Visible-infrared remote-sensing model and applications for ocean waters

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Visible-infrared remote-sensing model and applications for ocean waters

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Visible-infrared remote-sensing model and applications for ocean waters
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Lee, Zhongping
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Tampa, Florida
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University of South Florida
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English
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xvi, 145 leaves : ill. ; 29 cm

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Remote sensing ( lcsh )
Optical oceanography ( lcsh )
Raman effect ( lcsh )
Dissertations, Academic -- Marine Science -- Doctoral -- USF ( FTS )

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Thesis (Ph. D.)--University of South Florida, 1994. Includes bibliographical references (leaves 127-137).

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University of South Florida
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University of South Florida
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020798878 ( OCLC )
33835091 ( ALEPH )
F51-00189 ( USFLDC DOI )
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VISffiLE-INFRARED REMOTE-SENSING MODEL AND APPLICATIONS FOR OCEAN WATERS by ZHONGPING LEE A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Marine Science University of South Florida December, 1994 Major Professor: Kendall L. Carder, Ph D.

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Graduate School University of South Florida Tampa, Florida CERTIFICATE OF APPROVAL Ph.D Dissertation This is to certify that the doctoral dissertation of ZHONGPING LEE with a major in the Department of Marine Science has been approved by the Examining Committee on October 25, 1994 as satisfactory for the dissertation requirement for the Doctor of Philosophy degree Examining Committee ---------------Major Professor: Kendall L. Carder. Ph D Member : Paula G Coble, Ph.D Member : Mark E Luther, Ph.D. Member : Carmelo R. Tomas, Eh.D. Member: Gabriel A. Vargo Ph.D

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ACKNOWLEDGEMENTS Frankly, I owe too much to all the players in the ocean optics group at the Department of Marine Science in the University of South Florida. Especially, I would like to thank Dr. Kendall L. Carder for his encouragement and guidance in the research and the nice working environment under his leadership; Tom Peacock for his tireless help in and out of science; Steve Hawes, for his thought ful discussions about gelbstoff, algorithm, and mu s ic-politics; Bob Steward, for his kindly help in data acquisition and reduction; and Bob Chen and Joan He s ler for their nice assistance in administrative affairs. Al so, I would like to thank Dr. C. 0. Davis (Jet Propulsion Lab), Dr. J L. Mueller (San Diego State Uni versity) for their in-water optical measurements, and Dr. J. Marra (Columbia University) for his primary production measurements.

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TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS ABSTRACT INTRODUCTION Introduction to Remote Sensing The Present Study and Structure PART A. THE OPTICAL BASIS AND THE FORWARD PROBLEM 1. APPARENT AND INHERENT OPTICAL PROPERTIES 1.1 Introduction 1.2 Quantities Describing the Light Field 1.3 Apparent Optical Properties (AOPs) 1.3.1 Irradiance Reflectance, R 1.3.2 Remote-sensing Reflectance, Rrs 1.3.3 Diffuse Attenuation Coefficient of Irradiance 1.3.4 Distribution Function and Average Cosine 1.4 Inh e rent Opti c al Properties (lOPs) 1.4.1 Absorption Coefficient 1.4 .1.1 Absorption Coefficient of Water Itself 1.4.1.2 Absorption Coefficient of Gelbstoff 1.4 1.3 Ab so rption Coefficient of Phytoplankton Pigments 1.4.1.4 Absorption Coefficient of Detritus 1.4.2 Volume Sc a ttering Function and Scattering Coefficient 1.4. 2.1 Volume Scattering Function, {3(cx) 1.4.2. 2 Scattering Coefficient, b IV v IX XIV 1 1 8 12 13 13 14 16 16 17 19 20 2 1 22 23 24 25 26 27 27 27

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1.5 Relationships between AOPs and lOPs 1. 5 .1 Sub-surface Irradiance Reflectance 1.5.2 Remote-sensing Reflectance 1.5.3 Diffuse Attenuation Coefficient of Downwelling lrradiance 2. MODEL OF THE REMOTE-SENSING REFLECTANCE 2.1 Introduction 2.2 Remote-sensing Reflectance of the Water Column (elastic scattering only), Rrsw 2.3 Remote-sensing Reflectance of Bottom Reflectance, Rr/ 2.4 Remote-sensing Reflectance of Gelbstoff Fluorescence, Rr! and Water Raman Scattering, Rrs R 3. DATA AND METHODS 3.1 Introduction 3.2 Remote-sensing Reflectance, Rrs 3. 3 Absorption Coeffi c ient of Particles and Pigments, aP and a"' 3.4 Absorption Coefficient of Gelbstoff, ag 3.5 Measurements of In-water Optical Properties, Kd and Rrs(O ) 4 RESULTS OF Rrs MODELING 4 1 Validation of Rrs Model 4.2 Model Results and Discussion 4.3 Contributions by R r! and RrsR 5. CONCLUSIONS OF PART A PART B. THE INVERSE PROBLEM AND APPLICATIONS 6. THE INVERSE PROBLEM 6.1 Introduction 6.2 Simulation of a"'(A) 6.2.1 Mathematical Functions 6.2.2 Empirical Relationship 6. 3 Derivation of the Absorption Coefficient from Rrs 7. RESULTS AND DISCUSSION OF THE INVERSE PROCESS 7.1 Comparison of a(440), a(486) and a(SSO) Derived Using Rrs and Kd Methods 7.2 Comparison of Rrs-derived a(440), a(486) and a(SSO) Using Simulated a"' and Measured aP 11 31 31 33 34 36 36 36 40 42 44 44 45 46 49 49 51 51 53 60 62 65 66 66 68 69 75 77 80 81 84

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7.3 Comparison of Rrs-derived a0(440) to G0(440) 8. APPLICATIONS 8.1 Introduction 8 2 Estimation of Chlorophyll Concentration 8.3 Estimation of the Gelbstoff Absorption Coefficient 8.4 Algorithm for the Absorption Coefficient at 490 nm, a(490) 8.5 the Water Color at Depth 8.6 Estimation of Primary Production 8. 7 Total Radiance (L1 ) from a Low-flying Aircraft (Blimp Shamu) 9. CONCLUSIONS OF PART B 10. AND FUTURE WORK 10.1 Summary 10.2 Future Work REFERENCES CITED APPENDICES APPENDIX 1. EXACT SOLUTION OF NADIR R, s(O") BY THE RADIATIVE TRANSFER EQUATION APPENDIX 2. DIFFUSE ATTENU ATION COEFFICIENT OF AN EXTENDED RADIANCE SOURCE APPENDIX 3. REMOTE-SENSING REFLECTANCE FROM GELBSTOFF FLUORESCENCE (R,/) AND WATER SCA TIERING (R,/) Ill 89 91 91 91 92 94 94 100 116 121 124 124 125 127 138 139 141 143

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LIST OF TABLES Table 1. Cruise Information where Data Were Collected and Used in this Study 9 Table 2 Recent Results for "Beta Factor" of GF/F Filter Pad 47 Table 3. Station Chosen for the Rrs Model Demonstration 52 Table 4. Model Parameters for Stations in Table 3 58 Table 5. Optical Component Contributions to Rrs of Stations in Table 3 60 Table 6 Parameters for the Empirical a9(") Simulation 76 Table 7 Results about PP Calculation of ML-ML, May 1991 109

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L I ST OF FIGURES Figure 1. Schematic Relationships between Water Color and In-water Constituents 4 Figure 2a. Map of the Locations where Fiel d Data Were Used 1 0 Figure 2b. Stations where Data Were Used t o Demonstrate Rrs Model 11 Figure 3. Examples of Downwelling (a) and Upwe ll ing (b) Irradiance Spec t ra 1 5 Figu r e 4. Examples of Irradiance Reflectance for Different Waters 17 Figure 5 Light Geometry 18 Figure 6 Examp l es of Remote sensing Reflectance for Different Waters 1 8 Figure 7a. Absorption Coefficients of Pure Water 22 Figure 7b. Examp l es of Absorption Coefficients of Gelbstoff 24 Figure 7c. Examples of Absorption Coefficients of Phytop l ankton Pigments 25 Figure 7d. Examples of A b sorption Coefficients of Detritus 26 Figure 8a. Volume Scattering Funct ion of Pure Sea Water 28 Figure 8b. Volume Scatte r ing Function of Natural Waters 28 Figure 9. Spectrum of the Back-scattering Coefficients of Pure Sea Water 30 Figure 10. Examples of Bottom A l bedo Spectra 42 v

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Figure 11. Fresnel Reflectance of Sea Water (n ... = 1 .34) 46 Figure 12. Recent R esults for "Beta Factor" of GF/ F Filter Pad 48 Figure 13a Detailed R s Model Components for Station TAO 1 54 Figure 13b. Detailed R,s Model Components for Station G027 54 Figure 13c. Detailed R,s Model Components for Station C014 55 Figure 13d. Detailed R ,5 Model Components for Station CO 19 55 Figure 14. Measured vs. Modeled R,s for the Selected Stations 57 Figure 15a. Measured vs. Simulated a9 for Station G003 71 Figure 15b. Mea sured vs. Simulated a9 for Station G004 71 Figure 15c. Mea sured vs. Simulated a9 for Station G015 72 Figure 15d. Measured vs. Simulated a9 for Station C015 72 Figure 16a Param eter F of a9 Simulation vs. ai440) 7 3 Figure 16b. Parameter a2 of a9 Simulation vs. a9( 440 ) 73 Figure 16 c R at io a9/ a9 1 vs. a9(440) 74 Figure 17 a Comparison of R ,5-derived to K[derived a(440). For Detail s See Text 82 Figu r e 1 7 b. Comparison of R ,5derived to K[derived a(486) For Detail s See Text 83 Figure 17c. Comparison of R ,5derived to K [ derived a(550). For Details See Text 84 Figure 18a Comparison of R,5derived a(440) Using Simulated a9 and M easu red a P 86 Figure 18b Comparison of R ,5-derived a(486) Using Simulated a9 and Measured aP 87 VI

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Figure 18c. Comparison of R n -derived a(550) Using Simulated a0 and Measured a P 88 Figure 19. Comparison of Rrs Derived 440) to the Measured a9(440) 89 Figure 20. Rrs Derived X vs. Measured ai 440) 94 Figure 21a. a( 490) vs Rn( 442)/ Rn-(550) and Rn-(520)1 Rrs(560) 96 Figure 21b Comparison of the a(490) Algorithms 96 Figure 22a. Measured vs Modeled Ei440) of Station G010 98 Figure 22b. Mea s ured vs. Modeled E i 486) of Station GO 10 98 Figure 22c. Measured vs Modeled Ei520) of Station GO 10 99 Figure 22d Measured vs Modeled Ei550) of Station GO 10 99 Figure 23a. Measured vs. Modeled PAR of May 17 in ML-ML 107 Figure 23b. Measured vs Modeled PAR of May 20 in ML-ML 107 Figure 23c. Measured vs. Modeled PAR of May 22 in ML-ML 108 Figure 23d. Measured vs. Modeled PAR of May 24 in ML-ML 108 Figure 24a. Measured vs. Modeled PP of May 17 in ML-ML 110 Figure 24b Measured vs. Modeled PP of May 20 in ML-ML 110 Figure 24c. Measured vs Modeled PP of May 22 in ML-ML 111 Figure 24d. Measured vs. Modeled PP of May 24 in ML-ML 111 Figure 25. Measured vs. Modeled PP of ML-ML May 1991 112 Figure 26a. Measured vs Modeled L, of Station SH04 117 Figure 26b. Measured vs Modeled L, of Station SH34 117 Figure 26 c. Measured vs. Modeled L, of Station SH35 118 Vll

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Figure 27a. Measured vs. Modeled Rrs of Station SH04 119 Figure 27b Measured vs. Modeled Rrs of Station SH34 119 Figure 27c. Measured vs. Modeled Rrs of Station SH35 120 Figure 28. Schematic Light Field of an Extended Lambertian Source 141 Vlll

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LIST OF SYMBOLS Symbols units Description a m' Total absorption coefficient, a.,.. + a& + aP adg m' Absorption coefficient of t he sum of detritus and gelbstoff ad, g ,p,w , m Absorption coefficient of detritus, gelbstoff particles, water, and pigments, respectively a p .d. A v erage percentage difference, u s ed to quantify the d ifferen c e between the measured and mode l ed Rrs a<>I .<>2 m' Ab s orption coefficient of p i gments at the blue and red peak s, r espec t ively AI mg / m3 Leading parame ter for pigment concentration algorithm A 2 Exponent par ameter for pigment concentration algorithm AOP Apparent optical property AVG>-1 Al Avera g e val ue i n the range of 'AI to 'A2 b m' Scattering coeffic i ent bb ml Backscattering coefficient bbw,bp m Backscattering coefficient of pure sea waters particles, respective l y 1/ m Water Raman scattering coefficie n t B m Ratio of the volume filtered to the effective surface area o n t h e fil ter pad IX

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c m-1 Beam attenuation coefficient, a + b [C] mo/ m3 l:> Concentration of phytoplankton pigments plus phaeopigments [chl a] mg/m3 Concentration of phytoplankton pigments Dd,u Distribution function for downwelling, upwelling light field, respectively {Dd} Vertically averaged downwelling distribution function Ed,u W/m2 Downwelling, upwelling irradiance, respectively E o W/m2 Scalar irradiance Eod,ou W / m2 Downwelling upwelling scalar irradiance, respectively Eq 0 Ein/ m2 Quantum scalar irradiance E w u W/m2 Upwelling irradiance from water column (elastic scattering only) f Parameter to adjust the measured a F Parameter to simulate a g Con stant to r e l a te R s and b vf a G Constant to relat e R and bvfa H m Water depth I W /sr Radiant inten sity IOP Inherent optical property j radian Subsurface solar zenith angle k m 1 Dif fuse attenuation coefficient of radiance Kdu m 1 Diffuse attenuation coefficient of downwelling, upwelling irradiance, respectively L W / m2/s r Radiance X

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L A,G,R,I W / m2/ sr Radiance for aerosol, diffuse reflector, Rayleigh scattering, and total Ld,u W / m2/s r Radiance in downwelling, upwelling hemi s phere respectively Lsty W / m2/sr Radiance from sky light which enters a remote sensor by the surface reflectance Lw u W / m2/sr Upwelling radiance from water column (elastic scattering only) L.,.. W / m2/ sr Water-leaving radiance L bj.R,>< .... W /m2/sr Water-leaving radiance for bottom reflectance, gelbstoff fluore sce n ce, water Raman scattering and water column (elastic scattering only), respectively n.,.. Refractive index of sea water OD Optical density PAR Ein / m2/s Photosynthetic available radiance pp mol C / m3 Primary production Q sr Ratio of irradiance to radiance Qm sr "Q factor" for mole c ular scattering R Irradiance reflectance R G Reflectance of a diffuse reflector Rrs sr-1 Remote-sensing reflectance R bj.R, w rs sr-1 Remote-sensing reflectance from bottom reflectance, gelbstoff fluorescence, water Rama n sca ttering and water column (elastic scattering only) respectively R w Irradiance reflectance from water column (elastic scattering only) XI

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s d,g,dg nm1 Spectral slope of absorption coefficient of detritus, gel bstoff, and the sum of detritus and gelbstoff, r espective l y t A i r-sea interface transmittance Tb.p T ransmission spectra of the b lank pad, sample pad, respective l y [YS] Concen tra t ion of gelbs toff (yellow substance) a radian Scattering angle abJ radian Scattering ang l e in the backward, forward d irection, respective l y {3 m-1sr-1 Volume scattering funct i on (VSF) f3w,p m-1sr-1 VSF of pu r e sea water, particles, respective l y {3b m-1sr-1 Light-averaged-backwa r d-VSF f3ie m-1sr-1 Volume scattering functio n of inelastic scattering {3pad Path-length elongatio n factor of filter pad Offset of sun glint due t o waves or foam cp radian Azimuth ang l e cJ> mo l C/Ein Quantum yie l d of photosynthesis c/>m mo l C/Ein Maximum quantum yiel d of photosynt h esis 'Y Ratio of [ chi a ] to tota l pigment con centration [C] K m-1 Quasi-diffuse attenuation coefficient, a + bb f.. n m Wavelength A_, nm Excita t ion wavel ength for i nelastic scattering 'TJ Quantum efficie n cy of gelbstoff fluorescence Xll

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1Jb Exponent for particle backscattering coefficient Vt m -1nm-1 Inelastic scattering coefficient 'T = KH, diffuse optical length 'TA,G Optical length of air, gas, re spec tively J.l.d.u Average cosine for downwelling, upwelling irradiance, respecti ve! y p Bottom albedo r Fresnel reflectance e radian Zenith ang le e a w radian Zenith angle of water-leaving radiance in the air, water, respectively II m2/ Ein Photoi n hibition parameter w sr Solid angle X Ill

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VISffiLE-INFRARED REMOTE-SENSING MODEL AND APPLICATIONS FOR OCEAN WATERS by ZHONGPING LEE An Abstract Of a dissertation submitted in partial fulfillment of the requirement s for the degree of Doctor of Philosophy Department of Marine Science University of South Florida December 1994 Major Professor: Kendall L. Carde r Ph.D. XIV

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Remote sensing has become important in the ocean sciences, especially for research involving large spatial scales. To estimate the in-water constituents through remote sensing, whether carried out by satellite or airplane, the signal emitted from beneath the sea surface, the so called water-leaving radiance (L..), is of prime importance. The magnitude of L"' depends on two terms: one is the intensity of the solar input, and the other is the reflectance of the in-water constituents. The ratio of the water-leaving radiance to the downwelling irradiance (E d ) above the sea surface (remote-sensing reflectance, R r J is independent of the intensity of the irradiance input, and is largely a function of the optical properties of the in-water constituents. In this work, a model is developed to interpret Rrs for ocean water in the visible-infrared range In addition to terms for the radiance scattered from molecules and particles, the model includes terms that describe contributions from bottom reflectance, fluorescence of gelbstoff or colored dis s olved organic matter (CDOM), and water Raman scattering. By using this model, the measured Rrs of waters from the West Florida Shelf to the Missis s ippi River plume which covered a [chl a] (concentration of chlorophyll a) range of 0 .07-50 mg/ m3 were well interpreted The average percentage difference (a.p.d.) between the measured and modeled Rrs is 3.4%, and, for the shallow waters, the model-required water depth is within 10% of the chart depth. Simple mathematical simulations for the phytopl a nkton pigment a bsorption coefficient (a4>) are sugge s ted for using with the Rrs model. The invers e problem of Rm which is to analytically derive the in-w a t e r c on s tituents from Rrs data alone, XV

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can be solved using the a9 functions without prior knowledge of the in-water optical properties. More importantly, this method avoids problems associated with a need for knowledge of the shape and va lue of the chlorop h yll-specific absorption coefficient. The simulation was tested for a wide range of water type s, including waters from Monterey Bay, the West Florida Shelf and the Mississippi River plume. Using the simulation, the Rrs-derived in-water absorption coefficients were consistent with the values from in-water measurements (r2 > 0.94, slope 1.0). In the remote-sensing applications, a new approach is suggested for the estimation of primary production based on remote se nsing Using this approach, the calculated primary production (PP) values based upon remotely sensed data were very close to the measured values for the euphotic zone (r = 0.95, s lope 1.26, and 32% average difference), while traditional, pigment-based PP model provided values only one -third the size of the measured data. This indicates a potential to significantly improve the accuracy of the estimation of primary production based upon r emote sensing. Abstract Approved: ---------------Major Professor: Kendall L. Carder Ph.D. Date Approved: ctJd. c::?51 /CJ
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INTRODUCTION Introduction to Remote Sensing Remote sensing has become an important tool in the study of ocean science, especially for the synoptic research of large bodies of water, because a large region of the world oceans can be viewed by a remote sensor in a very short time. For example, the Nimbus-7 and TIROS satellites had repeat cycles of 2 days at the equator with > 1 km pixel diameter; at the other end of the scale, however a blimp can transit Tampa Bay in mere hours measuring at high resolution (-8 x 8 m2 ) and lingering long enough to observe changes with time. The main purpose of oceanic remote sensing in the visible-infrared region of the spectrum is to remotely derive concentrations of certain constituents in the water (principally phytoplank-ton dissolved organic matter and suspended inorganic sediments) to estimate the oceanic primary production and to understand ocean circulation The derivation of these constituents through remote sensing, whether by satellite or aircraft, depends on the signal emitted from beneath the sea surface, the so called water-leaving radiance L.,.,('A) (definitions of variables are in the List of Symbols ; the functionality of one variable to another may not be explicitly expressed unless it is needed for further clarity) or the spectrally digitized water color. There

