Citation
Photosynthetically active radiation in the Indian River Lagoon

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Title:
Photosynthetically active radiation in the Indian River Lagoon
Series Title:
Photosynthetically active radiation in the Indian River Lagoon
Creator:
Kornick, Adam Marcus
Place of Publication:
Gainesville, Fla.
Publisher:
Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Language:
English

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University of Florida
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University of Florida
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All applicable rights reserved by the source institution and holding location.

Full Text
PHOTOSYNTHETICALLY ACTIVE RADIATION
IN THE INDIAN RIVER LAGOON:
ANALYSIS USING THE PARPS MODEL AND STATISTICAL ANALYSIS
By
ADAM MARCUS KORNICK

A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF ENGINEERING
UNIVERSITY OF FLORIDA

1998




Copyright 1998
by
Adam Marcus Kornick




I dedicate this work to my father, Hank Kornick.




ACKNOWLEDGEMENTS

I would like to thank my graduate committee members, Dr. Peter Sheng, Dr. Bob Thieke, and Dr. Bob Dean, for their contributions.
I would like to thank all of the graduate students who helped me, particularly those who participated in the field work on the Indian River Lagoon, Justin Davis, Joel Melanson, Peter Seidle, Matt Henderson, Hugo Rodriguez, William Weber, Al Browder, Detong Sun, Chenxia Qiu, Kevin Barry, Dave Christian, Christian Schlubach, Haifeng Du, Jun Lee, and Kijin Park, and a second round of thanks to those who help me with proofreading, Justin Davis and Dave Christian. I would like to thank the Department of Coastal and Oceanographic Engineering as a whole. The UF synoptic data used in this study were collected by the Coastal and Oceanographic Engineering Department with funds from the St. Johns River Water Management District. I would like to thank all of the Coastal lab staff, Vik Adams, Sidney Schofield, Jim Joiner, Vernon Sparkman, and Chuck Broward, for their help and patience. BTR Labs, particularly Tom Price, gave me invaluable aid.
I could not have completed my work without the openness and aid of the following researchers, Ron Miller, Chuck Gallegos, and Dennis Hanisak. My chapter on statistical modeling could never have included so many analyses without the help of Ken Portier. I would also like to thank Robert Virnstein of the SJRWMD for providing me the data collected by HBOI and Becky Robbins at the SFWMD for helping me to get reports from their archives so quickly.




I never would have made it through UF without Dave Mickler, Chris Depcik, Scott Klein, William Weber, and Jen Harriss.
I thank NSF for supporting me for one year during my master's studies. In addition to other funding, this material is based upon work supported under a National Science Foundation Graduate Fellowship. Any opinions, finding, conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.




TABLE OF CONTENTS
ACKNOWLEDGEMENTS ............................ iv
LIST OF TABLES ................................. ix
LIST OF FIGURES ................................ xi
ABSTRACT ... ... .. ..... .. .. .. .. .. ... .. .... xvi
CHAPTERS
I INTRODUCTION ............................. 1
1.1 M arine Radiometry ......................... 9
1.2 Solar Energy . . . . . . . . . . . . . . 9
1.2.1 Effects of Sunlight ...................... 10
1.3 Radiometric Quantities ....................... 14
1.3.1 Photosynthetically Active Radiation ............ 14
1.3.2 R adiance . . . . . . . . . . . . . 15
1.3.3 Irradiance . . . . . . . . . . . . . 15
1.4 Optical Properties .......................... 17
1.5 Literature Review .......................... 17
1.6 Objectives and Hypotheses ..................... 23
1.7 Organization 24
2 LIGHT DATA 26
2.1 M easuring KPAR 26
2.1.1 Plane Attenuation . . . . . . . . 28
2.1.2 2 7r Sensors 28
2.1.3 Scalar Attenuation . . . . . . . . . . 29
2.1.4 4 -x Sensors 29
2.2 Collection of Light Data . . . . . . . . . . . 30
2.2.1 SERC Study 30
2.2.2 HBOI Study 31
2.2.3 UF Study 31
2.3 Sum m ary 31
3 WATER QUALITY DATA . . . . . . . . . . . . 33
3.1 Measuring Water Quality . . . . . . . . . . . 33
3.2 Water Quality Constituents . . . . . . . . . . 33
3.2.1 Dissolved Constituents . . . . . . . . . 33




3.2.2 Particulate Constituents ....................... 34
3.3 Collection of Water Quality Data ....................... 36
3.3.1 SERC Study ...... ......................... 36
3.3.2 HBOI Study ...... ......................... 37
3.3.3 UF Study ................................. 38
4 STATISTICAL MODEL ....... ......................... 40
4.1 Data Set Characterization 40
4.2 Principal Component Analysis (PCA) .............. 41
4.2.1 SERC PCA ................................ 44
4.2.2 HBOI PCA (Year 1) ...............46
4.2.3 HBOI PCA (Year 2) ..................... 47
4.2.4 UF PCA ........................... 48
4.3 Pearson Correlation Coefficients ..... .................. 49
4.4 Single Variable Regression ........................... 50
4.4.1 SERC Single Variable Regressions ................ 53
4.4.2 HBOI Year 1 Single Variable Regressions ............ 62
4.4.3 HBOI Year 2 Single Variable Regressions ............ 68
4.4.4 UF Single Variable Regressions .................. 74
4.4.5 Discussion of Single Variable Model Results ........... 84
4.5 Linear Multiple Variable Regression ..................... 88
4.5.1 SERC Multiple Variable Regressions ............... 89
4.5.2 HBOI (Year 1) Multiple Variable Regressions ....... ..90
4.5.3 HBOI (Year 2) Multiple Variable Regressions ....... 94 4.5.4 UF Multiple Variable Regressions ................ 97
4.5.5 Discussion of Linear Multiple Variable Models ........ 97
4.6 Non-Linear Factorial Multiple Variable Models ............. 102
4.6.1 SERC Factorial Regression ..................... 103
4.6.2 HBOI (Year 1) Factorial Regression ............... 103
4.6.3 HBOI (Year 2) Factorial Regression ............ 105
4.6.4 UF Factorial Regression ....................... 107
4.7 Comparison Between Non-Linear and Linear Models ......... 107
4.8 Data Variability ...... ........................... 110
5 PARPS NUMERICAL MODEL ..... ..................... 113
5.1 Attenuation ....... ............................. 113
5.2 Kirk's Monte Carlo Model ........................... 113
5.3 Absorptance ....... ............................. 114
5.3.1 Pure Sea Water Absorption .................... 115
5.3.2 Gelbstoff (Yellow Substance) Absorption ........... 116
5.3.3 Phytoplankton Absorption ..................... 117
5.3.4 Detritus Absorption .......................... 117
5.4 Scatterance ....... .............................. 119
5.4.1 Single Scattering Albedo ....................... 119
5.5 Model Construction ...... ......................... 120
5.5.1 Deterministic PARPS Model .................... 121
5.5.2 Monte Carlo PARPS Model ..................... 122
5.6 Sensitivity Analyses ...... ......................... 122
5.6.1 Turbidity ................................. 123
5.6.2 Chlorophyll a ............................... 125
5.6.3 Color ....... ............................. 125
5.6.4 [ .......... ........................... .... 127




