficult to determine the actual bottom albedo for a given location (Mobley a nd Sundman 2003, Farmer 2005). The real PAGE 275 257 albedo is a mix of different patches of albedo values with different BRDF functions so this method cannot completely remove the wa ter column attenuation to reveal a sharp, color, spectral, imag e of the bottom. High solar zenith angles were associated with errors in the albedo inversion. High zenith angles can lead to increased sun glint resulting in error in the Rrs() measurement. The assumption of Lambertian reflectance may not be valid for higher solar zenith angles. The light striking the surface at an angle close to the hor izon may not give the same percentage of reflectance towards a radiometer angled 30 from nadir when compared to the sun being more directly overhead. In examin ation of the stations where there were albedo inversion resu lts it was determined that at only 15% of the stations with a solar zenith angle of less than 30 wa s an error of greater than 30% at 440 nm observed while at 85% of those with solar zeni th angles of greater than 37 was an error greater 30% found (there were no stations with solar zenith angles between 30 and 37 that produced an albedo result). Examinati on of the areas that were possibly shallow enough to have some bottom influence on the Rrs() values revealed that at 96% of the stations with no results were found either sola r zenith angles greater than 30 or optical depths at 440 nm greater than 2. Of the st ations with no result, 63% had both high zenith angle and high optical depth while only 10% of stations with results had this combination. To reliably achieve a bottom al bedo inversion, both optic al depths less than 2 and a low solar zenith angle are needed. Further research is needed to determin e the maximum solar zenith angle for the technique. A controlled experiment at a single loca tion with a known bottom albedo would be necessary to fully understand the sources for the problems with high solar zenith angle. Sun glint may be s major factor in causing errors in the inversion. Since the average cosine of upwelli ng irradiance is the primary i ndication of bottom albedo, the error at larger zenith angles may be function of a change in u due to the zenith and scattering in the water column. To determine if the change in u produces the error further research is needed. Based on the actual data, Rrs() values collected at greater than 37 should be suspect when albedo inversions are attempted. Unfortunately optical data collected in the field is never absolutely perfect, so the practical limit of this method is a much lo wer optical depth than indicated by modeled data. There were no synchronous measurements of the albedo values at any of the stations in this study to conf irm the model results, so this limit may not be as low. The known albedo values consisted of standard m easurements used in the Hydrolight model and measurements collected just offshore from Sarasota, Florida. The Rrs() could contain excessive skylight or sun glint that could cause errors in the values. Since only the integrated value was used, the IOP input values could cause errors if the values change significantly over depth. It is difficult to statistically analyze the limit of the model based on the results usi ng real data from this study. Further testing of the algorithm with bottom albedo measurements collected in synchrony with the Rrs() and IOP values are required before a more definitive limit can be established. PAGE 276 2587.5. Applications for Albedo inversions The uses for a real spectral bottom al bedo could be many. Many surveys are performed with color video cam eras. Most cameras only have 3 colors, red, green, and blue. While three wavelengths can be used fo r some colorimetric identification of objects below the surface, spectral data can provide a more quantitative identification. If the bottom is covered with a photosynthetic organi sm like sea grass or algae, the spectral shape of the albedo may give some indication to the type of organism If the object is a manmade device, such as submersible vehicle, it would be very difficult to exactly match it's color and reflectivity to the substrate making it detectable using a spectral radiometer. This technique could be useful for applic ations ecological mappi ng to port security. The biggest drawback to using this te chnique with hyperspectral imagery would be the need for a less processo r intensive version of the Hydrolight model combined with a very powerful computer. A faster version of Hydrolight has been created for use with Phills imagery to generate look up tables to determine bathymetry and bottom type (Mobley et al. 2005). They involve matching the Rrs() to a set of preset values using estimated IOP data in conjunction with know n albedo values. The change in average cosine values with changes in depth a nd albedo would require model runs for each wavelength and IOP values using bottom albedo va lues of 0, 0.5, and 1. The wavelength range could be lowered if the depth is such that attenuation by water would increase the optical depth to greater than 2. While taking a large amount of computer time, this method is feasible even for highresolution imagery. If the IOPs are constant over the area of in terest then a series of regressions could be calculated for the albedo fits at 0, 0.5, and 1 over the depth range of the area. For coral reef off the Florida Keys, the depth rang e might be 1 to 20 meters. Instead of doing Hydrolight runs for each depth, runs could be determined for several depths and a second order polynomial equation calculated for each of those depths. A second regression using a logarithmic or polynomial fit is calculated for each of the terms as they change over depth. A correction for slight changes in so lar zenith angle during the time of collection could further increase the accuracy of the resu lts. To map the albedo of an area, it may only require as little as 12 Hydrolight runs to get this matrix. Th e computer time would not be a concern with this approach. The best time for mapping the albedo of an area would be during a period of constant IOPs with lower attenuation such as a high tide. Since the areas where this technique would be applied are most often near shore, a flood tide would provide the lowest attenuations. A flood tide would usuall y bring in clear offshore waters. The peak of high tide when the currents sl ow down may be the best time fo r mapping most regions. A problem could be possible resuspension of sediment caused by an incoming tide if the current is strong enough. The tidal period s hould be an important consideration in mapping an area especially if there is a signifi