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are two approaches to formulate this derivation from measured L,.. : one is empirical and the other is analytical The empirical approach, such as the Coastal Zone Color Scanner (CZCS) algorithm for pigments [Gordon et al. 1983], is most often used at present. 2 The empirical approach is based on observations of the change of water color (spectral ratios) as change of water constituents, and statistical methods are used to find the apparent relationship of one variable to another. Ocean waters show a wide variation of colors, ranging from dark blue through blue/ green, green, and green/yellow [Jerlov 1976]. For clear sky days, blue water is usually found in the open ocean, where the water is clear, deep, and very few light absorbers such as phytoplankton are present. Pure sea water (which means the sea water without su s pended particles and dissolved organic materials) is a good absorber for wavelengths longer than 570 nm [Smith and Baker 1981] For upwelling regions, water color turns to green due to the increased concentration of phytopl a nkton and its associated degradation products (gelbstoff and detritus) which are strong absorbers in the blue/green bands [Jeffrey 1980, Bricaud eta!. 1981 Ro es ler et al 1989] For coastal (especially shelf) regions gelbstoff (yellow substance) or colored dissolved organic matter (CDOM) is abundant due to land run-off and absorbs strongly in the blue, turning the water to greenish yellow colors Based on the above observations, it is easy to qualitatively scale the concentrations of in-water constituents such as chlorophyll a ([chi a]) and gelbstoff ([YS]) based on ocean color and this is the basis for the CZCS algorithm

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3 The CZCS algorithm is a power law of the ratio of L,..(443) /L,.. (550), which was empirically developed. Its accuracy in deriving pigment concentration is about a factor of 2 [Gordon and Morel 1983] for the oligotrophic ocean, and is much worse for coastal waters This is because the water color is affected by constituents in addition to chlorophyll alone, especially in coastal areas. Water color signals, as observed immediately above the ocean's surface, depend upon the incident irradiance and the concentration and distribution of the in-water constituents. The waters will appear bluer on a bright, sunny day than on an over-cast cloudy day as there is relatively more blue light entering the sensor from reflected sky light rather than cloud light. At the same time, in-water constituents which can affect the water color include chlorophyll, gelbstoff, detritus, bacteria, and inorganic particles. Transpectral responses (water Raman scattering gelbstoff fluorescence) and bottom reflectance further complicate matters. This is why simple ratios of L..,'s do not always work well to derive [chl a] [Carder et al. 1986], especially for coastal waters, when there may be a strong bottom influence Figure 1 illustrates the schematic relationships between water-leaving radiance and in water components. Since there are many components in the water which can affect the water color, it is necessary to separate their individual influences if we want to improve the algorithm. This favors the analytical approach. For the purpose of deriving in-water constituents first it is essential to understand how each component affects the optical signal. Only after this step, can we have the potential to analytically derive the individual component from the remotely measured signal alone. So, there are two

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4 x sensor I ---I Rrs('A) L.)'A) t Ej..'A) 'Lf I LR/ a(A.), chi a, YS, ... i L > > > > > > > 7 j 7 7 > ; ; ; 7 7 ) 7 7 ; ; ) ) /. / / / / I bottom I_--_J Figure 1 Schematic Relationships between Water Color and In-water Constituents. steps to the analytical approach as pointed out by Morel [19 80 ] For the remotesensing technique, first is the forward step (or the forward problem), i.e. to interpret the observed colo r based on the measurement of eac h component (solid arrow in the box of Figure 1); second is the backward step (or the inverse problem), i.e. to derive each component just from the remotely measured signal (dashed arrow in the box of Figure 1). The forward problem can largely be solved based upon measurements of the optical components. If a few parameters prove difficult to measure, they may be

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simulated based on theoretical grounds. This step is important not only for the understanding of the optical scenario, but also for the guidance of future theoretical and experimental studies In the forward problem, as upwelling light depends upon the intensity of input irradiance, subsurface irradiance reflectance (R(O-)) and remote-sensing reflectance (Rrs) are defined as the ratio of upwelling irradiance to downwelling irradiance just below the surface and the ratio of the water-leaving radiance (LJ to the downwelling irradiance (Ed) above the sea surface, respectively. In this way, R(O-) and Rrs will be independent of the intensity fluctuation of the input irradiance, and largely a function of the optical properties of the in-water constituents. Since Ed can be very precisely predicted from models [Gregg and Carder 1990 Bishop and Rossow 1991], it is easy to calculate Lw if we know how to accurately determine Rrs 5 Optical models have been developed for the subsurface irradiance reflectance R(O) [Gordon et al 1975, Morel and Prieur 1977 Gordon 1989b Kirk 1984, 1991], but satellites measure the upwelling radiance above the water surface To use satellite radiance data, it is necessary to know how to interpret remote-sensing reflectance instead of irradiance reflectance Models were suggested by Carder and Steward [1985] and Peacock et al. [1990] to explain the measured R m but in each case no bottom reflectance, gelbstoff fluore sce nce or water Raman scattering were included. Also in these works a somewhat arbitrary "Q factor" [Austin 1974] was used. For the open ocean, in-water constituents are dominated by phytoplankton particles and their derivatives As a result, Rrs is easier to interpret, and is largely

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dependent on the concentration of chlorophyll. For these "case 1" [Morel and Prieur 1977] waters, Monte Carlo simulations [Gordon et al. 1988, Morel and Gentili 1993] have been made for Rrs
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coefficient) to represent the "effective" attenuation coefficient. It is not clear, however how to express the "effective" attenuation coefficient for Rrs. The inverse problem is to use remotely measured data to derive the absorption and scattering properties and to estimate in water constituents such as [chi a], [YS], etc These derived values can be used to model the spectral light at depth [Sathyendranath and Platt 1988] and /or to estimate primary production [Morel 1988, Balch et al 1992] Analyti c ally, not much improvement has been made for the 7 inverse problem in the past studies, mainly becau s e it is not easy to accurately express the change of each component by a few parameters In the application of remote sen s ing, emp i rical and semi analytical approache s have been studied in the estimation of [chi a], and efforts have been made to estim a te the primary production based on pi g ment concentration and empirical chlorophyll specific ab s orption coefficients [Morel 1991, Platt et al. 1991, Balch et al 1992] But as the chlorophyll specific abs orption coefficient varies significantly from sample to sample [Morel and Bricaud 1981, Bricaud and Stram ski 1990 Carder et al. 1991, Carder et al. 1994], the concentration of chlorophyll cannot be derived accurately from remote sensing without prior knowledge of the chlorophyll-specific absorption coefficient, which will further influence the primary production Therefore for cases where only water-leaving radiance (or remote sensing reflectance) is available better methods are needed for the derivation of the in-water absorption coefficient and the estimation of primary production

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The Present Study and Structure This contribution uses in-water and remote-sensing optical data to develop methodologies that can be used with present and new aircraft and spacecraft sensors to quantify biological, chemical and physical properties of the surface waters from open ocean to coastal waters. In this study, a mathematical model is first developed to interpret the remote sensing reflectance (solid arrow in the box of Figure 1) based on previous theoretical and experimental studies. In the model, terms to describe contributions from bottom reflectance, gelbstoff fluorescence and water Raman scattering are developed In addition hyperspectral Rrs measurements taken from waters ran g ing from the West Florida Shelf to the Mississippi River plume are selected to demonstrate the model. Differences between the modeled and measured Rrs are discussed 8 Second, new approaches are suggested for the inverse problem (dashed arrow in the box of Figure 1), which include mathematical and empirical simulations for the absorption curves of phytoplankton pigments (aq,). With these simulations, R r s or upwelling radiance above the surface (L"(O+)) can be modeled when there are no in water measurements available Alternatively the in water absorption coefficient can be derived from remote signals alone, and the spectral light field at depth as well as the primary production can be calculated. Part A of this manuscript describes the optical basis of remote sensing and the model development. It is divided into 4 chapters: Chapter 1, the optical properties of

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Table 1. Cruise Information where Data Were Collected and Used in this Study. I Cruise Name I Location I Period I Water Type Monterey (MA) Monterey Bay Sep. 1989 green Monterey (MB) Monterey Bay Oct. 1989 green TBX1 (TA) West Florida Shelf Mar. 1990 shallow, green ML-ML1 (ML) North Atlantic May-June 1991 blue TBX2 (TB) Wes t Florida Shelf May 1992 green, blue GOMEX (GO) Gulf of Mexico April 1993 green, blue COLOR (CO) Gulf of Mexico May-June 1993 dark, green SHAMU (SH) Tampa Bay Jan. 1993 shallow Note: Characters in parenthe ses will be used in text and tables as a short name. pure sea water, gelbstoff and phytoplankton pig ments, and the relationships between the apparent and inherent optica l properties; Chapte r 2, model development for remotesensi n g refle ctance; Chapter 3, data u sed and measurement methods; Chapter 4, model r esults; and Chapter 5, conclusions of part A. Part B presents the ways to solve the inverse problem and discusses some applications of remote sensing: 9 Chapter 6, the m et hod s suggested to so lve the inverse problem; Chapter 7, comparisons of the derived absorptio n coefficient from R,s inversion and that from Kd; Chapter 8, discussion of the r emote-se n sing applications, with a focus on primary production ; Chapter 9, conclusions of part B; and Chapter 10, summa ry of this study and expectations for futur e work. Data used in this study came from cruises during the period of 1989 to 1993 I

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37" 36 45' 1---...-------r-'---......,....-----.,J 36 30' 122 15' 121' 121' 93 92 91 90 Figure 2a. Map of the Locations where Field Data Were Used. 89" 820" 15 r 2F / 10" -ATLANTIC OCEAN GULF OF MEXICO as a? 86 as FARROR IS LANDS t 84 30 29 28 27 26 83 lO

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II which covered a wide range of water types, such as h i gh-latitude North Atlantic waters; sub tropic waters of Monterey Bay; gelbstoff rich, shallow waters of the West Florida Shelf; clear waters in the Loop Current ; and the phytoplankton bloom waters in the Mississippi River plume Table 1 summarizes the cruise information, Figure 2a shows the locations of the data collection and Figure 2b zooms in on the stations where Rn curves are used for the model demonstration 31 *March 90 OA.pr i l 93 OJune 93 30 Q) "0 :J 29 ...., 0 _J 28 -92 -90 -88 -86 -84 -82 Longitude Figure 2b. Stations where Data Were Used to Demonstrate Rn Model.

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12 PART A THE OPTICAL BASIS AND THE FORWARD PROBLEM

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13 CHAPTER 1 APPARENT AND INHERENT OPTICAL PROPERTIES 1.1 Introduction There are two kinds of optical properties which relate to the in-water constituents [Presendorfer 1976]: apparent optical properties (AOPs) and inherent optical properties (lOPs) AOPs are functions of both the light field and the in-water constituents, whereas lOPs have no relation to the light field and are solely dependent on the distribution and optical character of the in-water constituents. AOPs are easy to measure routinely in optical ocean studies, but difficult to relate to in-water constituents. For lOPs, the situation is reversed. One goal of optical oceanography is to derive the lOPs from the AOPs, then to evaluate the physical biological and /or chemical conditions of the water and global ocean. This process involves some optical quantities that can be measured directly, such as the radiance and irradiance fields The connections between these optical quantities and the lOPs are through the AOPs In this chapter, we will briefly discuss these optical quantities and properties.

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14 1.2 Optical Quantities Describing the Light Field The optical quantities used most widely in describing the light field are radiant intensity, radiance, vector irradiance, and scalar irradiance: Radiant intensity, I(z, 8,
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,-... s C\l s .._.. t:;q 2 0 400 (a) 0.08 0.04 0.00 400 (b) 0 1m e 4 m \1 8 m 'Y 12m .... ---. .. 500 600 700 0 1m 4 m \1 8 m 0 0 _.\! 0 I ', '-" ev . ', \l \1. '\1. ---' --' 500 600 700 wavelength (nm) Figu r e 3. Examples of Downwelling (a) and Upwelling (b) Irr a diance Spectra (Courtesy of Dr. J. L. Muell e r ) 15

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16 measured at a poi nt in space, so Eo = J. L(6,q> )dw 4n (2) This term is appropriate for evaluating the flux received by a phytoplankton cell It is useful to divide the scalar irradiance into downwelling (00) and upwelling (Eou) components, which are integral s of the radiance distribution over the upper or lower hemisphere, respectively, Eod = J L(6,q> )dw 2 n E = J L(6,q>)dw ou -2n (3) Both vector and scalar irradiance have unit s of W 1 m2 1 3 Apparent Optical Properties (AOP s ) AOPs come from simple manipulation of the optical quantities and are jointly dependent on the lOPs and on the distribution of the amb i ent light field The important AOPs are the irradiance reflectance (R), remote-sensing reflectance (RrJ, and the diffu se attenuation coefficients for downwelling (K,J and upwelling (K") irradiance 1.3.1 Irradiance Reflectance, R Irradiance reflectance (or irradiance ratio) R(z), is the ratio of the upwelling to

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0 .04 I I 0 G010 G004 I -0 0.02 ,.... 0.00 400 I 500 600 wavelength (nm) Figure 4 Examples of lrradiance Reflectance for Different Waters. (Courtesy of Dr. J L. Mueller) the downwelling irradiance at a given depth z in the light field: R(z) = Eu(Z) Ej.z) 700 R has no units. Figure 4 shows examples of sub-surface R for two different water types, where [chl a] was 0.12 mg/m3 for GOlO, and 7.4 mg/m3 for G004. 1.3.2 Remote-sensing Reflectance, Rrs Remote-sensing reflectance, Rm is generally defined as the ratio of the upwelling radiance to the downwelling irradiance at a given depth 17 (4)

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Q Sun Jl E)z) Figure 5. Light Geometry 0.01 2 ---0 .006 -...... ---"' 0.000 400 500 600 700 wavelength (nm) water G022 G020 G005 GOO! 800 Figure 6. Examples of Remote sensing Reflectance for Different Waters. 18

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19 (5) where ew is the in-water zenith angle and !p is the azimuth angle from the solar plane, respectively, for the upwelling radiance L.,. Figure 5 shows the light geometry. Rrs has the units of steradian 1 (sr -1). Since a satellite or aircraft sensor measure s the radiance leaving the water surface, a very useful form of Rrs is Lw(0\8 a''P) EJ.O+) (6) i.e., the ratio of the water-leaving radiance to the downwelling irradiance just above the surface. Where ea is the in-air zenith angle of the water-leaving radian ce, and sin(8a) = n w sin(8,..) (n w is the refractive index of sea water). In most cases, 8a is within 30 and IP is about 900 from the solar plane for ship-board measurements In the following text, 8 and IP may not be explicitly shown for the sake of brevity. Figure 6 shows examples of Rrs of different waters, with [chi a] of 16 .2, 2.4, 0.6 and 0 5 mg/m3 for stations GOO 1, G005, G020, and G022, respectively 1 .3.3 Diffuse-attenuation Coefficient of Irradiance This property is divided into two components; one for the downwelling irradiance, Kd, and another for the upwelling irradiance, K.,. These represent the rate

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20 of change of the natural log of the irradiance with depth, d ln[Ejz)] Kd = ----dz d ln[E/z)] dz (7) The minus before the derivative is to force Kd and Ku to be positive, as z is positive downward. The units for K are m -1 Similar to Lambert-Beer's Law [Gordon 1989a], this definition clearly indicates that, in any absorbing and scattering medium (in this case sea water), all the quantities describing the light field change with depth z. The change is typically a decrease in Ed and Eu with increasing depth, in an approximately exponential manner. So it is convenient to specify the rate of change as the change of the natural logarithm of the value with depth. When the rate of change and value at one depth are known (e.g. Kd and EiO)), it is possible to estimate the value at another nearby depth for a well mixed ocean 1. 3.4 Distribution Function and Average Cosine Distribution functions (Diz) and Du(z)) and average cosines (""j;iz) and ""j;u(z)) for downwelling and upwelling light, respectively, are defined as

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21 Dj.z) 1 ---= EJ.z) Ej.z)' Dll(z) = _1_ = J.LII(z) (8) J.Lj.Z) These factors are simple means of characterizing the shape of the radiance distribution. For example, for completely diffused upwelling light, Du = 2.0, J.l.u = 0 5. For a collimated downwelling light beam, Dd = J.l.d = 1. In most oceanic cases, both Dd and D" increase with depth, and D)Dd ::::: 2 [Gordon et al. 1975] For the downwelling distribution function just beneath the surface, D).O) ::::: 1 / cos(J), with an error of less than 3 % for a clear-sky situation [Gordon 1989a], where j is the sub-surface solar zenith angle. 1.4 Inherent Optical Properties (lOPs) lOPs are those that are independent of the ambient light field (i.e. independent of the intensity and the angular distribut i on) The important lOPs of any medium are the absorption coefficient, a, the scattering coefficient b and the volume scattering function (VSF), {3(cx), which expresses the magnitude and angular distribution of scattered photons The angle ex describes the direction change of the scattered photons from the input photons An additional inherent optical property is the beam attenuation coefficient c, given as c =a+ b. The beam attenuation coefficient thus represents the fractional loss of photons from a collimated light beam due to absorption and scattering with units m 1

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--.. I s ,__.. 0.3 0 1 0 .03 0.01 400 Smith and Baker (1981) Tam and Patel (1979) Morel and P rieur ( 1977) : : 500 6 0 0 wavelength (nm) Figure 7a. Absorption Coefficients of Pure Water. 700 The absorption and scattering coefficients of water as a whole, at a given wavelength are equal to the sum o f the individual coeffic i en t s of the components present [Gordon eta!. 1980 ] 1.4 1 Absorption Coefficien t 22 There are three major components for the absorption coefficient of ocean water: water itself, a w ; suspended particles, a P ; and gelb s toff, a s a P can be further divided into two components: the absorption coefficient of phytoplankton pigments, and

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23 the absorption coefficient of detritus, ad. So : 1.4.1.1 Absorption Coefficient of Water Itself. The absorption coefficient of water itself is one of the most important optical components Figure 7a shows three measured absorption spectra Water absorbs light very weakly in the blue and green regions of the spectrum, but increa ses markedly as the wavelength rises above 570 nm, becoming quite significant in the red region Also notice in the figure that there are some differences in aw among researchers. The main reason is the difficulty in obtaining "pure" water for experiments (also see the discussion in Smith and Baker (1981)) and the long path length needed for accuracy at blue wavelengths We will use the aw values from Smith and Baker [1981] as their work is more re cent and widely used But it must be remembered that the accuracy of their aw was only +25% to -15% between 380 to 800 nm. For wavelengths in the visible, aw does not change much between fresh and salt waters [Morel 1974]. However, due to the dissolved ions in the sea water, aw can change markedly for wavelengths in the UV range [Morel 1974]. Hojerslev and Trabjerg [1990] reported that aw varies with temperature. However, their results differed from Pegau and Zaneveld [1993]. So, questions about how varies with temperature remain.