5.6.5 Monte Carlo Repetitions .. .. .. ... ... ... ....131
5.7 Model Results .. .. .. ... ... ... ... ... ... ... ..132
5.7.1 SERC Data .. .. .. .. .. ... ... ... .... .....136
5.7.2 HBOI Data (Year 1) ... .. .. .. .. .. .. 138
5.7.3 HBOI Data (Year 2)...... .. .. .. .. .. .. 140
5.7.4 UF Data .. .. .. .. ... ... .... ... ... .....142
5.8 Discussion of Numerical Model Results. .. .. ... ... .....144
5.8.1 Model vs. Data. .. .. .. ... .... ... ... .....148
5.8.2 Model vs. Model .. .. .. .. ... ... ... ... .....149
5.8.3 Sources of Error. .. .. .. ... ... ... ... ... ..149
6 CONCLUSION. .. .. ... ... ... ... ... ... ... ... ..152
6.1 Data........................152
6.2 Model Comparison .. .. .. .. .. .... ... ... ... .....153
6.2.1 Empiricism vs. Theory .. .. .. ... ... ... ... ..154
6.2.2 Process Information .. .. .. .. ... ... ... ... ..155
6.2.3 Robustness .. .. .. .. ... ... ... ... ... ....155
6.2.4 Variability. .. .. .. ... ... ... ... ... ... ..156
6.3 Hypotheses .. .. .. .. ... ... ... ... ... ... ... ..157
6.4 Future Work. .. .. .. ... ... ... ... ... ... ... ..163
6.4.1 Lab Work. .. .. .. .. ... ... ... ... ... ....163
6.4.2 Integration. .. .. .. .. .... ... ... ... ... ..164
6.4.3 Sediment Dynamics .. .. .. .. ... .... ... .....164
6.4.4 Radiative Transfer Model .. .. .. .. ... ... ... ..164
6.4.5 Tree Model .. .. .. .. ... ... ... ... ... ....164
6.5 Summary. .. .. .. .. ... ... ... ... .... ... .....166
REFERENCES. .. .. .. .. ... ... ... ... .... ... ... ... ..167
BIOGRAPHICAL SKETCH. .. .. .. .. ... ... ... ... ... ... ..172




LIST OF TABLES

1.1 SI Units for marine optics ...... ........................ 9
2.1 Summary of light data collection ...... .................... 31
3.1 Water quality parameters collected in SERC study ............. 36
3.2 Water quality parameters collected in HBOI study .............. 37
3.3 Water quality parameters collected in UF study ................ 39
4.1 Simple statistics for SERC study ...... .................... 40
4.2 Simple statistics for HBOI study (Year 1) .... ............... 41
4.3 Simple statistics for HBOI study (Year 2) .... ............... 42
4.4 Simple statistics for UF study ...... ...................... 43
4.5 PCA for SERC data set ...... ......................... 44
4.6 PCA for HBOI Year 1 data set ..... ..................... 46
4.7 PCA for HBOI Year 2 data set ..... ..................... 48
4.8 PCA for UF data set ....... ........................... 50
4.9 Correlation between parameters in SERC study ................ 52
4.10 Additional correlation between parameters in SERC study ........ 53 4.11 Correlation between parameters in HBOI (Year 1) study ......... 54 4.12 Additional correlation between parameters in HBOI (Year 1) study 57 4.13 Correlation between parameters in HBOI (Year 2) study ......... 59 4.14 Additional correlation between parameters in HBOI (Year 2) study 60 4.15 Correlation between parameters in UF study .................. 61
4.16 Additional correlations between parameters in UF study ......... 62 4.17 Comparison of single variable models for SERC study ............ 62




4.18 Comparison of single variable models for HBOI year 1 study ..... ..69 4.19 Comparison of single variable models for HBOI year 2 study ..... ..74 4.20 Comparison of single variable models for UF study ............. 84
4.21 Comparison of r2 for single variable models ................... 85
4.22 Comparison of r2 of linear multiple variable models ............. 101
4.23 Comparison of r2 of factorial and non-factorial models .......... 108
4.24 Approximate Indian River Lagoon segment boundaries .......... 111
4.25 F-test for individual parameters in spatial test ................ 112
5.1 Absorption by Pure Sea Water ........................... 116
5.2 Absorption by Phytoplankton ..... ...................... 118
5.3 Default Values of adjustable coefficients in deterministic PARPS runs 121 5.4 Ranges of adjustable coefficients for Monte Carlo PARPS simulations 122 5.5 Calibrated values of adjustable coefficients .................. 137
5.6 Comparison of high and low KPAR within UF data set .......... 147
5.7 Modeled and observed data ..... ....................... 148
5.8 r2 of observed data vs. PARPS model ...................... 149
6.1 Comparison of light attenuation models ..................... 156
6.2 Allowable KPAR for a series of depths ...................... 161




LIST OF FIGURES

1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 2.1 2.2 2.3 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9
4.10

The Indian River Lagoon ......................... 2
Halodule wrightii .. .... ... .... .. .. .. . ... ... .. 4
Syringodium filiforme ............................ 5
Halophila engelmannii .......................... 5
Thalassia testudinum ........................... 6
Halophila decipiens ............................ 6
Halophila johnsonii ............................ 7
Ruppia m aritim a ............................. 7
Sampling stations in the Indian River Lagoon . . . . . . 27
2 x Sensor . .... . . . . . . . . . . . . 29
4 r Sensor . .... . .. .... .. . ... 30
SCREE plot for SERC data set ..................... 45
SCREE plot for HBOI Year 1 data set . . . . . . . . 47
SCREE plot for HBOI Year 2 data set . . . . . . . . 49
SCREE plot for UF data set ....................... 51
Depth based statistical model for SERC data . . . . . . . 55
pH based statistical model for SERC data . . . . . . . 55
Color based statistical model for SERC data . . . . . . . 56
TOC based statistical model for SERC data . . . . . . . 56
DOC based statistical model for SERC data . . . . . . . 58
Po based statistical model for SERC data . . . . . . . . 58




4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4.24

Chlorophyll based statistical model for SERC data .......... Color based statistical model for HBOI year 1 data ............
Chlorophyll based statistical model for HBOI year 1 data ........ Turbidity based statistical model for HBOI year 1 data ......... Total suspended solids based statistical model for HBOI year 1 data Inorganic suspended solids based statistical model for HBOI year 1 data Organic suspended solids based statistical model for HBOI year 1 data TP based statistical model for HBOI year 1 data .............
Color based statistical model for HBOI year 2 data ............
Chlorophyll based statistical model for HBOI year 2 data ........ Turbidity based statistical model for HBOI year 2 data ......... Total suspended solids based statistical model for HBOI year 2 data Inorganic suspended solids based statistical model for HBOI year 2 data Organic suspended solids based statistical model for HBOI year 2 data

4.25 TP based statistical model for HBOI year 2 data . 4.26 UTM based statistical model for UF data ........ 4.27 Julian day based statistical model for UF data ... 4.28 Time based statistical model for UF data ........ 4.29 Temperature based statistical model for UF data . 4.30 Dissolved oxygen based statistical model for UF data 4.31 pH based statistical model for UF data ......... 4.32 Salinity based statistical model for UF data ...... 4.33 Total phosphorus based statistical model for UF data 4.34 Total nitrogen based statistical model for UF data.. 4.35 TSS based statistical model for UF data ....... 4.36 Color based statistical model for UF data ........ 4.37 Total carbon based statistical model for UF data .