cant change in optical properties with the tide. PAGE 277 259 A 3 dimensional color map of a coral reef could be created using this technique. A hyperspectralscanning imaging sensor like the Phills (Davis et al. 1999, Lesser 2007), a side scan sonar system, and a flow through optical system could provide a high resolution color map of a cora l reef region. A lower cost method could use a towed balloon with miniature black a nd white cameras using narrow band pass filters for several important wavelengths (Dave English, pers onal communication). Su ch a map would be invaluable to coral reef ecol ogists and natural resources offi cials. It would provide a baseline for future research and could be used to quantify coral coverage. A spectral threedimensional image could be used to identify hazards to coral reefs such as bleaching, cyanobacterial blooms, or black band disease. The spectral values could identify species of corals based on pigments through fourth deriva tive analysis of the spectral shape. Currently reef systems worldw ide are in decline. Management practices need to be geared to addressing the reefs in the greatest decline. By initially identifying the problems in these areas, more efficient allocation of resources and policy changes could be targeted to the indi vidual reefs. A threedime nsional spectral baseline map would provide a tool to focus rest oration and preservation efforts. Homeland security could benefit from sp ectral maps of specific bottom areas. Monitoring a harbor from below the surface can be very complex. It usually requires active systems like sonar. Coverage of a larg e area would be difficult. If the attenuation is low enough, the area could be monitored optically using the bottom albedo inversion technique. An object of inte rest could be camouflaged from a video camera since it only sees 3 colors across a narrow range. Camouf laging an object so that it spectrally blends in with the water column or bottom would be much more difficult. This difficulty would be compounded as the object moves across the bottom. An active camouflage system that changes in spectral reflectance would be difficult to implement. To provide real time indications of a ch ange in the bottom, an initial mapping of the area could be performed to determine th e albedo using an approach similar to the mapping of the reef area. A faster model like the Rrs() optimization routine could then be combined with the known albedos and de pths. The iterative portion of the model would not need to be run if the IOP inputs were provided in real time through moorings. The resulting Rrs() spectra could then be compared to measurements from a tethered balloon or autonomous air craft with an algor ithm to detect outliers in bottom albedo. The outliers could then be examined in more detail and determined if they represent a possible threat. Surveys at set intervals w ould be required to u pdate the bottom albedo values depending on seasonal changes in the bottom albedo due to changes in benthic biological organisms or sediment deposits. This system would provide a real time tool for monitoring the large area of a port without a need for a larg e array of acoustic moorings, a fleet of ships, or a fleet of AUVs. Sea grass coverage has declined in some areas due to anthropogenic influences and needs to be monitored for restoration efforts. Tampa Bay experienced a severe decline in sea grass coverage during the early 70s (Dawes et al. 2004). Efforts the last couple of decades have succeeded in restori ng several of these areas. Monitoring sea PAGE 278 260 grass using a radiometer can be difficult due to changes in patterns (Zimmerman 2003). Changes in current can result in more of the leaf being visible due to the grass either laying over or standing up. Changes in epiphy tes on the grasses can change their albedo. Changes in coverage or sediment between th e grasses can also change the albedo. A spectral albedo would make it easier to separate these changes in a sea grass bed. Other algorithms require an a priori input of sea grass and sand al bedos and attempt to estimate coverage based on the proportion of those valu es. With knowledge of the IOP values and depths, spectral values could be determined and then deconvolved into sand or grass areas to get coverage estimates (Diersson et al. 2003). The resulting sea grass coverage along with spectral changes due to epiphytes could be estimated from this method. PAGE 279 261 8. Conclusions An analytical inversion of an AOP meas urement can be more accurate than the more direct measurement for determin ing IOP values under many environmental conditions. The AOP inversi ons are especially accurate for low attenuation waters without a significant bottom contribution. This study assumed that no method was an absolutely perfect measurement of the select ed inherent optical pr operty but instead let statistics determine the best method. Instead of a single measurement, an idealized data set based on a nonparametric analysis of the different methods was assumed to represent the best value for the water column IOP tested. The Rrs() optimization algorithm performed the best under the most conditions fo r most of the IOP comparisons due to its analytical approach and longer effective path length. Both the quantitative filter pad method and Rrs() were best for determining aph() depending on conditions. The MODIS algorithm was best for determining ag() when using its semianalytical approach combined with an initial higher value for the ag() coefficient. The Kd() optimization model was best for anw() and the Hydroscat6 was best for bbp() when the bottom contribution to Rrs() was significant. The percent error terms had correlations with parameters that revealed areas for im provement for most met hods. The closure of results among the methods provided an appro ach for determination of spectral bottom albedo using Rrs(). The longer the effective path length of li ght in the method, the better the accuracy of the method in low attenuation waters. The closure study demonstrated that under conditions where there was no bottom present, the Rrs() inversions were more accurate than the Kd() inversions for calculating anw() due to an optical path length that is much larger than that of the Kd() values. The Kd() optimization method was more accurate than the ac9 for anw(). Kd() values have path lengths of several meters while the ac9 has a path length of only 0.25 m. The excep tion for the more direct methods was the aph() measurements using the quantitative filter pad method where effective path length can exceed 20 m for clear water and volumes of over 4 liters are filter ed. The increase in signal to noise from an increased