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.--..... -I s 1 .0 0.5 0 0 4 0 0 ' -. :"7'-' :.: 500 600 wavelength (nm) Figure 7b Examples of Absorption Coefficients of Gelbsto f f. 24 700 1.4.1.2 Absorption Coefficient of Gelbs t off. Figure 7b shows example s of the spectral absorption coefficient of gelbstoff. It i s a strong blue absorber with exponential decrease with wavelength. This absorption coefficient can be expressed as [Bric a ud et al. 1981, Carder et al. 1989, Roesler et al. 1989] a (.l..) = a (440)e -s,0.-4>) g g (9) The spectral slope S8 varies with different dissolved organic materials, which also varies slightly with wavelength range [Krijgsman 1994]. At 440 nm, Carder et al [ 1989 ] found th at S8 ::::: 0.011 nm' for a marine humic acid and 0.019 nm' for a marine fulvic acid. The average of S8 for ocean waters is reported as 0 0 1 4 nm' [Bricaud et a!. 1981, Kishi no et a!. 1984].

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--I s 0.4 0.2 -0.0 400 / --. ' -"" ... --. .... .. ..... 500 600 700 wavelength (nm) Figure 7c. Examples of Absorption Coefficients of Phytoplankton Pigments 1.4 .1.3 Absorption Coefficient of Phytoplan kto n Pigments. Figure 7c presents 25 examples of the spectral absorption coefficient of phytoplank to n pigments, which are the basis of oceanic photos y nthe s is. This s pectrum typic al ly has two peaks one arou nd 440 nm, another around 675 nm These are due to the presence of c hlorophyll a. The s houlders above 440 nm are due to the pre se nce of the accessory pigment s, suc h as chlorophyll b, c h lorop hyll c and carotenoids. The width of the peaks around 440 nm and around 675 nm varies from sample to sample, due to the change in accessory pi g ment s pre se nt and the "pa ckage effect" [Morel and Bricaud 1981, Kirk 1986]. The "pa ckage effect" and the accessory pigments/chlorophyll a ratio also cause the ratio ai440) to chlorophyll concentration to b e generally non linear

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0.08 s .._.. 0.04 I-. 1----0 .00 400 ... .... I I . .. . ... . -----.:. ::..:. .:. .:. .:.-.:. 500 600 700 wavelength (nm) Figure 7d Examples of Absorption Coefficients of Detritus 1.4 1.4 Absorption Coefficient of Detritus. Figure 7d presents examples of the 26 spectral absorption coefficient of detritus. Like gelbstoff, it is a strong absorber in the blue and exponentially decreases with wavelength, and can also be expressed as: = f440) -SJ>.-440) ad ad' e (10) The spectral slope Sd has been reported in the range 0.009 to 0.011 nm1 [Roesler et al. 1989]. It has been found that the absorption coefficients for fulvic acid and detritus can be combined. The sum can also be expressed in a form similar to Eqs 9 and 10, but with an average slope at 440 nm of 0 .011 nm1 [Carder et al. 1991].

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1.4.2 Volume Scattering Function and Scattering Coefficient The scattering property of a substance is determined by its volume scattering function, {3(a), which describes the probability of input photons being scattered to a specific angle, a The scattering coefficient b is a measure of the sum of all the scattered photons (at all angles) 27 1.4.2.1 Volume Scattering Function. {3(a). This property is defined as the scattered radiant intensity in the scattering angle a per unit scattering volume per incident irradiance. Figure 8a shows the VSF of sea water itself ({3...). As this is a molecular scattering mechanism, the scattering is symmetric between the forward and backward directions [Morel 1974]. Figure 8b shows the VSF of some natural waters [Petzold 1972] Due to the presence of larger "soft," low-index particles, natural waters scatter photons strongly in the forward direction due to diffraction and refraction effects, and very weakly in the backward direction. 1.4.2.2 Scattering Coefficient. b The integration of {3(a) over 4?r solid angle gives the total scattering coefficient. The scattering coefficient is divided into two parts: the forward scattering coefficient, b 1 and the back-scattering coefficient, bb. Mathematically they are

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4 -.-4 I rJl .-4 I s '-" 2 <::Q 0 0 60 120 Figure 8a. Volume Scattering Function of Pure Sea Water. 1000 100 -.-4 I 10 rJl 1 .-4 \ I \ s 0.1 ..._., Q:l. 0 01 ----------0.001 0.0001 0 60 120 ex (degree) Figure 8b. Volume Scattering Function of Natural Waters (From Petzold [1972]) 28 180 180

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29 1t b1 "' 21t J02 P(cx)sin(cx)dcx, bb "' 21t p(cx)sin(cx)dcx. 2 (11) and b = b 1 + bb. bb is the major contributor to the upwelling radiance The back-scattering coefficient of sea water can be divided into two components: back-scattering coefficient of pure sea water bbw' and back-scattering coefficient of suspended particles bbp Everything except molecular scattering is included in particle scattering Back-scattering coefficient of pure sea water, bb.., Many theoretical and experimental studies have been carried out [e.g Morel 1974 Smith and Baker 1981] on the back-scattering of pure sea w ate rs Figure 9 shows the spe c trum of the backscattering coefficient of pure sea water [Smith and Baker 1981] which can be expressed as (12) Due to the presence of ions and dissolved material, the scattering coefficient of pure sea water is -30% higher than that of pure fresh water [Morel 1974]. Back-scattering coefficient of particles, bbp There are rare measurements of spectral b for ocean waters although a few measurements at single wavelengths bp have been made (e.g Petzold 1972) and Whitlock et al. [1981] reported bb, for river

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-I 0 .004 0 .002 0 .000 400 500 600 700 wavelength (nm) Figure 9. Spectrum of the Back-scattering Coefficients of Pure Sea Water. samples It is believed that b bp('A) can be expressed as [Morel and Prieur 1977 Bricaud et al. 1981, Smith and Baker 1981, Bricaud and Morel 1986 Gordon et al. 1988 Sathyendranath et al. 1989a Morel and Ahn 1990] : 30 {13) with 7lb in the range of 0 3 for different particles while the data of Whitlock et al. [1981] imply an 7lb of 1. 7 for their river samples.

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31 1.5 Relationships between AOPs and lOPs 1.5.1 Sub-surface lrradiance Reflectance From Eq 4, the sub-surface irradiance reflectance, R(Q-), is (14) The major contribution to EiO) comes from the sun light and sky light. The contribution to E"(Q ), however is dominated by the following four components [Peacock 1992]: elastic scattering from molecules and particles in the water column (E "w(f..)) and from bottom reflectance (Eub(f..)), and inelastic scattering from gelbstoff fluorescence (Ef(/..)) and water Raman scattering (E"R(f..)). Work by Gordon [1979] and Carder and Steward [1985] dealing with chlorophyll a fluorescence have been reported, but because the fluorescence efficiency of chlorophyll a varies by an order of magnitude and peak chlorophyll a fluorescence occurs in a narrow band centered around 685 nm, chlorophyll a fluorescence is not cons i dered in this study For optically deep, homogeneous water, the irradiance reflectance due to the elastic scattering of molecules and particles, Rw(o-), can be expressed as [Gordon et al 1975]:

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32 (15) Recently, extensive Monte Carlo simulations have been performed for various sun angles and VSFs [Kirk 1984, 1991; Jerome et al. 1988, Gordon 1989b, Morel and Gentili 1991], and it is found that forb/a < 0.25, generally, where G(p.iO)), according to Kirk [1991], is G(!ljO)) = 1-LJ..O) M1 and M2 vary with VSF and range from 0.244 to 0 514 for M1 and from (16) (17) 0.303 to 0.326 for M2 (for VSFs reported in Petzold [1972]). Actually, the above expression can be approximated as G G(lljO)) = =-, 1-LJ..O) (18) for sun angles < 80 (0 .68 < p.iO) < 1.0) with G varying from 0 304 to 0 344, and averaged to 0.32 (%) for the above M1 and M2 values. Keeping G = 0 32 as a constant and putting the 7% error to the other terms then Eq. 16 is (19) This is a re-write of Eq. 16 but it more explicitly shows the variation of R""(O) with solar zenith angle, as DiO) = 11 p.iO) """ llcos(j) (section 1.3.4)

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33 For parts due to inelastic scattering and bottom reflectance, there are no simple expressions like Eq 19. Their contributions to the remote-sensing reflectance will be discussed in Chapter 2. 1 5. 2 Remote-sensing Reflectance Based on the above assumption about the major components which make up the sub-surface upwelling light field to first order (single s c atterin g and quasi-single scattering [Gordon 1994]) the water-leaving radiance can be expressed as (20) Breaking Eq 6 into contributions from the various me c hanisms lis ted in Eq 20 we have R Rw + Rb + R 1 + RR rs rs rs rs rs (21) From Austin [1974] there is (22) where t is the air-sea interface transmittance Since EiO+) = E iO-)/t, then from Eq. 6, (23)

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34 Similar to Zaneveld [1982, 1994], through the radiative transf er equation, the exact solution for nadir remote-sensing reflectance from the elastic scattering part of (24) where J A = _2_n ----p b f 21t (25) is the light-averaged-backward-VSF (detailed in Appendix 1). The terms for bottom reflectance and inelastic scattering will be discussed in Chapter 2 and appendices. 1.5.3 Diffuse attenuation Coefficient of Downwellin g Irradiance Through Monte Carlo simulation, Gordon [1989a] found tha t KjO) :::: l.04DjO)(a+bJ (26) and Kjav) :::: 1.08D jO)(a +bt) (27) where KiO) and Kiav) are the diffuse attenuation coefficient for the downwelling

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irradiance just beneath the surface, and an average of Kd between the sub-surface Ed and 10% of the sub-surface Ed value, respectively. 35

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36 CHAPTER 2 MODEL OF THE REMOTE-SENSING REFLECTANCE 2 1 Introduction One goal of ocean optics is to be able to interpret water color or remote-sensing reflectance in terms of the in-water constituents. From Eq. 21, we see that remotesensing reflectance can be broken down into many terms. To interpret the measured remote-sensing reflectance on the left side of Eq. 21, each component on the right side of Eq. 21 needs to be expressed in terms of the optical properties of the water. 2.2 Remote-sensing Reflectance of the Water Column (elastic scattering only), Rrs"' In Eq. 24, {3b = {3b.,.. + {3bP' as {3 = {3.,.. + {3P. {3b is the tight-field weighted average of the backward VSF. Thus, {3 bw and {3 bp can not be simply expressed using a few parameters, since they depend on the light field. Extensive calculations for different a, VSFs, and light fields are necessary. For j > 15 and a nadir viewing sensor, Gordon [1986] and Gordon et al. [1988] found through Monte Carlo simulation, that Rrs"'(CJ) can be expressed as

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37 (28) where gi = 0 0949, and g2 = 0.0794. More recently, Morel and Gentili [1993] made Monte Carlo calculations for "case 1" waters ([chl a] < 3 mg / m3 ) using one VSF shape for particles. For sun angles within 80 from zenith and for satellite viewing angles cea < 50) they found (29) where g averaged about 0.0936 (for 440 550 nm) and varied slightly with wavelength, sun angle and view angle. But, as pointed out by Mobley et al [1993], g may vary with Monte Carlo computation models, and this variation can be 12% for high scattering waters and much larger in high absorbing waters [Mobley et al. 1993]. Also, it is not clear yet how g varies for high [chi a] and "case 2" waters In another way, with the definition Q = Eu(O-)/ Lu(O) [Austin 1974] and Eq. 16, there is (30) This expression introduces a new parameter, the Q factor. However only a few measurements of Q exist. Q is extremely sensitive to sensor orientation, so its values have been reported from 3.2 to 12 [Gordon et al. 1980]. For example, Austin [1979] takes Q to be about 4. 7 and spectrally constant from 440 to 550 nm, while Kirk [1986] gives Q as -4.9, and Gordon et al. [1975, 1988] s uggest a value of -3.4. In

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38 some other studies, Q is somewhat arbitrarily chosen as a spectral constant [Carder and Steward 1985, Peacock et al. 1990] However, recent measurements [C O. Davis, unpublished] and Monte Carlo sim ulation s for "case 1" waters [Morel and Gentili 1993] show that Q increases with wavelength, which is an inverse trend compared to bbp [Carder et al. 1991]. Using the single and quasi-single scattering approximations of Gordon [1994] Lee et al. [1992 1994a] found that for a wide variety of waters, Eq. 30 can be expanded as (31) where <1n is the Q factor for molecular scattering. <2m can be estimated based on the molecular VSF shape and the illumination geometry [Lee et al. 1992, 1994a]. Eq. 31 can be seen as a simplification of Eq. 24 for wide situations, with the first term in the bracket of the right side representing the backscattered photons due to molecular scattering, and the second term representing the backscattered photons due to particle scattering. In Eq. 31, both G and Qn increase with sun angle [Gordon 1 989b, Kirk 1991 Lee et al. 1 992, 1994 a], so we expect that Rrs(O' ) is less sensitive to the solar zenith angle than R(O). To simplify matters, we can take average values of G and Qm and allow any errors due to these simplifications to be embedded into the empirical terms X and Y. G is about 0.32 according to Gordon et al. [197 5] Jerome et al. [1988] and Kirk [1991]. Qm is about 3.4 [Lee et al 1992, 1994a]. Thus, our equation becomes

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39 (32) Variations due to VSF, solar zenith angle, and view angle are now all embedded in the two parameters X and Y. Since there is a different wavelength exponent between the scattering coefficients of molecules versus that of particles, errors generated by using average G and
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40 model these optically shallow waters, we consider that the subsurface Eu w consists of two parts coming from two layers : one from the layer above the bottom, and one from the layer "below" the bottom. Then the subsurface E"w coming from the upper layer only can be obtained by reducing the optically deep expression by an amount equivalent to the contribution of the missing water column below H. Thus for shallow waters with depth Hand a totally absorbing bottom, with t = 0.98, and nw = 1.34, Rrs w is approximated by (33) with z positive downward from the surface. If we define the quasi-diffuse attenuation coefficient as K = a+bb, then Kd = DdK and Ku = DuK [Gordon 1989a] Since D /Dd = 2 [Gordon et al. 1975], we can rewrite Eq. 33 as R;; = 0.17[bbw+y{400)r}1_e-3lD.ixRJ, a 3.4 '} (34) where {Dd} is the vertically averaged downwellin g distribution func tion and {DA is approximate by 1.08Di0) [Gordon 1989a, Lee et al. 1994a]. 2.3 Remote sensing Reflectance of Bottom Reflectance, R ,/ Assuming that the bottom is an extended Lambertian reflector with bottom

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41 albedo p, then for a nadir-viewing sensor, Rrsb can be approximated by [Lee et al. 1992, 1994a] (35) where k is the effective attenuation coefficient for the radiance from an extended Lambertian source How k relates to the quasi-diffuse attenuation coefficient K is not well understood. Heuristically, it should be a value between c and K. It was found that k is from 1.36K to 1.62K for K.1i in the range of 0.5 2.0 based on the Monte Carlo simulations [Gordon 1989a] for an extended totally diffuse light source (detailed in Appendix 2). As an average in this work, k = 1.5K as is used by Marshall and Smith [1990]. Then Eq 35 becomes [Lee et al. 1992, Lee et al 1994a] R b O 17 -(ID)l.S)KH pe (36) This value depends not only on the optical properties of the water body, but also on water depth and the bottom albedo [Gordon and Brown 1974]. In the modeling work, the water depth was based on the Provisional Chart for the Gulf Coast (#1003), and the bottom albedo was based on measurements of bottom samples from the region with near-shore values of p = 0.1 to 0 2 (used for station TA01), and offshore values of p = 0.4 to 0.5 (used for stations TA02 and TA03). Figure 10 shows examples of those albedo spectra. The quasi-diffuse attenuation coefficient K is assumed to be equal to total absorption a as bb < < a for most of the world ocean [Morel and Prieur 1977]

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0 "0 Q) -ro s 0 .,._) .,._) 0 0 8 0.4 0 0 400 offshore near-shore 500 600 wavelength (nm) Figure 10. Examples of Bottom Albedo Spectra. 700 For sensors not viewing the nadir, kin Eq 35 needs to be adjusted to klcos(8w) In our experiments, e ... is generally within 20, i .e. 0.93 cos(8...) 1.0, so k/cos(8w) = 1.5K could still be used. 2.4 Remote-sensing Reflectance of Gelbstoff Fluorescence, R! and Water Raman Scattering, R,./ In general, these terms are due to inelastic scattering By considering (the volume scattering function for inelastic scattering) isotropic, remote -sensing reflectance due to gelbstoff fluorescence and water Raman scattering can be approximated as [Lee et al. 1992, 1994a] (detailed in Appendix 3) 42

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43 and (38) So combining Eqs. 34 36, 37 and 38, after calculat i ng Rrs R Rrf and Rrsb only X and Y remain as unknowns By matching the modeled Rrsw and the residual of Rrs R r / -Rrf -Rrsb, X and Y can be derived using the predictor-corrector approach to modeling as in Carder and Steward [ 1985]

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3.1 Introduction CHAPTER 3 DATA AND METIIODS 44 From 1989 to 1993 measurements of optical properties for a variety of waters were taken, including sites in the North Atlantic, Monterey Bay, the West Florida Shelf, the Gulf of Mexico and the mouth of the Mississippi River. In these waters [chi a] ranged from 0 .07-50 mg / m3 and a g(440) ranged from 0.005-0.5 m -1 Table 1 summarizes the cruise informat ion, whi le Figure 2a shows the locations o f data collection. For each station, hyperspectral R,s and particle and pigment absorption coefficients (aP and a9 ) of surface water samples were measured For the 1993 Gulf of Mexico stations, a long-path (50 em or 100 em) [Peacock et al. 1994] spectrophotometer was used to measure ag. In-water optical properties (K d and Rrs(O-)) were calculated based on the profiles of downwelling irradiance and upwelling radiance, which were measured by Dr. J. L. Mueller (San Diego State University) or Dr. C 0. Davis (Jet Prop Lab) using a Biospherical MER sensor (model 1048A).

