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Parameterization of the light models in various general ocean circulation models for shallow waters

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Title:
Parameterization of the light models in various general ocean circulation models for shallow waters
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Book
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English
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Warrior, Hari V ( Hari Vijayan ), 1974-
Publisher:
University of South Florida
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Tampa, Fla.
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Subjects / Keywords:
heat budget
optical models
Princeton Ocean Model
General Ocean Turbulence Model
hyper-salinity
Hydrolight
light attenuation
Dissertations, Academic -- Marine Science -- Doctoral -- USF   ( lcsh )
Genre:
government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
ABSTRACT: Solar energy is incident on the earth's surface in both short-wave and long-wave parts of the spectrum. The short-wave part of the spectrum is of special interest to oceanographers since the vertical distribution of temperature in the top layer of the ocean is mostly determined by the vertical attenuation of short-wave radiation. There are numerous studies regarding the temperature evolution as a function of time (see Chapter 2 for details). The diurnal and seasonal variation of the heat content (and hence temperature) of the ocean is explored in this thesis. The basis for such heat budget simulation lies in the fact that the heat budget is the primary driver of ocean currents (maybe secondary to wind effects) and these circulation features affect the biological and chemical effects of that region. The vertical attenuation of light (classified to be in the 300-700 nm range) in the top layer of the ocean has been parameterized by several authors. Simpson and Dickey (1981) in their paper have listed the various attenuation schemes in use till then. This includes a single-exponential form, a bimodal exponential form, and a spectral decomposition into nine spectral bands, each with their specific exponential functions with depth. The effects of vertical light attenuation have been investigated by integrating the light models into a 1D and a 3D turbulence closure model. The main part of the thesis is the inclusion of a bottom effect in the shallow waters. Bottom serves two purposes, it reflects some light based on its albedo and it radiates the rest of the light as heat. 1-D simulation including bottom effects clearly indicates the effect of light on the temperature profile and also the corresponding effect on salinity profiles. An extension of the study includes a 3D simulation of the heat budget and the associated circulation and hydrodynamics. Intense heating due to the bottom leads to the formation of hyper-saline waters that percolate down to depths of 50 m in the summer. Such plumes have been simulated by using a 3D numerical ocean model and it is consistent with observations from the Bahamas banks.
Thesis:
Thesis (Ph.D.)--University of South Florida, 2004.
Bibliography:
Includes bibliographical references.
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Mode of access: World Wide Web.
Statement of Responsibility:
by Hari Warrior.
General Note:
Includes vita.
General Note:
Title from PDF of title page.
General Note:
Document formatted into pages; contains 154 pages.

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oclc - 56389727
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usfldc doi - E14-SFE0000394
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ABSTRACT: Solar energy is incident on the earth's surface in both short-wave and long-wave parts of the spectrum. The short-wave part of the spectrum is of special interest to oceanographers since the vertical distribution of temperature in the top layer of the ocean is mostly determined by the vertical attenuation of short-wave radiation. There are numerous studies regarding the temperature evolution as a function of time (see Chapter 2 for details). The diurnal and seasonal variation of the heat content (and hence temperature) of the ocean is explored in this thesis. The basis for such heat budget simulation lies in the fact that the heat budget is the primary driver of ocean currents (maybe secondary to wind effects) and these circulation features affect the biological and chemical effects of that region. The vertical attenuation of light (classified to be in the 300-700 nm range) in the top layer of the ocean has been parameterized by several authors. Simpson and Dickey (1981) in their paper have listed the various attenuation schemes in use till then. This includes a single-exponential form, a bimodal exponential form, and a spectral decomposition into nine spectral bands, each with their specific exponential functions with depth. The effects of vertical light attenuation have been investigated by integrating the light models into a 1D and a 3D turbulence closure model. The main part of the thesis is the inclusion of a bottom effect in the shallow waters. Bottom serves two purposes, it reflects some light based on its albedo and it radiates the rest of the light as heat. 1-D simulation including bottom effects clearly indicates the effect of light on the temperature profile and also the corresponding effect on salinity profiles. An extension of the study includes a 3D simulation of the heat budget and the associated circulation and hydrodynamics. Intense heating due to the bottom leads to the formation of hyper-saline waters that percolate down to depths of 50 m in the summer. Such plumes have been simulated by using a 3D numerical ocean model and it is consistent with observations from the Bahamas banks.
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PAGE 1

Parameterization of the Light Models in Various General Ocean Circulation Models for shallow waters by Hari Warrior A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Marine Science College of Marine Science University of South Florida Major Professor: Kendall Carder, Ph.D. Robert Weisberg, Ph.D. Boris Galperin, Ph.D. Frank Muller Karger, Ph.D. Sethu Raman, Ph.D. Date of Approval: March 19, 2004 Keywords: light attenuation, Hydrolight, hyper-salinity, Princeton Ocean Model, General Ocean Turbulence Model, heat budget, optical models Copyright 2004, Hari Warrior

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DEDICATIONS To my mother and father, whose positive, unflinching attitude towards life and whose belief on education have become my precious assets. Also to my advisor whose support made the whole academic experience a pleasure.

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ACKNOWLEDGEMENTS I wish to express my deepest gratitude to Dr. Kendall Carder, my major advisor, who provided me this wonderful opportunity to develop my capability to work independently and to challenge myself intellectually. His guidance, insight and encouragement were critical for the successful completion of this study. I also want to express my appreciation to the advisory committee members. Drs. Robert Weisberg, Boris Galperin, Sethu Raman and Frank Muller-Karger for their stimulating ideas regarding this study. Thanks and appreciation extend to Dan Otis, Jim Ivey and Jen Patch who contributed to this study directly or i ndirectly through discussions on observations, modeling and written presentation. Special thanks go to Bob Chen who backed up the computer system and saved my work several times. I am also genuinely indebted to all my friends here and in India who have encouraged me to achieve success.

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Table of Contents List of Tables iii List of Figures v Abstract ix Chapter 1 Introduction 1 Chapter 2 Background and Theoretical Considerations 11 2.1 Introduction 11 2.2 Optical Background 14 2.3 Conclusions 21 Chapter 3 An Optical Model for Heat and Salt Budget estimation for shallow seas 23 3.1 Introduction 23 3.2 Background 27 3.3 Location and data 30 3.3.1 Meteorological data 33 3.3.2 Bathymetric data 36 3.3.3 AVHRR (Advanced Very High Resolution Radiometer) data 36 3.3.4 In-situ data 37 3.4 Inherent optical properties 37 3.5 Quantifying the bottom effects 41 3.6 Modifications to the GOTM code 43 3.7 Surface-flux calculations 48 3.8 Results and discussion 50 3.9 Sensitivity studies 58 3.10 Thermohaline effects 58 i

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3.11 Moisture effects 63 3.12 Conclusions 65 Chapter 4 3-D modeling of the thermohaline plumes near Bahamas 68 4.1 Introduction 68 4.2 Description of the model 73 4.2.1 Basic equations 75 4.2.2 Boundary conditions 77 4.3 Results and Discussion 81 4.3.1 Test for bathymetry slope error 81 4.3.2 Tides 81 4.3.3 Winds 81 4.3.4 Effect of bottom albedo 82 4.3.5 Heat budget 83 4.3.6 Water budget 89 4.3.7 Long-term simulation 90 4.4 Inclusion of wind and tides 99 4.5 Conclusions 100 Chapter 5 Conclusions 104 References 109 Appendices 122 Appendix A: Hydrolight 123 Appendix B: Comparison of the Light Models in POM 128 Appendix C: Turbulence Closure Submodel 138 About the Author End Page ii

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List of Tables Table 1.1 List of symbols and acronyms used in this chapter. 6 Table 2.1 Symbols used in this chapter 17 Table 2.2 Attenuation coefficients in POM (extinct. coefficient) 18 Table 3.1 List of symbols 28 Table 3.2 The inherent optical properties of the water column 40 Table 3.3 Empirical model parameters for the k-kL model. 44 Table 3.4 Flux rates averaged over a 12 hr. heating cycle during model simulation for a 2.5 m deep water column (in Wm -2 ) 46 Table 3.5 The various flux rates averaged over 12 hrs during model simulation for a 10 m-deep water column (in Wm -2 ). 47 Table 3.6 The final temperatures (C) obtained by model simulation after 12 hrs of heating. 53 Table 4.1 List of the symbols used in this chapter. 80 Table 4.2 Vertically integrated heat change (per unit area) in the water column after 15 days of simulation. 86 iii

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Table B1 Derived chl-a values for POM 129 iv

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List of Figures Fig. 1.1 A MODIS ocean color image of the Bahamas for April 18, 2000. 3 Fig. 1.2 Histogram showing the total area of earth and that in tropics less than 10m water depth. 4 Fig. 3.1a,b AVHRR image of SST for a) 15 April 2001 at 6:00 am. b) 17 April 2001 at 6:00 pm. 25 Fig. 3.2 Isohalines along the west coast of Andros Island (modified May curves from Cloud, 1962a). 26 Fig. 3.3 Chart showing the relative location of field of study. 31 Fig. 3.4 A MODIS ocean color image of the Bahamas for April 18, 2000 32 Fig. 3.5a-c Temporal variation of the meteorological parameters a) wind speed b) air pressure c) relative humidity 34 Fig. 3.5d Variation of light intensity at the Mote Marine Lab location. 35 Fig. 3.6 Curve showing a typical diurnal profile of total incoming radiation including cloud effects. 45 Fig. 3.7 Spectral albedo curves for sea grass and coral sand bottoms. 52 v

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Fig. 3.8 Temperature as a function of depth for the various types of bottoms after 7 days of simulation. 54 Fig. 3.9 Bathymetry (in meters) of the model simulation domain. 56 Fig. 3.10 Modeled SST (C) with uniform coral sand bottom after a 60 hour April simulation of the Bahamas banks. 56 Fig. 3.11a,b SST anomalies (C) after 60 hours when a sand bottom is replaced by a) seagrass b) black surface 57 Fig. 3.12a-f The salinity, temperature and density change after 24 days of model simulation for spring and summer, 2001 for the three bottom types. 60 Fig. 3.13 Evaporation Precipitation (E-P) in m for 150 days starting from February 1 st 61 Fig. 3.14 Increase in salinity from February with time for the various water depths using a coral sand bottom. 62 Fig. 3.15 Evolution of the moisture released into the air for various water depths. 65 Fig. 4.1 CDOM values near Andros Island for various months. 69 Fig. 4.2 Figure from Otis et al. (2004), to show the depth of salinity and Gelbstoff intrusions. 70 Fig. 4.3 Map of the Bahamas showing Adderly Cut. 72 vi

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Fig. 4.4 Bathymetry of model simulation. 73 Fig. 4.5a,b Temperatures after 15 days a) 6 am b) 6 pm. 85 Fig. 4.6a, b The heat fluxes and heat content change in the a) estuary b) deep ocean. 88 Fig. 4.7 Water budget analysis showing the various transport processes illustrating the conservation of water mass. 90 Fig. 4.8a,b Temperature distribution (C) after 30 days of simulation, at a) surface and b) bottom. 92 Fig. 4.9a,b Flow vectors around the channel. 93 Fig. 4.10a,b The temperature distribution after 60 days of the a) surface b) bottom waters at 6 AM. 95 Fig. 4.11a, b yz cross-section along the middle of the channel of a) temperature b) salinity after 60 days. 96 Fig. 4.12 Salinity cross-section after 75 days of simulation. 97 Fig. 4.13a-d. Cross-sections of the channel at various times. 98 Fig. 4.14a,b Salinity contours including wind and tides after a) 60 days b) 75 days. 102 Fig. 4.15 Salinity profile after 330 days. 103 vii

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Fig. A1 Diagram underlying the equation of transfer of radiance (taken from Kirk, 1994). 125 Fig. A2 Quad-partitioning in radiative transfer model (taken from Mobley, 1994) 126 Fig. B1 Comparison of Hydrolight and POM for Type 1 waters. 130 Fig. B2 Comparison of Hydrolight and POM for Type 1A waters 131 Fig. B3 Comparison of Hydrolight and POM for Type 1B waters. 133 Fig. B4 Comparison of Hydrolight runs for different sun angles for Type 2 waters. 134 Fig. B5 Comparison of Hydrolight and POM for Type 3 waters. 137 viii

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Parameterization of the Light Models in Various General Ocean Circulation Models Hari Warrior ABSTRACT Solar energy is incident on the earths surface in both short-wave and longwave parts of the spectrum. The short-wave part of the spectrum is of special interest to oceanographers since the vertical distribution of temperature in the top layer of the ocean is mostly determined by the vertical attenuation of short-wave radiation. There are numerous studies regarding the temperature evolution as a function of time (see Chapter 2 for details). The diurnal and seasonal variation of the heat content (and hence temperature) of the ocean is explored in this thesis. The basis for such heat budget simulation lies in the fact that the heat budget is the primary driver of ocean currents (maybe secondary to wind effects) and these circulation features affect the biological and chemical effects of that region. The vertical attenuation of light (classified to be in the 300-700 nm range) in the top layer of the ocean has been parameterized by several authors. Simpson and Dickey (1981) in their paper have listed the various attenuation schemes in use till then. This includes a single-exponential form, a bimodal exponential form, and a spectral decomposition into nine spectral bands, each with their specific exponential functions with depth. The effects of vertical light attenuation have been investigated by integrating the light models into a 1D and a 3D turbulence closure model. The main part of the thesis is the inclusion of a bottom effect in the shallow waters. Bottom serves two purposes, it reflects some light based on its albedo and it radiates the rest of the light as heat. 1-D simulation including bottom effects clearly indicates the effect of light on the temperature profile and also the corresponding effect on salinity profiles. ix

PAGE 13

x An extension of the study includes a 3D simulation of the heat budget and the associated circulation and hydrodynamics. Intense heating due to the bottom leads to the formation of hyper-saline waters that percolate down to depths of 50 m in the summer. Such plumes have been simulated by using a 3D numerical ocean model and it is consistent with observations from the Bahamas banks.

PAGE 14

Chapter 1 Introduction The sun is the major source of energy to the earths surface. Even if the sky is clear, the intensity of the solar irradiance is significantly reduced due to passage through the atmosphere. This reduction of intensity is partly due to scattering by the air molecules and dust particles and absorption and scattering by water vapor and other gases. Solar radiation reaching the surface is primarily found between the wavelengths = 250 nm and =4250 nm. Due to atmospheric gases (mainly CO 2 H 2 O, methane and ozone) acting as efficient absorbers in the near infrared region, the spectral composition of solar radiation at the surface is greatly modified. Therefore, it is a challenging task to tease out the effects of individual gases in the net radiation spectrum received by a remote-sensing satellite. It is important that we quantify the suns heat reaching the water column and the subsequent absorption by water. Study of the heat budget of oceans is important because the circulation of the ocean is driven primarily by it. This in turn determines the distribution of biological life in the oceans. Also the local weather and long-term climate of the earth is significantly affected by the heat budget. In this manner, the study of heat budget forms an important field of oceanography. An equally difficult task is parameterizing the absorption of the short-wave solar radiation by the water. Till now, work has been carried out in parameterizing and improving the spectral attenuation of light with depth in ocean models. Simpson and Dickey (1981a), made a comparison between the various light attenuation schemes in use until then for deep waters. They have illustrated through selective modeling (using a 2.5 level turbulence closure scheme) the relative errors associated with 1) a single exponential form, 2) a bimodal spectral exponential form, 3) the arc1

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tangent approach and 4) a spectral decomposition into 9 wavebands. The spectral model was found to be the most accurate. Few works have specialized in studying the coastal waters, where optical properties and physical processes are more complex than the deep ocean (an exception is the work of Chang et al., 2002, but they did not include bottom effects). In this thesis the spectral absorption of solar radiation with water depth is investigated, incorporating the salient point introduced in this workthe effect of bottom absorption and radiation. The effects of different types of bottom are investigated varying from coral sand to sea grass (also from white to black). There is found to be a very strong influence of the bottom albedo and depth on the development of the temperature profile in the overlying water column. Also hydrodynamic effects of this shallow water bottom heating are studied, which result in thermohaline plumes emanating from shallow waters sinking to depths commensurate with density. A MODIS image of the Bahamas (location of our studies), which illustrates some of the above-mentioned properties, is shown in Fig. 1.1. As mentioned in the last paragraph, this thesis is primarily concerned with the shallow-water short-wave radiative heating and its effects on the heat budget and circulation. The first question that springs to mind when we stress that these results are important is the total area of the earths surface that undergoes shallow-water heating effects. The total area of the ocean and also the area in the tropics (between +/30) which are less than a specified depth (1 m to 8 m) are shown in Figure 1.2. The data were taken from the NOAA ETOPO5 data set (web page can be found at http://www.ngdc.noaa.gov/mgg/global/seltopo.html). It is seen that about 1.6 million km 2 of the ocean is shallower than or equal to 1 m, of which about 0.2 million km 2 is in the tropics. It is interesting to note that about 25% of that area is in the Bahamas, so the region of Great Bahamas Banks is ideal to study the tropical shallow-water effects. Thus, the total ocean less than 10 m where the shallow-water effects are important is about 7.5% to the total area of the 2

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continental shelves in the world, which is about 41 million km 2 (the continental shelves in turn, occupy about 8% of the total oceanic area). To evaluate the enormity of the numbers, another comparison can be made with the Mediterranean Sea. The total ocean shallower than 10 m is approximately the same area as the area of the Mediterranean, which is about 2.5 million km 2 This dissertation will make it clear that the shallow water effects need to be addressed Fig. 1.1: A MODIS ocean color image of the Bahamas for April 18, 2000. 3

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depth (m) 0246810 Area (km2) 0.002.00e+54.00e+56.00e+58.00e+51.00e+61.20e+61.40e+61.60e+61.80e+62.00e+6 Total earth Tropics Fig. 1.2: Histogram showing the total area of earth and that in tropics less than 10 m water depth. 4

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properly in coupled air-sea models that predict weather or for climate models that need to accurately predict climate change. Solar radiation between the wavelengths of 300-700 nm, which is usually classified as short-wave and visible radiation, is especially important in oceanography, because it can penetrate to depth in the ocean, depending on the optical properties of the water column. This penetrating short-wave radiation is responsible for the varied biological life at various depths in the ocean. Variations in the attenuation of visible radiation in the upper ocean alter the vertical distribution of local heating. They have potential implications for thermal and dynamical processes as well as for ocean-atmosphere interactions. These variations are largely controlled by the concentration of light-absorbing pigments associated with phytoplankton that vary over a wide range of time and space scales. Chlorophyll concentrations from 0.05-2 mgm -3 are common in oceans with higher values at times in the coastal regions. These variations have been investigated in detail (described in detail in the next chapter), not only for their influence on the upper-ocean structure, but also for generating full spectral radiance profiles over a range of oceanic conditions (Denman 1973; Simpson and Dickey 1981a,b; Lewis et al. 1990; Ohlmann et al. 1996; Ohlman et al. 2000). A potential for the effects of stabilization of the mixed layer due to biological heat trapping, occurs due to light attenuation. This can lead to increased stratification, and, in turn, to favorable conditions for phytoplankton growth as was suggested by Sathyendranath et al. (1991) and other references. While this hypothesis can only be tested in a coupled ecosystem model, the influence of light attenuation due to phytoplankton growth on ocean circulation can be studied in Ocean General Circulation Models (OGCMs). One recent study in an isopycnal OGCM addressed the modulation of SST by surface chlorophyll for the Arabian Sea (Nakamoto et al. 2000). Chang et al. (2000) have analyzed physical and bio-optical data from the coastal zone by including simulations using the optical model (Mobley, 1994) Hydrolight (see Appendix) to 5