optical path length more than compensates for the empirical assumptions made in AOP inversions for clear waters. Low solar zenith angle can affect both Kd() inversions and Rrs() inversions. Under ideal conditions there were significant ne gative correlations with solar zenith angle and error from Kd() inversions for primarily 412 to 555 nm and error Rrs() inversions for primarily 532 to 676 nm. Kd() values are affected by increased wave focusing and Rrs() value are affected by sun glint when the sun is nearer to zenith. For solar zenith angles less than 15 more Kd() measurements are needed near surface to smooth out PAGE 280 262 wave focusing. Rrs() measurements may need to be collected at different view angles than the standard 30 observation zenith angl e to possibly minimize glint at low solar zenith angles. The ideal angles appear to be between 15 and 45 based on the data set used in this study. The lower solar zenith angles resulted in greater error for the AOP values than the higher angles. The Rrs() inversion models were less accura te when bottom reflectance was greater than 10% of the total R() for most IOPs. The exception was the Rrs() optimization for aph() values when bottom was present. While Rrs() optimization statistically did well for anw() under optimal conditions and significant bottom contribution to reflectance, it did not perfor m as well when used for albedo inversions under the same conditions. However, because the Rrs() optimization algorithm takes into account the bottom albedo, it did perform well for inversion of aph() when bottom reflectance was signifi cant. Since the aph() values do not have a spectral shape that decreases with increasing wavelength as does bbp() or ag(), it does not appear to be as influenced by bottom reflectance. The Kd() optimization method, developed in th is study gave the best result of the Kd() inversions tested. The model is ba sed on Preisendorfer's definition of Kd() and would give very accurate results for absorpti on values if the data were perfect and the average cosine of downwelli ng irradiance known. The Kd() optimization results have errors primarily due to wave focusing and empirical determination of the average cosine of downwelling irradiance. Kd() optimization did not perform well for bbp() due to the low signal from bbp() in the Kd() measurement but it did get closer to the ideal value when a number of outliers was removed. The anw() results from the Kd() optimization method were the best input for the albedo inversion algorithm. The anw() and aph() results from Kd() optimization, while not the abso lute best, were good under most conditions. Generally, the longer path length of the Rrs() values gave them a greater signal to noise ratio than the Kd() values. The Kd() optimization method does provide the best inversion of Kd() values to obtain IOPs. The MODIS semianalytical algorithm proved the best method of the Rrs() inversions for determining ag(). The CDOM fluorescence contribution to Rrs() affects the inversion of aph() by increasing Rrs() around 440 nm and bbp() by increasing Rrs() around 555 nm. The MODIS algorithm, us ing a higher coefficient for the ag(400) equation, increased the modeled Rrs() value at lower wavelengths to correct for the CDOM fluorescence. A lower coefficient was th en used after the model run to calculate the anw() and ag(), resulting in better agreement with the idealized values. This change in the method could be applied to other Rrs() inversions to improve them in areas where CDOM fluorescence is expect ed to be significant. The level of empiricism is a tradeoff that limits the accuracy of a model but requires less a priori knowledge of the study area and lo wer computational needs. The ranking of the accuracy of the AOP inversion proceeded from least empirical to most PAGE 281 263 empirical. Of the four Rrs() inversions, Rrs() optimization was the most accurate, followed by MODIS, QAA, and MODIS default band ratio algorithm. For the Kd() inversions, Kd() optimization was best followed by Kd Loisel and Kd Kirk. The more direct IOP methods required some empirical functions to correct for errors. The ac9 uses a ratio of estimated scatte ring to correct for losses in the absorption tube. The filter pad method uses an empirical function to correct for path length elongation. The Hydroscat6 uses an empirical function to correct for attenuation and convert bb(, 140) to bb(). Every method in this study employs so me form of empiricism, the level of which affects the accuracy of the method. There are some exceptions to the leve l of empiricism and accuracy of the algorithms since the complexity of the more analytical algorithms can sometimes lead to errors. The MODIS algorithm performed better than the Rrs optimization algorithm for anw(676). The better accuracy for MODI S may be due to adjustment of the phytoplankton absorption factors based on nitr ate depletion temperatures to account for changes in packaging. The fits at longer wavelengths for some of the methods represent extrapolations based on fits at the shorter wavelengths due to decreased signal to noise caused by water absorption at the longer wa velengths. MODIS uses an empirical function based on aph (440) and water temperature to estimate aph(676) that gave it very good results at that wavelength. While generally a more analytical a pproach is better, a more empirical approach can yield be tter results under certain condition. The results for Rrs() inversions in this study indi cate some improvement to the algorithms. To compensate for CDOM fluorescence, all the Rrs() algorithms would benefit from using a larger CDOM slope coe fficient for the initial iterative fit or a correction function that fits the emission from CDOM fluorescence. While it is standard practice to measure Rrs() at zenith angles less than 45, higher zeniths should be avoided to limit sun glint. Under most conditions, the MODIS algorithm could benefit from the simple iteration method used to determine bbp() by the QAA algorithm. When bottom contribution is significant, the Rrs() optimization method can be improved by basing the bbp() value on an empirically determined valu e similar to the approach used by the MODIS algorithm. The Kd optimization method can be improved by changes in measurement technique. Lower solar zenith angles lead to greater wave focusing and need to be compensated for by increasing ne ar surface measurements of Ed(). Collection of scalar downwelling irradiance synchronous along with planar measurement would provide a direct measurement of the average cosine of downwelling irradian ce and eliminate an empirical equation in the algorithm. The coefficient for ag() needs to be locked to a specific