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45 3.2 Remote sensing Reflectance R n Hyperspectral Rn was measured by the method developed by Carder and Steward [1985], using a Spectron Engineering spectroradiometer (Spectron Model SE-590) with 253 spectral channels covering the wavelength range from 370 1100 nm. With this instrument, the upwelling radiance above the surface (L.,(O+ ,ea,
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1.0 0 8 0 6 0.4 0 2 0 0 0 vertical component horizontal component unpolarized 30 60 angle (degree) Figure 11. Fresnel Reflectance of Sea Water (n ... = 1.34). 3 .3 Absorption Coefficient of Part icles and Pigments, a P and 90 The method described by Mitchell and Kiefer [1988] was used to measure aP, and the method developed by Kishino et al. [1985 ] and modified by Roesler et al [1989] was used to measure ad and to derive Briefly, water samples were filtered 46 onto Whatman GF/F filter pads immediately after collection. Another pad wetted with filtered sea water served as a blank. The transmission spectra from 380 nm to 800 nm of these pads (TP and Tb) were measured by the Spectron. The opti cal geometry was designed to illuminate the pad with diffuse light from a Lambertian diffuser added between the light source and the filter pad This geometry i s very similar to that of

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47 Table 2. Recent Results for "Beta Factor" of GF/ F Filter Pad. I Authors I "beta factor" expressions I Nelson and Robertson, 1993 (3pad = 1.0 + 0.46 OD/10 Cleveland and Weidemann, 1993 (3pad = (0.378 + 0.523 ODP)"1 Bricaud and Stramski, 1990 (3pad = 1.63 OD/2 2 Mitchell, 1990 (3pad = (0.392 + 0.655 ODP)"1 Bricaud and Stram ski [1990], who illuminated a pad in front of a diffusing window which was adjacent to an end-on photomultiplier tube. The volume filtered was about 500 1500 ml (depending on the water clarity). Using the mea sured transmission spectra, the optical density of the sample is Tb OD =log-P T p and the absorption coefficient of the sample is OD aP = 2 .3--P BR I-' pad (41) (42) where B is the ratio of the volume filtered to the effective surface area of sample on the pad (3pad is the so called "beta factor" [Mitch ell and Kiefer 1988], introduced to describe the optical-path-length elongation due to the filter pad. Table 2 and Figure 12 provide recent results of (3pad for GF/ F filter pad. Notice the significant differences of (3pad when ODP is around or less than 0.1 In our calculation of aP, (3pad from Bricaud and Stramski [1990] (their Eq. 2) was used. In the calculation of the absorption

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1 0 8 6 4 2 0 0.0 0.1 Nelson & Robertson, 93 Cleveland & Weidemann, 93 Mitchell, 90 Bricaud & Stramski, 90 0.2 on p 0.3 ..... :.:.:. :. :. : :.: : .: .:. : 0.4 0.5 Figure 12. Recent Results for "Beta Factor" of GF/F Filter Pad. coefficient, large-particle scattering was corrected by assuming a P(780) = 0 from the aP curve 48 After this measurement, the sample pad was soaked in hot methanol [Kishino et al. 1985, Roesler et al. 1989] for about 15 minutes to remove pigments and its optical density was again determined via Eq 41, and the detrital absorption coefficient ad was obtained by Eq 42. The difference between the particle and detrital absorption coefficients provided the absorption coefficient of phytoplankton pigments a<>: (43)

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49 3.4 Absorption Coefficient of Gelbstoff, a8 For stations before 1993, the absorption coefficient of gelbstoff (a8 ) was not explicitly measured for visible wavelengths However, from Eq 27, the total absorption coefficient could be derived from Kiav), and aw and aP were available, so a8 could be estimated from Kiav) values, using the expression a8 ::::: Kiav)l(l.OSDiO))aw-aP, as bb < < a At the 1993 GOMEX and COLOR stations, a8 of water samples were measured using 50-cm or 100-cm path-length instruments, respectively after filtering the sample through 0 2 JLm pore-diameter Gelman Supor200 filters [Peacock et al. 1994]. 3.5 Measurements of In-water Optical Properties, K d and Rrs(O-) A Biospherical Instrument MER (model 1048A) was used to determine the vertical structure of the water column. The depth profiles of downwelling irradiance (Eiz)) and upwelling radiance (Lu(z)) were determined for each cast. With these measurements, Kiav) and sub-surface downwelling irradiance (EiO-)) and upwelling radiance (Lu(CJ)) were derived. The process is similar to that of Smith and Baker [1981] Briefly, Ej.z) = EJ.O-)e -KJ.av)r. (44)

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50 then ln[EJz)] = ln[EJO-)] -KJav)z (45) Due to surface-wave-focusing and ship shadow effects [Gordon 1985], the measured Eiz) and z include errors associated in the field, and we cannot simply use values from two depths to derive Kjav) and EiO). In order to correct these errors linear regression between ln[Ejz)] and z were performed for the surface layer. The regression results gave K jav) and ln[E d(O.)]. The same process was applied to Lu(z) to get Lu(O ).

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51 CHAPTER 4 RESULTS OF Rrs MODELING 4.1 Validation of Rrs Model In previous studies [Carder and Steward 1985, Peacock et al. 1990, Lee et al. 1992, Lee et al. 1994a], qualifyin g words such as "excellent," "very good" or "good" were used to describe how well the modeled curve fit the measured curve, and they were usually justified visually There was no quantitative indication regarding the difference between the measured and modeled curves. H ere, a modified average percentage difference (a.p.d.) i s u sed to quantify and validate the model results of Rrs. It is defined as a.p.d. (46) where A VG;v >-2 means the average valu e in the wavelength range from f..1 to f..2 The cut-off between 660 and 750 nm is because there is no term included to model the chlorophyll a fluorescence in the measured signal. The 750 830 nm band is important for turbid waters. In the forward process, a 8 was measured or estimated, a P was measured, H for shallow waters came from published charts, and the predi cto r -co rrector method

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Table 3. Station Chosen for the Rrs Model Demonstration. Station Latitude Longitude Time/Date Bottom Mod. depth depth TAOl 27<>'2.7' N 82' w + 10.5/3-4-90 14m 13.7m TA02 27<>'2.0' N 83003' w +13.0/3-4-90 25m 25m TA03 27' N 83 11' w + 14 9 / 3-4-90 35m 36m G008 28' N 910)0' w "08.5/4-12-93 -G010 28' N 910)0' w "14.0/ 4-12-93 G027 290)2' N 85' w "09. 2/4-19-93 -C012 28' N 890)3' w ++ 10.8/6-5-93 -C014 28 N 90002' w ++16.1 /6-5-93 -C019 270)4' N 83<>'2.0' w ++o9.5/6-8-93 33m 35m Note : " indicates that the water is optically deep. + : East standard time, : Central daylight time, ++: East daylight time. 52 [Carder and Steward 1985] was used to obtain the values of X and Y. In this process, it was sometimes necessary to apply a factor f to the measured aP, such that the absorption coefficient of particles used in the model isf* aP. The purpose of thisfis to correct for possible errors due to patchiness, and /or the "beta factor" (see Figure 12). It is necessary to keep in mind that the process here was focused on testing the expressions developed in Chapter 2 using the measured components, so only minor adjustments were applied to the measured components before a small ( 0.05) a.p.d. was obtained. Most of the parameter derivation was concentrated on X and Y (and p for shallow waters), and the parameter fwas not varied much (usually 0.9 to 1.1) from 1.0 in reducing the a.p.d ..

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53 For the calculation of Rj, 1], s )y and u came from the measurements of Hawes et al. [1992] and Hawes [1992], while 11(/..j for R,./ came from Collins et al [1984] 4 2 Model Results and Discussion Measured Rrs curves for 9 stations were selected to demonstrate the model developed in Chapter 2. These 9 stations covered a wide range of water types: 1) the West Florida Shelf with shallow, gelbstoff-rich coastal waters; and 2) Gulf of Mexico waters with phytoplankton blooms in the Mississippi River plume (S > 17 %o). Table 3 provides the station locations as well as the measured and modeled water depths for the shallow stations Figure 2b shows the locations of these stations in the Gulf of Mexico As examples, Figures 13a 13d show the detailed model components for Rm and Figure 14 shows the results for the chosen stations. Table 4 lists the model parameters X, Y, ag(440), and aP(440) with a.p .d. and the measured values of aP(440) and [chi a] for each station. Table 5 details the fractional contributions that Rrsw RrsR, Rj and Rrsb make to the measured Rrs at 440 nm and 550 nm It can be seen from Figures 13a -13d that excellent fits were achieved between the measured and modeled Rrs curves for all of the selected stations except for the spectral region around 685 nm where chlorophyll a fluorescence is present in the field data This excellence can also be seen from the a.p .d. values (Table 4) for each station with the average a p.d. being 3.1%, which is within the measurement

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0.02 0.01 0.00 400 ........ ........ .. .. .. ...... \ \ .. '\\ .,... -...... ____ _ 500 ,, . . .. > > > > ' \ 600 Figure 13a. Detailed Rrs Model for Station TAO!. 0.008 ,.-... I rn 0.004 ..._.. tl) 0. 0 0 0 . -:' .. :':' .. .. .. .. .. ::-.. ,.. mea. R rs mod. R rs mod. R raw mod. R rsf mod. RrsR mod. Rrsb 700 mea. R rs mod. R rs mod. R rsw mod. R rsf mod. R rsR 400 500 600 700 wavelength (nm) Figure 13b Detailed Rrs Model for Station G027. 54

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..-...-4 I rJl -(J) !--ct; 0.008 0.004 0.000 400 500 --mea. R r s mod. R rs mod R TBW mod. R rsj mod. R TBR 600 700 Figure 13c Detailed Rrs Model for Station C014. 0.008 0 .000 400 --mea. R rs -mod. R TB .............. mod. R 500 600 rsw mod. RrsJ mod. RrsR mod. Rrsb 700 wavelength (nm) Figure 13d. Detailed Rrs Model for Station C019 55

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accuracy For such a small percentage difference, we can reasonably say the model developed here works very well for these waters 56 For the stations chosen, the aP that was required by the model was in general within 10% of the measured aP except near the Mississippi River at station C012 (20%), with very high [chi a] (38.6 mg/m3) The average difference between the measured and required aP is 8 .9% (9 stations) (7.5% when station C012 is excluded) The maximum 15% or 20% difference can perhaps be explained by the water patchiness and/or the accuracy involved in the method of aP measurement due to the "beta factor" which varies significantly between species and researchers [Bricaud and Stramski 1990, Mitchell 1990, Yentsch and Phinny 1992, Cleveland and Weidemann 1993, Nelson and Robertson 1993] (see Table 2 and Figure 12). This effect may be especially important for station C012 which was near the Mississippi River mouth where the heavy load of sediments and minerals might cause additional uncertainty in the optical path length elongation Also the influence of horizontal and vertical structure of the waters increases for mesotrophic eutrophic waters so patchiness can affect accuracies in the more hypertrophic waters. Finally, the low signal obtained for the upwelling radiance measurements at station C012 made the Rrs calculation sensitive to corrections for reflected skylight. It can be seen from Table 4 that the ratio of ag( 440) to aP( 440) among these waters was highly variable, with a range from 0 3 to 3.0, and the X value does not co-vary with the pigment concentration [chi a] for the waters studied. This illustrates that the model works well over a wide range of conditions, and also suggests why the

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--. I r:n '-' 1'1) !--0.008 0.004 0 .000 400 1. TA0 2 2 TA03 3 co 19 4. G01 0 5. G027 6. GOOB 7. C014 8. co 12 500 600 700 wavelength (nrn) Figure 14 Measured vs Modeled Rrs for the Selected Station s Solid: measured, d as hed: modeled. power-law pigment algorithm doe s not work well for coastal waters b ecause of the lack of co-variation of all optical components with [ chl a]. The highest X value, 0.0087 m 1sr t, was at the shallow, mesotrophic station TAOl, suggesting a large scattering effect due to detritus and suspended sediments Brisk northwesterly winds 57 suspended sediments in the shoal regions to the east and north of the station, and they likely were transported by the ebb t idal currents from Tampa Bay to the study site [Carder et al 1993] The Y values were within the range from 0 to 2.4 for the waters reported here, which might be interpreted as being partially due to bbp For bbp as mentioned in section 1.4.2.2, the wavelength exponent (17b ) is in the expected range 0-3.0 for a

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58 Table 4. Model Parameters for Stations in Table 3. Station X y a11z aD I a p.d. a ml!a "pl [chi a] TA01 .0087 1.2 .082 .041 .037 .045 1.05 TA02 .0022 2 4 .042 .033 .025 035 .61 TA03 .0012 2 3 .034 .027 029 .026 .70 G008 .0065 .24 .31 28 .033 .295 5.27 G010 .0010 1.8 .059 .023 023 .021 .12 G027 .0014 1.9 078 .029 .021 .034 .20 C012 .0030 0 .42 1.34 .044 1.12 38.58 C014 .0068 0 38 1.21 .031 1.16 20.26 C019 .0007 2 0 .023 .021 .037 .023 .22 range of particles (e.g. river sample [Whitlock et al. 1981], bacteria [Morel and Ahn 1990], phytoplankton cells [Bricaud and Morel 1986], and coccoliths [Gordon et al 1988]) For Y = 2.4, if the exponent for Q is 1.0, then Tlb = 1.4, which is within the 0 3.0 range reported elsewhere, also is within the range of 0 2 as used by Sathyendranath et al. [1989a]. Generally Y values were found to be low for turbid water, and high for clear water. The value 2.4 for stations TA02 and TA03 of the West Florida Shelf seems a little bit high for those waters. This might be due to errors in a8 as a8 was derived from Kd for those stations. For the world ocean the range of Y needs further study. At the optically shallow stations (TA01, TA02, TA03 and C019) the modelrequired depths were within about 10% of the chart depths without consideration of

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59 any tidal influence (typically <0. 5 m). This demonstrates that Eq 36 works well for shallow waters and it indicates a potential to use this model to survey (e g by aircraft overflights) dramatic changes in shelf bathymetry that can occur as a result of major storms. For station C019, an albedo value of about 0 1 was used in the model, suggesting the bottom might contain more heavy minerals or grass at that site. Direct bottom albedo measurements are lacking at individual stations and are needed for a wide variety of bottom types For stations TAOl, TA02, TA03, G008, C012 and C014, the general agreement between the modeled and measured Rrs values is very good ( -3. 5 % a p d ) with small differences around 580 nm, where the measured Rrs > modeled Rrs Other than modeling error there are at least three possible reasons for this : a) bottom albedo uncertainty, b) phycoerythrin fluorescence [Yentsch and Yentsch 1979, Yentsch and Phinney 1985], and c) water absorption coefficient uncertainty [Smith and Baker 1981, Tam and Patel 1979] A spectrally constant bottom albedo was u s ed for the shallow stations Soil reflectance [Tucker and Miller 1977] and earlier measurements of bottom albedo (Figure 1 0) did display some spectral dependence The amount of change spectral albedo could induce would not provide the sharp spectral increase and then decrease with wavelength in Rrs required for the measured and modeled Rrs curves to converge, however. There also was no bottom contribution toRr s at G008, C012 and C014. More realistic explanations include the lack of a term in the model for phycoerythrin fluorescence, the differences between the water absorption coefficients in this

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60 Table 5. Optical Component Contributions toRrs of Stations in Table 3. Station Rrsw/Rrs RjR! Rrs Rrsb/Rrs Rrs{440)/Rrs{550) 440 550 440 550 440 550 mea Rrs corr Rrs TA01 .95 .92 .02 .01 .02 .10 .87 .91 TA02 .91 82 .05 .06 .05 .11 1.48 1.77 TA03 87 .83 .10 .12 02 .04 1.87 1.96 G008 97 1.00 03 .02 -.49 .48 G010 92 .94 .08 .07 -1.64 1.61 G027 .91 .96 08 .07 1.34 1.26 C012 .92 1.03 .09 .03 -.31 28 C014 99 1.02 .03 .01 -.32 .31 C019 .92 96 .06 07 .01 .01 2.46 2.37 spectral region as reported by Smith and Baker [1981] and by Tam and Patel [1979], and the accuracy of the "beta fa c tor" for low absorbing portions of a9(A.) for detritus -rich stations Further study is requ i red in order to resolve this issue The differences between the measured and modeled Rrs curves around 685 nm, on the other hand are expected due to the fact that no term is included in the model to describe the chlorophyll a fluorescence [Carder and Steward 1985]. 4.3 Contributions by Rj and RrsR Model results at station T A03 sugg est relatively higher gelbstoff fluorescence and water Raman scattering influences since a higher 1J (1.5 % ) [Hawes et al. 1992]

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61 was used. This value is -3 times greater than the value suggested by Spitzer and Dirks [1985] for terrigenous gelbstoff If we exclude this station, 90% or more of the water-leaving radiance is accounted for by the sum of the elastic scattering from molecules, particles and the bottom, which leaves about 10% or less of the measured Rrs for gelbstoff fluorescence and water Raman scattering This is consistent with the reports of Marshall and Smith [1990] and Stavn [1990], as water Raman scattering makes more of a contribution when the water is clear It is interesting that the ratio RrsC440)/Rrs(550) did not vary widely due to inelastic scattering (see Table 5). Among stations without bottom influence, differences in the ratio were within 10%, which suggests the spectral radiance ratio algorithm is effective for most deep waters without consideration of gelbstoff fluorescence and water Raman scattering. However, it is obvious that as the bottom influence increases, the usefulness of the power-law algorithm decreases. Also, the power-law algorithm can not distinguish between the absorption of gelbstoff and that of pigments. Note that Rrsw(490)/Rrs(490) values as low as 0. 77 were determined (not explicitly shown), suggesting that great care must be taken when interpreting remote sensing curves for the intermediate wavelengths at shallow coastal stations.

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62 CHAPTER 5 CONCLUSIONS OF PART A 5.1 Contributions to the water-leaving radiance spectra for a variety of waters can be attributed to elastic scattering by water molecules, suspended particles, and bottom reflectance, and to inelastic scattering by water Raman scattering and gelbstoff fluorescence. Inelastic scattering by pigments was not considered For optically deep water, remote-sensing reflectance of the water column part (elastic scattering only), Rrsw(f..), can be mathematically simulated as follows (47) where bbw(f..) is known, X and Yare spectral constants, and Y was less than 2.4 for the waters considered For optically shallow waters, the expression for bottom-reflectance contribution, R b = 0 17 -CID)l.S)aH rs pe (48) works well for the shallow waters considered. Together, the water-column term and the bottom-reflectance term accounted for about 90% or more of the total remotesensing reflectance

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63 5.2 Close agreement between modeled and measured R was achieved for all rs selected stations when all of the scattering mechanisms mentioned (both elastic and inelastic) were included The average a.p .d. is 3 1%. The ratio az<440)/aP(440) ranged from -0.3 to 3 .0, indicating the broad usefulness of the model. For contributions other than from the water column, as much as 23% of Rrs(490) is attributable to water Raman scattering, gelbstoff fluorescence, and bottom reflectance for an optically shallow (25 m) station For pigment algorithms based on the power law of spectral radiance ratio most "error" comes from reflected bottom radiance for optically shallow coastal waters. The aP required by the model was generally within 10% of the measured a P with an average difference of 8 9% (9 stations) (7 5% when station C012 is excluded). This suggests a potential to remotely measure the pigment and gelbstoff absorption coefficients, although derivation of [chi a] will depend upon knowledge of the chlorophyll-specific absorption coefficient for a region 5 3 The model required bottom depths for the optically shallow waters are within 10% of the chart depth s, suggesting it s possible use to remotely measure bottom depth for the shelf waters. 5.4 The contribution of R,/ and Rr/ were generally within 10% or less of the total Rm covering the whole range from 400 nm to 600 nm. If these two terms were omitted, this 10% or less difference can be roughly compensated by a small increase in X value in the modeling. Also, R j and R/ do not significantly affect the Rrs(440)/RrsC550) ratio; thus the power-law pigment algorithm can be used without the

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64 correction of gelbstoff fluorescence and water Raman scattering with little error if the absorption and scattering properties co-vary with pigment concentration as happened for "case 1" waters. These imply that R,! and Rr/ could be omitted in the Rrs modeling to simplify the process.