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Table 1.1: List of symbols and acronyms used in this chapter. Symbol CDOM RHR C p E d E u E n Q (z) POM MLD EOF UV Explanation Colored Dissolved Organic Matter Radiant Heating Rate (in Csec -1 ) Density (kgm -3 ) Specific heat of sea water (Jkg -1 C -1 ) Wavelength (m) Downwelling irradiance (Wm -2 ) Upwelling irradiance (Wm -2 ) Net downward irradiance (E dE u ) Divergence of downward irradiance (Wm -3 ) Princeton Ocean Model Mixed Layer Depth (m) Empirical Orthogonal Function Ultra Violet study the transmission of light in an ocean mixed layer. The associated Radiant Heating Rates (RHR, see Table 1.1) can be incorporated in ocean models. Radiant Heating Rate (the symbols in this equation are defined in Table 1.1) is defined as, zCzEEzRHRpnn)]()0([)( (1.1) the symbols are defined in Table 1.1. Quantitative coherence analyses indicated cloud cover, chlorophyll and CDOM to have the greatest influence on solar transmission on weekly time scales. They showed that for low (0.1 mgm -3 ) and high chlorophyll conditions (5 mgm -3 ) the difference in RHR for a 12-hour period from 6 am to 6 pm 6

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was about 0.1C. The spectral difference between high chlorophyll and low chlorophyll spectral solar transmission to depth matched the shape of the phytoplankton absorption curve, with peaks at 440 and 680 nm. EOF (Empirical Orthogonal Functions, Table 1.1) analyses showed that mixed layer depth (MLD) is the dominant factor in the RHR in ocean models, and the RHR decreases as the MLD deepens. EOF analyses compress a data set into a series of modes (linear orthogonal functions) with associated vectors of ascending amplitudes corresponding to each mode. This method is an empirical technique used to rank the importance of a set of processes that results in the variance of a data set. The whole thesis is divided into five chapters. This chapter provides an introduction to the work contained in the remaining chapters. Here the concepts of light attenuation in the marine systems and its influence on the heat budget of these waters are introduced. It is stressed here that the study conducted in this thesis is for shallow waters and their influence on adjacent deeper water circulation. In the following chapters, the influence of short-wave radiation on the heat budget, and how it is attenuated with depth and wavelength is examined, based on the optical properties of the aquatic medium. Also, the errors associated with the various attenuation schemes in the OGCMs in use today are evaluated. Chapter 2 provides the background of various attenuation schemes in use currently, and how the schemes have gradually improved over the years. Then the inadequacies of using a simplified light model in a commonly used general ocean model, the Princeton Ocean Model are evaluated. The inadequacies in the single attenuation coefficient method have been reported by many scientists. Simpson and Dickey (1981a), made a comparison between the various light attenuation schemes in use till then. They have illustrated through selective modeling (using a 2.5 turbulence closure scheme) the relative errors associated with 1) a single-exponential form, 2) a bimodal spectral exponential form, 3) the arc-tangent approach and 4) a spectral decomposition into 9 wavebands. The spectral model was found to be the most accurate. They reported a 0.5C change in the mixed layer temperature over a 24hour period simply by using different types of light-attenuation schemes. 7

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In their paper, Simpson and Dickey (1981a) used a 1-D, second-moment turbulence closure (the same turbulence closure scheme employed by POM) scheme with modification to account for solar flux divergence (Eq. 1.2). The advantage of 1D models is that they can study the vertical temperature structure without the complicating effects of advection and horizontal diffusion. Their investigation of the role of downward irradiance in determining the upper-ocean structure showed that SST, mixed layer depths, eddy diffusivity of heat and the mean horizontal velocities were dependent on the particular form of solar irradiance divergence. The divergence of downward irradiance, Q (z), may be written as zzEzd)()( Q (1.2) where z is the depth and E d (z) is the downward irradiance. This is the radiant flux per m 2 of a horizontal surface due to contributions from the entire upward hemisphere (sun + sky light). One-dimensional studies such as these have been instrumental in driving home the point that proper representation of solar irradiance is required for accurate computation of SSTs. In Chapter 3, the shallow-water heat budget is introduced using a one-dimensional (1-D) turbulence model and realistic heat fluxes for the Bahamas Banks. This chapter contains the salient details of the new feature included in the thesis work (bottom heating). A new optical model including the effects of the bottom is introduced here and is then incorporated into the 1D turbulence module with simulations performed for the 3 spring months of 2001. Most of the meteorological data were derived from the AUTEC weather station in the Bahamas (explained in Chapter 3). It is shown that the influences of depth, the bottom absorption and radiation (depending on the bottom spectral albedo) have strong influences on the heat budget. We deal with natural two extremes in bottom albedo (reflectivity) of sea grass and coral sand as well as the errors in ignoring the bottom. These have corresponding effects on circulation features, when the study is later extended to a 3-D numerical model. 8

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A predominant effect of shallow water is the increased heating and evaporation of these waters. The increased evaporation can lead to the formation of especially saline water columns. The salinities of such regions have been observed and modeled as high as 45 psu. The presence of such hyper-saline features has been observed by Cloud et al. (1962) and subsequently by other scientists. Hyper-saline waters in the Bahamas are so dense that they can sink to depths of at least 45 m in summer and 75 m in winter (Smith et al., 1995 and Hickey et al. 2000). Hickey et al. came to the conclusion that subsurface salinity/turbidity maxima observed throughout the upper layers of Exuma Sound are the signature of dense plumes that originated on the shallow Bahamian banks and flowed off the platform during ebb tide. This process redistributes highly saline, frequently turbid water from the somewhat isolated banks to the semi-enclosed Exuma Sound. Physical factors induce biological and chemical changes which get very much modified by the presence of a bottom. It is believed that in addition to the thermal and UV (Ultra Violet radiation) effects on coral, there are drastic changes in the ecosystem where hot brine can spill into the offshore. Mass extinctions and migrations are associated with these features (Bird et al, 1979). Shallow water heating can also affect three-dimensional circulation through thermohaline effects. The influence of shallow water heating on hydrodynamics using a three-dimensional primitive-equations model are investigated in Chapter 4. There, the effects of penetrative radiation on the upper subtropical ocean circulation are investigated by using an ocean general circulation model (OGCM) with spectrally varying attenuation depths. This heat budget is found to have important ramifications for ocean circulation over and adjacent to the Banks. The intense heating and evaporation of the shallow surface waters can lead to density differences, which can initiate baroclinic circulation and thus an associated thermohaline flow (Hickey et al. 2000). These thermohaline plumes then flow off the shallow shelves to depth in deeper waters, diffusing and dispersing laterally. This occurs after a transition commonly referred to as Stommel transition (Stommel, 1961). This is a change from a flow induced by temperature to a flow induced by salinity. These hot brine 9

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plumes advect into the deeper seas, sinking to an equilibrium depth of 50 m (Hickey et al. 2000). The same three-dimensional flow structure is found off saline oceanic regions like the Mediterranean (with a saline-water outflow at the bottom along the Strait of Gibraltar and a fresher Atlantic plume flowing in at the surface). The study of the flow characteristics is followed up by a study of the heat and water budget. The general transfer of heat between the estuary and deeper seas is evaluated. A very large amount of heat was found to transfer back and forth between the two bodies of water before being lost as long-wave radiation at the air-sea interface. Finally the conclusion is drawn (Chapter 5) that the effects of bottom heating and absorption are not negligible when modeling shallow waters and that salinity dominates the thermohaline circulation for many shallow banks. The time frame of study in this thesis is springtime, when there is no or little precipitation. The current simulations can be extended to summer when precipitation slowly sets in. The atmospheric effects of evaporation and precipitation can be modeled by studying the moisture feedbacks. This can be performed using a coupled air-sea model that can correctly simulate such a scenario, but this was beyond the scope of the thesis. 10

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Chapter 2 Background and Theoretical Considerations 2.1 Introduction Numerous studies have been carried out on the heat budget in various parts of the world by combining field measurements and numerical modeling. For example, Ohlmann et al. (1996) have performed a global analysis of the heating of an oceanic mixed layer due to short-wave penetration. They showed that the thermal energy absorbed in the upper mixed layer of the ocean can be available for immediate interchange with the atmosphere, while the light that penetrates well below the mixed layer remains sequestered there (after getting converted to heat) until winter convective mixing returns it to the mixed layer. Solar penetration can be a significant portion of the heat budget of the upper-ocean mixed layer on annual scales in the tropics and must be considered seasonally at midand high-latitudes. In view of these modeling and experimental results, it has been established beyond a doubt that the attenuation of short-wave radiation with depth has a very strong influence on the heat budget of the upper oceanic layer. It is very important that we model the underwater light field very carefully using the available inherent optical properties of the aquatic medium. The effect of short-wave radiation on the heat budget of the water column was mentioned in the Introduction (Chapter 1). The absorption of short-wave radiation depends on the material in the water column. The energy thus absorbed by the various ocean constituents (mainly water) heats the water volume within which it is absorbed. In this thesis the main focus is in heating the water column due both to the absorption by the water column and by the bottom. The details of the effect of the bottom are 11

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considered in Chapter 3. In this chapter, the background materials and published works on the parameterization of the light budget schemes are examined. Liu et al. (2002) have provided a detailed account of inadequacies of photon budgets leading to inadequate heat budget estimations found in various general circulation models, which are discussed in this chapter. They have used an optical model called Hydrolight and have demonstrated that the single attenuation scheme (explained in the next section) of various general circulation models is in error. There are numerous schemes that characterize the light attenuation with depth in the marine system and the conversion of light into heat in the euphotic zone and below. Increased light attenuation has been found to accompany increases in turbidity and chlorophyll in ponds (Idso and Foster, 1974), in the oceans for Jerlov Types 1 (clear) to 9 (coastal) (Zaneveld, 1981). Similar calculations by Woods et al. (1984) for oceanic water Types 1 to 3 (Jerlov classification) showed that the seasonal rate of solar heating below the mixed layer increased as the attenuation of short-wave radiation in the mixed layer decreased. In addition to these studies, there are some field observations relating thermal behavior of water bodies to their optical properties. The main validation for the various optical models comes from studying the heating effects: the temperature profiles measured by either AVHRR or CTD profiler (see Table 2.1 for explanations). A non-dimensional parameter has been used to quantify the fraction of available energy that is converted to thermal energy within the mixed layer. Ohlmann et al. (1996), present values as small as 0.85, indicating that 15% of the total solar input will be lost from the mixed layer heating through solar penetration beyond the mixed layer on annual timescales. Inelastic scattering by water molecules and photosynthesis are other pathways and although the reemitted light by inelastic scatter (e.g. Raman scattering and fluorescence) has been shifted toward longer wavelengths it is typically reabsorbed locally because of the higher absorption coefficients at longer wavelength, again becoming a source of heat. This pathway (the inelastic scattered fraction of light as well as the light absorbed by phytoplankton for photosysnthesis) is usually ignored as the lost energy is immediately fluoresced and 12

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converted locally to heat by absorption. Lastly, a fraction of light energy is absorbed by phytoplankton and stored as chemical energy in the organic compounds resulting from photosynthesis and subsequent reactions. If, for example, the chlorophyll specific absorption coefficient is a* = 0.025 and the chlorophyll concentration is 0.1 mgm -3 the absorption coefficient of phytoplankton, a is 0.0025 m -1 which is a small number. It has been shown by Morel (1988) that the ratio of stored energy to available radiation at the surface for phytoplankton remains very small. It is just a few percent of the light absorbed by the phytoplankton even under eutrophic conditions. Of the light absorbed by phytoplankton, only about 5% is photosynthesized (e.g. Carder et al. 1992), the rest being fluoresced or converted to heat. Even this chemical energy is transformed into heat, at least partly, within the same layers due to animal consumption and respiration and the oxidation of detrital organic matter. Solar radiation passes beyond the air-sea interface and heats well below the surface. Just a 10 Wm -2 change in the quantity of solar radiation absorbed within the top 10 m layer can result in a temperature change of more than 0.6C month -1 (Ohlmann et al., 1996), so the accuracy of absorption of insolation calculations is important to the ocean heat budget. There are various parameterizations to simulate upper-ocean attenuation of solar insolation. Simpson and Dickey (1981a) have listed the various types of vertical attenuation schemes in use until that date. These include single-exponential forms (Denman 1973), bimodal exponential forms (Kraus 1972; Paulson and Simpson 1977) and spectral decomposition forms using up to nine spectral bands (Simpson and Dickey, 1981a), each with their specific exponential functions with depth. The utility of each parameterization method was judged as a function of its ability to accurately replicate heating effects of solar transmission attenuation within the water medium. Simpson and Dickey (1981a) reported a 0.5C range in mixed -layer temperatures over a 24-hour period derived by using different types of light-attenuation schemes. Such sensitivity to radiant heating processes demonstrates the need for having light-attenuation models in the upper ocean that accurately represent spatial and temporal variability in transmission of solar radiation. After the seminal 13

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paper by Simpson and Dickey, 1981a, there have been numerous similar studies on the vertical attenuation of light in ocean. Morel and Antoine (1994) have introduced a three-term form to represent the fully spectral solar transmission. Their solar transmission parameterization relies upon quantities that can be determined from in situ and remotely sensed data (mainly chlorophyll a, which can be determined by satellite sensors or by in situ sampling). This attenuation scheme is especially important, since the amount of air-sea interaction that occurs at the surface and the processes occurring within the mixed layer and thermocline are critically dependent on the vertical distribution (caused by the vertical attenuation) of short-wave radiation. It can be safely concluded that an understanding of the heating of the ocean due to solar radiation is quite important for an understanding of the various physical, biological and chemical processes that go on within the ocean and the heat and water exchange with the atmosphere. 2.2 Optical Background Natural waters exhibit enormous variations in inherent optical properties. Some oligotrophic (optically clear waters) oceanic waters are nearly optically equivalent to distilled water, whereas, some coastal and inland waters are so murky, they resemble mud. Based on the Jerlov classification (Jerlov 1976) all waters can be broadly classified as Types 1, 1A, 1B, 2 and 3 waters. These classifications are distinguished by the variation in their absorptive and scattering properties (basically the inherent optical properties). Type 1 waters are clear oligotrophic waters, while the Type 3 waters are the murkiest (most of the biologically productive coastal waters fall in this category). Water types have a significant impact on the attenuation of light with depth by primarily affecting the shortwave radiation. Most general ocean circulation models such as the Princeton Ocean Model (POM) use a simple light budget scheme, which leads to significant error. The POM is a sigma-coordinate, free-surface, primitive-equation ocean model, which includes a turbulence sub-model. It was developed in the late 1970's by Blumberg and Mellor, 14

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(1985, 1987), with subsequent contributions from other people. The model has been used for modeling of estuaries, coastal regions and open oceans. The model has several important features. First, it has an embedded turbulence-closure sub-model (Mellor and Yamada, 1974, 1982; Galperin et al., 1988) for parameterizing the vertical eddy coefficients. ). Secondly, it employs a sigma coordinate in the vertical, which, with the turbulence closure sub-model, is well suited to study nonlinear dynamics over a shallow continental shelf, since it produces realistic bottom boundary layers which are important in coastal waters (Oey et al., 1985a,b). By and large, the turbulence model seems to do a fair job of simulating mixed layer dynamics although there have been indications that calculated mixed layer depths are a bit too shallow (Martin, 1985). A recent paper (Mellor 2001) suggests ameliorative changes, which are incorporated in this model version. Also wind forcing may be spatially and temporally smoothed. In this chapter only the equations used for modeling the underwater light field are discussed. The equations of motion are discussed in Chapter 4. Again, the net solar radiation is the sum of the long-wave and short wave radiation components entering the sea surface. Various symbols are used in explaining the irradiance and optical schemes. These are given in Table 2.1. In the POM, the light model at the surface is installed as (1-tr)*srad where tr is the fraction of the incident solar radiation (srad) that is long-wave. This fraction is absorbed in the top layer of the ocean. The UV and visible light remainder are attenuated with depth according to: rad k =srad*(1-tr)*exp(extinc*z k ) (2.1) This short-wave (1-tr) fraction, varies as a function of which Jerlov water type is specified. Based on water type, the constants tr and extinc are set according to Table 2.2. A better approximation to Eq. 2.1 is the bi-modal exponential parameterization suggested by Kraus (1972), 15

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E d (z)= E d (0){R.exp(z/ 1 ) + (1-R).exp(z/ 2 )} (2.2) where R (constants for two wavelength bands) is a measured fraction and 1 and 2 are attenuation lengths. An attenuation length is defined as 1/K d where K d is the diffuse attenuation coefficient (see Table 2.1). The first term in Eq. 2.2 characterizes the rapid attenuation in the top 5 m due to absorption of red spectral components while absorption of blue-green spectral components penetrating to depths greater than 10 m is characterized by the second term ( 2 > 1 ). Zaneveld and Spinrad (1980) have suggested an arctangent approximation to Eq. 2.1 i.e. E d (z) = E d (0).exp(z/ 2 )[1-R.tan -1 (-z/ 1 )] (2.3) Simpson and Dickey (1981a) have made a comparison of these various models and they have come to the following conclusions: 1) The single-exponential form appears acceptable only at very high wind speeds when the deep mixed layer is homogenized. Even then, there is a large error associated with this idealized equation. 2) A spectrally (wavelength) decomposed attenuation is preferable, with the accuracy increasing with the number of spectral bands (i.e. by increasing the number of wavelengths in the visible spectrum). 3) The bi-modal exponential form and the arc-tangent form have the same number of degrees of freedom and produce nearly equivalent results. Morel and Antoine (1994) have used a parameterization of the attenuation coefficient for downwelling irradiance which depends upon the relation between the downwelling diffuse attenuation coefficient K d () and the chlorophyll pigment concentration (Morel, 1988) K d () = K w () + ()C e() (2.4) 16

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Table 2.1: Symbols used in this chapter. Symbol AVHRR CTD tr K d extinc OWS b() a(), a t () c() a w () a g () a* () a () chl-a 0 R 1 2 Definition Advanced Very High Resolution Radiometer Conductivity Temperature Depth Volume scattering function Long-wave radiation fraction Diffuse attenuation coefficient Oceanic Weather Station Wavelength Scattering coefficient Total absorption Total attenuation Absorption due to water Absorption due to Gelbstoff Specific absorption coefficient Absorption due to phytoplankton Chlorophyll a Average cosine ratio Attenuation lengths (e-folding depths) albedo Units m -1 ster -1 m -1 m m -1 m -1 m -1 m -1 m -1 m 2 mg -1 m -1 mgm -3 m 17