. . . . . 73
. . . . . 75
. . . . . 75
. . . . . 76
. . . . . 77
. . . . . 77
. . . . . 78
. . . . . 78
. . . . . 79
. . . . . 80
. . . . . 81
. . . . . 81




4.38 Silica based statistical model for UF data .................... 83
4.39 Chlorophyll based statistical model for UF data ............... 83
4.40 One variable maximum r2 statistical model for SERC data ...... .. 90 4.41 Two variable maximum r2 statistical model for SERC data ...... ..90 4.42 Three variable maximum r2 statistical model for SERC data ..... ..91 4.43 Four variable maximum r2 statistical model for SERC data ...... .. 91 4.44 One variable maximum r2 statistical model for HBOI Year 1 data 92 4.45 Two variable maximum r2 statistical model for HBOI Year 1 data 93 4.46 Three variable maximum r2 statistical model for HBOI Year 1 data 93 4.47 Four variable maximum r2 statistical model for HBOI Year 1 data 94 4.48 One variable maximum r2 statistical model for HBOI Year 2 data 95 4.49 Two variable maximum r2 statistical model for HBOI Year 2 data 95 4.50 Three variable maximum r2 statistical model for HBOI Year 2 data 96 4.51 Four variable maximum r2 statistical model for HBOI Year 2 data 96 4.52 One variable maximum r2 statistical model for UF data ........ .. 98
4.53 Two variable maximum r2 statistical model for UF data ......... 98 4.54 Three variable maximum r2 statistical model for UF data ....... ..99 4.55 Four variable maximum r2 statistical model for UF data ......... 99 4.56 r2 for multiple variable models as a function of number of variables 100 4.57 Two variable factorial statistical model for SERC data .......... 103
4.58 Three variable factorial statistical model for SERC data ........ ..104
4.59 Two variable factorial statistical model for HBOI data .......... 104
4.60 Three variable factorial statistical model for HBOI data .......... 105
4.61 Two variable factorial statistical model for HBOI data .......... 106
4.62 Three variable factorial statistical model for HBOI data .......... 106
4.63 Two variable factorial statistical model for UF data ............. 107
4.64 Three variable factorial statistical model for UF data ........... 108




5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9
5.10 5.11 5.12 5.13 5.14

PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test PARPS sensitivity test

of Po of P/0 of Po of PO

using using using using

HBOI data and time. . UF data and time . . SERC data and Julian day HBOI data and Julian day

5.15 PARPS sensitivity test of P0 using UF data and Julian day . . .

5 repetitions of Monte Carlo PARPS . 10 repetitions of Monte Carlo PARPS . 20 repetitions of Monte Carlo PARPS . 50 repetitions of Monte Carlo PARPS . 100 repetitions of Monte Carlo PARPS . 200 repetitions of Monte Carlo PARPS .

5.22 PARPS prediction using SERC data

Calibrated PARPS prediction using SERC Monte Carlo PARPS prediction using SERC PARPS prediction using HBOI year 1 data Calibrated PARPS prediction using HBOI y

. 133
. 133
. 134
. 134
. 135
. 135
. 136
ata 138
data 139
. . 139
ear 1 data 140

5.27 Monte Carlo PARPS prediction using HBOI year 1 data

of turbidity using SERC data . . of turbidity using HBOI data . . of turbidity using UF data . . . of chlorophyll using SERC data . . of chlorophyll using HBOI data . . of chlorophyll using UF data . . . of color using SERC data . . . of color using HBOI data . . . of color using UF data . . . . of Po using SERC data and time . .

. . 123
. . 124
. . 124
. . 125
. . 126
. . 126
. . 127
. . 128
. . 128
. . 129
. . 129
. . 130
. . 130
. . 131

5.16 5.17 5.18 5.19 5.20 5.21

5.23 5.24 5.25 5.26




5.28 PARPS prediction using HBOI year 2 data .................. 141
5.29 Calibrated PARPS prediction using HBOI year 2 data .......... 142
5.30 Monte Carlo PARPS prediction using HBOI year 2 data ......... 143 5.31 PARPS prediction using UF data ..... .................... 143
5.32 Calibrated PARPS prediction using UF data ................. 144
5.33 Monte Carlo PARPS prediction using UF data ................. 145
5.34 Calibrated PARPS prediction for all data sets ................ 145
5.35 Calibrated PARPS prediction at low values ................... 146
5.36 Calibrated PARPS prediction at high values ................. 146
6.1 A hypothetical tree model for KPAR ..... ................... ....165




Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering
PHOTOSYNTHETICALLY ACTIVE RADIATION IN THE INDIAN RIVER LAGOON:
ANALYSIS USING THE PARPS MODEL AND STATISTICAL ANALYSIS By
Adam Marcus Kornick
December 1998
Chairman: Dr. Y. Peter Sheng
Major Department: Coastal and Oceanographic Engineering
Many marine species spend some necessary portion of their lifespan within an estuary. Unfortunately, this habitat is suffering from seagrass loss, often attributed to water quality degredation. It is believed that this degraded water quality causes lower levels of light energy to be available beneath the water's surface. These lower light levels are then believed to result in seagrass decline and reduced habitat. This penetration of light is believed to be the primary determinant of depth limitation for seagrasses. The Indian River Lagoon, stretching 341 km from Ponce de Leon Inlet to Jupiter Inlet on Florida's east coast, provides an excellent study ground to examine issues affecting the estuarine environment.
This study examines several ways to predict light attenuation as a function of the water quality within the Indian River Lagoon. These include several statistical models (linear and non-linear, single and multiple variable) which have been developed for several other estuaries and a spectrally based numerical model. These




models are examined for both predictive and hindcasting ability, and conclusions are drawn about the applicability of these models to future coupled hydrodynamic/water quality/seagrass models.
Data variability was found to be best explained by multiple variable linear regressions, while spectral modeling using the PARPS (Photosynthetically Active Radiation Prediction System) model proved to be the most robust method to predict light attenuation. The PARPS model works particularly well with the SERC (Smithsonian Environmental Research Center) data set, with which the model was developed. The conclusion was reached that neither statistics nor physics allows us to perfectly predict attenuation in the photosynthetic spectrum, KPAR. Instead, the two should be used together as supporting tools. When their predictions begin to diverge, it is a clear signal that those data points should be examined with care, and that an attempt should be made to use those data points to improve each of the models.

xvii




CHAPTER 1
INTRODUCTION
The health of our global oceans is influenced by the health of our estuaries. Almost every marine species spends some necessary portion of its lifespan within an estuary. Furthermore, the large majority of commercial fish catch occurs in estuaries. On Florida's west coast, in the Gulf of Mexico, over 70 % of the total catch is estuarine related (McHugh, 1980). Unfortunately, our coastal habitats are disappearing and being degraded at an increasingly rapid rate as the global human population soars. The Indian River Lagoon provides an excellent study ground to examine these problems.
The Indian River Lagoon is located on the east coast of Florida, where it stretches approximately 341 km through six counties, from Ponce de Leon Inlet in the north to Jupiter Inlet in the south, see Figure 1.1. Its width varies from 0.4 to 12.1 km and the average depth is 1.2 m (Steward et al., 1994). It is one of the most diverse estuaries in the world, in terms of habitat and species, containing over 2000 identified species (Barile et al., 1987).
Unfortunately, anthropomorphic influence on the lagoon has led to an overall decline in the lagoon's health, including its water quality. Near areas of higher population loss, large areas of mangroves and seagrass have been documented (Vimnstein and Cambell, 1987). It is believed that this degraded water quality has caused lower levels of light energy to be available beneath the water surface. These lower light levels are then believed to result in seagrass decline and reduced habitat. The penetration of light is believed to be the primary determinant of depth limitation for




Indian River Lagoon
N
10 km I

Figure 1.1: The Indian River Lagoon




sea grasses (Virnstein and Morris, 1996), though other factors such as sediment type, sediment nutrients, and salinity can all affect sea grass growth and health.
The term seagrass applies to any flowering plant which evolved from terrestrial plants and then returned to the seas. Seagrasses are a subset of Submerged Aquatic Vegetation (SAV). The seven seagrasses that live within the Indian River Lagoon, in approximate order of decreasing occurrence are (Virnstein and Morris, 1996):
1. Halodule wrightii, shoal grass
2. Syringodium filiforme, manatee grass
3. Halophila engelmannii, star grass 4. Thalassia testudinum, turtle grass 5. Halophila decipiens, paddle grass
6. Halophila johnsonii, Johnson's seagrass
7. Ruppia maritima, widgeon grass
Images (Florida Department of Environmental Protection, 1998) of these seven seagrasses are shown in Figures 1.2 1.8. They are again listed from most common to most rare.