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65 PARTB THE INVERSE PROBLEM AND APPLICATIONS

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66 CHAPTER 6 THE INVERSE PROBLEM 6.1 Introduction As discussed previously, the ultimate goal of remote sensing is to derive the in water constituents through remotely measured signals Empirical and semi-analytical approaches have been discussed for derivation of pigment concentration [Clark 1981, Gordon and Morel 1983, Carder et al. 1991, Card e r et al. 1994], and diffuse attenuation coefficient [Austin and Petzold 1981, Gordon and Morel 1983] For the analytical approach, an inverse of the process described in Chapter 2, not much improvement has been achieved in the past studies One of the difficulties is that aP or change drastically from region to region, and it is not easy to accurately express these changes by a few parameters such as for ag or ad. For Rrs of deep waters at N wavelengths (A1 A2 ... AN), ignoring Rj and RrsR as discussed in section 4 3, there are N equations

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67 (49) Rrs(AN) 0.17 [bbw(')..N) +J 400lyl aw(')..N)+aagC>..N)+a4>(')..N) 3.4 ')..N in which ad8 can be expressed as [Roesler et al 1989, Carder et al. 1991] aag(>..) = aagC440)e -sdtc>--440) (50) There are at least N +4 unknowns for the N equations (N for 2 for adg(A.) (adg(440) and Sd8 ) and 2 for particle scattering (X and Y)). If only Rrs is available, there will be no certain solution for the above equations unless we dramatically reduce the unknowns regarding a9(A.). Bidigare et al [1990] pointed out that can be re-constructed by knowing concentrations and the specific absorption coefficients for each pigment but these cannot be known from remotely sensed data Hoepffner and Sathyendranath [1991] suggested that a9 can be modeled by the sum of 11 Gaussian bands. For these 11 Gaussian bands, their center wavelengths and half band-widths would vary from phytoplankton species to species Even if the center wavelengths and half band-widths can be fixed, we still need 11 parameters to simulate aq,. Methods are also suggested to use average specific absorption coefficient [Morel 1980 Sathyendranath and Platt 1988, Carder et al 1991] or average absorption curves [Roesler and Perry 1994]. With these approaches, only one unknown (the pigment concentration or a scale factor) is needed to model a9 Thus, if N is equal to or greater than 5, theoretically

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68 the series of N equations could be solved and the unknowns related to the absorption and scattering could be derived. But, due to the "package effect" and changing environments, it is well known that the curves vary widely from sample to sample [Morel 1980, Bricaud and Stramski 1990, Bidigare et al. 1990, Hoepffner and Sathyendranath 1991, Carder et al. 1994] No single shape or value for can be used globally. So, for the inverse problem in remote sensing, simpler expressions with adequate accuracy for a"' would be very useful. The following section will discuss the possible simple methods to s i mulate a9(A.) with the consideration of the change of shape with water sample 6.2 Simulation of aiA.) Generally there are two ways to simulate a9(A.): one is by the combination of mathematical functions [Hoepffner and Sathyendranath 1991, Lee et al 1994b] which use a few parameters to simulate the whole spectrum; another is to empirically relate a"' of each wavelength to a specific value such a s total pigment concentration [Morel 1980], or [chi a] [Carder et al. 1991] or a"' at one wavelength [Carder et al 1994, Roesler and Perry 1994]. The first method is simple and has more power to adjust the a"' curve This method, however creates a smooth a"' curve, and sacrifices the finesse of the a"' curve containing the pigment composition information when the number of simulation parameters is limited The second method shows the averaged finesse of

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69 the aq, curve, and has less potential to adjust the aq, curve as generally it is controlled by one parameter. 6.2.1 Mathematical functions By analyzing surface aq,(A.) data collected from the Gulf of Mexico in April, 1993, which covered a [chi a] range from 0 07 to 40 mg/m3 an expression for aq,(A.) was suggested by Lee et al. [1994b], which is a combination of 3 simple functions involving 6 parameters. Among the 6 parameters, 2 parameters vary only slightly for different waters and only 2 parameters have strong effects on the whole aq, curve. There were a few aq, curves from deep water samples which were greatly different from those of the surface samples, and could not be well simulated by the suggested simple expressions. But this is not important for remote sensing as 90% of the observed photons derive from the top attenuation depth (1/Kd) [Gordon and McCluney 1975]. For species recognition, the methods of Bidigare [1990] and Hoepffner and Sathyendranath [1991] might be better. For the wavelength range of 400 nm ::;; A. ::;; 700 nm, the simple mathematical simulation for aq,(A.) is:

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70 _din A.-A.,)2 (51) 400 l 570, a.._(l) = a e '\ too 'I' 570 < l < 656, a.._(l) = a.._(570) + aljl(656 ) 5 0 (52) 'I' 'I' 656 570 7 ), and (53) The wavelength range for Eq. 51 was 400-590 nm in Lee et al. [1994b], but it is better for Rrs modeling if the range is adjusted to 400 570 nm. With Eqs. 51 53, aq, curves can be simulated. Figures 15a 15d show examples of the simulated versus measured aq,. For the aq, samples, the normalized root-mean-square (rms) error is in the range of 5 20% with an average of 11%. Most of the variation occurred around 570 nm for clear water stations when the measured aq, values were low. In Eqs. 51 53, there are 6 parameters, aq,1 F, A1 aq,2 Az and u2 Parameter F describes the width of the aq, curve from 400 nm to -560 nm, 100 + A1 is the wavelength of the blue peak, A2 is the wavelength of the red peak and 2.355u2 determines the half band-width around the red peak. For the samples studied [Lee et al. 1994b], F varies from 1.6 to 4.2, A1 varies from 338 342 nm with 80% at 340 nm, Az varies from 672 to 675 nm with most at 674 nm, and 2.355u2 ranged from 21 to 34 nm. aq,1 varies from 0 .01 to 0.83 m1 while aq,/aq,1 varies from 0.21 to 0.85. So, for the 6 parameters, A1 and Az are almost fixed, and aq,2 and u2 only affect a small

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0.3 -0.2 ..... I s 11-d 0.1 0 0 400 500 measured mathematical empirical 600 700 Figure 15a Measured vs Simulated a.p for Station G003. 0.4 s 0.2 I .._, 0.0 400 : \ ', ' ', measured mathematical empirical 500 600 700 wavelength (nm) Figure 15b. Measured vs. Simulated a.p for Station G004. 71

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0.03 0 .02 ....... I "$ 0.01 I 0.00 400 500 ,., measured mathematical empirical ' .... ... .:. -.:."" ,/ 600 Figure 15c. Measured vs. Simulated aq, for Station G015. ...-... ....... I s .._... "$ 0 6 0.4 0.2 0.0 400 measured mathematical empirical , ' ' 500 600 wavelength (nm) Figure 15d. Measured vs. Simulated aq, for Station C015. 72 700 700

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1 0 I I 0 measured regression 3 0 0 0 -([) I I 0.01 0.03 0.1 0.3 Figure 16a Parameter F of aq, Simulation vs. aq,(440). 30 I ii I 0 bN 10 1-00 -5 I 0.01 I 0 measured e regression 0.03 0.1 0.3 -1 a4> ( 440) ( m ) Figure 16b Parameter u2 of aq, Simulation vs. aq,(440). 1 73

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74 1 .0 0 measured 0.8 expression 1 OJ i expression 2 ...... 0.6 """ 0 C\l 0.4 0.2 0.0 0.01 0.03 0.1 0.3 (m -1) Figure 16c. Ratio a(675)/a.p(440) vs. a(440). Solid curve: Eq. 54; filled circle: Eq. 55. region of the a curves. Thus, only 2 parameters, a.p1 and F, are important to the curve. F, a2 and a/a1 are indicators of the "package effect" The greater the "package effect," the smaller the parameter F, the bigger the band-width 2.355a2 and larger the ratio a.p/a1 That means, for in vitro phytoplankton pigment absorption coefficients (i.e. no "package effect"), from the above results, the "fatness" factor F will be close to 4.2, a/a1 around 0.2, and the half band-width around the red peak will be close to 21 nm (a similar value as reported by Hoepffner and Sathyendranath [ 1991]) Unlike Lee et al [1994b] who related the parameters to the

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75 parameters can be related to after nonlinear regression analysis. Figures 16a 16c show how those parameters relate to the measured ai 440) It is found that: aq,/aq,1 = 0.86 + 0.16ln(aq.J, normalized rms error : 17.2%, F = 2.89exp[-0.505tanh[0.56ln(aq./0 043)]], normalized rms error: 12.4%, u2 = 14.17 + 0.91n(aq,1), normalized rms error : 5.6% In this way, the curve can still be estimated if the measured Rrs is contaminated by bottom reflectance. 6.2 2 Empirical Relationship For the measured surface of cruises GOMEX and COLOR, Carder et al. [1994] found that for the SeaWiFS channels al'A)Iai675) can be expressed by a hyperbolic tangent function i.e. (54) where the parameters a0 a1 a2 and a3 are empirically determined for each SeaWiFS wavelength [Carder et al. 1994]. By the above expression, the value of approaches an asymptote at very high or very low values of ai675) (see Figure 16c). For in the range of 0.01 to 1.0 m 1 ([chi a] equivalent is in the range of 0.07 to 50 mg/m3), a simplified expression is (55)

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with parameters a0 and a1 empirically derived for each wavelength and presented in Table 6 Table 6. Parameters for the Empirical aq,(A) Simu l ation. I }.. I a o I a I I r II A I a o I a I I r2 390 5813 .0235 057 560 .3433 0659 .784 400 6843 0205 .081 570 .2950 0600 .806 410 .7782 .0129 .058 580 2784 0581 .834 420 .8637 .0064 .032 590 2595 0540 848 430 .9603 .0017 .005 600 2389 .0495 .845 440 1.0 0 -610 .2745 0578 .875 450 9634 .0060 .113 620 3197 0674 892 460 9311 .0109 .220 630 .3421 0718 898 470 .8697 0157 .235 640 3331 0685 .893 480 7890 0152 179 650 .3502 .0713 .891 490 .7558 .0256 .356 660 .5610 .1128 .884 500 7333 .0559 .710 670 8435 .1595 893 510 6911 0865 .815 680 .7485 .1388 .886 520 6327 0981 .836 690 .3890 .0812 .840 530 5681 .0969 .823 700 .1360 .0317 .751 540 5046 .0900 .805 710 .0545 .0128 .645 550 .4262 0781 .779 720 0250 0054 .531 76 Using these expressions (Eqs. 54 or 55) the number of unknowns related to aiA) is reduced to 1 (aq,(675) or a,p(440)). However, with 4 or 2 parameters for each wavelength, the a,p(A) shape will no lon ge r be the same for different waters, and the I

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changes of a.p(>..) due to "package effect" or pigment composition are considered, at least to the first order. 77 Due to the limited data sets, it is improper to claim that the values in Table 6 are final and universally usable. However, these values work very well for the waters in this study. Improved empirical results are anticipated with increased data sets and better measurements. In the following sections, simulations of a.p(A) by mathematical functions (Eqs. 51 -53) and by empirical relationships (Eq 55) are tested in the Rrs inversion for waters from the Monterey Bay and Gulf of Mexico, where both measured RrsC>-) and Ki>-) are available In the application chapter, efforts are concentrated on using the mathematical simulation, however 6.3 Derivation of the Absorption Coefficient from Rrs From the above a.p simulations, it is found that a9(440) is the most important parameter for the a.p(>..) curve. The other parameters can either be fixed or be estimated from a.p(440). For instance, for the mathematical simulation method, Az and >..2 can be fixed at 340 nm and 674 nm, respectively. If the relationships of a.p/a.p1 u2 and F versus a.p1 are used in the Rrs inversion, the number of total unknowns is reduced to 5 for theN equations: a.p1 adg(440), Sdg X and Y By minimizing the a.p.d. defined in section 4 1, it is possible to derive the 5 unknowns if N 5. Before we do this, however, ranges for the unknowns have to be set as there exist

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78 realistic limits for them It is possible that values outside of these limits may provide smaller a.p.d. values. For the exponent Y, there are no measurements available. Part of Y is 71b and as discussed in section 1.4.2, 71b changes with particle size. Generally, it is assumed that 71b 1.0 for open ocean and that 71b 0 for coastal waters [Gordon and Morel 1983, Morel 1988], although 71b can be as high as 1. 7 for river samples [Whitlock et al. 1981] and 3 0 for coccolithophorid blooms [Gordon et al. 1988]. Due to the similar curvature of the bb and adg spectra, the range for Y cannot be simply set as 0 ::5; Y < 3, because when the absorption is dominated by adg (very common for coastal waters), the compensation between the adg and bb parameters becomes strong Therefore a narrow range for Y for each station must be specified. Previous model results yield a rough relationship similar to that of Carder et al. [1994]: Y ::::: 0.86 + 1.2ln(x) with x = Rrs (440)/Rri490). Thus, the range for Y is set as: 0.9 (0.86+1.21n(x)) ::5; Y ::5; 1.1 (0.86+1.21n(x)), i.e., within 10% of the regression value and keeping Y 0 Sdg which depends on the relative abundance between detritus and gelbstoff, varies from sample to sample [Roesler et al. 1989]. By considering a detritus-to gelbstoff ratio less than 1.0, the range for Sdg is set as 0.012 ::5; sdg ::5; o 016, as Sg varies from 0.011 nm-1 to 0.019 nm-1 for different materials [Carder et al. 1989, Hawes et al. 1992], and averaged about 0.014 nm -1 for ocean waters [Bricaud et al. 1981].

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The ranges for aq,1 adg and X are much easier to establish: aq,1 > 0 adg(440) > 0, and X > 0. 79 By minimizing the a.p.d. defined in Chapter 4, the 5 unknowns are derived for each measured Rrs curve. Since there were Rrs values at -180 channels from 400 nm to 850 nm for each station there were about 180 equations available. By using the above method, Rrs curves measured from waters of Monterey Bay and the Gulf of Mexico were inverted to determine the unknowns. The results and discussion are summarized in Chapter 7.

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80 CHAPTER 7 RESULTS AND DISCUSSION OF THE INVERSE PROCESS For Rrs curves measured from waters of Monterey Bay and the Gulf of Mexico, the parameters aq, 1 ad8 ( 440), X and Y, as well as the total absorption coefficients a(440), a(486) and a(550), were derived by minimizing the a .p.d. for each station. The variable estimates were obtained using Quattro Pro 5.00, by applying the quadratic feature. For Rrs measurements, the measured Lsky may not be from the same part of the sky as that reflected off the sea-surface and entering the sensor when Lu(O+) is measured due to the sea-surface roughness. Cloudy conditions can worsen this mismatch. Therefore, instead of forcing r = 0.018, we let rand Ll in Eq. 39 be variables in the Rrs inversion; thus rand Ll were also derived when the a.p.d. was minimized. For the 45 stations available, the overall average a.p.d. is 3.4%. From Eq. 27, a(440), a(486) and a(550) were also derived from the measured Kiav). As Rrs >== 0.05b/a (Eqs. 23 and 29), Kjav) a = __ ___::....__ __ l.08D J_O)(l +20Rr) (56) In the calculation of a by Eq. 56, two sets of DlO) were used. One was 1/cos(J), and

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81 the other was derived by forcing the Kiav)-derived a(A.) to approximate a w(A) + aP(A.) + a8(A.) for A > 600 nm. In this way, errors due to sea surface roughness (wave focusing of light) and ship shadow can be reduced, and D iO) can be estimated for cloudy days when j is uncertain. 7.1 Comparison of a( 440) a( 486) and a(550) Derived Using Rn and Kd Methods Figures 17a 17c compare the results of the total absorption coefficients derived from the R n -inversion and those from K d methods (using derived D iO)) at 440 nm, 486 nm and 550 nm, respectively From Figure 17a, it can be seen that Rrs-derived a(440) is consistent with the K[derived a(440), with r = 0 94 (n=45), a slope equal to 1.03 and an average difference of 31% for a(440) in the range of 0.03 m1 to 2.5 m 1 However, the average difference dropped to 19% for a(440) le s s than 0.5 m 1 perhaps because patchy data are more likely for turbid stations When 1/cos(/) was used to replace DiO) to derive a(A.) from KiA.), the difference between the Rrs-derived and Ka-derived a( 440) was 73 % for the whole a ( 440) range. This indicates that the method used to derive a(A.) from KiA.) is preferable. These results al s o demonstrate that the method to obtain a(A.) from Rrs(A.) inversion works very well even for this wide range of water types. The 31% difference between the results can be caused by the following factors : 1) the errors in the measurements of L", LsJ:y' EiO+) and E iz), which will be transferred to Rn and Kd; 2) simplifications in the model development; 3) errors in

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-....c I s 1 0.1 0.01 0 01 R -derived rs 0 1 1 -1 a(440) from Kd (m ) Figure 17a. Comparison of Rn-derived to K[derived a(440). For Details See Text. simulation; 4) water inconsistencies between the Rn and Kd measurements (temporal 82 and spatial patchiness); and 5) method to obtain a from Kd. With the consideration of these possible sources of error, a 31% difference seems rather small and it can be claimed that we can not only qualitatively, but quite accurately derive the in-water absorption coefficient using remote-sensing techniques. Figures 17b and 17c compare a(486) and a(550) derived using the two methods r for a(486) is 0.97 (slope 1.04) between the two sets of results, with an average

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--. I s -C'lj s 0 C+-c --. OJ -0.1 0.01 0.01 e R -derived rs 1:1 0 1 1 -1 a(486) from Kd (m ) Figure 17b. Comparison of Rrs-derived to Kdderived a(486). For Details See Text. 83 error of 21% while r2 for a(550) is 0.97 (slope 0 87) with average error of 25% The 0 87 slope for a(550) means that the a(550) derived by Rrs inversion is consistently lower than that derived by K i av), with the implication that most of the 25% d i fference are systematic rather than random. One speculat i on is that simulated a.p(550) might be low because of a large F value This does not always happen however; for many clear water situations, where phytoplankton particles are small and less "package effect" oc c urs, the simulated a41(550) is usually great e r than the

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84 e R -derived TB -... .-4 1:1 I s '-"' 1'1) s 0 M 1M -... 0 lQ 0.1 lQ '-"' 0. 1 1 a(550) from Kd (m -l) Figure 17c Comparison of Rrs-derived to K [ derived a(550) For Details See Text. measured a.p(550). Furthermore, for clear water, most of a(550) come from aw(550) ( =0.064 m-1), so error in a.p(550) simu l ations has only littl e influence on a(550), and it could not exp l ain the 0 87 slope for clear water. Other possible sources of errors includ e the pure water absorption coefficient, the measurement of Eiz ), and the possibility that the actual D jO) for 550 nm might be higher than the derived values since Dd increases with scattering [Kjrk 1991]; and there were relatively higher b / a

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85 ratio at 550 nm for many waters. However, how much higher DiO, 550) should be is not clear. Further study is needed on this issue. 7.2 Comparison of Rrs-derived a(440), a(486) and a(550) Using Simulated and Measured aP In order to see how the simulated curve performs compared to the measured aP curve, the Rrs inversion process was also undertaken using the measured aP curve for each station. This time, it was assumed that we knew the curvature (shape) of aP for each station, but not the magnitude The factor fwas applied to the measured aP with no limitation set for its range fwas then derived by minimizing a p d .. Eq 9 was used for ag(A.) because ad was contained in aP. The range for S8 was set as 0.013 S8 < 0.017 nm-1 and the same range for Yas in section 6.3 was used. By the same process described in section 6 3, f, ag(440), S8 X and Y were derived by minimizing a.p.d .. Figures 18a-18c compare the results of Rrs-derived a(440), a(486) and a(550) values determined using the measured aP curves versus those determined using the simulated curves It can be seen that the results at all three wavelengths show close agreement. For the mathematical simulation (Eqs. 51 -53), the r2 values for a(440), a(486) and a(550) are 0.99 {n=48), while the average difference is 15.2% for a(440), 10.3% for a(486) and 10.5% for a(550). For the empirical relationships (Eq_ 55), the r2 is 0.98 for a(440), and 0.99 for a(486) and a(550) (n=48), while the average difference is 23.2% for a(440), 18.6% for a(486) and 10.6% for a(550)

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...-.. .....t I s -Q) > :;=j C,) ...-.. 0 -0.1 0.01 0 01 mathematical a 0 empirical a.p 1 : 1 0 1 a(440) by a p curve Figure 18a. Comparison of R1:J-derived a(440) Using Simulated and Measured ar The empirical simulation causes higher differences for the three absorption 86 coefficients, which might be due to the simplification in the expression From these results, we can say that the simulated curves work very well for the Rf:J inversion process and can be used to replace the measured aP curve. In this process the factors f for each station were also derived For all stations, it varied from 0 .18 to 2.34 with an average of 0.94, and more than 70% of the values fell in the range 0.7 to 1.3. Part of the/variation can be explained by

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..-.... ...-4 I s .._.... Q,) > :::::1 c.> d ..c ..-.... CD co .._.... d 0.1 0.01 0.01 mathematical a16 D empirical 1:1 0.1 a(486) by a p curve Figure 18b Comparison of Rn-derived a(486) Using Simulated a. and Meas u red ar patchiness and vertical structure, as the measured aP from one positio n may not represe n t th e effective particle absorptio n coefficien t of the upper water col u mn, especially when a strong vertical structure exists. Additionally, f includes the errors introd u ced in the model development, variation of aw, and compensation among the parameters. For ideal situations, i.e. the wate r co l umn is well mixed, correct values for aw, 87 a& an d scattering are used, and t h e Rrs-inversion process is well performed, fwill be a