value under certain cond itions. However, if wave focusing is minimized and the average cosine of downwe lling irradiance measured, solution to the CDOM slope coefficient could be iterated. By minimizing the effects of wave focusing and measuring the average cosine of dow n welling irradiance, the Kd() optimization method would be improved. PAGE 282 264 The more direct IOP measurements can be improved through changes in instrument design and path length corrections The ac9 can be improved by designs that would improve water flow through the instrume nt resulting in fewer entrapped bubbles. The ac9 needs a better light source that is more stable and produces lower heat. An LED light source and longer path length may impr ove the instrument. The Hydroscat6 needs a better post processing routine th at uses Morel's (1974) salt water scattering equations instead of assuming half the Morel (1974) va lues. The filter pad method could use beta factors that were more appr opriate to the species compos ition of the study area. The spectrophotometric ag() measurements need a longer path length instrument to achieve a higher signal to noise ratio. When compari ng the spectrophotometric methods to profiles or AOP inversions, a larger number of samp les need to be collected over depth and interpolated between to achieve an integrat ed water column value for the IOPs. These improvements could bring some of the more di rect methods closer to the AOP inversions in clear waters. The use of Hydrolight derived Rrs() values using input IOPs derived from Kd() inversions and the Hydroscat6 provided fo r determination of spectral bottom albedo values from the measured Rrs(). While the method does not require a priori knowledge of the bottom type, it does re quire accurate knowledge of Rrs(), anw(), bbp(), and depth for the water column. The algorithm is simpler than a direct measurement of the bottom albedo and can be used over a wider spat ial area. Since the algorithm assumes the bottom is a Lambertian reflector it may have e rrors at other angles for benthic surfaces with a bidirectional reflectance distribution func tion that is very different from isotropic. The algorithm functions best for optical depths based on Kd() times geometric depth that are less than 2 and solar zenith angles that are less than 30. This opt ical depth translates into a maximum depth of 20 m if the Kd() is 0.1 m1. However, greater depths and diffuse attenuation values may be possibl e with more accurate measurements. The algorithm is independent of the magnitude of the bottom albedo sin ce it is a function of the change in the average cosine of irradian ce by the presence of a bottom versus a deepwater column. Determining the color of the bottom would be useful in estimating the health of coral reefs and sea grass coverage. Spectral bottom albedo values are one of the resulting optical properties that can be dete rmined through the relationships between the different methods studied in this project as determined through the closure approach. PAGE 283 265 List of References Ackleson, S.G., W.M. Balch, and P.M. Holligan. 1994. Response of waterleaving radiance to particulate calcite and chlor ophyll a concentrations: A model for Gulf of Maine coccolithophore blooms. Journal of Geophysical Research. 99: 7483 7499. Agard, J.B.R., R.H. Hubbard, and J.K. Griffith. 1995. The relation between productivity and the biodiversity of Caribbean phytoplankton: applicability of Huston's dynamic equilibrium model. Journal of Experimental Marine Biology and Ecology. 202: 117. Agrawal, Y.C. and H.C. Pottsmith. 1989. Au tonomous, long term, in situ particle sizing using a new laser diffraction instrument. Proceedings. Oceans '89. 3: 15751580. Alldredge, A.L., U. Passow, and B.E. Logan. 1993. The abundance and significance of a class of large, transparent organic particle s in the ocean. Deep Sea Research. 40: 11311140. Andrfout, S., F.E. MullerKarger, E.J. Hochberg, C. Hu, and K.L. Carder. 2001. Change detection in shallow coral reef e nvironments using Landsat 7 ETM+ data. Remote Sensing of Environment. 78: 150162. Austin, R.W. 1974. Inherent spectral radian ce signals of the ocean surface. Ocean Color Analysis. SIO ref. 7410. Scripps Institute of Oceanography. La Jolla, Ca. 2.12.20. Austin, R.W., and T.J. Petzold. 1977. Consid erations in the design and evaluation of oceanographic transmissometers. Light in the Sea. J. E. Tyler. (Ed.) Dowden, Hutchinson and Ross, Stroudsburg. pp. 104120. Barnard, A.H., J.R. Zaneveld, and W.S. Pegau. 1999. In situ Determination of the Remotely Sensed Reflectance and th e Absorption Coefficient: Closure and Inversion. Applied Optics. 38: 51085117. Bellwood, D.R., T.P. Hughes, C. Folke, and M. Nystrm. 2004. Confronting the coral reef crisis. Nature. 429: 827833. PAGE 284 266 Bricaud, A., A. Morel, and L. Prieur. 1981. Absorption by Dissolved Organic Matter of the Sea (Yellow Substance) in the UV and Visible Domains. Limnology and Oceanography. 26: 4353. Bricaud, A., and D. Stramski. 1990. Sp ectral Absorption Coefficients of Living Phytoplankton and Nonalgal Biogenous Ma tter: A Comparison Between the Peru Upwelling Area and the Sargasso Sea. Limnology and Oceanography. 35: 562582. Behrenfeld, M.J., R.T. OMalley, D.A. Sieg el, C.R. McClain, J.L. Sarmiento, G.C. Feldman, A.J. Milligan, P.G. Falkowski, R.M. Letelier, and E.S. Boss. 2006. Climatedriven trends in contemporary ocean productivity. Nature. 444: 752755. Bryden, H.L., H.R. Longworth, and S.A. C unningham. 2005. Slowing of the Atlantic meridonal overturning circulation at 25 N. Nature. 438: 655657. Butler, W.L., 1962. Absorption of light by turbid materials. Journal of the Optical Society of America. 52: 292299. Campbell, J.W. 1995. The lognormal distribu tion as a model for bi ooptical variability in the sea. Journal of Geophysic al Research. 100: 13,23713,254. Cannizzaro, J.P. K.L. Carder, F.R. Chen, C.A. Heil, and G.A. Vargo. 2008. A novel technique for detection of the toxic dinoflagellate, Karenia brevis, in the Gulf of Mexico from remotely sensed ocean color data. Continental Shelf Research. 28: 137158. Carder, K.L., 1970. Particles in the eastern Equatorial Pacific O cean: their distribution and effect on optical parameters. Ph.D th esis. Oregon State University, Corvallis, Oregon. Carder, K.L., R.G. Steward, and P.R. Payne. 1985. Solidstate spectral transimissometer and radiometer. Optical E ngineering. 24: 863868. Carder, K.L. and R.G. Steward. 1985. A remotesensing reflectance model of a redtide dinoflagellate off west Florida. Li mnology and Oceanography. 30: 286298. Carder, K.L., W.W. Gregg, D.K. Costello K. Haddad, and J.M. Prospero. 1991. Determination of Saharan dust radiance and chlorophyll from CZCS imagery. Journal of Geophysical Research. 