Halodde lwrighti
SHOAL-GRASS

Figure 1.2: Halodule wrightii




SyringandimnfilifnJr~
MANATEIE-GRASS

Figure 1.3: Syringodium filiforme

11alophila englemannai
STAR-G~ASS

Figure 1.4: Halophila engelmannii




I /
Thasasia E tEIdidin
TURtTLE -GRlASS
Figure 1.5: Thalassia testudinum
Halophll dEcipiens
- ) PADDLE-GRASS
Figure 1.6: Halophila decipiens




l op hil j o h it,
*Inn
JOITNSOW"S SEAGRASS
Figure 1.7: Halophila johnsonii
n i ,-. V '.;
JFipiue1.7 ahl ohn:Monii

Ruppia narithima
mIDGEON-GRASS

Figure 1.8: Ruppia maritima




Seagrass beds are believed to provide habitat for adults and juveniles of many estuarine species (Lewis, 1984, Virnstein et al., 1983) as well as stabilizing sediment and providing food for waterfowl (Gallegos and Kenworthy, 1996). Seagrass habitats are one of the most productive biomes on Earth (Dawes, 1981, Zieman, 1982). They can be thought of as the estuarine analog to the tropical rainforest because of their biodiversity, productivity and fragility (Simenstad, 1994). For these reasons, this thesis will investigate the relationship between water quality and light attenuation.
Phytoplankton production is increased by nutrient enrichment, but total production remains nearly constant. This means that phytoplankton increases reduce cover of benthic plant (or macrophyte) populations such that the total organic carbon production of the estuary remains constant (Borum, 1996).
Before one considers the dynamics of a seagrass environment, it is important to consider the possible benefits of seagrass. It has been estimated that the Indian River Lagoon's seagrass meadows provide approximately a billion dollars annually of economic benefit (Virnstein and Morris, 1996). These estimates show that an acre of seagrass generates $12,500 each year through commercial and recreational fisheries.
Here at the Coastal and Oceanographic Engineering Department of the University of Florida, research work has been conducted (Sheng, 1997) since 1994 to develop a Pollutant Load Reduction (PLR) model for the St. Johns River Water Management District (SJRWMD). The PLR model includes a hydrodynamic model, a sediment transport model, a water quality model, a light attenuation model and a seagrass model (Sheng, 1997). The PLR model study also includes the collection and analysis of hydrodynamic, sediment, water quality, light, and seagrass data (Sheng, 1997). This study aims to develop a light model as part of the PLR model which is valid for the Indian River Lagoon.




1.1 Marine Radiometry

One tool for researching light within the Indian River Lagoon is marine radiometry, which is the study of radiant energy, i.e. sunlight, in the ocean. To describe marine optics clearly and precisely, this study uses the nomenclature recommended by the International Association of Physical Sciences of the Ocean (Morel and Smith, 1982) as illustrated in Table 1.1.

Table 1.1: SI Units

for marine

optics

1.2 Solar Energy
In the definition above we narrowed marine radiometry to sunlight in the ocean, neglecting other light sources. This is because other sources of light, including bioluminescence and artificial (man-made) light are a tiny fraction of the Earth's total radiant energy input.
Sunlight streams away from the sun, spreading photons equally in all directions. By conservation of energy, the total solar energy crossing any imaginary sphere around the sun is equal. The energy at a point on the surface of that sphere decreases as the radius, R, of that sphere increases. This is known as the inverse square law, the

Physical Quantity SI Unit Symbol
length meter m
mass kilogram kg
time second s
electric current ampere A
temperature Kelvin K
amount mole mol
luminous intensity candela cd
plane angle radian rad
solid angle steraradian sr
integral solar radiance Wm-2 E, radiant energy joule q
thermal energy joule Q




energy per unit area of a sphere around the sun, or any light source, is inversely proportional to R'. The integral solar radiance from photons at all wavelengths arriving at the Earth's atmosphere, E, is (Mobley, 1994),
-2
E, = 1367WTn (1. 1)
E, is commonly referred to as the solar constant, but it varies by a fraction of a percent. Moreover, this value is for the mean annual distance between the Earth's atmosphere and sun. The solar irradiance varies by an additional amount of approximately 50 W m-2 as the Earth orbits the sun. To complicate matters further, the spectral distribution of E, is a function of wavelength. It varies because the number of photons per wavelength interval varies, and because each photon possesses energy, q, as a function of its wavelength (Halliday et al., 1993),
hC
q = 1 (1.2)
A
where h is Planck's constant, c is the speed of light, and A is wavelength.
For better or worse, the solar irradiance as defined in equation 1.1 does not directly concern the optical oceanographer. Rather, one is usually concerned with the sunlight that reaches the sea surface. The magnitude and spectral dependence of this solar irradiance varies significantly with the position of the sun and atmospheric conditions.
1.2.1 Effects of Sunlight
Now let us examine three ways that sunlight in the visible spectrum might impact the ocean and the organisms beneath its waves. The first law of thermodynamics can be used to calculate the heat input due to sunlight (Mobley, 1994).
OT -1 aQ (1.3)
at C, M at




For this equation, T is temperature, t is time, c, is specific heat, m is the mass, and 2Q is heat absorbed or lost per unit time.
aT
Consider only the upper one meter of the ocean's surface layer. A typical irradiance would be 400 W m-2, so Q = 400 J1 for each square meter of the surface and c, = 3900 J kg-1 K-',. Let us assume that 5 % of this incident light is absorbed in this first meter by a mass of 1025 kg of sea water (1 m3 x 1025 kg/m3). We then discover (Mobley, 1994),
OT 1 (0.05)(400 J) 10 K(
at (3900 J kg-1)(1025 kg) 1 s
Twelve hours of sunlight would result in the upper meter's temperature increasing by
AT = (5 x 10-6)(12h)(360) s 0.22 K. (1.5)
This temperature change is significant as a boundary condition for ocean circulation models because of the importance of ocean temperature in global climate. Nonetheless, it would take about nine months to raise one m3 of typical sea water (31 C) to body temperature (37 o C) (Campbell, 1990)!
Dividing the total energy by the energy per photon will yield the number of photons incident upon the sea surface. We will assume the same irradiance of 400 W m-2 and again examine the upper meter of the ocean. Assuming a monochromatic average wavelength of 550 nm (Mobley, 1994),
QQA (400 J)(550 nrm) 102
q hc = (6.63 x 10-34)(3 x 108 ms-1) 1 photons. (1.6)
Mobley (1994) has also shown that the linear momentum of all these photons is,
1Q is simply E times surface area.