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Table 2.2: Attenuation coefficients in POM (extinct. coefficient) Type of water tr extinc (m -1 ) 1 0.32 0.037 1A 0.31 0.042 1B 0.29 0.056 2 0.26 0.073 3 0.24 0.127 the values of K w (), () and e() are given in Table 1 of Morel and Antoine (1994) for wavelengths 300-2600 nm. The radiant energy E, absorbed per unit of volume at a particular depth Z (positive downward) is expressed as (Gershun, 1936; Morel and Smith, 1982) 0EadzEd (2.5) where a is the absorption coefficient (m -1 ) and 0 E is the scalar irradiance (Wm -2 ) at the depth in question. The above Gershuns (1936) conservation of energy equation states that this amount of energy is simply the derivative with respect to depth of the downward vector irradiance E if the horizontal divergence is negligible, as in a horizontally homogeneous water body. The modulus of E is the net irradiance, which is the difference between downward irradiance E d and upward irradiance E u so that a 0 E = d(E d -E u )/dz (2.6) Following this, Morel and Smith (1982) express 18

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(2.7) 750300])(exp[),0()(ZdKEZEddd To simulate this propagation, they select a bimodal exponential function, as in Kraus, 1972 (Eq. 2.2). This is formulated as E vis =E vis (0-){V 1 .exp(-Z/Z 1 )+V 2 .exp(-Z/Z 2 )} (2.8) where V 1 and V 2 represent partitioning factors and Z 1 and Z 2 are the associated attenuation lengths (defined above). Note that the attenuating coefficients are constants and do not assume any relationship with the particulate and CDOM concentrations, as a complete model should. This idea was then incorporated by Morel and Antoinne (1994), where these four parameters themselves are functions of C (chlorophyll concentration). The variations of these four parameters as functions of log 10 C are conveniently described by polynomial expressions. In most of the ocean, the vertical structure of the chlorophyll profile shows either a near-surface peak or a deep-water peak. There are parameterizations (Mueller and Lange, 1989; Platt and Sathyendranath, 1988) that have been proposed to derive these pigment profiles from the near surface chlorophyll, C satellite detectable by remote sensor. Ohlmann et al. (1996) have developed a hybrid parameterization of the net flux of solar irradiation at depth and applied it to examining the global radiation penetration. They define the radiant heating rate (RHR) of the mixed layer as, RHR ml = mlpmlnnDcDEE)()0( (2.9) Where E n (0-) is the net flux of solar radiation (net irradiance) just beneath the sea surface and E n (D ml ) is the net solar flux at the bottom of the mixed layer. Ohlmann et al.s expression for the mixed layer heating rate and the net radiative heat flux at the mixed layer base, E n (D ml ), is 19

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soldDKEdDEmldmln ]})().{exp(,0()1()( (2.10) where is the Fresnel reflectance (albedo) at the air-sea interface. Ohlmann et al. calculated K d () values using the Baker and Smith (1982) parameterization, which is similar to Morels (1988) equation for K d by using chlorophyll concentrations (Eq. 2.4). The energy outside the evaluated portion of the solar spectrum (300 nm), mostly the infra-red radiation, will be quickly converted to thermal energy after passing through the air-sea interface and will penetrate only the shallowest mixed layers. Since knowledge of surface albedo over the global oceans is limited, it is not incorporated in their (Ohlmann et al., 1996) model. An additional feature of their model is the effect of clouds. Clouds have the ability to significantly affect the surface irradiance spectrum by altering the ratio of diffuse to direct light. They have shown that a comparison of the modeled clear-sky spectral decomposition with a cloudy sky irradiance spectrum illustrates that in the presence of clouds, the fraction of energy in the deep penetrating bands (blue band) can be as much as 14% higher than in the clear sky case. They have provided the readers with the seasonal variation of the mixed layer solar penetration and the corresponding heating rates for the tropics. They state that at Oceanic Weather Station, OWS N (November, 30N, 140W), from January through March, the radiant heating below the mixed layer is small due to the low incident flux and deeper mixed layers. In fact, at OWS N, monthly values of solar penetration range from near 1 Wm -2 in winter months to more than 30 Wm -2 during the summer. At this station, in April, the shoaling of the mixed layer would cause more of the sunlight to penetrate through the mixed layer if not for the seasonal increase in chlorophyll concentrations at that time. An increase in near-surface chlorophyll concentrations then is primarily responsible for reduced penetration in August in the mixed layer. After August, and through December, the mixed layer deepens and incident solar flux decreases, resulting in a solar penetration reduction of an order of magnitude from 25 to 2 Wm -2 Much of this solar penetration is converted to thermal energy within the seasonal 20

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pycnocline waters. Thermal energy deposited within seasonal pycnocline waters is entrained (mixed) into the mixed layer beginning in August when the mixed layer starts deepening. Thus, the thermal energy associated with mixed layer penetration occurring in May through July is unavailable for atmospheric exchange until at least August. They (Ohlmann et al., 1996) state that solar penetration thus is a significant portion of the upper ocean mixed layer heat budget on annual scales in the tropics and subtropics and so must be properly considered. Ohlmann et al. (2000) showed that results from radiative transfer calculations indicate that in-water solar fluxes can vary by 40 Wm -2 within the upper few meters of the ocean (based on a climatological surface irradiance of 200 Wm -2 ). They have shown that a significant portion of the variation can be completely accounted for by the chlorophyll concentration, solar zenith angle and cloud fraction. They have proposed a parameterization that is obtained empirically by fitting curves formed by expressing the irradiance as a sum of four exponential terms. Curve-fit parameters are then written as linear combinations of chlorophyll as cos -1 during clear sky periods, and chlorophyll concentration and cloud index during cloudy sky periods. They claim the two-equation solar transmission parameterization provides an improvement in skill of order 10 Wm -2 over existing full spectral parameterizations that ignore changes in chlorophyll and cloudiness. This parameterization relies upon quantities (chlorophyll) and cloudiness, which can be accurately determined using in situ and remotely sensible data. 2.3 Conclusions The nature of the underwater light field resulting from a given incident light field is determined by the incoming light field and the inherent optical properties of the aquatic medium. It is known that the attenuation of solar radiation across the entire photosynthetic waveband takes place at widely different rates for different parts of the spectrum. As a consequence, the spectral composition of the downwelling flux changes progressively with increasing depth. There are various parameterizations of 21

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the downwelling and upwelling underwater light field. The previous sections have shown that the light models (the parameterizations of K d ) used in the common ocean general circulation models need to be improved to correctly predict the underwater short-wave radiation. The assumption of a spectral K d (upto 12 wavebands in the visible part of spectrum) improves the simulation of the light field significantly, which produces improvements in the heat budget. The improvement in light irradiance due to a spectral model is shown in Appendix B. The effect of the other various types of parameterizations (Eq. 2.2 to Eq. 2.4) are not shown as applying the Princeton Ocean Model is the focus of this thesis. The attenuation of light with depth as predicted by POM and based on Mobleys Hydrolight model is given in Appendix B. There, the curves are given that show the inaccuracy by upto 5 times, in the constant parameterization of POM. It is seen there that K d of turbid waters can be represented by a constant value, or at the worst by two values, one for the surface and one for deeper waters, the constant varying with chlorophyll and particulate content. In homogenous Type I water columns, the net attenuation constant decreases with depth. The net K d or the attenuation constant integrated over wavelengths decreases with depth because the more attenuating wavelengths are absorbed near the surface while at depths light with only less attenuating wavelengths remain. But in water columns with increased chlorophyll concentration the attenuation coefficient can be constant or even increase with depth. This is because, the decrease of attenuation with depth is offset by higher attenuation because of increased scattering due to particles (chlorophyll or sediment specific scattering coefficient). More simulations need to be carried out to get an accurate K d for various particle concentrations. This improved K d can thereby give a better prediction for the heat budget of these waters and hence the associated circulation. So in summary, there is an almost 0.5C range in mixed -layer temperatures over a 24-hour period derived by using different types of light-attenuation schemes. Also results from radiative transfer calculations indicate that in-water solar fluxes can vary by 40 Wm -2 within the upper few meters of the ocean. But none of the existing models address the shallow water problem. 22

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Chapter 3 An Optical Model for Heat and Salt budget estimation for shallow seas 3.1 Introduction Understanding the effects of solar radiation and its penetration of the water column is important to improve models of coastal circulation, coral bleaching and benthic photosynthesis. Due to high absorption by water molecules at longer wavelengths, about 57% of the total radiation is absorbed in the top meter or less. The heating rate from infrared radiation is usually treated separately from absorption of visible (400-700 nm) radiation which is much more penetrative and thus sensitive to the water constituents (Smith and Baker, 1981; Pope and Fry, 1997). Numerous studies have been made on the heating effects of light (both the long-wave and short-wave components) in various parts of the world using both field measurements and numerical models. For example, Ohlmann and Siegel et al. (1996) provided a global analysis of the oceanic mixed-layer heating due to solar penetration. Thermal energy within the seasonal thermocline associated with solar penetration beyond the seasonal mixed layer will be sequestered there, lost to any atmospheric exchange until entrainment associated with fall and winter mixing occurs. In shallow waters, however, the thermal energy associated with solar radiation absorbed within the surface mixed layer is almost immediately available for exchange with the atmosphere. In this chapter, the influence of the penetration of the short-wave radiation in shallow waters is evaluated, where traditional circulation models (e.g. Princeton Ocean Model, POM), have ignored bottom effects. This is equivalent to having a transparent sea floor, with no light either absorbed or reflected by the 23

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bottom. This minimizes the heating effects on water columns less than about 20 m in depth. The actual thermal effects of shallow waters often have important consequences for the salt budget, chemical and biologic formations like whitings, aragonite precipitation (Broecker et al. 2000), hot brine effects on coral (Lang et al., 1988), high humidity, and even on cloud formation over shallow banks. For example, waters over shallow subtropical banks can become much hotter in the spring than waters found in adjacent deeper regions (e.g. Fig 3.1a, 3.1b). In addition to being warmer than the surrounding waters, some of these shallow regions are known to produce hyper-saline waters (waters with salinity greater than 37 psu) due to excessive evaporation. The presence of such hyper-saline features as high as 46 psu has been observed by Cloud et al. (1962) and later by many other scientists (Fig 3.2). Broecker et al. (1966), showed that these high-salinity pools of water have residence times of longer than 300 days. Physical observations have shown the seasonal pattern of these sinking waters. For the year 2000 of observations, it was found that these hyper-saline waters are so dense that they can sink to depths of at least 45 m in summer and 75 m in winter (Smith et al., 1995; Hickey et al. 2000; Otis et al. 2004). These particular depths of penetration are a function of the increase in salinity over the shallow banks, and the depth of the thermocline in the deeper waters. Since the atmospheric forcings are typically similar over the years, it can be assumed to first order that these depths of penetration are repeatable over the years. These observations led Hickey et al. to the conclusion that subsurface high salinity values observed throughout the upper layers of Exuma Sound indicate that the dense plumes originated on the shallow Bahamian banks and flowed off the platform during ebb tide. Certainly, a better understanding of the mechanisms affecting the temperature and salinity of shallow waters is warranted, especially if this water can be described by thermohaline circulation to depths where coral reefs are expected to flourish. There have been numerous observations of coral bleaching due to the excessive warming of shallow areas. Chiappone et al. (1997), studying the coral reefs around the greater Bahamas banks, ascribe factors associated with the lack of reef 24

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(a) (b) Fig. 3.1: AVHRR image of SST for a) 15 April, 2001 at 6:00 am. b) 17 April, 2001 at 6:00 pm, color scale in C (AVHRR images courtesy of F.Muller-Karger). 25

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Fig. 3.2. Isohalines along the west coast of Andros Island (modified May curves from Cloud, 1962a). 26

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development to include turbidity, sediment transport, and fluctuations in water temperatures. Contrary to the Grand Banks of the Bahamas, such adverse conditions do not prevail in the Exuma Cays, however, given the relatively high coverage (>25%) of massive coral species in many reefs. Lang et al. (1988) observed that heating and evaporation of water on the Great Bahamas bank during the summer could create a mass of warm, very saline (40 ppt) water, which is denser than the upper mixed layer of Exuma Sound. This can create underflows of very warm saline water, sometimes resulting in bleaching of corals. Coral reef bleaching has also been ascribed to increased ultra-violet radiation together with temperatures greater than 30C (Humann 1993). Waters over shallow subtropical banks can become much hotter than are found in adjacent deeper waters. Since coral bleaching has been attributed in part to elevated temperature, can summer heating and evaporation of shallow areas supply hot waters to the adjacent fringing coral reefs? Because of their low reflectivity, do sea grass and benthic algal mats significantly affect the amount of heat absorbed by a shallow water column and increase the resulting hyper salinity and the depth of penetration of hot waters? These are questions to be explore in this thesis, both in this chapter and the next. 3.2 Background There are numerous field observations relating the thermal behavior of water bodies to their optical properties. Idso and Foster (1974) found, that with algal blooms, increased solar radiation is trapped in the upper water columns. Zaneveld et al. (1981) carried out calculations on the rate of heating of the surface mixed layer of marine waters, ranging in optical character from the Jerlov (1976) oceanic Type I to coastal water Type III. 27

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Table 3.1: List of symbols. Symbol E d, E u, E net a w () a g () a () chl-a 0 r r C r B r dp b () r rs Q bot Q lost Q a Q b Q e Q c Q sd R B T a T w e w ea Definition Downwelling, upwelling and net radiation Absorption due to water Absorption due to Gelbstoff Absorption due to phytoplankton Chlorphyll a Average cosine Reflectance Reflection from the water column Reflection from the bottom Deep water reflectance Bottom albedo Remote sensing reflectance Heat generated due the bottom Heat lost from the water column Downwelling longwave radiation Upwelling longwave radiation Latent heat flux Sensible heat flux Downwelling shortwave radiation Bowens ratio Air temperature Water temperature Saturated vapor pressure Vapor pressure of air Units Wm -2 m -1 m -1 m -1 mgm -3 Wm -2 Wm -2 Wm -2 Wm -2 Wm -2 Wm -2 Wm -2 K K mbars mbars 28

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It has already been established beyond doubt that penetration of short-wave radiation to depths has a very strong influence on the heat budget of the surface layer and that higher-resolution optical models are more accurate (e.g. Simpson and Dickey, 1981, Liu et al.2002). In this thesis, a further step is taken to point out how a very critical factor, the bottom, has been virtually ignored in coastal heat budget calculations. In shallow regions of the coast, a large fraction of light reaches the bottom. For carbonate banks, a significant fraction of the visible light is reflected back from the bottom, depending on the bottom albedo, while the bottom absorbs the rest of it. The absorbed short-wave radiation is then radiated or conducted back from the sediments as long-wave radiation, heating the adjacent bottom layer of water. Figure 3.3 is a chart of the location of study. The locations of Andros Island, the Great Bahamas Banks, the TOTO (Tongue of the Ocean) etc. can be seen relative to the state of Florida in the Atlantic Ocean. Figure 3.4 is a MODIS ocean color image of the Bahamas. For coral sand areas as much as 50% of the light striking the bottom is reflected, while for thick grass regions only about 5% is reflected (Mobley, 1994), and up to 40% of the reflected energy exits the ocean surface, depending on the water column depth and bottom albedo. The regions of sea grass and coral sand bottom based on their reflectivity are marked in the figure (Fig 3.4). Some investigations of coastal areas have been performed recently using a black bottom, which assumes that all of the light energy hitting the bottom is placed in the bottom layer as heat (Weisberg et al. personal communication). They have also used a 100% reflecting bottom and have shown (Weisberg et al. 1996, 2001) how the generation of buoyancy (by heating and fresh-water input from the rivers) induces a baroclinic circulation that modifies the wind-driven circulation along the West Florida Shelf. This baroclinic circulation is in fact, responsible for the cold tongue found along the west Florida shelf in springtime. In winter, the coastal waters are coldest with waters getting progressively warmer as the depth increases. As spring sets in, the coastal waters heat up rapidly whereas the waters outside the continental shelf are also still warm. So the portion in between these two warm waters is coldest 29

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in the area and is the cause of the cold tongue. The true effect of bottom absorption lies somewhere between the extremes of no bottom and a black bottom. This chapter shows that neglecting the optical effects of a bottom can lead to large errors when predicting the heat budgets and thermal structure of shallow oceanic areas. The importance of shallow-bottom reflection on the under-water light field and the subsequent effect on interpretations of ocean-color remote sensing have already been demonstrated (Lee et al. 1998, 1999, 2001). A similar approach to that used by Lee is adopted here for determining bottom-reflected irradiance and its contribution to shallow-water heating. 3.3 Location and data Due to its extensive shallow bathymetry, the Bahamas region of the Atlantic is a very convenient location to study bottom effects. The location of the field area for simulations is a 200x200 km region near Andros Island. The very deep region to the east of Andros Island is called the Tongue Of The Ocean, TOTO, because of its shape (see Figs. 3.2 and 3.3). Figure 3.3 is a chart (with shelf break superimposed) of the location of the study area, and Figure 3.4 is a MODIS ocean-color image using the high-resolution (250 m and 500 m) Landsat-like bands. The Bahamas Platform, of which the Banks is a part, is a barely submerged plateau (depth < 10 m) constructed of Pleistocene lime stone on Tertiary and Cretaceous lime stone and dolomite covered with a film of recent carbonate sediments (Hildegard, 1968). These bottoms are covered in places with layers of sea grass or algae. The brighter regions of Figure 3.4 30

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Fig. 3.3: Chart showing the relative location of field of study. 31

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Fig. 3.4: A MODIS ocean color image of the Bahamas for April 18, 2000. 32

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near Andros Island show shallow sandy areas with very high reflectance (albedos of about 0.5). The slightly darker areas are bottoms with sea grass or algal matter beds with much lower albedos (about 0.05). Mixture of the two within a given pixel accounts for most of the intermediate values. The islands are surrounded by shallow-water reef material. The island of Andros is bordered by the shallow (less than 10 m deep) Great Bahamas bank to the west and the deep Tongue Of The Ocean to the east. To the east of the Tongue Of The Ocean, lies the Exuma Cays. In this chapter, we deal with the part of the Great Bahamas Bank along the northwestern part of Andros Island. Only around the edges of the Bank does the sea floor slope steeply from 10 m to 200 m over a distance of 2 km or less. The presence of these shallow regions with rocky shoals and islands, combined with the lateral extent of the Bank, greatly reduces the tidal exchange of water with the surrounding deep areas (Broecker, 1966) and this isolation (~ 300 day residence time)has led to the development of an extensive region of relatively sheltered undisturbed water, ideal for one dimensional simulations. 3.3.1 Meteorological data The meteorological data used in this study came from the AUTEC (Atlantic Underwater Test Center) site run by the U.S. Navy. The Weatherpak-100 is an automated weather station installed 10 meters above the sea surface, 1 mile offshore of the eastern side of Andros island and it records the mean, high and low air temperatures, wind speed and direction, maximum wind gust and direction, barometric pressure and relative humidity. The data from this weather station are collected and updated every 10 minutes, and sent to shore by radio link to a dedicated computer (referenced from AUTEC website). Figure 3.5a-d shows the variation of meteorological parameters with time. The figure shows the temporal evolution of the wind speed, air pressure, relative humidity and total incoming radiation. Representative total radiation data for these latitudes were taken from the Mote 33