96: 53695378. Carder, K.L., R.G. Steward, G.R. Harvey and R.B Ortner. 1989. Marine humic and fulvic acids: their effects on remote sensing of ocean chlorophyll. Limnology and Oceanography. 34: 6881. PAGE 285 267 Carder, K.L., Z.P. Lee, J. Marra, R.G. St eward, and M.J. Perry. 1995. Calculated Quantum Yield of Photosynthesis of P hytoplankton in the Marine LightMixed Layers (59N, 21W). Journal of Geophysical Research. 100: 66556663. Carder, K.L., F.R. Chen, Z.P. Lee, S.K. Hawes, and D. Kamykowski. 1999. Semianalytic ModerateResolution Imaging Spectrometer algorithms for chlorophyll a and absorption with biooptical domains ba sed on nitratedepletion temperatures. Journal of Geophysical Re search. 104: 54035422. Carder, K.L., C.C. Liu, Z.P. Lee, D.C. Englis h, J. Patten, F.R. Chen, and J.E. Ivey. 2003. Illumination and turbidity effects on obs erving faceted bottom elements with uniform Lambertian albedos. Limnology and Oceanography. 48: 355363. Carder, K.L., F.R. Chen, J.P. Cannizzaro, J.W. Campbell, and B.G. Mitchell. 2004. Performance of MODIS semianalytic o cean color algorithm for chlorophylla. Advances in Space Research. 33: 11521159. Carder, K.L., J.P. Cannizzaro, F.R. Chen, and Z.P. Chen. 2006. MODIS SemiAnalytic Algorithm for IOP. Remote Sensing of Inherent Optical Properties: Fundamentals, Tests of Algorithms, and App lications. Lee, Z.P. (Ed.). Reports of the International O ceanColour Coordinating Group, No. 5, IOCCG, Dartmouth, Canada. pp. 6372 Catia M.D., J.A. Church, N.J. White, P.J. Gleck ler, S.E. Wijffels, P.M. Barker, and J.R. Dunn. 2008. Improved estimates of upperocean warming and multidecadal sealevel rise. Nature. 453: 10901093. Cattrall, C., K.L. Carder, K.J. Thome, and H.R. Gordon. 2002. Solarreflectancebased calibration of spectral radiometers. Geophys ical Research Letters. 29: 21 24 Chen, F.R., K.L. Carder, and D.K. Costello. 2004. Hyperspectral retrievals of bottom depth and albedo using a genetic optimization code. Ocean Optics XVII Proceedings. Office of Naval Research. Arlington VA. 6 p. Chen, R.F., and J.L. Bada. 1992. The fluor escence of dissolved organic matter in seawater. Marine Chemistry. 37: 191221. Clark, D.K. 1981. Phytoplankton algorithms for the Nimbus7 CZCS. J.F.R. Gower (Ed.). 'Oceanography from Space'. Plenum Press, New York. 227 P. Cleveland, J.S., and A.D. Weidemann. 1993. Quantifying absorption by aquatic particles: a multiple scattering correction for glassfiber filters. Limnology and Oceanography. 38: 13211327. PAGE 286 268 Costello, D.K., K.L. Carder, and J.E. Ivey 2002. Measurement a nd Interpretation of Diffuse Attenuation and Reflectance in Cl ear, DeepWater Environments: The Effects of TransSpectral Phenomena. 'Ocean Optics XVI Proceedings'. Davis, C.O., M. Kappus, J. Bowles, J. Fish er, J. Antoniades, and M. Carney. 1999. Calibration, characterization and firs t results with the ocean PHILLS hyperspectral imager. SPIEInternati onal Society of Optical Engineering Proceedings. 3753:160168 Dawes, C.J., R.C. Phillips, and G. Morrison. 2004. Sea grass communities of the Gulf Coast of Florida: Status and ecology. Florida Fish and Wildlife Conservation Commission Fish and Wildlife Research Institute and the Tampa Bay Estuary Program. St. Petersburg, FL. 74 pp. Dierssen, H.M., R.C. Zimmerman, R.A. Leathe rs, T.V Downes, and C.O. Davis. 2003. Ocean color remote sensing of seagrass and bathymetry in the Bahamas Banks by highresolution airborne imagery. Limnology and Oceanography. 48: 444455. Duntley, S. Q. 1942. The Optical Propertie s of Diffusing Materials. Journal of the Optical Society of America. 32: 6170. English, D.C., and K.L. Carder. 2006. Determining Bottom Reflectance and Water Optical Properties Using Unmanned Underwater Vehicl es under Clear or Cloudy Skies. Journal of Atmospheric and Oceanic Technology. 23: 2,3142,324. Esaias, W., M. Abbott, I. Barton, O.B. Brown, J.W. Campbell, K.L. Carder, D.K. Clark, R.H. Evans, F.E. Hoge, H.R. Gordon, W.M. Balch, R. Letelier, and P.J. Minnett. 1998. An overview of MODIS capabilities for ocean science observations. IEEE Transactions on Geosciences and Remote Sensing. 36: 12501265. Field, C.B., M.J. Behrenfeld, J.T. Rande rson, and P.G. Falkowski. 1998. Primary production of the biosphere: Integrati ng terrestrial and oceanic components. Science. 281: 237240. Garver, S.A., D.A. Siegel, and B.G. Mitchell. 1994. Variability in near surface particulate absorption spectra: what can a satellite ocean color imager see? Limnology and Oceanography. 39: 13491367. Gattuso. J.P., B. Gentili, C.M. Duarte, J.A. Kleypas, J.J. Middelburg, and D. Antoine. 2006. Light availability in the coastal o cean: impact on the distribution of benthic photosynthetic organisms and contri bution to primary production. Biogeosciences. 3: 895959. Gershun, A. 1939. The light field. Journal of Mathematics and Physics. 18: 51151. PAGE 287 269 Gregg, W.W., and K.L. Carder. 1990. A simple spectral solar irradiance model for cloudless maritime atmospheres. Li mnology and Oceanography. 35: 16571675. Gregg, W.W., M.E. Conkright, P. Ginoux, J.E. OReilly, and N.W. Casey. 2003. Ocean primary production and climate: Global d ecadal changes. Geophysical Research Letters. 30: 31 34. Gordon, H. R. and W. R. McLuney. 1975. Estim ation of the depth of sunlight penetration in the sea for remote sensing. Applied Optics. 14: 413416. Gordon, H.R., O.B. Brown, and M.M. Jacobs 1975. Computed Relationships Between the Inherent and Apparent Optical Prope rties of a Flat Homogeneous Ocean. Applied Optics. 14: 417427. Gordon, H.R., and D.K. Clark. 1980. Remote sensing optical properties of a stratified ocean: an improved interpretation. Applied Optics. 19: 34283430. Gordon, H.R., D.K. Clark, J.W. Brown, O.B. Brown, R.H. Evans, and W.W. Broenkow. 1983. Phytoplankton pigment concentrati ons in the Middle Atlantic Bight: comparison of ship determinations and CZCS estimates. Applied Optics.22:2036. Gordon, H.R., O.B. Brown, R.H. Evans, J.W. Brown, R.C. Smith, K.S. Baker, and D.K. Clark. 1988. A semianalytic radiance model of ocean color. Journal of Geophysical Research. 93: 10,90910,924. Gordon, H.R. 1989. Can the LambertBeer mo del be applied to the diffuse attenuation coefficient of ocean water? Limnology and Oceanography. 34: 13891409. HallockMuller, P, F.E. MllerKarger, and J. C. Halas. 1993. Coral Reef Decline. National Geographic Research a nd Exploration. 9: 358378. Hallock, P. 2005. Global change and m odern coral reefs: New opportunities to understand shallowwater carbonate depos itional processes. Sedimentary Geology. 