p = N h = 10 216.63_x 10-34 j 1.2 x 10-r kg m s- (1.7)
A 550 nm
This momentum is 9 orders of magnitude less than that of a 75 kg human walking down the street at 3 m s1
Finally, we can calculate the amount of energy that this same amount of sunlight will produce if it is all used in photosynthesis. Photosynthesis absorbs certain wavelengths preferentially, but every photon results in the same amount of usable energy. From Einstein's Law of the Photochemical Equivalent, it can be stated that each molecule taking part in a chemical reaction which is the direct result of light absorption requires one quantum of radiation (Gregory, 1977). This means that any photochemical reaction (such as photosynthesis) depends on the number of absorbed quanta and not the energy content of the absorbed quanta'. Any additional energy is re-emitted as a photon or retained as heat.
Beadle et al. (1985) have estimated the fraction of incident sunlight energy that terrestrial plants convert to stored energy as follows. Only about 50 % of solar radiation is photosynthetically active radiation (PAR, see section 1.3.1). Of that 5 10 % is reflected, scattered or re-emitted from the plant. Another 2.5 % is lost due to absorption that does not result in a reaction (inactive absorption). Another 8.7 % is lost due to pigment inefficiencies and approximately 20 % is lost in carbohydrate synthesis. Finally another 6.8 % is lost in respiration in 03 plants '. This would leave 2 7 % of incident light to be stored as chemical energy (Beadle et al., 1985). Again, using the same irradiance, and thus the same 400 J of irradiance, we find that
2-7%x400J =8-28J (1.8)
'It should be noted, however, that quanta of different wavelengths will be absorbed preferentially (Jerlov, 1976)
'All seagrasses are believed to be exclusively C3 (Kirk, 1983), but some evidence has been found of limited C4 pathways in marine algae (Nielson, 1975).




Dividing equation 1.8 by seconds gives the power produced,
8-28J= 8 28 W (1.9)
8
This means that as little as 2 m2 and at most roughly 7.5 m2 of plant filled ocean produces enough energy to power a light bulb!
Admittedly, this estimation procedure was intended for terrestrial plants. However, Nielson (1975) states that "we can hardly expect any difference in this respect [light absorption] between terrestrial and marine". Still, let us undertake a second estimate to be sure that our calculations are reasonable.
The overall reaction of photosynthesis is summarized (Campbell, 1990) in equation 1.10.
C02 + 2H20 8 (CH20) + H20 + 02 (1.10)
Only 2 6 % of incident light is lost by surface reflection (Kirk, 1983). On the order of 5 % of remaining light is lost due to backscattering (Kirk, 1983). As stated before, only 50 % of this light is in the PAR spectrum. Of the PAR remaining in the water column, as much as 70 80 % can be absorbed by high concentrations4 of chlorophyll (Kirk, 1983).
For a wide range of water types 1 J of energy in the PAR spectrum requires approximately 2.5 x 1018 quanta (Morel, 1976). Therefore, the energy is
1 J 6.02 x 1023
mol photons 1 x = 240 kJ (1.11)
2.5 x 101squanta lmole
This means that 8 Einsteins of light will contain 1.92 MJ. Equation 1.10 shows that 1 mole of carbohydrate (CH20) will be produced for every 8 Einsteins of light. From stoichiometry, converting one mole of C02 to one mole of carbohydrate requires
4These absorbtion levels were observed in concentrations of 100 m4




472 kJ Therefore, the maximum possible theoretical efficiency for converting light energy to chemical energy is
efficiency 47 = x 100 % = 24.6 % (1.12)
1.92 MJ
The efficiency in equation 1.12, assumes that the plant is producing only carbohydrates when in fact it is also producing lipids, proteins, nucleic acids, etc. These require additional energy and bring the maximum efficiency down to about 18 % (Kirk, 1983). Thus, our total efficiency in estimating by this method becomes
.96 x.95 x.50 x.18 x.75 = 0.06 = 6% (1.13)
This estimate of 6 % for marine plants is reasonable when compared to the earlier estimate of 2 7 % for terrestrial plants (Beadle et al., 1985).
1.3 Radiometric Quantities
1.3.1 Photosynthetically Active Radiation
From analyses in Section 1.2.1 we see that the importance of sunlight comes first from its ability to produce biologically available energy (through photosynthesis), second from its energy transport (heat), and lastly, from its momentum transport. These calculations support this work's focus on the biological influence of marine light.
To study photosynthesis as a function of sunlight we must define photos ynthetically active radiation, EPAR, the sunlight available for photosynthesis by plants (Kirk, 1983),
I700 rim A
EpAR ~ i hcEo (x, A) dA (photons s-' m) (.4
EPAR can also be expressed in einst .s-~ m1 where one Einstein is one mole of photons. Equation 1.14 is then simply,




1 p700 nm A
EPAR 6.02 1023 ] -Eo(x, A)dA (einst s-1 m) (1.15)
6.02 x 350 nm hc0
E, is a measure of irradiance defined in Section 1.3.3. The lower bound of the integral in equation 1.14 is often approximated as 400 nm so that the entire integral range is included within the visible spectrum. This approximation is acceptable because most of the near UV band (350 400 nm) is rapidly absorbed in the water column (Mobley, 1994), particularly in eutrophic estuaries such as the Indian River Lagoon. We will use this approximation for the remainder of this investigation.
1.3.2 Radiance
Before using EPAR, it is necessary to understand other important radiometric measures of hydrological optics. The most fundamental measure of a light field is the spectral radiance, L (Mobley, 1994)
L(xt,,/A) AQ (W m-2sr-'nm-1). (1.16)
L~xt,,A -At AA AQ AA
A Q is the solid angle subtended by the instrument measuring radiance. A A is the area on which light of energy A Q is falling. A A is the range of wavelengths impacting A A over A T seconds. Note that spectral radiance defines the spatial
(x), temporal (t), directional (i), and wavelength (A) structure of the light field. All other optical quantities can be derived from spectral radiance.
1.3.3 Irradiance
The only other radiometric quantity of interest to this investigation is irradiance, which measures the energy absorbed over some constant solid angle, generally a hemisphere or sphere. Examples of photometric instruments which measure irradiance are shown in Figures 2.2 and 2.3. To obtain the irradiance we merely integrate the radiance using one of two definitions (scalar and plane) of irradiance.
First let us examine the spectral downward plane irradiance, Ed (Mobley,

1994),




Ed(x, t,A) E: L(x, t, 0, , A) I cos O sin OdOdo (W m-2sr-'nm-'). (1.17)
Z=0 f0
This is essentially the radiance integrated over all downward directions. If the instrument measuring this quantity was inverted, so that it collected all the photons traveling upward, it would measure spectral upward plane irradiance, E,5,
E,,(x, t, A) j L(x, t, 9, , A) I cos 01 sin OdOd (W m-2sr-nm-1). (1.18)
Note that identical light beams with different incident angles (0) will cause plane irradiances proportional to the cosine of the incident light angle. This is because a beam traveling at angle 0 sees an effective surface of AA cos 0. For this reason, instruments that measure spectral plane irradiance are often called cosine collectors or cosine meters6 Gallegos (1993b).
The other definition of irradiance is spectral scalar irradiance. It includes the contributions of all photons over a fixed solid angle equally, i.e., they are not weighted by the cosine of their direction of travel. The spectral downward scalar irradiance, denoted Eod7 is defined (Mobley, 1994) as
Eod(X,t,A ) = L(x,t,O,,A))sin OdOd(W m-2 sr- nm-1). (1.19)
f=0 f=0
Like plane irradiance scalar irradiance can also be used to measure upwelling photons. This quantity is called the upward scalar irradiance, E,, (Mobley, 1994),
E. (x,t,A) -- L(x,t,0,,A)sinOdOd (W m Sr nm1). (1.20)
f= 2F
5Eo can be twice Ed in turbid water, but Ko is within a few percent of Kd (Kirk, 1973, p. 121).
6The eager reader can skip ahead to Figure 2.2 for an example of an instrument which measures plane irradiance.
7Figure 2.3 shows an instrument which measures downward scalar irradiance.