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(c) (a) (b) Fig. 3.5: Temporal variation of the meteorological parameters a) wind speed b) air pressure c) relative humidity for 90 days. (Continued on the next page) 34

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(Fig 3.5 continued) (d) Fig. 3.5d) Variation of light intensity at the Mote Marine Lab location. 35

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Marine Laboratory (Sarasota, FL) web site, where light data are provided every 15 minutes. It is known that the Bahamas lie in the trade-wind belt. From March to the end of August, the prevailing wind is from the east or southeast, while in September it veers (flows towards) to the north (Hildegard, 1968, Boultbee, 1989). As a result of the seasonal pattern of winds, there is, in summer, a net northward drift of water across the bank. In winter the residual current is southward and, during the southeasterly gales, eastward. 3.3.2 Bathymetric data Navigation charts (BBA Chart kit, 1991) were used to digitize and interpolate the bathymetry of the bank regions. This was accomplished by laying a regular grid printed on a clear sheet of plastic over the bathymetric chart and reading off values from the chart box by box. By interpolation a digital map of bathymetry was created for the northern portion of the Great Bahamas Bank. 3.3.3 AVHRR (Advanced Very High Resolution Radiometer) data The AVHRR satellite sensor provides sea-surface temperature data. The data are used here to compare deep-water temperatures with temperatures of the shallow waters on the Bahamas Banks. The spatial and temporal coverage is very good for cloud free days, with three satellites (NOAA-12, NOAA-14 and NOAA-15) providing daily coverage of the entire study area. Real-time high-resolution (1 km at nadir) data have been acquired through the HRPT (High Resolution Picture Transmission) receiving station at the University of South Florida (courtesy of Frank Muller-Karger). 36

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3.3.4 In-situ data In-situ data sets of optical properties used as input to the heat budget simulation were collected during the SIMBIOS (Sensor Intercomparison and Merger for Biological and Interdisciplinary Studies) experiment carried out in the Tongue of the Ocean region from April 24-28, 2000. The simulations in this study were run for dates near April 17 th but the water properties are assumed to remain constant over this period. Measurements of absorption due to gelbstoff (yellow substance or colored dissolved organic matter) were made by first filtering seawater through a 0.2 m pore-sized nylon filter and freezing the samples. At the lab, samples were thawed and the absorption was measured in a spectrophotometer by comparing it to a Milli-Q water blank (Mueller and Austin 1995). Chlorophyll a concentration, [chl a] was determined fluorometrically [Holm-Hanson and Rieman 1978; Mueller and Austin, 1995]. Vertical profiles of salinity, temperature and various optical properties were carried out at each station during the experiment using a slow-drop package consisting of a CTD (Conductivity, Temperature and Depth, SeaBird serial microcat ,SBE-37) and several optical instruments, including a Wet Labs ac9, which was used to measure absorption and attenuation at 9 wavelengths. Scattering was determined using the following equation, (Preisendorfer, 1961) b() = c ()a() (3.1) where b is the total scattering, a is the total absorption, and c is the beam attenuation coefiicient. 3.4 Inherent optical properties Types 1, 1A and 1B waters, which are found usually in the open ocean, are the clearest natural waters based on Jerlovs classification. Morel Case 1 waters are waters in which the phytoplankton concentration dominates variations in absorption 37

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and scattering. Absorption by chlorophyll and related pigments therefore plays a major role in determining the total absorption coefficient in such waters. Case 1 waters can vary from very clear (oligotrophic) water to very turbid (eutrophic) water, depending on the phytoplankton concentration. Prieur and Sathyendranath (1981) developed a pioneering bio-optical model for spectral absorption of Case 1 waters. The essence of the Prieur and Sathyendranath model is contained in a more recent and simpler variant given by Morel (1991b): a()={a w ()+0.06a c ().C 0.65 }{1+0.2exp(-0.014(-440)} (3.2) where, a w () is the absorption coefficient of pure water and a c *() is the non-dimensional statistically derived chlorophyll-specific absorption coefficient. One of the limitations of this model is that the model assumes that the absorption by yellow matter co-varies with that due to phytoplankton. Note that the formulation of Smith and Baker (1981) must be used in this expression rather than the clearer values of Pope and Fry (1997). Otherwise the 0.2-factor must be changed to compensate for the yellow matter inherent in the Smith and Baker (1981) clear-water values. For Types 2 and 3 waters, which are more turbid waters with a higher concentrations of gelbstoff and suspended sediments, the absorption and scattering are calculated based on field measurements. They are then input into the Hydrolight model (Mobley, 1994) as ac9 data files. The total absorption coefficient can be expressed as a sum of the absorption coefficients of pure water, Gelbstoff and phytoplankton pigments respectively: a t () = a w () + a g () +a () (3.3) Absorption values for pure water are taken from Pope and Fry (1997), whereas absorption for phytoplankton pigments and Gelbstoff has been modeled with simple bio-optical models, which give a realistic simulation for a variety of waters. 38

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The phytoplankton pigment absorption coefficient is simulated using the empirical model, a () = {(a 0 () + a 1 ()ln[a (440)]} a (440) (3.4) where values for a 0 () and a 1 () are provided in Lee et al.(1994, 1998). In the Hydrolight calculations, a (440) can be input by itself or can be linked to another parameter such as the chlorophyll a concentration. To be consistent with the calculations of other researchers such as Morel (1988), and to compare with the POM, [chl-a] has been used as an input to determine the a (440) and the particle scattering (b p (550)) values: a (440) = 0.06[chl-a] 0.65 (3.5) b p () = B[chl-a] 0.62 (550/) (3.6) Here B is an empirical value, which was 0.3 in Gordon and Morel (1983). It could vary among 0.3,1.0 and 5.0 to simulate a range from normal to highly turbid waters. It was set to 0.3 m -1 for this study. The gelbstoff absorption is expressed as (Sathyendranath 1981, Carder et al. 1991); a g ()=a g (440)exp[-0.014(-440)] (3.7) Based on the input absorption and scattering, Hydrolight can be used to calculate the attenuation of light with depth for these waters. An appropriate expression for more rapidly determining the diffuse attenuation function can be derived. Kirk (1984a) found an analytical relationship by systematically varying the optical properties which was comparable to a Monte Carlo study: 39

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2/1020)]19.0425.0([1)(abaavgKd (3.8) where, is the average value of the attenuation coefficient in the euphotic zone, which is actually the value of K )(avKd d at the midpoint of the euphotic zone. This equation has been further extended by Bissett (1999) to incorporate the effects of the variation in the average cosine with depth. In the present simulations, this equation for K d is adopted. For a listing of the symbols used in this study see Table 3.1 and also Table 2.1. Also refer to Table 3.2 below for the inherent optical properties used in this study. Table 3.2: The inherent optical properties of the water column. Chl concentration [chl-a] : 0.15 mgm -3 a w () : Pope and Fry (1997) b w () : Morel (1974) a (440) : 0.06[chl-a] 0.65 = 0.00856 a g (400) : 0.05 b p () : B[chl-a] 0.62 (550/) ; B=0.3 The average cosine used is the cosine of the sub-surface solar zenith angle, and it provides the effective slant path of photons to depth for a shallow water column (Lee et al., 1999). 40

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3.5 Quantifying the bottom effects Lee et al. (1999, 2001) have modeled the effect of shallow waters to derive bottom depth and albedo using the in-water remote sensing reflectance r rs They simulated the output from a large number of Hydrolight runs for a wide variety of bottom and water types. The Lee model is used to calculate the irradiance reflectance r. r= E u /E d =Q.r rs ; where r rs = L u /E d (3.9a,b) E u and E d are the upwelling and downwelling irradiances and L u is the upwelling radiance. While for shallow waters, 2.5
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C D u =1.03 (1+2.4u) 0.5 B D u = 1.04 (1+5.4u) 0.5 (3.13a,b) H is the total water column height and cos is the cosine of the subsurface solar zenith angle, r dp = (0.084 + 0.17u)u (3.14) Once the reflectance r is determined, the upwelling light field can be calculated using E u =r*E d (Mobley 1994). The net irradiance at any depth is E net =E d -E u and the dE net /dz is converted into heat (Kirk, 1988) and is added as a heat source for each water layer. The amount of light absorbed by the bottom per second is assumed to be radiated and conducted into the bottom layer and is determined by, Q bot = (1b )*E d (H b ) (3.15) where H b is the depth of the bottom layer. A portion of the total upwelling light is internally reflected at the water-air interface, while the rest escapes back into the atmosphere. Gordon et al. (1988) expressed this relationship and Lee et al. (1999) used it in a semi analytical model for nadir-viewing remote-sensing reflectance R rs using Hydrolight 3.0, rsrsrsrrR5.115.0 (3.16) 42

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3.6 Modifications to the GOTM code In many applications of estuarine and coastal models the realistic reproduction of vertical heat-exchange processes is at least as important as the horizontal transport processes. A study of vertical processes using one-dimensional models is the first step towards a more complete analysis of three dimensional ocean circulation studies. For a one-dimensional analysis of the development of thermal structure without the complicating effects of advection and horizontal diffusion, a simpler version of the turbulence model called the General Ocean Turbulence Model (GOTM) was adopted (Burchard et al. 1998, Burchard et al. 1999). The kand k-kL models are the only two two-equation models that have been extensively applied to geophysical flows. In our simulations, the model was run with the Mellor-Yamada, k-kL and not the kturbulence closure, since most ocean models follow MY (k-kL) scheme for calculating the turbulent kinetic energy. Both k-kL model and kmodel have been applied independently for many years but have only recently been compared in detail (Burchard et al. 1998). MY (k-kL model) is the same turbulence closure model (level 2.5) as used in the Princeton Ocean Model (POM) for parameterization of the vertical turbulent eddy coefficients. The MY, k-kL equation can be written as follows 223112)(2)(zzlztLLEBEPELkLLkSkL (3.17) For the empirical parameters occurring in the equation above, see Table 3.3. These are calibrated using laboratory experiments and are similar for the kmodel (Baumert and Peters, 2000). In the GOTM model used in the current simulations, the values adopted for the constants are as those modified by Burchard et al. (1998). 43

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Table 3.3. Empirical model parameters for the k-kL model. B 1 E 1 E 2 E 3 S q 16.6 1.8 1.33 1.8 0.2 For the buoyancy production related parameter E 3 which corresponds to c 3 in the kmodel, the same problem arises as for the kmodel. Mellor and Yamada (1982) chose the same empirical co-efficient for the buoyancy production and for the shear production, arguing that it might be preceded by another constant if data can be found to unambiguously support a value other than unity, where unity here is related to the ratio of E 1 /E 3 as Rodi (1980) for the kmodel. It was again Kantha (1988) in his unpublished manuscript, who first suggested a completely different value for E 3 based on limitations of the macro length scale for stably stratified flow. In the same year, Galperin et al (1988) suggested application of an algebraic length scale limitation proportional to the buoyancy length scale, 056.0222lim2NforNkLL (3.18) when using the k-kL with E 3 =E 1 in order to reflect the limiting effects of stable stratification on the size of the turbulent eddies. 44

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day 100.25100.50100.75 SW radiation (Wm-2) 0200400600800 Fig. 3.6: Curve showing a typical diurnal profile of total incoming radiation including cloud effects. 45

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Table 3.4: Flux rates averaged over a 12 hr. heating cycle during model simulation for a 2.5 m deep water column (in Wm -2 ). Clear represents a transparent bottom. Q solar is short-wave radiation from 350-700 nm. Q lost represents short-wave reflected light to the atmosphere plus short-wave light transmitted through a transparent bottom. Bottom type Q a (+) Q b (-) Q e (-) Q c (-) Q solar (+) Q lost (-) Q net (+) SST in 12 hrs Black 365.07 440.18 75.02 14.49 375.10 10.3 200.18 0.83 Sea grass 365.07 440.11 74.97 14.43 375.10 12.00 198.66 0.80 Coral sand 365.07 439.59 74.59 13.97 375.10 40.8 171.22 0.61 Clear 365.07 437.76 73.28 12.35 375.10 218.86 -2.08 -0.04 46

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Table 3.5: The various flux rates averaged over 12 hrs during model simulation for a 10 m-deep water column (in Wm -2 ). Clear represents a transparent bottom. Bottom type Q a (+) Q b (-) Q e (-) Q c (-) Q solar (+) Q lost (-) Q net (+) SST in 12 hrs Black 365.07 438.75 74.00 13.22 375.10 10.3 203.9 0.29 Sea grass 365.07 438.75 73.99 13.22 375.10 11.3 203.99 0.29 Coral sand 365.07 438.71 73.96 13.19 375.10 18.1 196.21 0.27 Clear 365.07 438.4 73.75 12.93 375.10 70.4 144.69 0.16 47

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Burchard (2001a) recently showed that the consequence of not using the limitation leads to a pronounced, unphysical maximum of the macro length scale L in the entrainment region below a stably stratified boundary layer. However, after calibrating E 3 Burchard (2001a) could show that the model performs properly without the length scale limitation Eq. 3.18. If the energy resulting from the solar insolation absorbed and reflected by the bottom is not considered, the same errors in the GOTM will also be manifested in the POM (it is demonstrated in the next chapter). The General Ocean Turbulence Model has been developed in a modular format with a series of subroutines. The calculation of the underwater light field has been modified by using inherent optical properties (instead of the spectrally constant, or wavelength-independent K d with depth). Though not sensitive to this particular study, we replace the constant fluxes used in the GOTM by actual measurements of the total heat fluxes from the meteorological data. The sum of the latent, sensible, incoming long-wave and outgoing long-wave radiation is used as a boundary condition at the surface. The absorbed short-wave radiation is treated as a source of heat at each water depth. An additional upwelling radiation term from the bottom is also included, which is characterized as mentioned before. There is an additional source of heat now in the bottom layer from the long-wave radiation emitted or conducted from the bottom as a result of absorption of the short-wave radiation incident upon it. The explanations of all of the equations of motion and the parameterization of the turbulent exchange coefficients in the Mellor-Yamada model are too complicated to be included here and can be referenced from their papers. The basic equations of the turbulence closure are provided in Appendix C. 3.7 Surface-flux calculations The heat fluxes have been parameterized by many scientists. In this paper the state-of-the-art formulae of Doney et al. (1996) have been adopted. Q sd is the short-wave radiation measured at the surface of the water column. The rest of the terms in the heat budget are computed using the formulae of Doney (1996): 48

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Q sens = a c pa C H U 10 (T a -T s ) (3.19) Q lat = a L a C E U 10 (q a -q s ) (3.20) Q lw (net)= 0 [T a 4 (0.39-0.05e a 0.5 )F(CI)+4T a 3 (T s -T a )] (3.21) F(CI)=1-0.63CI (3.22) where a is the air-density (1.22 kg -3 ), c pa is the specific heat of air at constant pressure (1003 Jkg -1 K -1 ), C H and C E are bulk transfer coefficients (9.7x 10 -4 and 1.5x10 -3 both unitless), U 10 is the wind speed at 10 m above the sea surface (ms -1 ) T a and T s are air and sea surface temperatures in K respectively, L v is the latent heat of vaporization (2.45x10 6 Jkg -1 ),q a and q s are air and sea surface humidity respectively (both unitless), 0 is emissivity of sea surface (0.985, unitless), is Stephan Boltzmann constant (5.7x10 -8 Wm -2 K -4 ), e a is the vapor pressure, CI is the cloud index. The net rate of heat uptake by the surface layer, resulting from the combined effects of solar energy absorption and these various surface heat exchange processes is Q net =Q sd (1) + Q a -Q b -Q e -Q c +Q bottom (1) (3.23) where Q sd (j) is the short-wave flux (from 400 nm) at the j th level of depth obtained from the downwelling light field. Q bottom (1) is a new extra term that we are emphasizing in this chapter. This Q bottom (j) is the sum of the upwelling light flux from the bottom that is absorbed by the j th layer and the heat diffused upwards from the bottom (heat that is radiated by the bottom), in this case, the top layer. The total energy that is lost from the water column as light from the surface is designated as Q lost in the Table 3.4 and Table 3.5. A typical curve showing the diurnal variation of the short-wave radiation is given in Figure 3.6. The background radiation value just taking into account nocturnal infrared radiation is about 30 Wm -2 49

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The rate of heat uptake by a typical 2.5 m water column is given in Table 3.4. This experiment was carried out for 12 hours of diurnal heating. The Q lost term is the term that is ignored by many modelers. This is the heat that is lost out of the water column. Mostly, the loss is through the surface as light (which the remote sensing instruments measure as the water-leaving radiance, L w ). In case of a transparent bottom (when the bottom is ignored), there is a very large heat loss of about 218 Wm -2 showing that ignoring the bottom creates quite erroneous results. Also the water column is about 0.2C warmer after 12 hours of heating when the bottom is black as opposed to coral sand but only 0.03C warmer than when the bottom is grass. A similar run is carried out for a 10 m water column (seen in Table 3.5). The Q lost term for 10 m water depth (70 Wm -2 ) is not as high as for the 2.5 m depth since more light is absorbed by the deeper water column. 3.8 Results and discussion The aim of this study was to emulate the evolution of water-column temperature profiles in response to external forcing (wind, solar radiation, fluxes) using the optical properties of the water column and those of the bottom. As mentioned before, Table 3.2 shows the inherent optical properties used in the following simulations. Simulations were run with various bottom conditions in the GOTM for 1 m, 2.5 m, 5 m, 7.5 m, 10 m and 20 m deep water columns for 12 hours of solar heating. The results for the various types of bottom are tabulated in Table 3.6. Simulations with black bottoms produce water columns that are warmer than using the other bottom properties. The spectral albedos for the two types of bottom are provided in Fig 3.7. Coral sand is highly reflective (albedo of about 0.5) while sea grass is not (about 0.05). The bottom serves two purposes: it reflects the short-wave radiation incident on it depending on its albedo, and absorbs the rest of the radiation. This absorbed radiation is then conducted and radiated back as long-wave radiation and immediately absorbed in the bottom layer. Note that the effects observed in the 50