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...-.. I s -v > M ;j Q -e. ...-.. 0 lO lO -0.1 0 mathematical a9S empirical a9S 1:1 0.1 a(550) by a p curve Figure 18c Comparison of Rrs-derived a(550) Using Simulated and Measured aP. factor correcting the "beta factor" used in the aP calculation since it is difficult to determine which "beta factor" is appropriate for our field samples (see Table 2 and Figure 12) as discussed in section 4 2 For offshore waters, pigment absorption coefficient is generally low If the volume of filtered sea water is not enough, it is quite possible that the filer pad ODp is less than 0 10 (ap equivalent is -0.06 m if the volume is 500 ml with GF/F 25 mm filter and using the "beta factor" of Bricaud and Stramski [1990]) where {3JXUI varies most. Thus for better measurement of aP 88

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0 1 0.01 0.001 0.001 0 measured f measured 1:1 0 0 0.01 0 1 1 derived a41(440) (m -t) Figure 19 Comparison of Rn-derived a.p(440) to the Measured a41(440). regardless of the "beta factor" used, a large volume of water sample must be filtered in order to reduce the "beta factor" uncertainties; this is consistent with a recent independent study by Patch et al. (in preparation). 7.3 Comparison of Rn-derived a41(440) to Measured a41(440) Using the a41 simulations described in section 6 2, surface layer a41 values 89

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90 could be derived just from Rrs without prior knowledge of the "package effect" or the chlorophyll-specific absorption coefficients Figure 19 compares the derived to the measured ai440). The r is 0.55 (n=36), but it becomes 0 92 (with 46% difference) ifjis applied to the measured values, where thefvalues were derived as in section 7 2 As pointed out by Gordon and Clark [1980] and Gordon [1992], derived values from Rrs-inversion are optical averages of the upper water column, which can not be directly compared to in-water measurements made at a discrete position when the water is not homogeneous. Hence, f might be needed to compensate for possible differences due to water patchiness, vertical structure, and/or the "beta factor." These results indicate that at this stage, the values derived by the Rrs-inversion method can be accurate to within 50 % of the phytoplankton absorption at 440 nm in the upper water column

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8 1 Introduction CHAPTER 8 APPLICATIONS 91 Since an overflight can view a large area of the ocean in a short time period, applications of remote sensing via aircraft or satellite have become increasingly popular and important. These applications include surveys of pollutant flow sediment transport, ocean circulation, estimation of [chl a] and [YS], modeling the water color at depth, and estimation of primary production, etc In the following sections, some of these applications will be discussed, as well as the modeling of upwelling radiance of Tampa Bay measured from a low flying aircraft. 8.2 Estimation of Chlorophyll Concentration The amount of phytoplankton in the ocean, often measured by the concentration of chlorophyll a ([chi a]), contributes significantly to regulation of the global climate system through its effect on the carbon cycle It also indicates the trophic status of waters, and contributes to the conversion of light into heat. Since the 1970's efforts have been made to remotely estimate [chi a] in the

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92 ocean. Empirical and semi-analytical algorithms have been reported for different waters and seasons [Gordon et al. 1980; Gordon and Morel 1983 and references cited there; Carder et al. 1991 ; Carder et al. 1994]. Applying the analytically derived and the relationship between and [chl a] can be derived through [chl a] = a;(675) where is the chlorophyll-specific a bsorption co e fficient at 675 nm. (57) In addition to the ai440) value derived from Rr:r-inversion the derivation of [chl a] depends on if we use Eq. 57. This value varies regionally and seasonally, but it has been shown to be more stable than as there is less influence due to the "package effect" at 675 nm [Carder et al 1994] Thus, if we know the value of [chi a] can be derived using Eq. 57 with the Rrs derived It is necessary to keep in mind that Rrs -derived [chl a] is an optically averaged value of the upper water column [Gordon and Cl ar k 1980, Gordon 1992] Only when the water column is well mixed, can Rrs-derived [chl a] be directly compared to measured [chi a] from a discrete location. 8.3 Estimation of the Gelbstoff Absorption Coefficient Generally a and a have similar absorption spectra in the vis i ble wavelengths, d g

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93 so it is not easy to clearly separate a8 from ad8 unless by active remote sensing such as laser induced gelbstoff fluorescence [Hoge et al 1993]. The scattering effects of detritus and gelbstoff are different, however, making it possible to estimate ai 440) from the X or Rrs values. Then ag(440) can be separated from the Rrs-derived adg(440) as discussed in sections 6 3 and 7.1. Figure 20 shows the relationship between measured ai440) and the derived X values In the log-log format r2 between ai440) and X is 0.89 (n = 39); and the best regression fit is aj440) = 61.44Xu1 Thus, with the ad8(440) and X values derived by Rrs in section 7.1, ag(440) = ad8(440) 61.44X' 3 1 (58) Eq. 58 might be strongly driven by the sediments from the Mississippi River. For other regions, different regression results may occur. Also, there may be a difference between the "beta factor" of detritus and that of phytoplankton [Bricaud and Stramski 1990, Nelson and Robertson 1993]. More data sets and better measurements are expected to improve Eq. 58 As ag(440) = a8.(440) [YS], it is possible to estimate the gelbstoff amount if we know the gelbstoff-specific absorption coefficient, a8.(440). Unfortunately, as with the chlorophyll-specific absorption coefficient, a8.(440) varies for different sources of gelbstoff [Carder et al. 1989, Hawes 1992], making it difficult to estimate [YS]. How a8 ( 440) varies is beyond the scope of th i s research, although we can choose an averaged a8 ( 440) value for the calculation of [YS]

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-.. ...-4 I s ._... -.. 0 ._... "d t3 1 I 0.1 1-0 01 0.001 0.0001 I I I I 0 0 0 measured I I regression I 0.00001 0.0001 0.001 0 01 0.1 -1 -1 X (m sr ) Figure 20 Rrs -derived X vs. Measured ai440). 8.4 Algorithm for the Absorption Coefficient at 490 nm, a(490) 94 --Optical water types can be classified by the attenuation or absorption coefficient at 490 nm [Jerlov 1976; Austin and Petzold 1981], and 11Ki490) yields a measure of the penetration depth of solar light [Gordon and McCluney 1975] in meters By analyzing the diffuse attenuation coefficient K(490) (which is proportional to Ki490)) and the in-water upwelling radiance ratio at 443 and 550 nm, Austin and Petzold [1981] developed the algorithm

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95 K(490) = 0 0883 +0.022 ( L (443)]-1.491 Lu(550) (59) where the 0.022 is the attenuation coefficient of pure sea water at 490 nm [Austin and Petzold 1981] in units of m1 Applying this algorithm to the West Florida Shelf data and other stations, Carder et al. [1992] found that the correlation between a(490) and the ratio Rrs(442)/Rrs(550) is less than that between a(490) and Rrs(520)/Rrs(560) (Figure 21a). This may partly be explained by the influence of bottom reflectance and other components that do not co-vary with chlorophyll for "case 2" waters. For regions that include shallow, coastal and "case 2" waters, an algorithm similar to Eq 59 is presented for the calculation of a( 490) based on the study of 45 stations. These stations include blue-sky and cloudy sky conditions Alternatively, a(490) could be analytically derived by using high-resolution Rrs values as discussed in sections 6. 3 and 7 .1. For the algorithm development, Kd-derived a(490) (::::: a(486), using derived DiO)) is considered as the true value. Figure 21a shows the relation between the reflectance ratio and K[derived a(490). For a(490) ranged from 0.03 to 1.5 m1 it is found that r2 is 0.96 (n=45) between ln(a(490)) and ln(RrsC520)/Rrs(560)), while r2 is 0.89 between ln(a(490)) and ln(Rrs(442)/Rrs(550)) Thus, for the best fit, an algorithm for a( 490) is

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96 10 I I 0 0 0 ""'4 +.1 1 1-0 r:t) !,.. 0 Rr/442)/Rr/550) 0 Rr8(520 )/ Rr/560) 0.1 I I 0.01 0.1 Figure 21a a(490) vs. Rn(442)/Rn(550) and R n (520) / R n (560) ..-.. I s 0 by R (442)/R (550) .._.. rs rs ..-.. 1 by R (520)/R (560) 0 rs rs O:l --1:1 .._.. d '"d (1) > 0 1 ""'4 (1) '"d 0 ""'4 +.1 0 0.01 I 0 .01 0. 1 1 fll -1 !,.. Kd derived a(490) (m ) Figure 21b. Comparison of the a(490) Algorithms

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97 a(490) = O.lJ Rr.s(520)]-3.11 -\ R,3(560) (60) with average error of 32 .5%. However, if the ratio Rr.r(442)/Rr:r(550) is used instead, the best fit generates a(490) = 0 15(R,.s( 442)]-1.37 R,3(550) (61) with average error of 49.6% Remember that the error was only 21% when the hyperspectral Rr.r-inversion method (section 7 .1) was employed Figure 21b shows the results from Eq. 60 and Eq. 61. 8.5 Modeling the Water Color at Depth Combining Eqs. 27 and 44, one can derive Ej.z) Ej..O-)e -l.OSD.,.(O)az (62) Since Dd(O) = 1/cos(J) [Gordon 1989a], Eiz) can be modeled if EiO) and a are known. From sections 6 .3 and 7.1, a can b e derived from Rr:r inversion, and EiO) can be calculated by models [Gre gg and Carder 1990, Bishop and Rossow 1991] As examples, Figures 22a 22d show the modeled versus measured Eiz ) for statio n GOlO at wavelengths 440 486 520 and 550 nm, r es pectively with EiO")

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98 Ed(440) (W/m2 ) 0.1 0 3 3 0 0 measured modeled --s .._... 10 ,.Q -+-) Q) '0 20 Figure 22a. Measured vs. Modeled Ei440) of Station GOlO. Ed( 486) (W /m 2 ) 0 1 0 .3 3 0 0 measured modeled --s .._... 10 ,.Q -+-) Q) '0 20 I' Figure 22b Measured vs. Modeled Ei486) of Station GOlO

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99 E d(520) (W /m 2 ) 0.1 0.3 3 0 0 measured modeled -s _.. 10 ....., 0-4 a> '"d 20 Figure 22c. Measured vs. Modeled Ei520) of Station GOlO. Ed(550) (W/m2 ) 0.1 0.3 3 0 ,_ I 0 measured modeled -s '-"' 1 0 ....., 0-4 Q) '"d 20 I Figure 22d Measured vs. Modeled E d(550) of Station GOIO.

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calculated by the model of Gregg and Carder [1990]. It can be seen that the model gives very close subsurface irradiance (about 10% difference) compared to the measured values; and the calculated irradiance profiles were consistent with the measured for the upper water column. 8 6 Estimation of Primary Production 100 In the past decades, primary production models have been based on pigment concentration, either by light available (P-I relationship of Platt et al [1991]) or light absorbed (P-AQ relationship of Bidigare et al. [1992]), using spectral or non-spectral expressions Recent popular models use the light absorbed approach, i.e. : chlorophyll a concentration multiplied by the irradiance and two factors: averaged chlorophyll specific absorption coefficient, and the quantum yield for carbon fixation. Thus the photosynthesis rate at depth z is [Kishino et al. 1986, Smith et al. 1989, Cullen 1990, Morel 1991 Marra et al 1992, Zaneveld et al. 1993]: PP(z) = cf>(z)[chl a]a;PAR(z) (63) where cb(z) is the quantum yield for carbon fixation and [chi a] is the chlorophyll a concentration (mg / m3). a/ is the spectrally-averaged chlorophyll-specific absorption coefficient over 400 700 nm (m2(mg chi aY1):

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101 (64) and PAR(z) is the photosynthetically available irradiance computed by (65) where E/(z,f..) in Equations 64 and 65 is the spectral scalar irradiance in quanta/m2/ nm /s. From Sathyendranath and Platt [1988], (66) Quantum yield , a measure of the phytoplankton growth rate [Platt 1986], varies with light intensity, physiological status, temperature and nutrient stress of the phytoplankton population [Langdon 1988, Cleveland et al. 1989, Smith et al. 1989]. We choose the empirical formula suggested by Kiefe r and Mitchell [1983] to express how

(z) = m PAR, +PAR(z) (67) where =
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102 4> PAR PP(z) = AP(z) m cll e -vPAR(z) PAR41 + PAR(z) (68) with AP(z) = y[C]a;PAR(z) (69) where v in Eq. 68 is a parameter to describe photoinhibition. Eq. 69 accounts for the absorbed photons by the phytoplankton pigments, in which 'Y determines the fraction of chlorophyll a relative to the total pigment and phaeo-pigment concentration [ C]. Traditional estimates of primary production based upon remote measurements are accomplished using Eqs. 68 and 69, i.e. [C] is estimated first from remotely measured signals [Vargo et al 1987, Platt et al. 1991, Balch et al. 1992] using, for example, the CZCS algorithm: [ L (443)f A [Rrs<443)fz [C] = Al L:(550) 0.95 zAl -R=rs(-5-50-) (70) where A1 = 1.13 and A2 = -1.71 [Gordon et al. 1983]. The 0. 95 value comes from Ed(443)1Ei550) 0.95. With this estimated [C], the diffuse attenuation coefficient of irradiance can be approximated by the empirical relationship suggested by Morel [1988]: (71) in which values for Kw, d and e are found in tables calculated by Morel [ 1988]. With the measured or calculated E/(0") and Kd, PAR at any depth can then be

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103 estimated However 'Y, v, 4>m, PARq, and aq, must be estimated for the calculation of PP. 'Y varies from 0.3 to 0 9, with an average of 0 75 [Morel and Berton 1989, Balch et al. 1992], the value used for our calculation m, and PARq, vary with phytoplankton physiological status, which at this point cannot be derived based upon remotely sensed measurements and must be estimated from other information. m has been reported to range from 0 .03 mol C (E i n absorbedY1 to 0 1 mol C (Ein absorbed)-1 [Bannister and Weidemann 1984 Sm ith et al 1989 Morel 1991]. As a kind of average for productive waters, 4>m is assumed to equal 0.074 mol C (Bin absorbed) -1 a value suggested by Cullen [1990]. There is little literature information, however, about the values of v and PARq,. Platt et al. [1980] found v varied from 0 to 0.0028 (W/m2Y1 I f we choose 0 0028 (W/m2)"1 for v, its equivalent value is ::::: 0 .01 (Ein/m2/dayY1 Kiefer and Mitchell [1983] found that PARq, equals about 10 Ein/m2/day a value assumed for the waters in this study The only unknown remaining is aq, This value varies with phytoplankton condition (aq,.(A)) and the light environm e nt [Morel 1978, Kish i no et al 1986]. If only remote sensing information is available aq, must be estimated from other data or an empirical value has to be p i cked for aq, In many studies an aq, value of 0 015 (mg chl a/m2)"1 has been used [Bannister 1974, Dubinsky et al. 1984, Smith et al. 1989 and Marra et al 1992] and assumed to be vertically constant. Using the CZCS algorithm, [C] is found to be a c cur a te to about a factor of 2 [Gordon and Morel 1983], and aq,(440) can v ary by a factor of 4 [Morel and Bricaud 1981 Bricaud et al. 1988, Laws et al 1990 Stram ski and Morel 1990, Carder et al.

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104 1991] due to pigment composition, "package effects," and the color of the light field That means the combined variation of [ CJ and a 4> for AP could be off on a global scale by a factor of 8 when other terms are known, although the range of uncertainty is probably significantly less than 8 here as we are not in subtropical waters (e g see Laws et al. 1990). Eq. 63 is actually a simplified version of a complete spectral expression as noted by Sathyendranath et al. [1989b], Morel [1991] and Platt et al [1991]; i.e. (72) and the absorbed photons are (73) However, those full spectral models were based on the pigment or chlorophyll a concentration, similar to Eq. 63. If aq,(f..) and a(J.) can be obtained directly and analytically from remotely measured signals (e g remote-sensing reflectance), instead of using the pigment concentration based model and the empirical relationships to obtain [CJ and the attenuation coefficient for AP(z), the problems involved in the estimation of [CJ and choosing values for 'Y and aq, will be avoided, and the accuracy of estimating AP and PP would be improved when E/(0-) m, v and PARq, are certain. From the discussions in Chapters 6 and 7, we know aq,(A) and a(J.) can be derived solely from measured Rrs(A). Thus, scalar irradiance at depth z can be

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105 calculated through Eq. 66 with Kd = 1.08 DiO) a [Gordon 1989a] E/(O ) can be determined from models of Gregg and Carder [1990] or Bishop and Rossow [1991]. Therefore, when 4>m, PAR41 and "are known, PP for any depth can be calculated through Eqs. 68 and 73 data collected from the Marine Light-Mixed Layer (ML-ML) study (21W/59N) of May 1991 (PAR and primary production measurements are in Marra et al. [1994]), two sets of calculations were made One set is derived using Eqs. 68 and 69 (referred to as the "pigment" method hereafter) as discussed at the beginning of this section. The other set is derived by Eqs 68 and 73 (referred to as the "absorption" method hereafter), where the absorption coefficients of the pigments and the total absorption coefficients are analytically derived from measured remote sensing reflectance. In both calculations, measured PAR(O) for each station was used for the calculation of PAR(z) and comparisons of the two methods, because most of the stations were taken during cloudy weather. DiO) is approximated as 1.2 [Platt et al 1991] in the "absorption" method as most of the stations were under clouds The calculated results for each day at each depth were compared with the measured primary production values and the water column-integral production. Comparisons of calculated to measured PAR and calculated to measured PP are presented in Figures 23a 23d and Figures 24a 24d, respectively. All data are summarized in Table 7 and all PP data in Figure 25 It can be seen that the "absorption" method yields close estimates of PAR(z),

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106 while PAR(z) values calculated by the "pigment" method were consistently higher, particularly at depth. One reason for this is that the CZCS pigment algorithm estimated [chl a] as much as a factor of 5 lower than the measured surface values for these waters. This had the consequence that Kd values calculated from these [C] ([chl a]/0. 75) were small. This difference could be the result of an incorrect CZCS algorithm for that environment [e.g. Balch et al 1989 Mitchell and Holm-Hansen 1991], or less likely there were substantial errors or discrepancies in the measurements of R n or "sea truth" [chi a] Additionally, the empirical relationship between Kd and [C] (Eq. 71) might not hold for these water s. The s ame field data, however, are used for both methods; so models and algorithms will be largely responsible for differences between the methods Primary production values calculated using the "absorption" method were highly comparable to the measured values, whereas the "pigment" method significantly underestimated PP, particularly in the surface waters. The aver a ge difference of the water column integrated PP is 20 % between the measured and the "ab s orption" method while it is 61% between the measured and the "pigment" method (Table 7). The r2 is 0.95 (n=24) for a linear regression between the value s calculated by the "absorption" method and that of the mea s urem e nts with a slope of 1.26 and + 32% difference; whereas the r is 0.85 (n=24) between the values calculated by the "pigment" method and that of the measurements, with a slope of 0.34 and-78% difference (see Figure 25). These results indicate that there is a factor of 3

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10 7 P A R (Ein/m2/day) 0.1 0.3 1 3 10 30 100 0 r-7 I I \1 May 1 7 aJ 10 1- o -\1 s 0 ..._., 20 0 ...c: \1 .+) 30 1Q) 0 '"d 40 r-0 "absorption" 0 "pigment" 50 I \1 mea. Figure 23a Measured vs. Modeled PAR of May 17 in ML ML. 0.1 0.3 3 1 0 30 100 0 'r7 I v May 20 1 0 i-aJ \1 - o s 20 1- o ..._., ...c: \1 .+) 30 1- 0 -Q) '"d "absorption" 40 1- 0 0 "pigment" \1 mea. 50 I I Figure 23b Measured vs Modeled PAR of May 20 in ML-ML.

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108 PAR (Ein/m2/day) 0.3 3 1 0 30 100 0 I ......,. I v May 22 I() 1 0 f-o -.. \1 s o "--"' 20 I-o ,.Q \1 -+.J 0-4 30 f-Q) 0 '"d 40 f- 0 "absorption" 0 ''pigment" 50 I \11 mea. Figure 23c. Measured vs. Modeled PAR of May 22 in ML-ML. 0.3 3 10 30 100 0 ......,. T T \1 "" May 24 I() 10 o \1 -.. o s 20 f- 0 ..._.... ...0 \1 -+.J 0-4 30 0 Q) '"d "absorption" 40 -. 0 0 "ptgment" \1 mea. 50 I I Figure 23d Measured vs. Modeled PAR of May 24 in ML-ML.