If a collector is allowed to collect all of the photons traveling both upward and downward, it then measures spectral total scalar irradianice, E,,. This quantity is simply the sum of the upward scalar irradiance and the downward scalar irradiance.
I21r 0=7r
Eo (x, t, A) ] L(x, t,,$, A) sin OdOdq$(W m-2 sr -1nm'). (1.21)
1.4 Optical Properties
Now that we have quantified the fundamental aspects of the light field, we must relate these quantities to the medium through which they move, salt water. Oceanic waters, particularly those close to the coast, are a stew of dissolved substances and particles. These solutes and suspended particles are generally more optically important than the pure water in which they reside. The concentration and distribution of these substances can vary over a wide range, both spatially and temporally.
The way that optical properties interact with a medium and the substances within that medium, allow us to create two mutually exclusive classes, inherent and apparent. Inherent optical properties (IOP's) are properties that depend solely on the medium in which they are measured. Examples of IOP's include the index of refraction and the single-scattering albedo. Apparent optical properties (AOP's) are those properties that depend on the medium in which they are measured and the ambient light field. The diffuse attenuation coefficients are examples of commonly used AOP's. So, the index of refraction for a given sample should be the same regardless of light conditions. However, that same sample will have a different diffuse attenuation coefficient under different light conditions.
1.5 Literature Review
We can now review the literature to date that has investigated light attenuation. Relevant studies of related natural phenomena, such as seagrass growth and physical processes governing attenuation will also be considered in this section.




First, let us examine several studies have been published which relate the diffuse attenuation coefficients to the biological and chemical properties of coastal waters. Mcpherson and Miller (1987) have worked extensively on predicting attenuation coefficients as a function of water quality, particularly in Tampa Bay. Over a decade ago, they identified the importance of non-chlorophyll matter in attenuating visible light. They found that in Charlotte Harbor non-chlorophyll matter accounted for 72 % of the light attenuation (Mcpherson and Miller, 1987). Their more recent work has focused on the importance of incident light angle in attenuation (Miller and Mcpherson, 1995). Attenuation in central Florida can vary as much as 50 % due to changes in solar angle alone (Mcpherson and Miller, 1994). Both of these important factors will be examined in this thesis.
Kirk (1984) has searched for the exact relationship between optical properties and the angle of incident photons at the water surface. He has accomplished this through Monte Carlo simulations (Kirk, 1991).
Hogan (1983) has used simulated Rayleigh scattering, Mie scattering, and absorption as an alternative to Monte Carlo simulations in the St. Lucie Inlet. His results confirmed both a large difference between estuarine waters around the inlet and surrounding coastal (oceanic) waters and the strong dependence of transmittance on turbidity.
In the Indian River Lagoon, the two dominant seagrasses, Halodule wrightii and Syringodium filiforme only grow to the depth where 23 37 % of the surface irradiance penetrates (Kenworthy, 1992).
Gallegos and Correll (1990) have taken a physics based approach by separating IOP's and predicting attenuation coefficients. He found that an optical model based on separated absorption resulted in an error of 15 % or less for data collected in the southern portion of the Indian River Lagoon. (Gallegos and Kenworthy, 1996). Only




three calibration coefficients needed to be adjusted between data sets from the Rhode River and Hobe Sound in the Indian River Lagoon.
Gallegos (1994) modeled the spectral diffuse attenuation coefficient of downwelling irradiance in Chincoteague Bay and the Rhode River. His model was spectrally based, allowing calculation of both PAR and Photosynthetically Usable Radiation (PUR) PUR is the amount of radiation actually absorbed by photosynthetic organisms, which can be contrasted with the amount available for absorption, PAR. These two differ because sea grasses do not absorb all wavelengths of visible light equally, though they can absorb any visible light. There is evidence that PUR has real world significance. Macrophyte depth limits in lakes have been shown to be lower in lakes high in humic acids, because of selective absorption in the blue range (Jerlov, 1976). Because scattering and absorption combine nonlinearly to produce total attenuation, statistical regression equations cannot predict beyond the envelope of values observed. Scattering was not viewed as independent of wavelength, but rather as a sediment specific, i.e. site specific, function of wavelength and turbidity.
Gallegos (1993a) found that Indian River seagrasses require a long term (multiannual) average of 20 % of the surface sunlight. Because the bottom slopes gently in most of the lagoon, a slight increase in attenuation can make large benthic areas uninhabitable for seagrasses. Normalized attenuation (via a ship mounted deck cell) was used rather than actual irradiances for profiles. Attenuation was studied at two sites in the lagoon, the mouth of Taylor Creek and one near channel marker 198 of the Intracoastal Waterway, both in the southern end of the lagoon.
Freshwater discharge from Taylor Creek formed a color plume which significantly reduced available light to seagrass. At both stations, color and turbidity were found to be much more variable than chlorophyll. The exception to this was a freshwater chlorophyll plume that sometimes accompanied the color plume from Taylor Creek. Sediment specific coefficients for relating turbidity and/or TSS to detrital




absorption were determined for Hobe Sound in Indian River Lagoon. These coefficients will be used for initial model calibration of other data in the lagoon, and later compared with those for the fully calibrated models. Turbidity was found to be the predominant component of total absorption. The fact that color was present as a thin lense did not alter prediction significantly, despite the fact that it violated the assumption of a uniform water column. Lagoonal color was often 5 8 Pt. units8,) while the freshwater plume was 70 90 Pt. units. Gallegos and Correll (1990) first applied Kirk's model to very turbid waters in the Rhode River and Chesapeake Bay, which have photic depths 9 of 1 4 m. Because attenuation in estuaries is governed by a complex and poorly understood set of processes, empirical regressions and Monte Carlo simulations have been the only way to predict light attenuation from water quality. In this study, Gallegos and Correll (1990) used simultaneous attenuation and water quality measurements to extract absorption and scattering coefficients for use in later models. Typically, no light was detectable at the bottom of the water column so only surface water quality measurements were used'0. Scattering, b, was assumed to be wavelength invariant, and was found to be well correlated with the concentration of mineral suspended solids. The model predicted both the magnitude of attenuation over the water column and its slope well. Gallegos mentions that the direct measurement of ap and ad 11 might be easier and less error prone than measurement of the water quality parameters that predict them. The PARPS model developed in this study will be based on Gallegos's model.
The St. Johns River Water Management District (SJRWMD) has made a commitment to monitor PAR and water quality simultaneously in an attempt to
8Color was measured in this study using the Hazen method which compares water samples to known standards.
'Photic depth is the depth to which biologically usable light penetrates.
"I1n Chapter 4, it will be shown that the Indian River lagoon is not extremely turbid, i.e. no scattering whatsoever. The entire water column, not just the surface, is therefore relevant to studies of light attenuation.
"These optical coefficients are defined in Chapter 5




relate the two (Morris and Virnstein, 1993). They used data from 1990 to 1992, and found low correlations (r 2 < 0.45) for turbidity, total suspended solids, and chlorophyll as predictors of light attenuation across the lagoon.
When the SJRWMD divided the lagoon by the three counties containing it (Volusia, Brevard, and Indian River), they found no statistically significant temporal or spatial variability that could be attributed to water quality in any of the three counties. They concluded that low sampling frequency and different sampling techniques led to poor correlations between water quality and light attenuation. However, this study aims to determine if water quality can predict a significant amount of the variation in light attenuation or if there is any significant temporal or spatial variability within the lagoon.
Much of the work into light transmission in the coastal setting is driven by interest in submerged aquatic vegetation (SAV) and the relationship between light and SAy. Because of this, it is important to review literature relating SAV growth, particularly seagrass growth, and optical oceanography. The most relevant work to date was actually performed within the Indian River Lagoon itself.
Kenworthy (1993) has attempted to relate the attenuation of light to the maximum depth to which sea grasses can grow in the Indian River Lagoon. He calculated a broad range of percent surface light reaching the bottom (16 % 37 %) as the minimum for sea grass growth. He explains this apparent discrepancy in necessary light levels in terms of photosynthetically usable radiation (PUR)'2.
We also must examine research concerning the color of estuarine waters. Chapter 3 demonstrates that color is a very important factor in the attenuation of natural waters It is regarded as representative of the humic substances in the water which can significantly attenuate light in the visible (and thus PAR) wavelengths. 12PUR is defined on 19