175: 1933. Hawes, S.K., 1992. Quantum fl uorescence efficiencies of marine fulvic and humic acids. Master's Thesis. Dept. of Marine Science. University of South Florida. St. Petersburg, FL. 92 pp. Henyey, E.D., and J.L. Greenst ein. 1941. Diffuse radiation in the galaxy. Astrophysics Journal. 93: 7083. Hochberg, E.J., M.J. Atkinson, A. Apprill, S. Andrfout. 2003. Spectral reflectance of coral. Coral Reefs. 23: 8495 PAGE 288 270 Hochberg, E.J., and M.J. Atkinson. 2003. Capabilities of remote sensors to classify coral, algae, and sand as pure and mixed spectra. Remote Sensing of Environment. 85: 174189. Holden, H, and E. LeDrew. 2001. Effect s of the water column on hyperspectral reflectance of submerged cora l reef features. Bulletin of Marine Science. 69: 685 699. Hou, W., Z.P. Lee, and A.D. Weidemann. 2007. Why does the Secchi disk disappear? An imaging perspective. Optics Express. 15: 27912802. Hu, C., K.L. Carder, and F.E. MullerKarger 2000. Atmospheric co rrection of SeaWiFS imagery over turbid coastal waters: a practical method. Remote Sensing of the Environment. 74:195206. Hu, C., F.E. MullerKarger, D.C. Biggs, K.L. Carder, B. Nababan, D. Nadeau, and J. Vanderbloemen, 2003. Comparison of ship a nd satellite biooptical measurements on the continental margin of the NE Gulf of Mexico. International Journal of Remote Sensing. 24: 25972612. Ivey, J. E. 1997. A Comparison of the ac 9 Attenuation and Absorption Meter with the Quantitative Filter Pad Method within Turbid Estuarine Environments. Master Thesis, University of Sout hern Mississippi. 123 pp. Ivey, J. E., K.L. Carder, H. Hochman, J. Pa tch, and R. G. Steward. 1998. The Modulation of Optical Properties of Sombrero Key, Florida. Ocean Optics XIV proceedings. Ivey, J.E., K.L. Carder, F.R. Chen, and Z.P. Lee. 2002. Absorption measurements in optically clear waters. Ocean Optics XVI proceedings. CDROM. Jerlov, N.H. 1957. A transparencymeter for ocean water. Tellus. 9: 229233. Jerlov, N.H. 1976. Marine Optics. Elsevier. Amsterdam. 231 P. Kiefer, D. A., and J.B. Soohoo. 1982. Sp ectral Absorption by Ma rine Particles of Coastal Water of Baja California. Limnology and Oceanography. 27: 492499. Kirk, J.T.O. 1975. A theoretical analysis of the contribution of algal cells to the attenuation of light within natural waters. I. General treatment of suspensions of pigmented cells. New Phytology. 75: 1120. Kirk, J.T.O. 1981. Monte Carlo Study of the Nature of the Underwater Light Field in, and the Relationships between Optical Properties of, Turbid Yellow Waters. Australian Journal of Marine and Freshwater Research. 32: 517532. PAGE 289 271 Kirk, J.T.O. 1991. Volume Scattering Func tion, Average Cosines, and the Underwater Light Field. Limnology a nd Oceanography. 36: 455467. Kirk, J.T.O. 1992. Monte Carlo modeling of the performance of a reflective tube absorption meter. Applied Optics. 31: 64636468. Kirk, J.T.O. 1994. 'Light and Photosynthe sis in Aquatic Ecosystems'. Cambridge University Press. New York, New York. 509 P. Kirk, J.T.O. 1997. Pointsource integrat ingcavity absorption meter: theoretical principles and numerical modeli ng, Applied Optics. 36: 61236128. Kishino, M., M. Takahashi, N. Okami, and S. Ichimura. 1985. Estimation of the spectral absorption coefficients of phytoplankton in the sea. Bulletin of Marine Science. 37: 634642. Kramer, C.J.M. 1979. Degradation by sunlight of dissolved fluorescing substances in the upper layers of the Eastern Atlantic Ocean. Netherlands Journal of Sea Research. 13: 325329. Langebrake, L.C., C.E. Lembke, R.H. Weisberg R.H. Byrne, D.R. Russell, G. Tilbury, and R. Carr. 2002. Design and Initial Results of a Bottom Stationing Ocean Profiler. Oceans 2002 MTS/IEE Conf erence Proceedings. 1: 98103. Lee, Z.P., K.L. Carder, C.D. Mobley, R.G. Steward, and J.S. Patch. 1998. Hyperspectral remote sensing for shallow waters: I. a semianalytical model. Applied Optics. 37: 63296338. Lee, Z.P, K.L. Carder, C.D. Mobley, R.G. Steward, and J.S. Patch. 1999. Hyperspectral remote sensing for shallow waters: 2. de riving bottom depths and water properties by optimization. Applied Optics. 38: 38313843. Lee, Z., and K.L. Carder. 2000. Bandratio of spectralcurvature algorithms for satellite remote sensing? Applied Optics. 39: 43774380. Lee, Z.P., K.L. Carder, R.F. Chen, and T.G. Peacock. 2001. Properties of the water column and bottom derived from Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data. Journal of Geophys ical Research. 106: 11,63911,651. Lee, Z.P., and K.L. Carder. 2002. Effect of spectral band number s on the retrieval of water column and bottom properties from ocean color data. Applied Optics. 41: 21912201. Lee, Z.P., K.L. Carder, and R.A. Arnone. 2002. Deriving inherent optical properties from water color: a multiband quasianalytical algorithm for optically deep waters. Applied Optics. 41: 57555772. PAGE 290 272 Lee, Z.P., K.L. Carder, and K. Du. 2004. E ffects of molecular and particle scatterings on the model parameter for remotesensing re flectance. Applied Optics. 43: 49574964. Lee, Z.P. and C. Hu. 2006. Global distri bution of Case1 waters: An analysis from SeaWiFS measurements. Remote Sens ing of Environment. 101: 270 276. Lee, Z.P. (Ed.) 2006. Remote Sensing of I nherent Optical Properties: Fundamentals, Tests of Algorithms, and Applications. Re ports of the International OceanColour Coordinating Group, No. 5, IOCC G, Dartmouth, Canada. 126 pp. Lenes, J.M., B.P. Darrow, and C. Catt rall. 2001. Iron fertilization and the Trichodesmium response on the West Florida shelf. Limnology and Oceanography. 46: 12611277. Lesser M. P. and C. D. Mobley. 2007. Bat hymetry, water optical pr operties, and benthic classification of coral reefs using hyperspe ctral remote sensing imagery. Coral Reefs. 26:819829. Lewis, M.R., M.E. Carr, G.C. Feldman, W. Esaias, and C. Mc Clain. 1990. Influence of Penetrating Solar Radiation on the Heat B udget of the Equatorial Pacific Ocean. Nature. 347: 543545. Libes, S.M. 1992. 'An Introduction to Mari ne Biogeochemistry'. John Wiley & Sons, Inc. New York, NY. 734 pp. Loisel, H., D. Stramski, B.G. Mitchell, F. Fe ll, V. FournierSicre, B. Lemasle, and M. Babin. 2001. Comparison of the ocean i nherent optical properties obtained from measurements and inverse modeling. Applied Optics. 40: 23842397. Maffione, R.A., and D.R. Dana. 1997. Inst ruments and methods for measuring the backwardscattering coefficient of ocean waters. Applied Optics. 36: 60576067. Maritorena, S., A. Morel, and B. Gentili. 1994. Diffise reflectan ce of oceanic shallow waters: Influence of water depth and bottom albedo. Limnology and Oceanography. 39: 16891703. Mazel, C. H. 1997. Diveroperated instrument for in situ measurement of spectral fluorescence and reflectance of benthic ma rine organisms and substrates. Optical Engineering. 