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109 Table 7. Results about PP Calculation of ML-ML, May 1991. Day May 17 May 20 May 22 May 24 PAR(O) (Ein/m2/day) 38.27 16.25 65.72 28.73 I Rrs( 443)/ Rrs(550) I 1.2 I 1.6 I 1.8 I 1.8 I I surface [chi a] (mg/m3 ) I 2.9 I 1.3 I 1.5 I 1.0 I I CZCS [chl a] (mg/m3 ) I 0.67 I 0.43 I 0.36 I 0.34 I Mea. integral PP 190 98 89 99 (m mol C/m2/day) Est. integral PP: "absorption" 235 94 105 89 (m mol C/m2/day) Est. integral PP: "pigment" 77 34 62 40 (m mol C/m2/day) improvement in the accuracy of PP calculation from remote sensing for ML-ML waters using the "absorption" method. For May 17, the calculated PP values by the "absorption" method in the euphotic zone were generally greater than the measured values. Factors that can account for these differences include possible errors in measurement and Rrs inversion, grazing effects on the measured values, and either the photoinhibition factor used was smaller than the "real" situation, or
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110 pp (umol C/1/day} 0.1 0.3 3 10 30 0 I I May 17 0 \1 1 0 I-0 -.. s 0 ... _... 20 I-0 ._. ..c: -+-) 30 Q) I-0\1. '"0 40 "absorption" I-\JC. 0 "pigment" \1 mea. 50 I I Fig ure 24a. Measured vs. Modeled PP of May 17 in ML-ML. 0.1 0.3 3 10 30 0 I I May 20 0 If 10 I-0 w -.. 0 a' s _... 20 t-0 If ..c: -+-) 30 I-0 -Q) '"0 40 I-0 \711 "absorption" 0 "pigment" \1 mea. 50 I I Figure 24b Measured vs. Modeled PP of May 20 in ML-ML

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111 pp (umol C/1/day) 0.1 0.3 3 1 0 30 0 I I May 22 O'V 10 O'V ...-.. s 0 \II --20 I-OV ..c: +) 30 Q) 0 'V '"d 40 0 .'V "absorption" 0 "pigment" 50 I 'V mea. 1 Figure 24c. Measured vs Modeled PP of May 22 in ML-ML. 0 1 0.3 1 3 10 30 0 I T May 24 0 117 10 0 117 ...-.. 0 .'V s 20 I-0 .v ---..c: +) 30 0 117 Q) '"d 40 0 .'V "absorption" -0 "pigment" 'V mea. 50 I I Figure 24d. Measured vs. Modeled PP of May 24 in ML ML.

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112 "absorption" 10 0 "pigment" ..-.. 1""'"'4 --1:1 "'-... u 1""'"'4 0 0 3 s 0 ..._.. 1 "'t:1 0 Q) .+-) ro 1""'"'4 0 :;:j 0 .3 C) 0 1""'"'4 ro C) 0 0 1 0 1 0.3 3 10 measured PP (umol C/1) Figure 25. Measured vs Modeled PP of ML-ML, May 1991. "pigment" and "absorption" methods occurred on the only sunny day of the cruise May 22, where measured surface layer production was smaller than in the second layer. Other than measurement errors this is an indication of increased photoinhibition, as suggested by the calculated values of the "ab s orption" method The calculated PP values by the "absorption" method however are greater than the measured values for the fust four depths (40 % ) Possible reasons for thi s dif ference might be an overestimation o f
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this environment, since m and might be a function of light history The other 3 cruise days were overcast with an expected adaptation of the plants to a low light environment. The sudden exposure to the bright light probably caused extreme photoinhibition in the dark-adapted phytoplankton population with the resultant overestimation of PP by the "absorption" method. 113 The PP values calculated by the "pigment" method for the sunny day, however, do not show a photoinhibition response in the surface waters (Figure 24c). One reason for this is that aq, not only varies with the chlorophyll-specific absorption coefficient, but it also varies with the light field (Eq. 64). An aq, value for surface water is not necessarily appropriate for the whole water column, even for well-mixed oceans [Kishino et al. 1986]. So, the a"' value is one of the major sources of error in PP calculations by the traditional method. For the waters studied, PP values calculated by the "pigment" method were significantly lower than the measured rates. Since PP values calculated by the "absorption" method were close to measured values, our value of m, 0.074 mol C (Ein absorbedY1 is apparently close to the actual value. Therefore, the differences between the "pigment" method calculated and measured PP are largely due to the estimation of [C] and the product of ')'[C]aq, However, when only remote-sensing data are available, it is difficult to know which are the "correct" aq, and 'Y[C] values, as they depend upon empirical parameters. What makes things interesting is that a factor of 2 increase in both [ C] and a"'. will make calculated PAR and P P both close to the measured values. Table 7 pigment data, however, suggest that the CZCS

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algorithm accounts for most of the error. This is consistent with the speculation of Platt et al. [1988] that determination of biomass by remote sensing dominates the error in primary production estimation. 114 Comparing Eqs. 69 and 73, the main difference between the "absorption" and "pigment" methods is how AP(z), the absorbed energy by phytoplankton pigments, is obtained from remote-sensing data. In the traditional method, calculation of AP depends heavily on 4 parameters: -y, A1 A2 and a"'. When only remote-sensing signals exist, it is difficult to verify which values should be used for each of these parameters, although each of them could be tuned empirically to specific regions and specific seasons [Platt et al. 1991]. Since there are errors associated with each number the cumulative error in AP could then be very high even if PAR is correct. In the AP calculation by the "absorption" method, however, the phytoplankton absorption and the total absorption are analytically derived from measured Rrs. Thus, most of the error comes from the Rrs-inversion process. It is believed that absorption coefficients derived from Rrs inversion have an accuracy better than 50% for "case 1" and "case 2" waters (Chapter 7). This means that the accuracy in the AP calculation by the "absorption" method could be within 50% compared to the errors as great as 400% derived using the traditional method In this "absorption" method suggested here, the mid-step, i.e. deriving [chl a] and estimating a value for a"', is eliminated. The result is highly improved accuracy in deriving AP and PP. The remaining challenge for the calculation of PP through remote sensing is how to remotely obtain accurate estimation of the physiological parameters [Balch et al. 1992] such as 4>m,

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115 PAR.p and v that could perhaps be based on light history, chlorophyll fluorescence efficiency [Chamberlin et al. 1990], and surface temperature anomalies [Kamykowski and Zentara 1986]. In conclusion of this section: a) Based on the results presented here, the a.p simulation works very well in modeling PAR(z) from PAR(O) and measured Rrs. Combined with parameters regarding photosynthesis, the PP values calculated by the "absorption" method were close to the measured ones with r2 = 0.95 and slope = 1.26; which is a factor of 3 improvement in PP estimation accuracy over the traditional method These results also indicate that the combined PP model, 4> PAR PP(z) = AP(z) m ell e -vPAR(z) PARI!>+ PAR(z) (74) works well for the ML-ML waters. b) It is not necessary to know [chi a] and a .p for the calculation of P P In the traditional method, the estimation of [chi a] (or [C]) and a.p separately is an inherent disadvantage in calculating PP based upon satellite or aircraft remote sensing of ocean color From the remote-sensing point of view with regard to remote estimation of PP, what is really needed is the absorbed energy by phytoplankton and the physiological parameters regarding the photosynthesis by phytoplankton So, it is preferable to shift the primary production model from the pigment-concentration based to the pigmentabsorption based

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8. 7 Modeling Total Radiance (L1 ) Measured from a Low-flying Aircraft (Blimp Shamu) 116 In January 1993, the total radiance, L0 of Tampa Bay was measured from the Sea World blimp "Shamu". These L1 measurements covered waters over sandy and grassy bottoms and dark, gelbstoff-rich waters. Although values of Ed were measured before and after the flight, no Ed or proper LsJ.y data could be collected when L1 was measured, so no precise Rrs could be derived using standard methods. However, LsJ.y from part of the sky was measured, and its spectral shape might be considered approximately correct. Then, with the method discussed in Chapter 7, the parameters r and .!l were used to estimate the sky radiance which enters the sensor. Thus the measured L1 could be modeled, and the in-water absorption coefficient and the water depth for optically shallow water could be derived. The total radiance entering a sensor in clear air is [Gordon and Wang 1994] (75) where LR is the contribution due to Rayleigh scattering in the atmosphere, LA is the contribution due to aerosol scattering, and exp(-rA r d determines the attenuation of atmosphere to the upwelling radiance. Since the altitude of the blimp was only about 50 m over the water surface, exp( -rA rG) is = 1 and the small contributions due to LR and LA are combined into rLsty and !lEd of Eq. 40, so

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6000 ......-..,. 2 4000 ::s 0 C) 2000 --measured ---modeled 0 400 500 600 700 800 Figure 26a Measured vs Modeled L, of Station SH04. 6000 4000 ..., 2000 0 400 --measured -----modeled 500 600 700 wavelength (nm) Figure 26b. Measured vs Modeled L, of Station SH34 800 117

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-.. rn .+-) ::;j 4000 0 2000 C,) 0 400 measured modeled 500 600 700 wavelength (nm) Figure 26c. Measured vs. Modeled L, of Station SH35 1tL 118 800 L1 = (Rrs +11)--0 +rLsJcy (76) RG L0 was estimated by interpolation between the preand post-flight measurements of LG. With the aq, simulation discussed in section 6 .2 L, of waters over sandy bottoms (SH04), grassy bottoms (SH35), and dark waters (SH34) were modeled. Since Rrs and L, are interchangeable when other terms are certain, Rrs curves of above situations were also modeled at the same time Figures 26a 26c show the measured and modeled L,, while Figures 27a 27c show the measured and modeled Rrs. It can be seen that excellent model results were achieved for these waters. The bottom albedo of the sandy bottoms came

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0.02 0.01 0 .00 400 500 600 ' measured modeled 700 800 Figure 27a Measured vs. Modeled Rrs of Stat io n SH04 0.008 0.004 0.000 400 measured modeled 500 600 700 wavelength (nm) Figure 27b. Measured vs. Modeled Rrs of Station SH34. 800 119

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0.004 measured modeled bottom albedo fl) 0 .002 / .. ....................................... 0 .000 400 500 600 700 wavelength (nm) Figure 2 7c Measured vs. Modeled Rrs of Station SH35. 0 1 0.0 800 120 0 "'0 Q) ,.c s 0 -+-' -+-' 0 ,.c from Figure 10, while the bottom albedo of the grassy bottoms came from reflectance of vegetation [Tucker and Miller 1977].

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121 CHAPTER 9 CONCLUSIONS OF PART B 9.1 The phytoplankton absorption coefficient, a"'(f.) can be simulated using the following expressions: 1) mathematical functions : ,j A.-A-,)2 400 1 570, a (.i..) = a e -.\In too (77) acp(656) a41(570) (78) 570 < .A < 656, a,(.A) = a41(570) + 656 570 (.A 570) and (79) 2) empirical r e lationsh i ps: (80) The mathematical expression involves 6 par a m e ters, but only 4 of them (a"'1 F, a"'2 and u2 ) vary significantly amon g differ e nt wat e r s 3 of the 4 parameters, F u2 and a"'/a"'1 could be estimated from the value of a"'1 throu g h

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F = 2.89exp[-0 505tanh[0 56ln(aq,/0.043)]], U2 = 14 .17 + 0.91n(aq,1 ) ao(A.) and a1(A.) of Eq 80 for each wavelength were empirically derived 122 (Table 6) So, using either method, aq,(X.) curve can be simulated when aq,(440) is known Comparing the two methods, mathematical functions create a smooth aq, curve, but with more potential to adjust the curve shape The empirical relationships, however, provide empirical spectral finesse to the a curves 9 2 With the above aq,(A) expressions, the inverse problem of Rrs can be reasonably well solved. For waters of Monterey Bay and the Gulf of Mexico, the Rrs-derived total absorption coefficients at 440 nm, 486 nm and 550 nm were consistent with the values derived from Kd. When using the mathematical simulation the average difference is 31% for a(440), 21% for a(486) and 25% for a(550) for a(440) ranged from 0 03 m1 to 2 5 m1 These results were also consistent with the values derived using measured aP curves These results demonstrate that the aq,(X.) simulations can be used in remote-sensing applications without prior knowledge of the in-water optical properties, such as chlorophyll-specific absorption coefficient. 9.3 The ranges for the 5 variables (aq,1 adg(440), Sdg X, and Y) are close to realistic situations 9.4 With the aq,(X.) simulation, the e s timation of primary production in the euphotic zone can be carried out just from measured Rrs and surface PAR The problems associated with the traditional method, i.e. estimating [chi a] and using a chlorophyll-specific absorption coefficient are avoided For data collected in the ML-

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123 ML May 1991 waters, r is 0.95 between the calculated and measured PP values, with a slope of 1.26 and 32% average error This is a factor of 3 improvement in the accuracy of PP estimation by using the suggested method over the traditional method for those waters. However challenges remain to remotely estimate the physiological parameters since they might be functions of nutrient stress, life stage, light history, etc.

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10.1 Summary CHAPTER 10 SU1\1MARY AND FUTURE WORK a. A remote-sensing reflectance (Rrs) model is developed, including terms for the contributions of bottom reflectance, gelbstoff fluorescence, and water Raman scattering. 124 b The remote-sensing reflectance model is tested for a wide range of water types, and an average error of 3.4% is obtained between the measured and modeled remote-sensing reflectance curves. This result indicates that the forward problem, to interpret the water color or remote-sensing reflectance in terms of in-water constituents, is well solved. c. A six parameter model is developed to simulate the spectral absorption coefficient of phytoplankton pigments with an average error of about 11%. It can be used in the remote-sensing reflectance modeling and inversion. d. Using the model and the Rrs-inversion methodology developed above, in-water absorption and scattering coefficients can be analytically derived solely from the remotely measured signals. For a(440) ranging from 0.03 to 2.5 m, the remote sensing-derived a(440) values are within 31% of the in-water measured values. This

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125 indicates that the inverse problem, to analytically derive in-water optical components from remotely measured signals alone is reasonably well solved. e A new approach is suggested for the estimation of primary production based on remote-sensing measurements. In this new approach, the primary production model is based on the phytoplankton pigment absorption coefficient, instead of the phytoplankton pigment concentration. f Using the new approach for a study in the North Atlantic during May 1991 the estimated primary production at depth in the euphotic zone based on remote sensing was within 32% of the measured values This result is about a factor of 3 improvement in the estimation accuracy over a traditional method, which is based on the pigment concentration. 10.2 Future Work a Validation for values of X and Y is not complete which requires independent in-water measurements of the values and distributions of the spectral volume scattering function and radiance field. Hopefully, this will be solved in the coming years with the development of new, sophisticated instrumentation b Further coupled in-water and remote sensing measurements for a wide range of waters are necessary in order to i mprove and expand the usefulness of the model and simulations suggested in this study.

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126 c. Part of the errors in the component derivation come from the internal compensations among the parameters In order to improve the accuracy of derived in-water components from remotely sensed signals alone theoretical and experimental studies about the parameters need be carried out. For example, how great is the compensation among the parameters? What should be the right ranges for Y and Sd8? How to determine their ranges? etc d. Methods to accurately derive a(f.) from Kif-) need further study e Coupled investigations between primary production and remote-sensing reflectance measurements need to be carried out widely to generate more data to test and improve the suggested new approach f. For the remote estimation of primary production, methods must be pursued to remotely or empirically estimate changes of the physiological parameters, perhaps by their co-variance with some remotely measured variables such as sea-surface temperature anomalies, wind-stress history, and light history, etc

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127 REFERENCES CITED Austin, R. W. 1974 Inherent spectral radiance signatures of the ocean surface. Ocean Color Analysis. S/0 Ref. 7410. Austin R W. 1979. Coastal zone color scanner radiometry Ocean Optics VI Proc. SPIE. 208: 170-77. Austin, R. W., and T. J. Petzold. 1981. The determination of the diffuse attenuation coefficient of sea water using the coastal zone color scanner. In Oceanography from space, ed. J. F. R. Gower, 239-56. New York: Plenum Press Balch, W. M R. W. Epp1y, M. R. Abbott, and F M. H. Reid. 1989. Bias in satellite-derived pigment measurements due to coccolithophores and dinoflagellates. J. Plankton Res 11:575-81. Balch, W. M., R. Evans, J. Brown, G. Feldman, C. McClain and W Esaias. 1992. The remote sensing of ocean primary productivity: use of a new data compilation to test satellite algorithms. J. Geophys Res 97 : 2279-293. Bannister, T. T. 1974. Production equations in terms of chlorophyll concentration, quantum yield, and upper limit to production Limnol. Oceanogr 19:1-12. Bannister, T. T. 1979. Quantitative description of steady state, nutrient-saturated algal growth, including adaptation. Limnol. Oceanogr. 24 : 76-96. Bannister, T T., and A. D. Weidemann. 1984 The maximum quantum yield of phytoplankton photosynthesis in situ J. Plankton. Res. 6:275-94 Bidigare, R. R., M. E. Ondrusek, J. H. Morrow, and D. A. Kiefer. 1990. In vivo absorption properties of algal pigments Ocean Optics X, Proc. SPIE 1302:290302. Bidigare, R R., B. B. Prezelin, and R C. Smith. 1992. Bio-optical models and the problems of scaling. In Primary production and biogeochemical cycles in the sea, ed P G. Falkowski and A. D Woodhead, 1175-212. New York: Plenum Press.

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Bishop J. K., and W. B. Rossow. 1991. Spatial and temporal variability of global surface solar irradiance. J. Geophys. Res. 96: 16,839-16,858 128 Bricaud, A., A. Morel, and L. Prieur 1981. Absorption by dissolved organic matter of the sea (yellow substance) in the UV and visible domain s. Limnol. Oceanogr. 26:43-53. Bricaud A., and A. Morel. 1986. Light attenuation and scattering by phytoplanktonic cells: a theoretical modeling. Appl Opt. 25:571-80 Bricaud, A., A. L. Bedhomme and A. Morel. 1988. Optical properties of diverse phytoplanktonic species: experimental results and theoretical interpretation. J Plankton Res. 10:851-73. Bricaud, A., and D. Stramski 1990. Spectral absorption coefficients of living phytoplankton and nonalgal biogenous matter: A comparison between the Peru upwelling area and the Sargasso Sea Limnol. Oceanogr. 35 : 562-82. Carder, K L., and R. G. Steward. 1985. A remote-sensing reflectance model of a red tide dinoflagellate off West Florida Limnol Oceano gr 30:286-98. Carder, K. L., R. G. Steward, J. H. Paul and G. A Vargo. 1986. Relationships between chlorophyll and ocean color constituents as they affect remote-sensing reflectance models. Limnol. Oceanogr. 31:403-13. Carder, K. L., R. G. Steward, G R. Harvey, and P. B. Ortner. 1989. Marine humic and fulvic acids : their effects on remote sensing of ocean chlorophyll. Limnol. Oceanogr. 34:68-81. 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. J Geophys. Res. 96:5369-378 Carder, K. L., S. K. Hawes, K. A. Baker, R. C Smith, R G. Steward, and B. G. Mitchell. 1991. Reflectance model for quantifying chlorophyll _gin the presence of productivity degradation products J. Geophys. Res. 96: 20,59920,611. Carder, K. L., Z. P. Lee, T. G Peacock, R. G. Steward, and C 0. Davis. 1992. Aircraft algorithms for water absorption coefficients: rain or shine EOS 73, April. Carder, K. L., P. Reinersman, R. F. Chen, F. Muller-Karger, C 0. Davis, and

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M Hamilton 1993. AVIRIS calibration and application in coastal oceanic environments Remote Sens Environ. 44:205-16. Carder, K. L., S. K Hawes, and Z P. Lee 1994. SeaWiFS algorithm for chlorophyll a and colored dissolved organic matter in a subtropical environment. SeaWiFS working group repon. 129 Chamberlin W. S C R. Booth, D A Kiefer, J H Morrow, and R. C. Murphy. 1990. Evidance for a simple relationship between natural fluorescence, photosynthesis and chlorophyll in the sea. Deep-Sea Res 37 : 951-973. Clark, D K 1981. Phytoplankton algorithm for the Nimbus-? CZCS. In Oceanography from space ed J R. F. Gower, 227-38. New York : Plenum Press Clark, R. K., T H. Fay, and C. L. Walker. 1987. Bathymetry calculations with Landsat 4 TM imagery under a generalized ratio assumption Appl. Opt. 26: 4036-4038 Cleveland, J. S. M. J Perry, D A Kiefer, and M C. Talbot. 1989. Maximal quantum yield of photosynthesis in the northwestern Sargasso Sea. J Marine Res. 47: 869-86 Cleveland, J. S and A. D Weidemann 1993 Quantifying absorption by aquatic particles: A multiple scattering correction for glass-fiber filters Limnol. Oceanogr 38:1321-327. Coble, P. G., S. A. Green, N V Blough and R. B. Gagosian 1990 Characterization of dissolved organic matter in the Black Sea by fluorescence spectroscopy. Science 348:432-35. Collins, D J., J. A. Bell, R Zanoni, I. S. McDermid, J B Breckinridge, and C. A. Sepulveda. 1984 Recent progress in the measurement of temperature and salinity by optical scattering. Ocean Optic s VII Proc SPIE 489 :2 47-69 Cullen, J. J. 1990. On models of g r owth and photosynthesis in phytoplankton Deep Sea Res 37:667-83. Dubinsky, Z T Berman, and F Schanz 1984. Field experiments for in situ measurements of photosynthetic efficiency and quantum yield J. Plankton Res. 6:339-49 Gordon, H. R., and 0 B Brown 1974. Influence of bottom depth and albedo on the diffuse reflectance of a flat homogeneous ocean. Appl Opt 13:2 153-159.