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simulation were accentuated for a shallow (1 m) water column with an almost 0.9C temperature difference between the black and coral-sand bottom cases. Ignoring the bottom in heat budget models results in water temperature some 2.5C cooler than one would expect with a grass bottom. In 20 m of water, however, the difference becomes negligible over a single heating cycle. Figure 3.8 shows a simulation for a 7.5 m water column, with the winds set to a very low value of 0.5 m/s to facilitate the comparison among various bottom types for a stratified water column. These shallow regions completely mixed when the winds exceeded 1 m/s for this dry (70% RH) spring period. For this 7-day simulation, the starting temperature profile at 6 am was set constant with depth at 20.5C. The water-column temperature was then allowed to develop for a week reproducing temperature profiles at the end of the seventh day. Most light hitting a sea-grass bottom for example is absorbed and radiated as long-wave radiation or conducted into the bottom of the water column. Convection then mixes this hot water upwards due to buoyancy effects producing a well-mixed water column except at surface due to local infra-red absorption. The bottom of the water column was heated more for the sea grass than for coral sand, and less light was reflected upwards. This provided a warmer water column for the sea grass case except just beneath the surface. Here, the extra light reflected by the sand bottom that hit the sea surface at angles greater than the critical angle ( v > 48.5) is totally reflected and trapped. Due to its oblique, relatively horizontal path, much of it is absorbed near the surface. At the end of a week, the sea grass produced a warmer water column than did the coral sand bottom. This is because more light is lost by bottom reflection through the air-sea interface when the bottom is coral sand (e.g. Q lost in Table 3.4). 51

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lamda 300400500600700800 albedo 0.00.10.20.30.40.50.60.7 coral sand sea grass Fig. 3.7: Spectral albedo curves for sea grass and coral sand bottoms. 52

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Table 3.6: The final temperatures (C) obtained by model simulation after 12 hrs of heating. The solar radiation values and fluxes are as before. The starting temperature at 6:00 am in the morning of simulation was 26.5C. Depth (m) Black (C) Sea grass (C) Coral sand (C) Transparent Bottom (C) 1.0 27.90 27.80 27.04 25.32 2.5 27.32 27.30 27.11 26.46 5.0 27.00 26.99 26.92 26.67 7.5 26.86 26.86 26.83 26.65 10.0 26.79 26.78 26.77 26.66 20.0 26.67 26.67 26.67 26.63 53

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20212223242526272829depth(m) 012345678 initial profile clear bottom coral sand sea grass temperature (oC) Fig.3.8: Temperature as a function of depth for the various types of bottoms after 7 days of simulation. Depth of the water column is 7.5m and winds have been set to 0.5 m/s. 54

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Bathymetry contours for the study area are shown in Figure 3.9. There are regions of extremely shallow depth (note that the regions below 1 m depth are treated as 1 m by the model). The model domain has been set up with 4 km bins in the x and y directions. Figure 3.10 shows a 1D simulation for conditions measured from 15 to 17 April 2001 for comparison with the AVHRR images shown in Fig 3.1a and 3.1b. The simulation was for 60 hours starting at 0600, 15 April with an initial uniform 26.5C water column with a coral sand bottom. The final sea-surface temperatures, for the coral-sand bottom simulation are provided in Figure 3.10. Results from similar runs are shown in Figure 3.11a (the temperature anomaly) where coral sand is replaced by sea grass. Figure 3.11b shows the simulated temperature anomalies when the bottom is completely black. As can be seen from Figure 3.11b, there is a very appreciable change in the horizontal temperature structure after only 60 hours when results from a black bottom are compared to those with coral-sand bottom. Note that the shallow-water temperatures can be 1.55C warmer for black rather than for coral sand bottoms. Figure 3.10 can be compared with the bathymetry map (Fig. 3.9) to locate the shallow and deep areas. The regions where the bathymetry falls off to very deep regions are found to be regions of sharp temperature fronts when lateral convection and mixing are neglected. A temperature contrast of about 1.7C (warmer at the shallow end) can be observed at the interface of these thermal fronts. Note that high temperatures of up to 27.7C in Figure 3.10 are in the smaller, very shallow regions with depths less than 1.5 m. The black-bottom temperatures are modeled as high as 29.2C in Figure 3.11b. As a reality check, Figure 1b shows AVHRR temperatures exceeding 28.5C, falling between sea-grass and coral-sand temperatures. 55

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051015202530354045 05101520253035404550 00.51.52357.51015Andros Island Fig 3.9: Bathymetry (in meters) of the model simulation. 051015202530354045 05101520253035404550 02626.526.752727.2527.527.627.7Andros Island Fig. 3.10: Modeled SST (C) with uniform coral sand bottom after a 60 hour April simulation of the Bahamas banks. 56

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051015202530354045 05101520253035404550 00.010.10.20.30.50.81.4Andros Island (a) 051015202530354045 05101520253035404550 00.010.10.20.30.50.91.41.55Andros Island (b) Fig. 3.11a,b: SST anomalies (C) after 60 hours when a sand bottom is replaced by (a) sea grass or (b) black surface. 57

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Note that, much of the shallow area near Andros Island and the Berry Islands is, actually less than 1 m in depth, which was modeled as 1 m deep. Also, the skin temperature viewed by AVHRR on calm days can be 0.5 to 1C higher than the bulk temperature (Brown and Minnett 1999). But vast areas with depths of about 3-7.5 m can be seen to be at about 27C in both Figure 3.10 and Figure 1b (which is a daytime image, at the end of a heating cycle, taken near 6 pm). 3.9 Sensitivity studies A temperature anomaly plot is provided for the study area comparing the effects of sea-grass and coral-sand bottoms (Fig. 3.11a). We can see that when the coral sand bottoms are replaced by sea grass, the water column heats more. Based on pure energy conservation laws, we can explain this as being due to the fact that coral sand is highly reflective (albedo of about 0.5), and significant light energy is reflected from the bottom and out of the water column. Intuitively, this heat decrease is maximal for shallow highly reflecting areas where the water-leaving radiance is highest. This water-leaving radiance is perceived as the very bright regions by ocean color sensors as shown in Figure 3.4. This loss of energy reduces the springtime temperature of water columns over sand versus those over grass. The anomaly contrast is seen clearly in Figure 3.11a, especially in the shallows. 3.10 Thermohaline effects From the above discussions, the effect of bottom albedo on heat budget calculations and hence on the temperature of the water column has been demonstrated. In addition to this direct effect on water-column temperature, the heat budget also has an indirect effect on salinity. As the water evaporates, salinity increases, as does density. In this section, we revisit the effects of net evaporation on salinity changes during both spring and summer (Fig. 3.12a-f). 58

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A comparison between transparent and sea-grass bottoms shows the strong influence of bottom absorption and reflection on the salinity and corresponding density. As expected, salinity changes are greater for sea grass bottom, since thermal heating is greater with a sea grass bottom and hence so is net evaporation. There is an almost 0.4 psu difference between the transparent-bottom model and the implementation of the sea grass bottom over a period of 24 days. This could lead to serious errors when we try to simulate circulation over coastal areas (hydrodynamic simulations are described in Chapter 4). Salinity increases more in the shallow areas as compared to the deeper areas (Fig.3.12a-f), and is responsible for the thermohaline circulation found in these regions as described by Smith et al. (1995) and Hickey et al. 2000. The highest temporal variation in the salinity values occurs during the spring season (due to high insolation, low humidity and reduced precipitation). The salinity values start decreasing by summer. By May, precipitation begins to set in and salinity then start to slowly decrease. Figure 3.13 shows that evaporation is high in spring and summer, but summer salinities decrease because the E-P curve shows a decline. Note that this curve was derived for a 2 m water column as is found in Adderly Cut (the 3D numerical simulation of next chapter). An interesting feature of the curves 3.12a-f is an abrupt decrease in the temperature and salinity changes for depths shallower than about 6 m for transparent bottom. Remember that a transparent bottom ignores the light reaching the bottom. Shallow water depths cause nighttime cooling (loss of heat to the atmosphere, which is distributed over a shorter water column) for hot water columns over dark bottoms. With transparent bottoms, much less heat builds up during the day, so less evaporation (and hence smaller salinity change) occurs. Of course, the final temperature attained for the three types of curves (sea grass, coral sand and transparent bottoms) converges by a bottom depth of about 20 m. For deeper depths little reflected light from the bottom escapes through the sea-air interface before being absorbed by the water column. 59

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depth (m) 0246810121416182022 change in salinity (psu) 1.11.21.31.41.51.61.7 Sea grass Coral sand transparentbottom depth (m) 0246810121416182022 change in temperature (o C) -4-202468 depth (m) 0246810121416182022 change in density -0.6-0.4-0.20.00.20.40.60.81.0 depth (m) 0246810121416182022 change in salinity (psu) 1.11.21.31.41.51.61.7 depth (m) 0246810121416182022 change in temperature (oC) -4-202468 depth (m) 0246810121416182022 change in density -1012 AprilAugust (a) (d) (b) (e) (f) (c) Fig. 3.12(a-f): The salinity, temperature and density change after 24 days of model simulation for spring and summer, 2001 for the three bottom types. (Legends for the three types are in Fig.3.12a.) 60

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Fig. 3.13: Evaporation Precipitation (E-P) in m for 150 days starting from February 1 st Note the precipitation is the monthly average value for the AUTEC TOTO site. 61

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days 020406080100120 salinity 3638404244464850 1m1.5m2m2.5m4m5m Fig. 3.14: Increase in salinity from February with time for the various water depths using a coral sand bottom. 62

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Fig. 3.14 shows the evolution of salinity with water depth that has been simulated for the Bahamas Banks. Recall that the advective and diffusive effects and rainfall and river runoff over these regions are not incorporated in the model at this time. The salinity change represents then, a maximal salinity change possible for each depth. As incredible as it may seem, the salinity for these water columns can reach about 46 psu in late spring, as seen from observations (Smith 1940; Cloud, 1962a). The roughly concentric arrangement of the isohalines in the pool of hyper-saline waters, which develops in the summer months off the west coast of Andros (recall Figure 3.2). As observed from the bathymetry (Fig. 3.9) these are the shallowest isolated regions along Andros Island with depths less than 2 m. These pools of hyper saline waters formed in spring and summer are never completely destroyed by the winds in winter and they escape dilution by waters of lower salinity due to their isolation from the ocean. Broecker et al. (1966) estimated residence times upto 300 days for this hyper-saline region west of Andros Island. The presence of these hyper-saline plumes extends to winter, as seen from sampled data, though the salinity values are much lower (about 39 ppt). In the next chapter, we show the results obtained from a 3-D model of a coastal Bahamian setting for a full year using realistic winds and tides (Fig. 4.17). The reasons for the persistence of this salinity pattern are primarily due to the moderate tidal exchange with deeper waters and the shelter from the full vigor of the trades provided by Andros Island. So, even though there is a slow intrusion of less saline water from the Tongue Of The Ocean, it is clear that the dilution is not enough to offset the effects of evaporation on salinity. 3.11 Moisture effects It has been known from ancient times that low-level cumulus clouds are associated with the sea-land boundary. Sailors knew from the early days to anticipate land as close by whenever they saw large low-lying clouds in the open ocean. In fact, in his memoirs in 1495, Columbus has described the observations of landmass on his 63

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famous expedition to discover the Americas by the occurrence of low-lying clouds and birds. In addition to clearly delineating land boundary, the clouds also decide the amount of precipitation that the region obtains. As the clouds are formed from the moisture formed from the water evaporated that convectively updrafts, it would be interesting to study the moisture feedbacks along the land-sea boundaries. These clouds formed near the boundaries can of course be advected many miles by the prevailing sea and land breezes. Following up on the results of the chapter, it can be seen that one of the main ramifications of the study is the influence of shallow-water heating on moisture feedbacks. Figure 3.15 shows the moisture evolution of shallow waters using a 1D model. It can be observed that for a 1-m deep-water column, about 0.35 m of precipitable water is released in 4 months. To gain an understanding of the magnitude of shallow-water evaporation, the moisture released from a 1 m 2 water column of depth D is multiplied with the total area of the earth surface in the tropics with that depth (Fig. 1.2) for all depths less than 10 m. This cumulative value is then divided by the total mass of precipitable water vapor in the air (13*10 15 kg). This provides a value of 4%. That is, about 4% of the total water vapor in the earths atmosphere can be formed due to shallow-water (less than 10 m) heating effects of the Tropics. Of course, it is assumed here that the meteorological forcings in the calculation of all the regions of the tropics are identical to that of the Bahamas. Even so, it is clear that global models, which neglect any depth less than 50 m is seriously underestimating the water vapor injected into the atmosphere through evaporation. Water vapor is such an important green house gas that it is important to correctly quantify its amount. 64

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days 020406080100120 evaporation (m) 0.000.050.100.150.200.250.300.35 1 m2 m4 m5 m8 m10 m100 m Fig. 3.15: Evolution of the moisture released into the air for various water depths. Simulations were performed for the summer months with sea grass bottom. 3.12 Conclusions This chapter emphasizes the errors that can be expected when running a General Ocean Model without inclusion of proper bottom absorption and reflection of on short wave radiation. The sea surface temperature in shallow areas can be severely underestimated if the bottom is ignored and is overestimated if it is assumed to be black. There is a significant fraction of the light energy reaching the bottom in these shallow waters. This fraction can decrease to some extent in case of waters with very high turbidity or high chlorophyll content. The current model takes into consideration the effect of variable chlorophyll conditions while the original POM and GOTM model do not. A fraction of the light hitting the bottom is diffusely reflected back 65

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depending on the bottom albedo (high for coral sand and low for sea grass and algal mats). The rest of the light gets absorbed by the bottom and is reemitted as heat convectively heating up the water column from below. Light reflected through air-sea interface is considered and does not heat the water column. It can be safely concluded that the surface temperature in the shallow areas is wrongly predicted if the bottom effects are neglected or inaccurately represented for waters shallower than 20 m. In any simulations over a period of a couple of days, the errors can be expected to be appreciable if the bottom absorption and radiation are not property quantified and accounted for. This, in turn, will have effects on the salinity by evaporation and hence density variations of the water column, thus changing the hydrodynamics as well. The generation of hyper-saline plumes that slowly advect along the bottom into the deeper seas is shown in the next chapter. These hyper-saline plumes can be seen to percolate down to depths of 45 m to 50 m in summer (Hickey et al. 2000, Otis et al., 2004). Thus, it can be said with certainty that shallow-water effects are important when dealing with the heat budget of shallow estuaries and lagoons like the Tampa Bay where the depths average less than 10 m. These heating effects and the corresponding salinity increase are expected to have strong implications to the existence of the biological ecosystems at that location. It is known, that these salinity excursions can cause damage to the coral reefs at that depth (Lang et. al. 1988). The damage to coral reefs is not an isolated phenomenon, for the entire bio-diversity in such locations is affected. It was also seen that these variations of the evaporative flux affect the relative humidity over these shallow areas and adjacent land areas due to differential evaporation. These effects of water vapor on the cloud processes and hence local weather effects are expected to be seriously compromised if the effects of bottom were neglected in weather and local climate models. Fig 3.15 showed the development of the moisture and subsequent formation of clouds for the summer months. 66

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The effect of bottom heating in the presence of a salinity gradient becomes much more complicated due to the process of laminar double diffusion. This topic has been extensively studied by Turner (Turner et. al 1964) and could be included in the calculations in future studies. 67

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Chapter 4 3-D modeling of thermohaline plumes near the Bahamas 4.1 Introduction In the previous chapter the effects of bottom reflection and absorption on the heat budget of the water column off the coast of Andros Island were studied using a 1D numerical model (GOTM). In this chapter the study explores the hydrodynamics and water flow associated with such shallow-water heating. The time frame for the study in this chapter is again the springtime, when the atmosphere is dry and the solar radiation increases. The optically driven heat-budget model of Chapter 3 is used here with the POM. A 3D numerical ocean model (the Princeton Ocean Model or POM) is used to simulate the baroclinic circulations associated with this springtime heating. As seen in the last chapter, hyper-saline plumes are generated on shallow platforms with long residence times. It will be demonstrated using a 3D numerical ocean model that these hypersaline waters cascade down into the deeper waters and spread out significant distances from land. There are also observations of this phenomena such as Figure 4.1 after Otis et al. (2004). The 26 May panel with the arrow in the image shows how the Gelbstoff from the shallow margins or continental shelves flows off into the deeper waters of Exuma Sound, due both to thermohaline circulation and wind effects. Note that Gelbsotff is a proxy for salinity since there is a one-to-one relation between them for this region (Otis et al., 2004). Also, Figure 4.2 (Otis et al., 2004) shows salinity maxima penetrating to depths of 50 m in the Exuma Sound. This depth of 50 m is important as it can be used as a direct validation for our model results. 68

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Fig. 4.1: CDOM values near Andros Island for various months. 69

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Fig. 4.2: Figure from Otis et al. (2004), to show the depth of salinity and Gelbstoff intrusions. 70

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Thermohaline flows refer to flows in the ocean that are modulated and driven by differences in density resulting in a baroclinic circulation. Changes in density for surface waters are produced by either thermal differences or salinity differences or both. Observations indicate that the oceanic salinity distribution may change significantly from a few months to decades, thereby changing thermohaline circulation. Gordon (1991) describes two stable modes of ocean stratification and a feature referred to as the Stommel transition. These results have been verified by several numerical ocean models (summarized by Marotzke, 1994 and Whitehead, 1995). Physically, however, only a few measurements from laboratory experiments (Whitehead, 1996, 1998) support the existence of Stommel transitions. In this chapter, the occurrence of Stommel transitions in a shallow estuary is demonstrated using a numerical model, confirming the laboratory measurements. As mentioned in the previous chapter, the shallow areas of the banks west of Andros Island have been known to produce hyper-saline waters. This is due to water in such shallow regions being evaporated by intense spring and summer heating. The presence of such features has been observed by Cloud et al. (1962; Fig 3.2). Runoff of hyper-saline waters extend down to depths of 45 m in the summer (Fig. 4.2) and more than 75 m in the winter in Exuma Sound (Hickey et al. 2000). In addition to their observations, Hickey et al. (2000) have used a simple 1D hydrological model to show that such plumes are transported to these depths. In this chapter, plumes are simulated for the shallow basin region drained by Adderly Cut found just north of Lee Stocking Island (LSI) (Fig 4.3). This narrow channel then opens out into the deeper regions of Exuma Sound. Figure 4.4 shows bathymetry representative of such a region. Shallow regions 2 m in water depth are located behind LSI, which are connected by a channel 4 m deep, to the deeper offshore regions. This narrow channel widens out toward deeper waters (the white section of the figure indicates land). Since the shallow regions behind LSI are only about 2 m deep, the type of bottom (coral sand or sea grass) should have significance on the heat budget and the corresponding circulation. 71

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Fig. 4.3: Map of the Bahamas showing Adderly Cut. 72

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4.2 Description of the model There have been numerous recent simulation studies using the Princeton Ocean Model (Li et al. 1999a, 1999b, Weisberg et al. 2001, He et al. 2002) for coastal waters. These simulations have been performed without including the effects of bottom (e.g. using a transparent bottom) or have assumed a white, reflecting bottom. 02345671050100150200 ENWS Fig. 4.4. Bathymetry of model simulation. Since these simulations were intended for waters deeper than 20 m, the errors for such waters incurred were small. In this chapter we emphasize the significance of bottom heating on the generation of hyper-saline waters that results in thermohaline flow from shallow waters down to depths offshore. 73