36: 26122617. PAGE 291 273 McIntyre, M.L. 2003. Testing a model for deriving bathymetry from airbourne hyperspectral data by comparisons with multibeam data. Thesis. University of South Florida. 79 P. McPhaden, M.J. and D. Zhang. 2002. Slowdown of the meridional overturning circulation in the upper Pacific Ocean. Nature. 415: 603608. Mitchell, B. G. and D. A. Kiefer. 1988. Chlorophyll a specific absorption and fluorescence excitation spectra for li ghtlimited phytoplankton. Deep Sea Research. 39: 639663. Mobley, C.D. (1994). 'Light and water: radiativ e transfer in natural waters'. San Diego, Academic Press. 592 P. Mobley CD, and L. K. Sundman. 2003. Effects of optically shallow bottoms on upwelling radiances: Inhomogeneous a nd sloping bottoms. Limnology and Oceanography. 48: 329336. Mobley, C.D., H. Zhang, and K.J. Voss. 2003. Effects of optica lly shallow bottoms on upwelling radiances: Bidirec tional reflectance distribution function effects. Limnology and Oceanography. 48: 337345. Mobley, C. D., D. Stramski, W. P. Bisse tt, and E. Boss (2004). Optical modeling of ocean waters: Is the Case 1 Case 2 clas sification still useful? Oceanography. 17: 6067. Mobley, C.D., L.K. Sundman, C.O. Davis, T. V. Downes, R.A. Leathers, M.J. Montes, J.H. Bowles, W.P. Bissett, D.D.R. Kohl er, R.P. Reid, E.M. Louchard, and A. Gleason. 2005. Interpreta tion of hyperspectral remotesensing imagery via spectrum matching and lookup tabl es. Applied Optics. 44: 35763592. Moore, C., M.S. Twardowski, and J.R.V. Zaneveld. 2000. The ECO VSFA multiangle scattering sensor for determination of the volume scattering function in the backward direction. Proceedings from Ocean Optics XV, Monaco Morel, A., 1974. Optical properties of pure wa ter and pure sea water. In: Jerlov, N.G. and E.S. Nielsen (Eds.). Optical Aspects of Oceanography. Academic Press, London. pp. 124. Morel, A., and L. Prieur. 1977. Analysis of variations in ocean color. Limnology and Oceanography. 22: 709722. Morel, A., and R. C. Smith. 1982. Terminology and units in optical oceanography. Marine Geodesy 5: 335349. PAGE 292 274 Morel, A., and B. Gentili. 1993. Diffuse refl ectance of oceanic wate rs. I. Bidirectional aspects. Applied Optics. 32: 68646879. Mueller, J.L., and R.W. Austin. 1992. O cean Optics Protocols for SeaWiFS Validation. S.B. Hooker and E.R. Firestone (Eds.) NASA Technical Memo. 104566, Vol. 5. NASA Goddard Space Flight Center Greenbelt, Maryland. 43 P. NASA. 2008. NASA Spacecraft Confirms Ma rtian Water, Mission Extended. Press Release. Ohlmann, J.C., D.A. Siegel, and C. Gautier. 1996. Ocean mixed layer radiant heating and solar penetration: a global analysis Journal of Climate. 9: 22652280. O'Reilly, J.E., S. Maritorena, B.G. Mitchell, D.A. Siegel, K.L. Carder, S.A. Garver, M. Kahru, and C. McClain. 1998. Ocean color chlorophyll algorithms for SeaWiFS. Journal of Geophysical Res earch. 103: 24,93724,953. Otis, D. B., K.L. Carder, D.C. English, and J.E. Ivey, 2004. CDOM transport from the Bahamas Banks. Coral Reefs. 23: 152160. Palandro, D. A., S. Andrfout, C. Hu, P. Hallo ck, F. E. MllerKarger, P. Dustan, M. K. Callahan, C. Kranenburg, and C. R. Beav er. 2008. Quantification of two decades of shallowwater coral reef habitat decline in the Florida Keys National Marine Sanctuary using Landsat data (19842002). Remote Sensing of Environment. 112: 33883399. Peacock, T.G. 1992. Some marine light s ources and their effects on remote sensing reflectance models. Thesis. Univer sity of South Florida. 72 P. Pegau, W.S., D. Gray, and J.R.V. Zaneveld 1997. Absorption of visible and nearinfrared light in water: the dependenc e on temperature and salinity. Applied Optics. 36: 60356046. Pettersson, H. 1934. A transparencymeter fo r seawater. Medd. O ceanographic Institute. Gothenberg, Ser. B 4. Petzold, T.J. 1972. Volume scattering functions for selected waters. Scripps Institute of Oceanography. 79 pp. Philander, S. G. 2004. Our Affair With El Ni o. Princeton University Press. Princeton, N.J. 274 pp. Poole, H.H., and W.R.G. Atkins. 1926. On the penetration of light in to sea water. Journal of the Marine Biological Associati on of the United Kingdom. 14: 177198. PAGE 293 275 Pope, R., and E. Fry. 1997. Absorption spectrum (380700nm) of pure waters, II, Integrating cavity measurements Applied Optics. 36: 87108723. Preisendorfer, R.W. 1961. Application of radia tive transfer theory to light measurements in the sea. Monograph. Inte rnational Union of Geodesy and Geophysics. Paris 10: 1130. Rahmstorf, S. 1994. Rapid climate transiti ons in a coupled oceanatmosphere model. Nature. 372: 8285. Reynolds, R.A., D. Stramski, V.M. Wright, and S.B. Wozniak. 2006. Measurement of the Volume Scattering Func tion using a Multiinstrume nt Approach. Proceedings. Ocean Optics OOXII Conference. CDROM. Sathyendranath, S., A.D. Gouveia, S.R. Sh etye, P. Ravidran, and T. Platt. 1991. Biological control of surface temperature in the Arabian Sea. Nature. 349: 5456. Siegel, D.A., J. Ohlmann, L. Wahburn, R. Bidi gare, C. Noose, E. Fields, and Y. Zhou. 1995. Solar Radiation, Phytoplankton Pigments, and Radiant Heating of the Equatorial Pacific. Journal of Geophysical Research. 100: 48854891. Siegel, DA, S. Maritorena, N.B. Nelson, M.J. Behrenfeld, and C.R. McClain. 2005. Colored dissolved organic matter and its influence on the satellitebased characterization of the ocean biosphe re. Geophysical Research Letters. 32: L20605. Smith, R. C. 1981. Remote Sensing and Depth Distribution of Ocean Chlorophyll. Marine Ecology Progress Series. 5: 359361 Smith, S.V., and J.T. Hollibaugh. 1993. Coastal metabolism and the oceanic organic carbon balance. Reviews of Geophysics. 31: 7589. Spinrad, R.W., K.L. Carder, and M.J. Perry. (Ed.) 1994. Ocean Optics. Oxford University Press. New York. 263 P. Subramanian, A., E. J. Carpenter, and P. G. Falkowski. 1999. Biooptical properties of the marine diazotrophic cyanobacteria Trichodesmium spp. II. A reflectance model for remote sensing. Limnology and Oceanography. 44: 618 627. Sweeney, C., A. Gnanadesikan, S.M. Griffies M.J. Harrison, A.J. Rosati, and B.L. Samuels. 2005. Impacts of shortwave penetration depth on largescale ocean circulation and heat transport. Jour nal of Physical Oceanography. 35: 11031119. PAGE 294 276 Truper, H. and C. S. Yentsch. 1967. Use of Glass Fiber Filters for the Rapid Preparation of in vivo absorption Spectra of Photosynthetic Bacteria. Journal of Bateriology. 94: 12551256. Twardowski, M.S., and P.L. Donaghay. 2002. Photobleaching of aquatic dissolved materials: Absorption removal, spectral alteration, and their interrelationship. Journal of Geophysical Resear ch. 107: 61 to 612. Tyler, J.E. and R.C. Smith. 1966. Submersible Spectroradiometer. Journal of the Optical Society of America. 56:13901396. Vastano, A. C., and S. E. Borders. 