Unfortunately, several different methods (Cuthbert and del Giorgio, 1992) exist for measuring color Traditionally, the Hazen method has been used. It entails the visual comparison of sample water to Pt-Co standard solutions. Cuthbert and del Giorgio (1992) has shown that these standard solutions do not accurately mimic the spectral properties of colored natural waters. Another method which has come into more prevalent use since the 70's, is the spectrophotometric determination of color. The absorbance of light by the sample is measured at one or more wavelengths in the PAR range. The most commonly used wavelength is 440 nm (Kirk, 1983, Gallegos, 1993a) and the absorbance is denoted as 9440. Even though both are still in use, Cuthbert and del Giorgio (1992) has developed a reliable conversion method. He found that true color measured in Pt, I' is given by,
true color (Pt, Mg= 18.216 X 9440 0.209. (1.22)
At Ft. Pierce Inlet, regression analysis was used to find relationships between water quality and attenuation at 445 n, 542 nm, and 630 nm. Scattering by suspended particulate material was the primary mechanism controlling the attenuation of dowuwelling irradiance at all three wavelengths. Cross sectional area of particles was found to be significant, demonstrating that suspended rather than dissolved materials dominate. The spectral distribution of the downwelling energy varied seasonally (i.e., over a span of several months) (Thompson et al., 1979).
Finally, it is worth noting that two fundamentally different types of sensors are commonly being used to measure PAR. The details of these two types of sensors, known as 27r and 47r sensors, will be explained in detail in Chapter 2. The reader should know at this point that two studies have reached very opposite conclusions about the differences between these sensors.
Moore and Goodman (1993) concluded that the two sensors are fundamentally identical for measurements of light attenuation. Gallegos (1993b) used simultaneous




measurements to show that a significant difference exists between attenuation calculated using a 2 7r versus a 4 7r sensor.He acknowledges that this conclusion is counter to the fact that the two are expected to be theoretically equal.
All of these previous studies provide an important foundation for the work presented herein. As we analyze data and reach conclusions, we will return to the literature reviewed in this section as a source of comparison. Now, let us turn our attention towards the objectives of this thesis.
1.6 Objectives and Hypotheses
The objectives of this study are:
1. Develop regression and numerical models of PAR attenuation in the Indian
River Lagoon;
2. Compare the two light attenuation models within the Indian River Lagoon;
3. Compare the IRL light attenuation models to those for other Florida estuaries;
and
4. Develop a strategy for coupling the IRL attenuation models with the IRL water
quality and seagrass models.
The hypotheses are as follows:
Hypothesis 1 Numerical modeling13 will provide more accurate prediction of PAR attenuation because it treats AOP's and IOP's separately. Hypothesis 2 Numerical modeling will provide more accurate hindcasting of PAR attenuation for the same reason.
13modeling based on integration of the spectrum of light penetrating the water column to a reference depth




Hypothesis 3 Nutrient loading of the Indian River Lagoon is primarily responsible for increases in light attenuation.
Hypothesis 4 The annual average PAR at depths greater than 2 m is too low to allow seagrass growth.
Hypothesis 5 Solar angle will have a significant effect on light attenuation. Hypothesis 6 Monte Carlo modeling of spectral slope in the spectral model will provide significantly different results.
Hypothesis 7 The same optical coefficients will be applicable to all data sets in the Indian River Lagoon
Hypothesis 8 Regression models for different water bodies will be different.
1.7 Organization
This study is organized in 6 chapters. Chapter 1 contains an introduction to the concepts of optical oceanography, a literature review of previous work focusing on light attenuation and seagrass's light needs, and a description of the hypotheses and objectives of this study. Chapter 2 explains the different methods for collecting light attenuation data. It also gives a brief overview of the three data sets used within this study. The next chapter, Chapter 3, gives an overview of the interaction between sea water constituents and sunlight, as well as discussing the three data sets in more detail. These chapters are designed to give the reader an overview of the work to date and an introduction of both the concepts of marine optics and marine chemistry.
Chapter 4 begins this thesis's data analysis. Statistical methods are applied to each data set to attempt to understand the data and explain the data. Chapter 5 continues to examine the three data sets. This chapter uses a modeling approach derived from physical equations, rather than the purely empirical approach of Chapter
4.




25
Finally, Chapter 6 attempts to conclude the study. Models from both Chapter 4 and Chapter 5 are compared to each other. In addition, the hypotheses and concepts presented in this chapter are examined again with this study's findings. Furthermore, results of this study are compared with those of previous modeling studies. The chapter concludes with a discussion of how this thesis can be applied and what future work can be undertaken to improve it.




CHAPTER 2
LIGHT DATA
This thesis uses three different studies as data sources. The data for each study was collected using somewhat different methods. However, each had the same objective, to measure a diffuse attenuation coefficient, specifically KPAR. The three studies are:
1. A short term study conducted by Dr. Chuck Gallegos of the Smithsonian
Environmental Research Center (SERC).
2. A two year monitoring program conducted by Dr. Dennis Hanisak at Harbor
Branch Oceanographic Institute (HBOI).
3. A long term, lagoon wide analysis conducted by Dr. Peter Sheng at the University of Florida (UF).
The sampling locations for these three studies are illustrated in in Figure 2.1. The SERC station is shown as a broad region rather than as specific points because exact locations were not reported. The methods for measuring light data in the studies above are described in the following sections of this chapter.
2.1 Measuring Kp,4
The most important difference between these studies lie in how they measure irradiance in the visible spectrum and how they gather water quality data (see Chapter 3). Light measurements in the photosynthetic range allow the calculation of KPAR. There is a long lasting debate (Jerlov, 1976, Mobley, 1994, Gallegos, 1993b) as to the differences between the two types of spectral diffuse attenuation coefficients