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Details of the Princeton Ocean Model (POM) are described by Blumberg and Mellor (1987). The model has several important features. First, it has an embedded turbulence closure sub-model (Mellor and Yamada 1974, 1982, Galperin et al., 1988 and Kantha and Clayson 1994) for parameterizing vertical eddy-diffusion coefficients (viscosity and eddy diffusivity). Secondly, it employs a sigma coordinate in the vertical, which, with the turbulence closure sub-model, is well suited to study nonlinear dynamics over a shallow continental shelf. It produces realistic bottom boundary layers, which are important in coastal waters (Oey et al., 1985a,b). The sigma coordinate system is probably a necessary attribute in dealing with significant topographic variability such as that encountered in estuaries or over continental shelf breaks and slopes. The main advantages of sigma model for a shallow shelf are the following: 1) They provide a smooth representation of the solid earth boundary, and so provide for a natural representation of bottom boundary layer physics and bottom intensified currents and 2) thermodynamic effects associated with the equation of state are well represented. The main problem using a sigma co-ordinate model is that, in the presence of arbitrary topography, the PBL (Planetary Boundary Layer) cannot be as well represented using sigma as with the z-coordinate. The reason is that the vertical distance between grid points generally increases as one moves away from the continental shelf regions, hence leaving the PBL with potentially coarse vertical resolution in the middle of an ocean basin. The horizontal grid uses curvilinear orthogonal coordinates and an Arakawa C grid-differencing scheme and is based on a fourth order version of the scheme of Arakawa and Lamb (1981) that conserves the potential enstrophy and energy when applied to the shallow water equations (Takano and Wurtele 1982). The differencing of the thermodynamic energy and water vapor advection equations is also based on a fourth-order scheme.. The horizontal time differencing is explicit whereas the vertical differencing is implicit (e.g. semi-implicit). The latter eliminates time constraints for the vertical coordinates and permits the use of vertical resolution in the surface and bottom boundary layers. The model also has a split time step. The external mode 74

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portion of the model is two-dimensional and uses a short time step based on the CFL (Courant-Fredrick-Levy) scheme. The CFL computational stability condition on the vertically integrated, external mode, transport equations limits the time step according to 2/122111yxCttE (4.1) where C t = 2(gH) 1/2 + U max ; U max is the expected maximum velocity (for a list of symbols, see Table 4.1). There are other restrictions but in practice the CFL limit is the most stringent. x and y are the grid spacings. The external mode calculation results in updates for surface elevation, and the vertically averaged velocities. The internal mode calculation results in updates for u,v,t,s and the turbulence quantities. There are numerous successful applications of the POM to studies of estuarine and continental shelf circulation, (e.g. Blumberg and Mellor 1985, Ezer and Mellor, 1994 and Miller and Lee 1995a, b, Weisberg et al., 1996, 2001). 4.2.1 Basic equations The basic equations have been cast in a bottom-following, sigma coordinate system. x* = x, y* = y, = Hz t* = t (4.2a,b,c,d) where x, y, z are the conventional Cartesian coordinates; D=H+ where H(x, y) is the bottom topography and (x, y) is the surface elevation. Thus ranges from =0 at 75

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z= to =-1 at z=-H. After conversion to sigma coordinates and deletion of the asterisks, the basic equations may be written as, )3.4(0tyDVxDU )4.4('''''0022xMFUDKdxDDxgDxgDfVDUyUVDxDUtUD )5.4('''''0022yMFVDKdyDDygDygDfUDVyDVxUVDtVD 6.4RFTDKTyTVDxTUDtTDTH 7.4sHFSDKSySVDxSUDtSD is defined as the velocity component normal to sigma surfaces. By transformation to the Cartesian vertical velocity the equations become )8.4(ttDyyDVxxDUW 76

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where f=2sin is the Coriolis parameter, =7.29*10 -5 s -1 is the angular velocity of the earth, is the latitude; g is the acceleration due to gravity; T is temperature, S is salinity; and 0 (=1023.8 kgm -3 ) is the mean density; = (T,S) as given by Mellor (1991). R is the term describing the penetration of solar radiation into the water interior and will be discussed with the surface boundary conditions and K M and K H are the vertical eddy coefficients for the mixing of momentum, and temperature and salinity, respectively (Table 4.1). The horizontal viscosity and the diffusion terms are defined according to: )()(xyxxxHyHxF (4.9) )()(yyxyyHyHxF (4.10) where xx = 2A M xU xy = yx =A M ,xVyU yy = 2A M yV (4.11a,b,c) Also, )()(yxHqyHqxF (4.12) where xAqHx yAqHy (4.13) where represents T,S, q 2 or q 2 l. It should be noted that these horizontal diffusion terms are not what one would obtain by transforming the conventional forms to the sigma coordinate system. 4.2.2 Boundary conditions The vertical boundary conditions for Eq. 4.3 are (0) = (-1) = 0 (4.14a,b) 77

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The boundary conditions for 4.4 and 4.5 are ),15.4(0),)0(,)0((,bawvwuVUDKM where the right hand side of (4.15a,b) is the input value of the surface turbulent momentum flux (the stress components are opposite in sign), and ),16.4(1),(][,2/122baVUVUCVUDKzM ),17.4(0,01baSDKCQTDKMpM where )18.4(0025.0,}]/)1[ln{(2012zHkMaxCkbZ Also, k=0.4 is the von Karman constant, z 0 is the roughness parameter, and kb-1 is the position of the grid point next to the bottom. The bottom drag coefficient (Eq. 4.18), along with the bottom boundary conditions (Eq. 4.16a,b) and the turbulence closure scheme, are expected to conform to a numerical solution fitting the logarithmic law of the wall (Mellor, 1996; Weatherly and Martin, 1978) in the bottom boundary layer if enough resolution is provided. For example, in the shallow regions inshore of the 200 m isobaths, kb-1 is usually within the bottom boundary layer since there are adequate sigma levels (to fully resolve the velocities in the bottom Ekman layer) within the bottom boundary 78

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layer. Thus the calculated bottom stress from Eq. 4.16a,b may represent the actual boundary condition. However, for deeper regions, kb-1 may not be necessarily within the bottom logarithmic layer. Thus Eq. 4.18 may underestimate the bottom drag coefficient, so a somewhat larger empirical value of 0.0025 must be specified in such a case. The actual algorithm is to set the drag coefficient to the larger of the two values. The parameter z 0 is the bottom roughness constant, which depends on the local bottom roughness of the continental shelf. The study of the oceanic bottom boundary layer on the West Florida continental shelf, conducted by Weatherly and Martin (1978) using the Mellor-Yamada level 2 turbulence closure scheme, found that the modeled boundary layer characteristics were not sensitive to z 0 A similar conclusion was also drawn by Dickey and Van Leer (1984) who, by using the Mellor-Yamada level 2.5 turbulence closure scheme that is also included in the POM as a critical element, studied the bottom boundary layer on the Peruvian shelf. In equation 4.17a, Q 1 is the net heat flux at the surface. The surface boundary conditions for the temperature are related to the surface heat flux. The solar short-wave irradiance at the surface is Q s thus Q 1 =(1-T r ) Q s +Q l The details of the short-wave radiation penetration used in POM were already mentioned in Chapter 2 (Table 2.1). No-slip and no-normal flow conditions are employed along the coastal boundaries. At the open boundaries the Orlanski (1976) radiation condition is adopted for all the dynamic variables, where the radiation speed is calculated from the corresponding interior field. This treatment of the open boundaries is sufficient to maintain mass conservation over the model domain. In the following simulation, the northeastern boundary (lower edge of Fig. 4.4) is kept open and the other three boundaries are closed. The POM model was run for the bathymetry shown in Fig. 4.4 with 60 grid points in the x-direction and 50 grid points in the y direction with each grid spacing equal to 600 m. There are 21 sigma levels in the vertical with the origin at the free surface. 79

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Table 4.1: List of the symbols used in this chapter. Symbol U max C t C p D U,V, f K M K H F x, F y F A M A H xx yy T S q 2 l C z k z 0 Q 1 Q s Explanation Expected max. velocity External wave velocity Latitude Specific heat Sigma coordinate Elevation H+ Velocities in x,y, coordinates Coriolis parameter Vertical kinematic viscosity Vertical diffusivity Horizontal viscosity term Eq. 4.9, 4.10 Horizontal diffusion term Eq.4.12 Horizontal kinematic viscosity Horizontal heat diffusivity Shear stress in x, y dir. Temperature Salinity Turbulence kinetic energy doubled Turbulence length scale Bottom drag coefficient Von karman constant Bottom roughness length Net heat flux at surface Short-wave radiation units ms -1 ms -1 Jkg -1 K -1 m m m/s s -1 m 2 s -1 m 2 s -1 m 2 s -2 m2s-2 m 2 s -1 m 2 s -1 m 2 s -2 K psu m 2 s -2 m m Wm -2 Wm-2 80

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4.3 Results and discussion 4.3.1 Test for bathymetry-slope error Before making actual runs with the 3D model, the model was initiated to make certain that the features simulated are real and not an artifact of the step-wise geometry of the model domain. It is not desirable that the steep slopes (a function in the model called slpmin imposes a minimum slope for the simulation) present in the bathymetry trigger artificial flows. The model was run first for 30 days with no forcing (no heat flux and no wind stress). There was no flow generated, which demonstrated that the simulations were free of error due to the slope values. 4.3.2 Tides Tides are incorporated into the model using a specified sinusoidal elevation at the open boundary. In this model simulation, tidal constituents were specified based on actual measured values. From the measured observations for the Bahamas, the main tidal constituent is found to be the M 2 tide, with amplitude of 0.405 m. This low value of the tidal amplitude indicates that the tidal effects on these shallow waters off LSI would be relatively small except in the passes. Though not shown here, tides tend to act as a disturbance to the total flow. Since we are more interested in the thermohaline flow, the simulations performed below have been done first without the effects of tides. Finally at the end of the chapter, the effects of tides and winds are incorporated as a sensitivity experiment. 4.3.3 Winds Actual meteorological data were available for the time of study. The main purpose of this study was to simulate the thermohaline plumes caused due to differential heating of the waters. It was found that in such shallow waters, if the 81

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winds were set to their actual values, the surface-flow was dominated by wind. The following hydrodynamic simulations were done with low wind speed (1 ms -1 ), the direction of which oscillates at every time-step. This is to remove net effects of wind flow on the hydrodynamics of these studies. But it needs to be clarified here that actual winds were used in the heat-flux calculations. 4.3.4 Effect of bottom albedo In the last chapter, the effects of shallow-water heating and bottom albedo on the temperature development of the water column were pointed out. Those studies were performed using a 1D model, and ignored the hydrodynamics associated with the process. In this section, we do similar simulations using a 3D numerical model, which incorporates the hydrodynamics related to this heating. Initial simulations were performed for 15 days using bathymetry of Figure 4.4. The right side of the shallow region was uniformly covered using sea grass, and the left side as coral sand (Fig. 4.5). The spectral albedo curves for sea grass and coral sand are provided by Figure 3.7. The simulation output was for February 15 th 2000 (starting from February 1 st and extending to February 15 th ) for which we have the meteorological input data. These simulations employed the same meteorological data set that was used in the previous chapter. The fluxes of momentum and heat (sensible and latent heat) were calculated every 10 minutes from the meteorological data after a 15-day initialization run. Results from the POM simulation had the temperature distribution of Figure 4.5a. The subsequent temperature development was calculated every external time step for the entire domain for each water depth. The contribution of the bottom type to the heat budget of these shallow waters is determined using the same approach as in the previous chapter (Eqs. 3.10 .15). The right or grassy side of the domain (Fig. 4.5b) in the shallow region is observed to be warmer than the left side by almost 0.4C at the end of a heating cycle. This is consistent with the finding in Chapter 2 that sea grass produces warmer waters than coral-sand bottom. The deeper middle part of the domain, which is the channel, is 82

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found to be cooler than the shallower sides. This, in turn is consistent with the previous findings of the effect of depth on the temperature evolution of the water column. The deeper the water column, the more mass over which scalar heating is to be distributed and hence, the less the temperature rises (Fig. 3.12 a-f). 4.3.5 Heat budget Since there are no wind and tidal effects in the current scenario, there are no strong undulations of the thermocline in the lateral and vertical directions in the open part of the ocean. The heat transfer experiment to be described below can be approximately described by the equation which captures its essence (He et al. 2002), netapQThvtThC. (4.19) where is the mean density of sea water, C p is the specific heat of sea water, h is the depth of a chosen isotherm across which there is minimal heat transfer rate and from which the depth-averaged temperature T and depth-averaged horizontal velocity v a are calculated. An order of estimate of velocity can be computed in the above transport equation. Using the above approximate equation, assuming a 1 C difference at the mouth of the estuary and remembering the pixel size to be 600 m, the average velocity v a is roughly of order 10 -3 m/s which is what is observed in the calculations. Expanding Eq. 4.19 to a simpler variant (He et al. 2002), )20.4(HCQyTAyxTAxzTKzzTwyTvxTutTpnetHHH 83

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which matches the local rate of change of temperature to a combination of the flow field advective rate of change, the rates of change by vertical diffusion and horizontal diffusion and the net heat input. In this section, heat budget calculations are performed similar to those in the previous chapter (Tables 3.4 and 3.5). There are three principal heat-budget terms to focus on: the net heat increase of the estuary, the air-sea flux across the water-air interface; and the heat transfer due to advection and diffusion between the estuary and deep ocean. The values of heat accumulated in the estuary and the open ocean during 15, 15.5 and 16 days of simulation are found in Table 4.2. There is more diurnal heat fluctuation (of the heat content) per unit area in the open ocean than in the estuary, though there is more diurnal fluctuation for the temperature in the estuary (due to the shallow nature of the estuary) than in the deep ocean. This high diurnal heat change in the open ocean is due to the significant advection of heat from the estuary. Flows in both the upper and lower vertical structure of the channel (colder fresher water flowing in at the surface and warmer saline waters flowing out at the bottom, after 30 days) promote heat transfer from the shallow estuary to the deeper ocean during daytime. Also the heat change is concentrated in the upper regions of the water column since these are the regions of heat input (mainly the solar radiation and the heat transferred from estuary rarely diffuses below about 8 m in the deep ocean in the early stages of the study). A time series of heat budget and flux terms of the estuary and deeper ocean is presented in Figure 4.6a and 4.6b. Figure 4.6a shows the fluxes (sum of the short-wave and long-wave radiation, sensible and latent heat fluxes) and the change in heat content of the estuary. The slow increase in the first couple of days indicates the time required for temperature differences to be generated between the shallow and deep 84

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0172022242526 (a) 0202224262727.4 (b) Fig. 4.5a,b: Temperatures after 15 days a) 6 am b) 6 pm. 85

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Table 4.2: Vertically integrated heat accumulated (per unit area) in the water column during 15 days of simulation. 15 days Heat Content (6 am) Jm -2 (*10 6 ) 15.5 days Heat Content (6 pm) Jm -2 (*10 6 ) 16 days Heat Content (6 am) Jm -2 (*10 6 ) Estuary 4.04 5.68 4.5 Open Ocean 1.84 18.7 5.53 86

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waters from a state of rest. As can be seen, only a small fraction (about 20%) of the flux is converted into temperature increase for the estuary. The rest is lost by reflection to the atmosphere and advected into the deeper ocean and replaced by cooler waters. Figure 4.6b shows the heat balance for the deeper ocean. As noted from the figure, a comparison between the total heat input into the open ocean (sum of the net air-sea heat flux and the heat advected from the shallow estuary) is close to the heat content increase there. Note that little energy is lost by reflection to the atmosphere for this deep region. This close match is a confirmation of the validity of our heat flux calculations and the first law of thermodynamics (that the total energy of a system is constant). An interesting point to note is that the heat input to the deeper ocean by advection during day is mostly lost from the deeper seas during nighttime. This is due to a combination of heat transfer back to the estuary and radiative air-sea fluxes. Fig. 4.6b clearly illustrates this feature. As a result, a large quantity of heat (about 2*10 6 Jm -2 for 12 hours) oscillates back and forth between the deeper ocean and the estuary in a diurnal cycle simply due to thermohaline effects. The net radiative and evaporative loss at night from the estuary is greater due to higher mixed-layer temperatures and convective overturn than in the deep seas (not shown here). The combination of these two factors indicates increased cooling of surface temperatures at night in the estuary compared with the deep ocean as suggested from Fig. 4.5. The temperature of the estuary fluctuates to a large extent (even though the heat content there does not) with the temperatures running below that of the deeper region at night and extending above the deeper region during daytime. It is this fluctuation in temperature that promotes the heat-flux transfer between the estuary and deep ocean. 87

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Estuary -1.50E+07-1.00E+07-5.00E+060.00E+005.00E+061.00E+071.50E+072.00E+072.50E+073.00E+070246810121416 Qnet heat increase (a) Deep Ocean -3.00E+07-2.00E+07-1.00E+070.00E+001.00E+072.00E+073.00E+0705101520 heat increase Qnet (b) Fig. 4.6a, b: The heat fluxes (air-sea flux) and heat content change in the a) estuary b) deep ocean. The heat content change of the deep ocean equals the sum of advection and heat flux. 88

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4.3.6 Water budget It is important that the above calculations conserve the quantity of water being transferred among the atmosphere, the estuary and the open ocean. So a water budget analysis is conducted to verify the results. There are three important measurements of the transport processes of water occurring in the system: 1) Heat is transferred between the estuary and open-ocean through advection and diffusion (Eq. 4.20). 2) The actual velocity calculated by the POM model through the mouth of the estuary. This is an average for the pixels across the channel mouth. 3) The evaporation occurring across the air-sea interface in the estuary. Note that the evaporation plotted is the area-normalized (evaporation multiplied by the total surface area of the estuary divided by the cross-section of the channel). If the total water mass in the estuary is to be a constant, as it should be, the net normalized evaporation in the estuary should equal the net water transport through the cross-section averaged over a day. The above three processes are compared in Figure 4.7. As can be observed, there is a fairly good match among the three curves. The difference between the advection process and the actual velocity measured by the model can be attributed to diffusion, which is found to be an order of magnitude smaller than advection. As can be noted from the graph (Fig 4.7) the net velocity (average over the channel cross-section, over one day) is into the estuary at all times. This is understandable and expected since the water lost as evaporation for the hotter estuarine water is being replenished by the transport process in order to maintain the water mass-balance. It should be noted however, that the heat advection through the channel cross-section changes direction at day and night times due to a fluctuation in the sign of temperature gradient across the channel (dT/dy in Eq. 4.20). The effects of long-term temperature and salinity are studied in the next section, where 60-day and 75-day scenarios are simulated. 89

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4.3.7 Long-term simulation For this long-term simulation, the same meteorological data were used as in the previous chapter, from the AUTEC weather site run by the US Navy. The data are acquired every 10 minutes and include date, time, atmospheric pressure, air temperature, relative humidity and wind direction and speed. In the following simulations, the winds were set to the low value (1 m/s) mentioned before. Using this, Eqs. 3.17 .21 were used to calculate the various flux terms, including the long-wave radiation, sensible and latent heat fluxes, and short-wave radiation. These simulations were run for February-May 2000. time (days) 0246810121416 velocity (m/s) -0.0020.0000.0020.0040.0060.0080.0100.0120.0140.016 advection+diffusion model Area normalised evaporation Fig. 4.7: Water budget analysis showing the various transport processes illustrating the conservation of water mass. 90