1984. Sea surface motion over an anticyclonic eddy on the Oyashio Front. Remote Sensi ng of the Environment. 16: 8790. Voss, K.J., C.D. Mobley, L.K. Sundman, J.E. Ivey, and C.H. Mazel. 2003. The spectral upwelling radiance distribu tion in optically shallow waters. Limnology and Oceanography. 48: 364373. Walsh, J.T. 1991. Importance of continenta l margins in the marine biogeochemical cycling of carbon and nitrogen. Nature. 350: 5355. Walsh, J. J., and K. A. Steidinger. 2001. Saharan dust and Florida red tides: The cyanophyte connection. Journal of Ge ophysical Research. 106: 11,597 11,612. Walsh J. J., J. K. Jollif, B. P. Darrow, J. M. Lenes, S. P. Milroy, A. Remsen, D. A. Dieterle, K. L. Carder, F. R. Chen, G. A. Vargo, R. H. Weisberg, K. A. Fanning, F. E. MullerKarger, E. Shinn, K. A. Stei dinger, C. A. Heil, C. R. Tomas, J. S. Prospero, T. N. Lee, G. J. Kirkpatrick, T. E. Whitledge, D. A. Stockwell, T. A. Villareal, A. E. Jochens, and P. S. Bo ntempi. 2006. Red tides in the Gulf of Mexico: Where, when, and why? Journa l of Geophysical Research. 111:146. Warrior, H., and K. Carder. 2007. An optical model for heat and salt budget estimation for shallow seas. Journal of Geophysical Research. 112: C12021. Werdell, P.J. and C.S. Roesler. 2003. Remote assessment of benthic substrate composition in shallow waters using multispectral reflectance. Limnology and Oceanography. 48: 557567. Wernand, M.R. 2008. The arcane colouring of natural waters: from Hudson(1600) to Raman (1930). IOCCG Report. 128 pp. Yentsch, C.S., 1962. Measurement of visible light absorption by part iculate matter in the ocean. Limnology and Oceanography. 7: 207217. PAGE 295 277 Zaneveld, J.R., R. Bartz, and J.C. Kitchens. 1990. A refletivetube absorption meter. Proceedings. Ocean Optics X. 1302: 124136. Zaneveld, J.R. 1994. Optical closure: from theory to measurement. Spinrad, R.W., K.L. Carder, and M.J. Perry. (Ed.) Ocean Optics. Oxford University Press. New York. pp. 5972. Zaneveld, J.R., J.C. Kitchen, and C. Moore. 1994. The scatteri ng error correction of reflectingtube absorption meters. Pr oceedings. Ocean Optic s XII Proceedings. 2258: 4455. Zaneveld, J.R., E. Boss, and A. Banard. 2001. Influence of surface waves on measured and modeled irradiance profiles. Applied Optics. 40: 14421449 Zaneveld, J.R., and E. Boss. 2003. The in fluence of bottom morphology on reflectance: Theory and twodimensional geometry model. Limnology and Oceanography. 48: 374379. Zar J.H., 1994. Biostatistical Analsysis. Pr entice Hall. Upper Saddle River, New Jersey. 662 P. PAGE 296 About the Author Jim Ivey took a round about way to his Ph.D. in optical oceanography. He graduated from the University of Georgia in 1986 with a BS in economics. He spent 7 years at various sales jobs before starting his Masters degree in Ma rine Science at the University of Southern Mississippi. He completed his Masters in 1997 and started at University of South Florida. Jim went on 43 research cruises, coau thored 5 papers, and authored 2 papers while at USF. He curre ntly works as a resear cher studying harmful algal blooms at the Fish and Wildlife Research Institute. xml version 1.0 encoding UTF8 standalone no record xmlns http:www.loc.govMARC21slim xmlns:xsi http:www.w3.org2001XMLSchemainstance xsi:schemaLocation http:www.loc.govstandardsmarcxmlschemaMARC21slim.xsd leader nam 2200397Ka 4500 controlfield tag 001 002029588 005 20090918081659.0 007 cr mnuuuuuu 008 090918s2009 flu s 000 0 eng d datafield ind1 8 ind2 024 subfield code a E14SFE0002939 035 (OCoLC)436998319 040 FHM c FHM 049 FHMM 090 GC11.2 (Online) 1 100 Ivey, James Edward. 0 245 Closure between apparent and inherent optical properties of the ocean with applications to the determination of spectral bottom reflectance h [electronic resource] / by James Edward Ivey. 260 [Tampa, Fla] : b University of South Florida, 2009. 500 Title from PDF of title page. Document formatted into pages; contains 277 pages. Includes vita. 502 Dissertation (Ph.D.)University of South Florida, 2009. 504 Includes bibliographical references. 516 Text (Electronic dissertation) in PDF format. 520 ABSTRACT: This study focuses on comparing six different marine optical models, field measurements, and laboratory measurements. Inherent Optical Properties (IOPs) of the water column depend only on the constituents within the water, not on the ambient light field. Apparent Optical Properties (AOPs) depend both on IOPs and the geometric underwater light field resulting from solar irradiance. Absorption (a) and scattering (b) are IOPs. Scattering can be partitioned into backscattering (b[subscript b]). Remote Sensing Reflectance (R[subscript rs]), the ratio of radiant light leaving the water to the light entering the water surface plane (E[subscript d]), is an AOP. R[subscript rs] is proportional to b[subscript b]/(a + b[subscript b]). Using this relationship, R[subscript rs] is inverted to determine both absorption and backscattering. The constituents contributing to both absorption and backscattering can then be further deconvolved using modeling techniques.The in situ instruments usually have a fixed path length while AOP measurement path length depends on the penetration and/or return of downwelling solar irradiance. As a consequence, AOP measurements use a longer path length than in situ instruments. If the path length of a direct IOP measurement instrument is too short, there may not be sufficient signal to determine a change in value. While the AOP inversions require more empirical assumptions to determine IOP values than in situ instruments, they provide a higher signal to noise ratio in clearer waters. This study defines closure as the statistical agreement between instruments and methods in order to determine the same optical property. No method is considered absolute truth. An R[subscript rs] inversion algorithm was best under most of the test stations for measuring IOP values.One exception was when bottom reflectance was significant, an inversion of diffuse attenuation (the change in the natural log of E[subscript d] over depth) was better for determining absorption and a field instrument was better for determining backscattering. The relationships between AOPs and IOPs provide estimates of unmeasured optical properties. A method was developed to determine the spectral reflectance of the bottom using IOP estimates and R[subscript rs]. 538 Mode of access: World Wide Web. System requirements: World Wide Web browser and PDF reader. 590 Advisor: Kendall L. Carder, Ph.D. 653 Absorption Irradiance Oceanography Backscattering Albedo 690 Dissertations, Academic z USF x Marine Science Doctoral. 773 t USF Electronic Theses and Dissertations. 4 856 u http://digital.lib.usf.edu/?e14.2939 