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Gordon, H. R., and W. R. Mcluney. 1975. Estimation of the depth of sunlight penetration in the sea for remote sensing. Appl. Opt. 14:413-16 Gordon, H. R., 0. B Brown, and M. M Jacob s. 1975. Computed relationship between the inherent and apparent optical properties of a flat homogeneous ocean. Appl. Opt. 14:417-27. 130 Gordon, H. R. 1979. Diffuse reflectance of the ocean: the theory of its augmentation by chl a fluorescence at 685nm. Appl. Opt. 18: 1161-166. Gordon, H R., and D K. Clark. 1980. Remote sensing optical properties of a stratified ocean: an improved interpretation Appl. Opt. 19:3428-430 Gordon, H. R., D K Clark, J. L. Mueller, and W A. Hovis. 1980. Phytoplankton pigments from the Nimbus-7 coastal Zone Color Scanner: Comparisons with surface measurements. Science 210:63-66. Gordon, H R., R C Smith, and J R V. Zaneveld 1980 Introduction to ocean optics Ocean Optics VI, Proc. SPIE. 208:1-43. Gordon, H R., and A. Morel. 1983 Remore assessment of ocean color for interpr e tation of sarellire visible imagery: A review. pp 44 New York: SpringerVerlag Gordon, H. R., D K Clark, J. W Brown 0 B Brown, R. H. Evans, and W. W Broenkow 1983 Phytoplankton pigment concentrations in the Middle Atlantic Bight: Comparison of ship determinations and CZCS estimates Appl. Opt. 22:20-36. Gordon, H. R. 1985. Ship perturbation of irradiance measurements at sea 1: Monte Carlo simulations. Appl. Opr. 24 :4 172-182 Gordon, H. R. 1986. Ocean color remote sensing : Influence of the particle phase function and the solar zenith angle Eos Trans. AGU 14:1055. Gordon, H. R., 0. 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. J Geophys. Res. 93 : 10,909-10,924 Gordon H R. 1989a Can the Lambert-Beer law be applied to the diffuse attenuation coefficient of ocean water? Limnol Ocean.ogr. 34:1389-409 Gordon, H. R. 1989b Dependence of the diffuse refle c tance of natural waters on the s un angle. Limn.ol. Ocean.ogr. 34: 1 484-489.

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132 Kiefer, D. A and B G. Mitchell. 1983 A simple, steady state description of phytoplankton growth based on absorption cross section and quantum efficiency. Limnol. Oceanogr 28:770-776. Kirk, J. T 0 1984 Dependence of relationship between inherent and apparent optical properties of water on solar altitude Limnol Oceanogr 29 : 350-56. Kirk, J. T 0 1986. Light and photosynthesis in aquatic ecosystems pp 117 Cambridge: Cambridge University. Kirk, J. T 0 1991. Volume scattering function average cosines, and the underwater light field Limnol. Oceano gr. 36:455-67 Kishino, M., C R. Booth, and N. Okam i 1984. Underwater radiant energy absorbed by phytoplankton, detritu s dissolved organic matter, and pure water. Limnol. Oceanogr. 29:340-349. Kishino, M., M. Takahashi, N. Okami, and S Ichimura 1985. Estimation of the spectral absorption coefficients of phytoplankton in a thermally stratified sea. Bull Mar. Sci 37:634-42. Kishino, M., N. Okami, M. Takahashi, and S Ichimura. 1986 Light utilization efficiency and quantum yield of phytoplankton in a thermally stratified sea. Limnol. Oceanogr 31: 557-66. Krijgsman, J. 1994. Optical remote sensing of water quality parameters: Interpretation of reflectance spectra Ph.D. dissertation Delft University. Netherlands Langdon, C. 1988 On the causes of interspecific differences in the growth-irradiance relationship for phytoplankton J. Plankton Res 10 : 1291-312. Laws, E. A G R Ditullio, K. L. Carder, P R. Betzer and S K Hawes. 1990. Primary production in the deep blue sea Deep-Sea Res 37:715-730 Lee, Z. P., K L. Carder S. K Hawes, R G. Steward, T G Peacock, and C. 0. Davis. 1992 An interpretation of high spectral resolution remote sensing reflectance. Optics of the Air -Sea Interface Proc SPIE. 1749:49-64. Lee z P K. L. Carder, S. K. Hawes, R. G. Steward, T G Peacock, and C. 0 Davis 1994a A model for interpretation of hyperspectral remote sensing reflectance Appl Opt 33: 5721-732. Lee, z P., K L. Carder and T. G Peacock. 1994b Hyperspectral modeling of

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133 remote sensing reflectance: from the Florida Shelf to the Mississippi river. Eos Trans AGU 75 : 193. Lyzenga, D. R. 1978 Passive remote-sensing techniques for mapping water depth and bottom features Appl Opt. 17:379-83. Marra, J., T. Dickey, W. S Chamberlin, C. Ho, T Granata, D.A. Kiefer, C. Langdon, R. C Smith, K. S Baker, R. R. Bidigare, and M. Hamilton 1992. Estimation of seasonal primary production from moored optical sensors in the Sargasso Sea. J. Geophys. Res. 97 : 7399-412. Marra, J., C Langdon, and C. A Knudson 1994 Primary production and water column changes and the demise of a phaeocyst is bloom at the Marine Light Mixed Layers site (59 N/2!0W, North Atlantic Ocean). J. Geoph ys. Res Accepted Marshall, B. R., and R C. Smith 1990 Raman scattering and in-water ocean properties Appl. Opt. 29:71-84. Mitchell, B. G., and D. A Kiefer. 1988. Chi-a specific absorption and fluorescence excitation spectra for light limited phytoplankton. Deep-Sea Res 35:635-63. Mitchell, B G 1990. Algorithms for determining the absorption coefficient for aquatic particles using the quantitative filter technique. Ocean Optics X, Proc. SPIE 1302:137-48 Mitchell, B. G., and 0 Holm-Hansen. 1991. Bio-optical properties of Antarctic Peninsula waters: differentiation from temperate ocean models. Deep-Sea Res. 38:1009-1028. Mobley, C. D., B. Gentili H R. Gordon, Z Jin, G W. Kattawar, A Morel, P. Reinersman, K. Stamnes, and R. H. Stavn. 1993 Comparison of numerical models for computing underwater light fields Appl. Opt 32:7484-504 Montgomery K., J J Petrovic, and N P Murarka. 1994 Guidance and control of unmanned air veh i cles. Association for unmanned vehicle systems symposium. Detroit, MI. May 23-25. Morel, A. 1974 Optical properties of pure water and pure sea water. In Optical aspects of oceanography, ed. N G. Jerlov and E. S. Nielsen, 1-24. New York : Academic Morel, A., and L. Prieur 1977 Analysis of variations in ocean color. Limnol Oceanogr. 22:709-22.

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135 Peacock, T. G. 1992. Some marine light sources and their effects on remote sensing reflectance models. Master's Thesis. Dept. of Marine Science, University of South Florida. Peacock, T. G., K. L. Carder, P. G. Coble, Z. P. Lee, and S. K. Hawes. 1994. Long-path spectrometer for measuring gelbstoff absorption in clear waters. Eos Trans. AGU 75:22. Pegau, W. S and J. R. V. Zaneveld. 1993. Temperature-dependent absorption of water in the red and near-infrared portions of the spectrum Limnol. Oceanogr. 38:188-92. Petzold, T J. 1972. Volume scattering functions for selected natural waters. Scripps lnst. Oceanogr. Visibility Lab. SIO Ref 72-78. Platt, T., C L. Gallegos, and W. G. Harrison. 1980 Photoinhibition of photosynthesis in natural assemblages of marine phytoplankton. J. Mar. Res. 38:687-701. Platt, T. 1986. Primary production of ocean water column as a function of surface light intensity: algorithms for remote sensing. Deep-Sea Res 33:149-63. Platt, T., S. Sathyendranath, C. M Caverhill, and M. R. Lewis. 1988. Ocean primary production and available light: further algorithms for remote sensing. Deep-Sea Res. 35:855-79. Platt, T., C. Caverhill, and S. Sathyendranath. 1991. Basin-scale estimates of oceanic primary production by remote sensing: the North Atlantic. J. Geophys. Res. 96: 15,147-15,159. Polcyn, F. C., W. L. Brown, and I. J. Sattinger. 1970. The measurement of water depth by remote-sensing techniques. Report 8973-26-F, Willow Run Laboratories, the University of Michigan, Ann Arbor. Preisendorfer, R. W. 1976. Hydrologic optics vol. 1: introduction. NTIS PB259 793/8ST. National Technical Information Service, Springfield, Ill. Roesler, C. S., M. J. Perry, and K. L. Carder. 1989. Modeling in situ phytoplankton absorption from total absorption spectra in productive inland marine waters. Limnol. Oceano gr. 34:1510-523. Roesler, C .S., and M. J. Perry. 1994. A robust model for determining in situ phytoplankton absorption and fluorescence emission spectra from reflectance. J. Geophys. Res .. Submitted.

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136 Sathyendranath, S., and T Platt 1988. The spectral irradiance field at the surface and in the interior of the ocean: a model for applications in oceanography and remote sensing. J Geophys Res 93:9270-280. Sathyendranath, S., L. Prieur, and A. Morel. 1989a A three-component model of ocean colour and its application to remote sensing of phytoplankton pigments in coastal waters. Int. J. Rem o te Sensing 10:1373 394 Sathyendranath S T. Platt, C M. Caverhill, R. E. Warnock, and M. R. Lewis, 1989b Remote sensing of oceanic primary production : computations using a spectral model. Deep-Sea Res. 36:431 53. Smith, R C., and K. S. Baker. 1981. Optical properties of the clearest natural waters. Appl. Opt. 20:177-84. Smith R C., B. B. Prezelin, R. R Bidigare, and K S Baker. 1989. Bio-optical modeling of photosynthetic production in coastal waters. Limno l Oceano gr. 34: 1524-544 Spitzer, D., and R W J Dirks. 1985 Contamination of the reflectance of natural waters by solar-induced fluorescence of dissolved organic matter. Appl. Opt. 24 : 444-45. Spitzer, D., and R. W J Dirks 1987 Bottom influence on the reflectance of the sea Int J. R e mote Sensing 8 : 279-90. Stavn, R. H., and A. D. Weidemann. 1988. Optical modeling of clear ocean light fields: Raman scattering effects. Appl. Opt. 27 : 4002-4011. Stavn, R. H. 1990 Raman scattering effects at the s horter visible wavelengths in clear ocean waters. Oc ean Optics X, Pr oc SPIE 1302:94-100 Stramski, D., and A. Morel. 1990 Optical properties of photosynthetic picoplankton in different physiological states as affected by growth irradiance Deep-Sea Res. 37:245-66 Tam, A. C., and C K. N. Patel. 1979 Optical absorptions of light and heavy water by laser optoacoustic spe c troscopy. Appl. Opt. 18: 3348-358 Tucker, C. J., and L. D Miller. 1977. Soil spectra contributions to grass canopy spectral reflectance Photogrammetric Engineering and Remote Sensing 43(6): 721-26

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Vargo, G A ., K. L. Carder, W. Gregg, E Shanley, and C. Heil. 1987 The potential contribution of primary production by red tides to the west Florida shelf ecosystem. Limnol. Oceano g r 32:762-67. Whitlock, C. H., L. R. Poole, J. W. Usry, W. M. Houghton W. G. Witte 137 W. D. Morris, and E. A. Gurganus. 1981. Comparison of reflectance with backscatter and absorption parameters for turbid waters. Appl Opt 20:517-22 Yentsch, C. S., and C. M. Yentsch. 1979. Fluorescence spectral signatures: the characterization of phytoplankton populations by the use of excitation and emission spectra J. Mar. Res 37 : 471-83. Yentsch, C. S., and D. A. Phinney 1985 Spectral fluorescence : an ataxonomic tool for studying the structure of phytoplankton populations J. of Plankton Res 7: 617-32 Yentsch, C. S., and D. A. Phinney. 1992. Spectral diffuse attenuation of phytoplankton measured by the filter pad technique are we on the right track? Ocean Optics XI, Proc SPIE 1750 : 180-86. Zaneveld, J R. V 1982 Remote sensed reflectance and its dependence on vertical structure: a theoretical derivation. Appl Opt. 21: 4146-150 Zaneveld, J. R. V, J. C. Kitchen, and J. L. Mueller. 1993. Vertical structure of productivity and its vertical integration as derived from remotely sensed observations. Limnol. Oceanogr. 38:1384-393 Zaneveld, J. R. V 1994. A theoretical derivation of the dependence of the remotely sensed reflectance on the inherent optical properties. Eos Trans. AGU 75 : 192

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138 APPENDICES

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APPENDIX 1 EXACT SOLUTION OF NADIR R r s ((}) BY THE RADIATIVE TRANSFER EQUATION The radiative transfer equation for nadir radiance L.,(z) is where L., is dL,/z.) dz L,: = f p(a)L(81, q/,z)dw1 4rt If we separate the radiance field L into two pa r t s : L d for the radiance in the 139 (1) (2) downwelling field, and, L" for the radiance in the upwelling field, then Eq. 2 can be re-written as (3) Define the light-averaged-backwardVSF {3 b and VSF-averaged-upwellingradiance L" similarly to Zaneveld [1982, 1994], re s pectively: (4) then Eq 1 becomes

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140 (5) If we define the diffuse-attenuation-coefficient for nadir-viewed radiance Lu as (6) then from the Rrs definition, the nadir in-water remote-sensing reflectance Rrs(Q) is (7) where E =-(8)

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141 APPENDIX 2. DIFFUSE ATTENUATION COEFFICIENT OF AN EXTENDED LAMBERTIAN RADIANCE SOURCE Ej.:z.) I el I I I I z Figure 28. Schematic light field of an extended Lambertian source. Figure 28 illustrates the light field illuminated by an extended Lambertian source. L0 is the source radiance and it is the same for all directions. Define k as the diffuse attenuation coefficient of radiance, then the radiance at distance z in direction e is (1) and the irradiance at that distance is

PAGE 161

It kz Ej_z) = 2rtL0J02 ecosc e>cos(8)sin(8)d8 Notice that the source irradiance is then, Ej_O) = rtL0 Ej_z) n kz = 2 J02 e -cos(e) cos(8)sin(8)d8 EJO) From Gordon [1989a], we have Ejz) EJO) -l.OSD j.O )..-;z z e and for a Lambertian distribution, DiO) = 2 so It kz e-2 16KZ z 2fo2e -coo(S)cos(8)sin(8)d8 142 (2) (3) {4) (5) (6) Define k = !;K, KZ = 7, then for 7 in the range of 0.5 to 2.0, !: varies from 1.37 to 1.62 for Eq 6 to hold So, in a general cas e, !: :::::: 1.5 is used as an average. Also, from Eq 36, for bottom albedo p = 0 .5, 7 = 0.5 means R r / :::::: 0 022 sr 1 and r = 2 means Rr/ :::::: 0.0004 sr1 If the average remote-sensing reflectance from the water column is 0.005 sr 1 r = 0 5 means R r / may contribute -99% of the total signal, and r = 2 means R,./ contribute less than 10% of the total signal, which indicates 0 5 to 2 of r is the general range where remote-sensing reflectance from the bottom could be verified

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APPENDIX 3. REMOTE-SENSING REFLECTANCE FROM GELBSTOFF FLUORESCENCE (RJ) AND WATER RAMAN SCA TIERING (RrsR) 143 For z positive downward from the surface (Figure 5), with the consideration of isotropic to first order the inelastic radiance in the direction 8 and the upwelling irradiance (E.,,ie) at depth z due to the depth interval dz are simplified to (1) and dE (z,A.) = -21tJn dL (z,8 J..)cos(8)sin(8)d8 u ,re n/2 u,re = 21tJ p ().. ,A.)E (z,A.x)d)..xdz, A r.e X o z (2) = Dll +2R(f....))El z,f..x ) Considering that R(f..x ) is small ( <0. 05) and D/Dd = 2 (Gordon et al 1975] is independent of depth, the subsurface irradiance due to the inelastic scattering for a deep water column is (3) Defining Qie as the "Q factor" for the inelastic scattering field the subsurface upwelling radiance due to inelastic scattering is

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144 (4) The inelastic total scattering coefficient 1/J{Ax,A) (m-1/nm) is defined as (5) Since f3;e{a,Ax,A) is considered isotropic, then (6) According to the definition of remote-sensing reflectance, with Eq. 4 and Eq. 6, we have (7) For gelbstoff fluorescence, defining 17 (A) as the quantum efficiency for the emission band excited by Ax, then [Gordon 1989, Carder and Steward 1985] (8) 1/;(Ax,A) can be characterized by a log-normal curve [Hawes et al. 1992], so (9) in which

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145 I A = J e -11n dA. .). (10) where TJ(A..J, Ap s and a may vary with the type of gelbstoff and Ax In general, bb < < a for most oceanic waters [Morel and Prieur 1977], so K is close to a. And, based on the calculation for chlorophyll a fluorescence made by Gordon [1989], the Qie factor for inelastic scattering is -3. 7 Then combining Eq. 7 and Eq. 9 with t ::::: 0.98, nw ::::: 1.34, the remote-sensing reflectance due to gelbstoff fluorescence can be reduced to f A. a (A. )E f0-A. ) -{1n >.:>.,r (11) R1(A.) z 0.072 t'I(A.) x g x d' 'x e dA.. rs x A. [2a(A.)+a(A.)]EJO-,A.) A x Unlike broad-band ( -100 nm) gelbstoff fluorescence, the water Raman emission has a half-band width of about 20 nm [Collins et al. 1984]. Omitting this band width, i.e. assuming a narrow Raman emission, the inelastic scattering coefficient 1/;(A.x,A.) for water Raman can be related to Raman scattering coefficient as and from Eq. 7, with K ::::: a, the remote-sensing reflectance for water Raman is b R(A. )E f0-A. ) R R(A.) 0.072 X d' X rs [2a(A.)+a(A.)]EJO-,A.) (12)


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