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The primary objective was to simulate the thermohaline effects, which have been observed by Hickey et al. (2000) and Smith et al. (1995). The domain is the same as described before (Fig. 4.3), with the channel connecting the shallow and deeper regions. The simulation started at a uniform 36.6 ppt salinity and 20.5 C for the surface layer, with a thermocline at 45 m where the temperature decreases to 16.5C By 60 m. The circulation initially was thermally dominated for the first 2 months (the so-called T mode of Stommel, 1961). Figure 4.8 shows the temperature distribution around the channel after 30 days of simulation. The bottom albedo signature is evident in these figures with the grass bottoms warmer than the sand bottoms. The surface velocity vectors flow out the channel into the deeper regions while the bottom flow vectors flow into the channel. This can be explained on the basis of thermally driven buoyancy. The waters over the shallow banks are heated more than offshore due to the bottom effect on short-wave radiation (see Chapter 2 for details) and expand. Thus, the sea surface height is higher at the shallow end of the channel driving the surface waters outside in a baroclinic flow. This outward mass transport is balanced by near-bottom inflow of cooler waters from the offshore region (Fig. 4.9a). The arrows indicate the direction of flow. The colder deeper waters are upwelled and advected along the bottom into the shallow regions. Also there is a convergence zone at the channel mouth where the flow from the north and south converge and upwell into the channel. After 60 days of simulation, the flow became salinity-dominated (the so-called S mode of Stommel, 1961). The waters over the shallow banks became hyper-saline with salinities reaching 40 ppt. The flow along the channel reversed direction, with the deeper hyper-saline waters flowing out along the bottom of the channel and the less saline surface waters flowing in at the surface (Figure 4.9b). This is similar to the scenario found in various hyper-saline basins. For example, such flows have been found in the Mediterranean Sea with dense hyper-saline waters flowing out at the bottom through the Strait of Gibraltar into the Atlantic Ocean with less saline Atlantic waters flowing in at the surface (e.g. Pickard and Emery, 1982). 91

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01618202224252627 (a) 016182022242627 (b) Fig. 4.8a,b: Temperature distribution (C) after 30 days of simulation, at a) surface and b) bottom at 6 AM. 92

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020406080100120140160180200 Land (a) (b) Fig. 4.9a,b: Flow vectors around the channel. a) yz cross-section at the middle of the channel after 30 days b) same section after 60 days. 93

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This is quite similar to the situation the following study simulated near these shallow regions. Figure 4.10 shows the temperatures at the surface and bottom after 60 days of simulation. As is evident from Figure 4.10a, there is almost a 1.5C difference between surface waters over the coral sand versus sea-grass bottoms (as shown by the left and right sides of the shallow areas). The shallow regions are completely well mixed while the deeper regions show the imposed thermal difference between the surface and bottom waters. A section along the channel at the middle (a yz section with constant x=30), shows temperature (Fig.4.11a) and salinity (Fig.4.11b). Since one motivation of this research was to observe thermohaline flow, the salinity distribution provides a measure of estuarine waters that flow to depths offshore. The saline waters from the shallow banks flow along the bottom through the channel and sink to about the 50 m isobath. This trend has been observed in field data by Hickey et al. (2000) and Otis et al. (2004). The advection and diffusion were limited to this depth by the thermal gradient found at about 50 m in both field data and the model, which acts as a barrier to further downward advection of the saline plume. Figure 4.12 shows the salinity cross-section after 75 days. The saline plume has enlarged and spread laterally, again limited by the 50 m thermocline. Sections of salinity across the channel mouth are shown in Figure 4.13a-d. The slopes of isohalines due to the Coriolis effect are observed. It tends to deflect the water to the right of the flow direction in the northern hemisphere. Thus water concentrates as shown on the right side of the flow, and manifests itself at the bottom of the channel whether it is flowing in (as is the case after 30 days) or out (after 60 days). 94

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016182022242627.5 (a) 016182022242627.5 (b) Fig. 4.10a,b: The temperature distribution after 60 days of the a) surface b) bottom waters at 6 AM. 95

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020406080100120140160180200 0161820222426Land (a) 020406080100120140160180200 03636.737383940Land (b) Fig. 4.11a, b: yz cross-section along the middle of the channel a) temperature b) salinity after 60 days. 96

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020406080100120140160180200 03636.737383940Land Fig. 4.12: Salinity cross-section after 75 days of simulation. The lateral spreading of the hyper-saline plume can be observed. 97

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Fig. 4.13a-d: Cross-sections of the channel at various times. 98

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After the intense evaporation of spring, the Bermuda high pressure system sets up SE winds with more humidity and precipitation.. As precipitation continues through May and June, E-P (evaporation-precipitation) decreases. This decrease reduces the intensity of saline plumes and hence the thermohaline circulation (e.g. see Hickey et al. 2000). 4.4 Inclusion of wind and tides The previous simulations were performed with a low oscillating wind and no tides to insure some turbulent mixing but no wind driven advection. Now to comprehend a more realistic situation, we need to include the effect of wind and tides. It can be observed intuitively that the wind effect now can dominate the horizontal flow pattern (e.g. see Otis et al 2004). Vertically however, it was observed in our simulations that the classic two-layer pattern still existed. The stommel transition (as explained in section 4.1) still took place during the same time period (after about 45 days) of simulation. It was also noticed that the depths of saline extrusions from the estuary now spread over a larger horizontal distance due to the influence of wind but only penetrated to about 40-45 m. The tides imposed at the open boundary were of the M 2 semidiurnal kind. Tides affect the oscillatory transfer of water across the channel and the turbulent mixing. Figure 4.14 demonstrates the salinity cascades to depth in the open ocean after 60 and 75 days but its larger extent and shallower penetration are likely due to greater mixing near the channel mouth. The extremes of salinity generated in the non-tidal model do not seem to survive advection and mixing out the channel. Since meteorological data were available, the model was run for a year with actual winds and tides. The simulation progressed through to winter, the thermohaline plumes cascaded down to depths of 75 m (Fig. 4.15) by December. This resulted from cooling and evaporation of the surface waters due to reduced solar fluxes and cold dry winds from N. American land masses. After a depth of about 75 m, the flow advected 99

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laterally offshore. These results are consistent with the observational results of Hickey et al. (2000). 4.5 Conclusions In this chapter, a 3-dimensional general circulation model (POM) of the thermohaline advection and diffusion of a shallow Bahamian estuary was run with and without tides. A springtime scenario was simulated, with realistic optical properties used in the heat-budget model to calculate the heat fluxes that forced the model. The thermohaline flow structure was consistent with the Stommel transition observed in laboratory flows. Initially the flow was thermally controlled with a flow of hotter water out at the surface of the channel and a flow of cooler water in at the bottom in accordance with geostrophy. After about 45 days, a transition occurred followed by the flow becoming dominated by salinity effects at this time the high salinity water inside the estuary flowed out at the bottom of the channel with cooler return flow at the surface. This is a classic two-layer pattern observed in many hyper-saline basins (the Mediterranean for example). The high salinity was predominantly formed in the shallow 2 m-deep waters and flowed into the channel and then out into the deep seas. This flow pattern of the saline waters was found to be bottom hugging. Simultaneously, less saline waters from the ocean side flowed into the estuary at the surface. The saline waters cascaded down to depths of 45-50 m within 60 days, and then spread laterally. These saline intrusions are in agreement with observations of Hickey et al. (2000) and Otis et al. (2004). The deflection of the flowing waters due to the Coriolis effect was also observed resulting in a salinity wedge along the bottom. Calculations have been made of the heat, salt and water budgets. The water flowing into the estuary replenishes the water lost there as evaporation (water being lost by evaporation is calculated and forced by the model). The same is true in the open ocean too, where water advects from the open boundary into the deep ocean. 100

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The the amount is much less, but it carries a heavier load of salt. This process increases the salinity of the waters in the estuary and creates a hyper-saline basin by the end of spring. The increase in salinity to about 40 ppt by the end of spring for a 2 m-deep water column was discussed in this and the previous chapter. There is a continuous transfer of heat between the two basins. A fairly large amount of heat oscillates back and forth between the estuary and the deep sea in a diurnal cycle driven by differential heating and cooling. The difference between the total air-sea heat flux of the estuary and the local rate of heat change is attributed to advection to the open ocean through the channel and has been calculated as such. This heat transfer occurs through the channel at its narrow cross-section. The advective velocity derived from this heat transfer was compared to the actual model velocities in the channel. The difference was found to be minor (~10%) and was attributed to diffusion. A next step in the research would be to study the moisture dynamics associated with this shallow heating. A preliminary study of the moisture released due to shallow-water heating is shown in the next chapter. This should be followed up by coupling the ocean model with a three dimensional hydrostatic atmospheric model. Such a coupled model would facilitate the study of both coastal oceanographic and meteorological phenomenon such as the development of cumulonimbus clouds for precipitation and modifications to sea breeze intensity. 101

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2040 020406080100120140160180200 03636.73740 (a) 2040 020406080100120140160180200 03636.73740 (b) Fig. 4.14a,b: Salinity contours including wind and tides after a) 60 days b) 75 days. 102

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020406080100120140160180200 036.536.75373839 Fig. 4.15: Salinity profile after 330 days. Note that the 36.75 psu salinity contour cascades down to about 75 m. 103

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Chapter 5 Conclusions The inadequacies of light models used in various general ocean circulation models, like the Princeton Ocean Model (POM) and the General Ocean Turbulence Model (GOTM) have been demonstrated in the previous chapters. These include discussions by several authors regarding inadequacies of the single-attenuation coefficient method. The need for higher spectral resolution and a good average cosine model were also discussed in the literature. Various parameterizations have been proposed to improve the downwelling light field (see Chapter 2). The particular advantage of each parameterization depends on the in-situ conditions in the ocean and atmosphere and has to be incorporated accordingly into general ocean models. Cloud cover is another issue that has been dealt with recently. Clouds affect the incoming radiation by varying the ratio of direct to diffuse radiation. Inclusion of this parameterization has been vital demonstrating that in-water solar fluxes can vary by 40 Wm -2 in the upper few meters of the ocean. Most of this variability can be accounted for by chlorophyll, solar zenith angle and cloud fraction, factors addressable with satellite data. In the current thesis, a fully spectral light model was found to be most accurate and has been added to the GOTM and POM models to correctly simulate the temporal temperature and salinity evolution. It has been shown in Chapter 3 how a very important factor has been neglected in most heat-budget and circulation models of shallow seas. A bottom affects the light reaching it in two ways. A fraction of the light incident on the bottom is reflected based on the albedo of the bottom. The rest of the light is absorbed and then reemitted as heat from the bottom. Thus the bottom effect can seriously modify the temperature of the water column if the bottom is shallow and dark. 104

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There are various types of bottoms varying from coral sand (~50%) to sea grass (~5%). Algal mats are also common, having an albedo nearly as low as that of sea-grass. Most of the light hitting sea grass beds gets converted to heat, warming up the water column more than coral sand. It has been shown that various general circulation models can produce significant errors in predicting water temperature when the bottom effects on light are neglected. Ignoring the bottom is tantamount to having a transparent bottom losing all of the energy from the light that hits it. High heating rates of shallow water lead to a high rate of evaporation and to increased salinity. For waters 1 m deep salinity in the Bahamas can reach as high as 48 ppt by summer based on field measurements. The General Ocean Turbulence Model (GOTM) is a one-dimensional model (details given in Chapter 3) used to simulate the temperature and salinity of the Bahamas Banks near Andros Island for which meteorological data were available. A model run for a 1 m water column over coral sand developed salinities of almost 48 ppt after three months of spring simulations with GOTM where a grass bottom heat and salt increased even more rapidly than sand bottoms. In addition to the physical effects, the biological implications of such shallow water heating are varied. Various authors have noted the excessive bleaching of coral reefs due to enhanced salinity and heat content of summer waters. Deaths of various marine organisms due to these adverse environmental factors are also common. Adding to these biological effects, the actual thermal effects of shallow waters often have important consequences for chemical and biologic formations such as whitings, or aragonite precipitation. A feature that makes 1D simulations suitable for these regions is the fact that advection and mixing are low in the study region with the residence times of the waters as high as 300 days. The one-dimensional model simulation has been expanded to fully three-dimensional model simulations using the Princeton Ocean Model (POM). This was applied to the shallow banks near Adderly Key, which enclose a shallow basin about 2 m deep, with a narrow channel that opens into deeper seas. Simulations were made 105

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for a shallow estuary with average depth of 2 m) connected by a narrow channel 4 m deep to the open ocean. The hydrodynamics occurring on a diurnal and a seasonal scale in these waters were studied and a strong seasonal signal was apparent in the thermohaline flow. The model was run with a very low rapidly oscillating wind of 1 ms -1 to avoid wind dominance of the circulation, although actual meteorological conditions were applied to the heat flux terms. The seas were initially dominated by the temperature variation but after about 2 months, the flow became salinity dominated. This transition, observed in the laboratory is called Stommel transition (Stommel, 1961). After transition, there is an outflow pattern similar to the flow in the Mediterranean, with salty deep waters flowing out and less salty, fresher waters flowing in at the surface. This is in keeping with the variation of sea level. Various aspects of the flow were then noted such as Coriolis acceleration and deflection on the thermohaline flow. Finally the salty water was observed to flow out the mouth of the channel and advect and mix downwards to a depth of approximately 45 m in the spring. This pattern is consistent with the field observations. A study was also been carried out of the heat and water budgets in association with the thermohaline circulation. There was found to be a fairly large amount of heat transferred between the estuary and the deeper ocean due simply to thermal pumping. This transfer is on a diurnal basis and occurs as an advective transport. The difference between the flux and the heat content change in the estuary was consistent with the observed advection and the heat was eventually transferred to the ocean. This heat transfer to the deep ocean during the day reversed at night. The heat transferred to the shallow estuary at night is radiated out as outgoing radiative fluxes. This cycle repeats itself on a continuous basis over the course of the time the model was run. Different comparisons were made, which were used to validate the accuracy of our simulations. As far as the water budget of the estuary-ocean combination is concerned, there are three independent water transport calculations that should match. These are 1) the velocity measured from the advection of heat following equation 4.19. This velocity was found to be into the estuary at all times. The heat advection direction changes 106

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sign though due to the change in the sign of temperature gradient across the channel. 2) The actual velocity calculated by the POM model in the simulations. The difference of this from the advection is due to diffusion. 3) The normalized evaporation occurring across the air-water boundary in the estuary. Figure 4.7 showed the comparisons among the three processes, which were found to closely match. One of the serious limitations in the three dimensional model is that the scenario were simulated with winds set to a low value of 1ms -1 (except for calculating fluxes). This was done of course, so that the features associated with the Stommel transition can be displayed clearly in the simulations. Realistic winds and tides were included in the final set of simulations (Fig 4.16a, b and Fig 4.17) to study its sensitivity. Winds did not break up the Stommel transition, which still occurred, but the flow vectors of the circulation became wind dominated. Tides also tend to act as a perturbation to the net flow. In this doctoral dissertation the light absorption and scattering features associated with a shallow bottom have been newly introduced in the heat-budget calculations. This heat budget modification has a significant impact on the temperature and salinity evolution and the associated hydrodynamics. This development of the water temperature and salinity, along with the associated flow pattern using the modified heat budget is found to be comparable to field data and observations by previous researchers. Generation and development of thermohaline flows associated with this salinity increase were evaluated. Shallow heating along the coast has influences on the local circulation. It has been shown (Weisberg et al. 1996, 2001) how the generation of buoyancy (by heating and fresh-water input from the rivers) induces a baroclinic circulation that modifies the wind-driven circulation along the West Florida Shelf. This baroclinic circulation is in fact, responsible for the cold tongue found along the west Florida shelf in springtime. The model developed here will aid in coastal heating calculations through usage of more accurate expressions of light scattering and absorption by shoal-water environments. 107

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The next step in this research would be to couple the three-dimensional model to a three-dimensional atmospheric model to study both local weather and large-scale climate. This coupled model could then be utilized for studying the moisture feedbacks. In local effects, this study could show the occurrence of the cloud cover associated with this moisture rising up. Occurrence of precipitation fronts near the coasts especially where shallow waters exist could be explained by this model. The precipitation then has a negative feedback effect on the formation of salty waters near the coast. This dilution of the salty water formation could even arrest the thermohaline circulation. This will be followed by a transition to the T-mode of Stommel transition. 108

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Lang, J.C, R.I.Wicklund and R.F.Dill, Depth and habitat related bleaching of zooxanthallate reef organisms near Lee stocking island, Exuma Cays, Bahamas, Proc. of the 6 th international coral reef sym. Australia, vol 3, 1988. Large,W.G and S.Pond:Sensible and latent heat flux measurements over the ocean. J.Phys.Oceanogr.,12,464-482, 1982. Lee, Z.P, K. Carder, Curtis Mobley, Robert Steward and Jennifer Patch, Hyperspectral remote sensing for shallow waters;1 A semianalytical model, Applied Optics, 6329-6338, 1998. Lee, Z.P, K. Carder, Curtis Mobley, Robert Steward and Jennifer Patch, Hyperspectral remote sensing for shallow waters;2. Deriving bottom depths and water properties by optimization, 38, Applied Optics, 3831-3843, 1999. Lee, Z.P, K. Carder, R.Chen and T.Peacock, Properties of water column and bottom derived from Airborne Visible Infrared Imaging Spectrometer (AVIRIS) data, J.Geophys. Res., 106, 11639-11652, 2001. Lewis, M., M.Carr, G.Feldman, W.Essias, and C. McClain: Influence of penetrating solar radiation on the heat budget of the equatorial Pacific Ocean. Nature, 347, 543-545, 1990. Li,Z., Weisberg, R.H. West Florida continetal shelf response to upwelling favorable wind forcing, part I, kinematic description. J.Geophys. Res, 104, 13507-13527., 1999a. Li, Z, Weisberg R.H.. West Florida continental shelf response to upwelling favorable wind forcing, part II: dynamicsl analyses. J.Geophys. Res, 104, 23427-23442, 1999b. 114

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Nakamoto,S, S.Prasanna Kumar, J.Oberhuber, K. Muneyama and R.Froiun: Chlorophyll modulation of sea surface temperatures in the Arabian Sea in a mixed isopycnal general circulation model., Geophys.Res.Lett., 27, 747-750, 2000. Oey, L.-Y., G. L. Mellor and R. I. Hires, A three-dimensional simulation of the Hudson-Raritan estuary. Part I: Description of the model and model simulations. J. Phys.Oceanogr., 15, 1676-1692, 1985a. Oey, L.-Y., G. L. Mellor and R. I. Hires, A three-dimensional simulation of the Hudson-Raritan estuary. Part II: Comparison with observation. J. Phys. Oceanogr., 15, 1693-1709, 1985b. Ohlmann,J.C, D.Siegel and C.Gautier: Ocean Mixed Layer Radiant heating and solar penetration: A Global Analysis, Journal of Climate, 9, pp2265-2280, 1996. Ohlmann, J.C and D.Siegel: Ocean radiant heating. Part II: Parameterizing solar radiation transmission through the upper ocean, J. Phys.Ocanogr., 30, 1849-1865, 2000. OReilly,J., S.Maritorena, B.G.Mitchell, D.Siegel, K.L. Carder, S.Garver and C.McClain, Ocean color chlorophyll algorithms for Seawifs, J.Geophys. Res,, 103, 24937-24954, 1998. Orlanksi, I., A simple boundary condition for unbounded hyperbolic flows, J.Comp. Phys., 21, 251-269, 1976. Otis. D., Kendall L. Carder, David C. English, CDOM transport from the Bahamas Banks, Coral Reefs, 2004. 117

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Appendices 122

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Appendix A: Hydrolight The optical model used to calculate the underwater irradiance properties in this thesis is Hydrolight. Hydrolight 4.0 (and its modified version 4.1) is a radiative transfer model prepared by Mobley (1994) that computes the radiance distributions and the related apparent optical properties for natural water bodies. Briefly, Hydrolight solves the radiative transfer equation to compute the spectral radiance distribution as a function of depth, direction and wavelength within the water. Version 4.1 of Hydrolight allows a choice of phase functions. Input to the model consists of the absorption and scattering properties of the water body (either directly or derived as an output from various models), and to second order, on the nature of the wind-blown sea surface. Additional input parameters include bottom depth and type, and sky and sun radiance incident on the surface. Output files consist of the various inherent optical properties, the radiance and irradiance fields (both upwelling and downwelling light fields) with depth, and the reflectances (defined as the ratio of upwelling to downwelling irradiance), all as functions of wavelength. In these shallow-water runs, we ignore the inelastic scatter by chlorophyll fluorescence and by Raman scattering. Hydrolight is designed to solve a wide range of problems in optical oceanography and limnology. The various input properties of the water column can be specified as a function of depth and wavelength. In our present studies, though, we assume a vertically homogeneous water column. These properties can be either obtained from measurements (as in the case of ac 9 input data files) or can be the output from some other model, or specified to be a function of chlorophyll (as is the case here). In its most general mode, Hydrolight includes the effects of inelastic scatter by chlorophyll fluorescence, by colored dissolved organic matter (CDOM) and by Raman scattering by the water itself. The effect of CDOM can also specified to be a function of the chlorophyll as in Case 1 waters. 123

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Appendix A: (Continued) A complete description of Hydrolight is given in Mobley (1994). Only a brief outline of the basic equations is given here. The spectral radiance L(z,,, ), which provides a complete description of the in-water light field as a function of depth z, direction (,) and wavelength () can be used to calculate the net irradiance profiles, E n (z). Hydrolight computes spectral irradiance throughout a water body by solving the one-dimensional, source free radiative transfer equation '''sin),,',',(),',',(),,,(),(),,,(cos ddzzLzLzcdzzdL (A1) where c(z,) is the beam attenuation coefficient and ( ),,',', z is the volume scattering function, which describes scattering from direction , to direction ,. The radiative transfer equation calculates the variation with depth of the spectral radiance values, from the attenuation (absorption and scattering) of the radiance. Figure A1 shows diagrammatically the equation of radiative transfer showing the input and output terms to the radiance. To solve the radiative transfer equations, Hydrolight discretizes the set of all directions, into a finite set of quadrilateral regions or quads bounded by lines of constant and Figure A2 shows the quad partitioning of the earths atmosphere. By applying such a discretization, Hydrolight ends up calculating the radiance values averaged over a quad. Integrating over all directions in Eq.A1 gives the sum over all quads. There is a similar decomposition of the wavelength into finite wave bands. Invariant imbedding theory is used to reduce the set of radiance equations, which is quad and band averaged, to a set of Riccatti differential equations governing transmittance and reflectance functions. Solution of these differential equations gives the spectral radiance as a function of wavelength, depth and direction. The net 124

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Appendix A: (Continued) irradiance profile E n (z) defined as the difference between downwelling and upwelling irradiance is then computed from spectral radiance using E d (z)= dddzLsincos),,(2/020 (A2) Fig. A1: Diagram underlying the equation of transfer of radiance (taken from Kirk, 1994). 125

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Appendix A: (Continued) Fig. A2: Quad-partitioning in radiative transfer model (taken from Mobley, 1994). 126

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Appendix A: (Continued) and E u (z) which is defined to be the upwelling radiance (which is integrated over the entire wavelength range) E u (z)= dddzLsincos),,(2/20 (A3) Inputs to Hydrolight are the absorption and scattering properties of the water column, which determine c (z,) and ),,',',( z in Eq. A1. These inherent optical properties are specified through the chlorophyll content for various case waters. 127

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Appendix B: Comparison of the Light Models in POM B.1 Introduction Since we are concerned with comparing our results with the POM, we need to calibrate our calculations to the chlorophyll concentrations used by POM for the various case waters. This is the only way by which we can make a quantitative comparison between the use of a constant K d as in POM and by a spectrally varying K d which the Hydrolight uses for its simulations. This has been done using an inverse approach. The Case 1 waters described by Morel (1988) are the clearest natural waters possible. These are the waters where light penetrates to the maximum possible depths. They are marked by the dependence of the inherent water properties on the chlorophyll concentration (Morel, 1988). He calculates the total attenuation coefficient as a function of the chlorophyll content. K d () = K w () + c () C e() (B1) where, K w () is the attenuation for pure water, and c and e are coefficients. The values of these coefficients for each wavelength are given by Morel et al. (1988 and 1994). If the net attenuation (defined by a K d ) of light for both the POM and Hydrolight models is the same for some depth of water column, the net irradiance E d at that particular depth (say 10 m) would be the same for both methods. That is, the light field at 10 m is the same when modeled by Hydrolight with spectrally varying K d values as when using a constant K d by the POM model. Thus we can substitute K d as obtained from Table 2.2 of Chapter 2 for the K davg () for various case waters using the following equation: 128

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Appendix B: (Continued) dEdeEzKdzKdavgdd)()(ln1)()( where, z=10 m. (B2) Using this equation, get the corresponding values of K d () used in the integrals. These K d () values used in the integrals are then substituted in the equation (B1). Now by using an inverse method, we can find a chlorophyll value for equation B1 that will give these K d () values. This gives the following chlorophyll values for the various case waters (Table B1). The above formulas could give an error of up to an order of magnitude when dealing with turbid (Type 2 and 3) waters. So, we classify the Type 2 and 3 waters into a single category of turbid waters with a chlorophyll concentration C>0.5 g/l. It should be noted that these are an average value for the chlorophyll and it can vary quite a bit from these. Table B1: Derived chl-a values for POM Type of water Type 1 Type 1A Type 1B Type 2,3 Chlorophyll concentration (g/l) 0.05 0.09 0.19 >0.5 It is important to note here that the waters have been assumed homogeneous with depth. In case of waters with a varying absorption and scattering properties with depth (this can happen in water column with chlorophyll pigment concentration varying with depth, like a near-surface maxima), as is the case in most oceanic waters, the errors associated with the POM simulations become very large. In this thesis we ignore such variations and assume a well mixed layer of euphotic zone. 129

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Appendix B: (Continued) B.2 Oligotrophic water (Type 1, 1A and 1B) Simulations were run for this Type 1 water by using the bio-optical model Hydrolight by specifying a chlorophyll concentration of 0.05 g/l. The results are then compared to the light model in POM by using a constant K d as in Table 2.2 in Chapter 2. Fig. B1 shows a comparison between the two curves. As already mentioned, Hydrolight has the option of prescribing the sun angle for the simulations. Sun angle differences can produce changes in the underwater light flux by the variation of incident radiation. The figures B1 through B5 have been carried out by specifying a constant sun angle of 45. Note that the x-axis is the logarithm of the irradiance light field. This is to facilitate the comparison of the two curves since the constant K d curve (as for the POM case) then becomes a straight line. ln(Ed) 0123depth (m) 020406080 Hydrolight POM Fig. B1: Comparison of Hydrolight and POM for Type 1 waters. 130

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Appendix B: (Continued) ln(Ed) 0123depth (m) 0204060 Hydrolight POM Fig. B2: Comparison of Hydrolight and POM for Type 1A waters. As can be seen from the curves, the irradiance fields are started with the same E d at the surface, but as the light penetrates deeper, they diverge with the attenuation increasing for the Hydrolight simulated case. As the solar radiation penetrates the water column, it becomes progressively impoverished for wavelengths which the aquatic medium absorbs strongly with residual light left at those wavelengths that are absorbed weakly. Or, we can say that the more attenuated wave bands already been absorbed, we are left with the less attenuating wave bands. Thus the attenuation coefficient for the total photosythetically available radiation (PAR) is higher in the upper few meters and falls to lower value with increasing depth. This means that the slope of the ln (E d ) curve for the Hydrolight simulation will decrease with depth. Finally, the curve becomes linear, indicating that the downward flux is now confined to wave bands all with the same, but low attenuation coefficient. In this particular case, these are primarily the blue wave bands, since the green and red bands are absorbed more quickly than the blue for the clear waters. 131

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Appendix B: (Continued) An important parameter that can be derived from this light field attenuation is the euphotic depth. This depth (defined as the depth where the irradiance falls to 1% of the subsurface value), which is the region with enough light for photosynthesis, is of great interest to biologists. The actual depth of euphotic zone varies considerably with the transparency for the penetration of light in the waters. Many biological models calibrate and measure the depth of chlorophyll blooms or production based on the euphotic depth. In case of a uniform attenuation coefficient, the euphotic depth can be calculated as 0.46/K d Assumption of a constant K d by the POM predicts a euphotic depth of 64 m for the clear Type 1 waters, which is fairly similar to what the Hydrolight predicts (read from Fig.B1). A similar plot has been given for Type 1A optical waters in Figure B2. This figure follows the similar pattern of Fig. B1 with the irradiances from the two simulations (POM and Hydrolight) diverging at the surface and then coming closer at depths. As is expected, the attenuation with depth in these waters is more than in Case 1 waters. The irradiance field with depth for the Type 1B water is shown in Figure B3. Curiously enough, the irradiance field in this case can be approximated with two K d values, one near the surface till 10 m depth and another one after that. The K d near the surface is dominated by highly attenuating wavelengths like red. After 10 m the less attenuating wavelengths like blue and green remain. The constant K d after the 10 m depth can be explained by the countervailing tendency, which exists at all wavelengths, for the attenuation to increase as a result of increased scattering. This increased scattering is due to the higher chlorophyll particulate concentration of Type 1B waters. So, in such a scattering medium K d in Type 1B waters over the clearer type waters is increased also because of the altered angular distribution of the down welling light. The higher turbidity is commonly associated with increased absorption 132

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Appendix B: (Continued) at the blue end of the spectrum; it is also true that in such waters the blue waveband is removed at shallow depths. In such profiles (Fig. B3 and Fig. B4), the change in slope of the E d curve occurs quite near the surface. More diffuse light increases the path length of the radiance field and thus its chances of getting absorbed or scattered (attenuated). So, as the light goes deeper into the water column the lower ln(Ed) 0123depth (m) 01020304050 Hydrolight POM Fig. B3: Comparison of Hydrolight and POM for Type 1B waters. 133

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Appendix B: (Continued) ln(Ed) 0123depth (m) 0204060 0 0 600 Fig. B4: Comparison of Hydrolight runs for different sun angles for Type 2 waters. attenuating wavelengths remain but its lower attenuation is offset by an increased attenuation due to heavy scattering from the particles. These two opposing factors tend to cancel the change in attenuation and hence contribute to the constant K d observed. Attenuation of light in such a water body can be characterized by a single K d or at worst, by two values, one above and one below the change in slope. The above argument holds good for all sun angles, but as the sun angle becomes more vertical, this compensating effect decreases (see Fig.B4, both the curves obtained from Hydrolight). Figure B4 shows a comparison between the irradiance field with depth for the two sun angles of 0 and 60 as simulated by Hydrolight. The irradiance flux is curved more at the higher depths when the incident beam became more vertical (0 ). This shows how the attenuation is not just a function of the particle scattering alone but depends on the incident angle of light beam too; 134

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Appendix B: (Continued) higher the sun angle, the less vertical the incident radiation is; and the less vertically a photon is traveling, the greater the path length and hence more the chances of getting absorbed. Eventually as the light reaches deeper into the water medium, the angular distribution of light intensity takes on a fixed form referred to as the asymptotic radiance distribution which is symmetrical about the vertical, and whose shape is determined only by the values of the absorption coefficient and the volume scattering function. Rigorous proofs of such an asymptotic function have already been well established (Preisendorfer 1961). An important point to note here is that, these curves demonstrate the minimum possible errors for any given Case water. As the chlorophyll concentration varies within the same case water, it will produce a significant change in the irradiance light field with depth (as simulated by Hydrolight) and hence will generate higher errors in the light field predicted by POM. Also within each case water bodies, for a particular scattering coefficient, based on the incident angle of light beam we can expect an error between the two curves to be varying from that between the curves in Figure B4. B.3 Eutrophic or turbid waters The observations now need to be extended to the case of more turbid waters. We simulate the case of the West Florida shelf waters during the summer of 1998. 1998, being an El Nino year was marked by higher than average rainfall in the West Florida region. The waters off the West Florida shelf had a very high Gelbstoff content during this period presumably due to the increased runoff from Mississippi and Charlotte harbor. From the measured data from the ECOHAB experiments over the West Florida shelf, chlorophyll concentrations as high as 1 g/l have been observed. We can now set the Hydrolight to run with this chlorophyll concentration, 135

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Appendix B: (Continued) which is homogeneous with depth with the Gelbstoff absorption value set to be proportional to chlorophyll absorption at a specified wavelength. This is found to be close to Type 3 waters when we run POM simulations. Figure B5 shows the irradiance flux predicted by POM for Type 3 waters and by Hydrolight. As we can see from the Figure B5, the Hydrolight run predicts a significant deviation from the constant K d across the spectrum predicted by POM when we categorize it as a Type 3 water type. The near linear profile of the Hydrolight simulation is not surprising, and can be attributed to the counteracting tendencies already mentioned above that affect the attenuation characteristics with depth. The Type 3 waters are highly attenuating at all wavelengths thus reducing the euphotic depth to 20 m. In addition to these factors, if we had a chlorophyll concentration that also varied with depth and space, we will be looking at errors that are much higher. These results clearly illustrate the inadequacies of the constant K d parameterization in the POM model. And since the scattering effect of particles leads to an almost constant K d with depth for turbid waters, we can try to find better values for the K d This constant K d will be a function of the chlorophyll content and other particulate matter in the water column. This can be the basis for future work on improving the light models of general ocean models. 136

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Appendix B: (Continued) ln(Ed) 0123depth (m) 05101520 Hydrolight POM Fig. B5: Comparison of Hydrolight and POM for Type 3 waters. 137

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Appendix C: Turbulence Closure Submodel The eddy coefficients for the vertical mixing of momentum primarily used in this numerical study are the instantaneous outputs of the Mellor-Yamada level 2.5 turbulence closure submodel. The following paragraphs briefly describe the end formulation of this submodel. The details can be found in Mellor and Yamada (1982), Galperin et al. (1988), and Kantha and Clayson (1994). The turbulence closure submodel in the POM is basically established on the work of Mellor and Yamada (1974,1982) and Mellor (1996). It was developed through systematic scaling of the governing equations for the turbulent fluxes of heat and momentum. The dissipation and triple correlation terms in these equations were based on the Rotta and Kolmogoroff hypothesis (see Mellor and Yamada, 1982), and the empirical constants were determined from laboratory measurements of homogeneous turbulence. Galperin et al. (1988) further modified this submodel by demonstrating that a more robust quasi-equilibrium model could result from a slightly different systematic expansion procedure. This Mellor-Yamada turbulence closure submodel characterizes the turbulence kinetic energy q 2 and a turbulence macroscale l as follows, )1()(()(22)()(2)()1()(212121213022212212221CKDhhDAhhqDAhhDqKgvuDKhhqhhDqhtDqhhhhhhm 138

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Appendix C: (Continued) )2()(()()()()()1()()(22121212130122121221222221ClqKqDhhDAhhlqDAhhBDqKglEvuDKlEhhlqhhlDqhlDuqhtlDqhhhhhm where a wall proximity function = 1+ 22)(LlE is introduced with (L) -1 = (-D) -1 +(H 0 +D) -1 (C3a,b) With the closure assumptions described by Mellor (1974) and summarized by Mellor and Yamada (1982), the mixing coefficients K m K h and K q are reduced to K m =lqS m K h =lqS h and K q =lqS q (C4) Here S m S h and S q called stability functions are analytically derived algebraic relations functionally dependent on qgvu,,,10 and l. With the introduction of 2/12222)()(vuDqlGm and 022gDqlh G, the stability functions become, S q = 0.2 (C5) S m [6A 1 A 2 G m ]+S h [1-2A 2 B 2 G h -12A 1 A 2 G h ]=A 2 (C6) S m [1+6A 1 2 G m -9A 1 A 2 G h ]-S h [12A 1 2 G h +9A 1 A 2 G h ]=A 1 (1-3c 1 ) (C7) A necessary closure assumption is that all length scales are propotional to each other, i.e., (l 1 ,l 2 1 2 ) = (A 1 ,A 2 ,B 1 ,B 2 )l. The empirical constants are assigned as, 139

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140 Appendix C: (Continued) (A 1 ,A 2 ,B 1 ,B 2 C 1 )= (0.92,0.74,16.6,10.1,0.08) and (E 1 ,E 2 )=(1.8,1.33), they are derived from laboratory data. The boundary conditions for the turbulence kinetic energy q 2 and a turbulence macroscale l in this turbulence closure submodel are, q 2 (0)=B 1 2/3 u s (0), q 2 (-1)= B 1 2/3 u b (-1) (C8) q 2 l(0)=0, q 2 l(-1)=0 (C9) where u s and u b are the frictional velocities calculated from the applied surface wind and modeled from the bottom frictional stress, respectively.

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ABOUT THE AUTHOR Hari Warrior was born in Kerala, India. He did his schooling in his native town followed by a Bachelors in Naval Architecture and Ship design at the Indian Institute of Technology, Madras in 1997. He followed up his B-Tech with a Masters in Atmospheric Sciences at North Carolina State University in 1999. He worked in the local and regional sea breeze simulations for the east coast of India. After his Masters, he came for a PhD to University of South Florida where he did his doctorate in Oceanography. For his PhD he worked on remote-sensing and ocean circulation modeling working with Dr. Ken Carder, USF. Haris interests are in modeling, which include ocean circulation dynamics, air-sea interaction and remote-sensing. He has a couple of publications to his merit and has also made presentations at a number of conferences. His hobbies include ping-pong, tennis and listening to soft music.