A
A tAk AA A A
AAA A

* SERC
. HBOI
SUF
grid

Figure 2.1: Sampling stations in the Indian River Lagoon

N
+E
S




collected in these three studies 1, downwelling plane irradiance (Kd) and downwelling scalar irradiance (Kod).
2.1.1 Plane Attenuation
The difference between these two diffuse attenuation coefficients,Kd and Kd, depends how we choose to define the irradiance being attenuated in the water column. The downwelling plane irradiance spectral diffuse attenuation coefficient (Kd) is defined as a function of plane irradiance (equation 1.17), so that it depends on the azimuthal angle of each photon. Since the diffuse attenuation coefficient decreases approximately exponentially with depth, we represent it with the following equation (Mobley, 1994),
p0
Ed(z,A) _= Ed(zo, A) expI -Kd(z',A)dz' (W m-2 nm-1). (2.1)
This diffuse attenuation coefficient has little dependence on depth in well mixed coastal waters, so we will assume here that it has no depth dependence, allowing us to eliminate the integral (Jerlov, 1976) 2,
Ed(z,A) = Ed(zo, A) exp(-Kd(A) x z) (W m-2 nm-1). (2.2)
2.1.2 2 7r Sensors
In order to measure plane irradiance, a flat light detector (also called a 2 7r sensor) is used (see Figure 2.2). The surface of the collector is equally sensitive to individual photons from any angle. However, as noted in Section 1.3.2, the collector as a unit does not detect photons from different angles equally well. Imagine a beam traveling perpendicular to the collector that completely illuminates the collector. If A A is the area of the detector, then the beam illuminates the entire area. For
'As we shall see, the differences between these two coefficients correspond to the two definitions of irradiance given on p. 15.
2We are in fact measuring the average spectral diffuse attenuation coefficient,!(Kd) but for our purpose we will assume Kd(A) and Kd(z, A) are equal.




the same light beam traveling at some angle 0' relative to the collecting surface, the collector has an effective area of AA cos 0. Because the light beam generates a response proportional to the cosine of the incident light these instruments are also referred to as cosine collectors.
Diffuser
_Filter
~Detector
Figure 2.2: 2 7r Sensor
2.1.3 Scalar Attenuation
The downwelling scalar irradiance spectral diffuse attenuation coefficient (Kod) is defined analogously to Kd. The only difference is the choice of the scalar irradiance equation (equation 1.19) over plane irradiance to define the irradiance in the water column4:
Eod(z, A) = Eod(zo, A) exp (-Kd(A) x z) (W m-2 rn-1). (2.3)
2.1.4 4 7r Sensors
4 7r sensors detect light from different directions with equal sensitivity. This means that the radiance it measures is scalar irradiance. The spherical shape of the instrument allows light to be collected from any direction (see Figure 2.3). It is
3When the light source of interest is the sun, the variable I'o denotes the cos0
4Note that we have again assumed that the attenuation coefficient is invariant of depth.




now obvious how the sensors received their names, while the 2 ir sensor only collects energy over a range of 2 7r in one polar direction, the 4 7r sensors collects energy over
2 7r in both polar directions for a total of 4 7r.

Diffuser Opaque Shield

--J Detector
Figure 2.3: 4 7r Sensor

2.2 Collection of Light Data

2.2.1 SERC Study
In the SERC study, Gallegos (1993b) measured profiles of downwelling spectral irradiance using a cosine (27r) corrected submersible radiometer. Interference filters were used to divide the visible spectrum into 5 nm increments. Downwelling PAR was measured with a Licor 192B underwater quantum sensor (which is a 27r sensor). Each channel of the spectral radiometer was normalized to readings from a deck cell on board the sampling vessel (Gallegos, 1993a). These light measurements were concurrent with and at the same frequency as the water quality measurements to be described in the next chapter.




2.2.2 HBOI Study
Hanisak used 47 and 27 Licor sensors to measure downwelling plane attenuation and integrated scalar attenuation. This study again used concurrent light and water quality sampling, but at different frequencies. Light attenuation was measured hourly, while water quality parameters were often sampled at only once a week. Detailed procedures for the HBOI study are listed in their Florida Department of Environmental Protection (FDEP) Quality Assurance and Quality Control (QAQC) manual.
2.2.3 UF Study
In the UF study, profiles of total downwelling irradiance were measured using three 47- submersible Licor sensors. One sensor was deployed just below the surface, one at 50 % of depth, and one at 80 % of depth. The average light attenuation for the water column was calculated based on the attenuation from the surface to 80 % of depth. All of these measurements were synoptic in nature. They and the water collection that accompanied were always instantaneous measurements at roughly a monthly frequency. These collection methods are also detailed in an FDEP QAQC prepared by the University of Florida and the SJRWMD.
2.3 Summary
Table 2.1: Summary of light data collection Data Set 47 sensor 27 sensor concurrent single frequency
SERC NO YES YES YES
HBOI NO YES YES NO
UF YES NO YES YES
Table 2.1 summarizes the differences and similarities between data sets. Because the HBOI study does not measure water quality and light data at the same frequency, we might expect to see some differences between it and the other data




32
sets. Additionally, due to quality assurance worries data collected in the first three weeks of November was removed from the HBOI study.




CHAPTER 3
WATER QUALITY DATA
3.1 Measuring Water Qual ty
Because this report examines the relationship between optical characteristics and the water in which light is being transmitted, measurements of water quality are just as important as measurements of light attenuation. Water quality can be defined as a measure of the water and all of its contents. Before detailing how this study collected and measured water to obtain its water quality, it is important to understand how the makeup of sea water affects light transmission.
3.2 Water Quality Constituents
Estuarine waters, such as those of the Indian River Lagoon, contain a continuous size distribution of particles. These particles range from the size of water molecules (0.1 nm) to the size of sediment 106 times larger than water (800 ym) (Henderson, 1997) all the way to organisms, such as manatees, 109 larger (I m). Even though we can then think of water as completely composed of these particles, constituents are traditionally divided into particulate and dissolved components.
This division is a fairly empirical one. Water samples are passed through a filter with a pore size of 400 nm. Anything that remains in the aliquot is termed dissolved, and the material on the filter are particulates. This traditional distinguishing line lies at the shortest wavelength of the visible spectrum (400 nm). So, our dividing line falls exactly at the limit of optical microscopy's ability to resolve particles.
3.2.1 Dissolved Constituents
Far offshore, oceanic water consists of pure water plus a very consistent relative amount of dissolved salts. These salts average 35 ppt by weight in most of the ocean.




In enclosed coastal areas, dissolved salts can rise above this average from evaporation or fall below it due to freshwater input. These salts have a negligible affect on attenuation in the visible wavelengths, and hence the photosynthetic wavelengths (Mobley, 1994).
In addition to salts, sea water also contains dissolved organic materials. Most of these organic compounds are derived from the decay of terrestrial material and consist of humic and fulvic acids (Kirk, 1983). These dissolved organic constituents are often referred to as yellow matter or gelbstoff. This is because they are generally brown to yellow brown in color and give the water a similar hue. In estuaries heavily influenced by river runoff, gelbstoff can dominate the absorption at the blue end of the spectrum (Mobley, 1994, Bricaurd et al., 1981).
3.2.2 Particulate Constituents
Once particulate material is removed from the filter and quantified, it is often further subdivided into two subclasses; biological and physical. These subclasses are based on the origin of the particles. Biological, also called organic, particles are created as living organisms grow, reproduce, and die.
Mobley (1994) has characterized organic particles into the following subdivisions:
Virii occur in natural waters in concentrations of 1012 to 1015 particles m-3 These
particles are much smaller than the smallest wavelength of visible light. It is unlikely that virii are significant absorbers, but they may influence backscatter. Note that although virii are distinct particles, they are dissolved matter
according to the traditional size definition.
Colloids are amorphous uncrystallizable amalgations of liquid found in the water
column. They are only significant as backscatters.




Bacteria range in size from 0.2iim to 1.0/m and occur in concentrations of
1012m-3. They are significant causes of attenuation only in clear oceanic waters. Phytoplankton are a very diverse set of microscopic marine plants. Individual cells
range in size from lpm to 200pm, and some colonial species form larger clusters of individual cells. Phytoplankton are often seen as the dominant particle responsible for determining the optical properties of oceanic water (Mobley, 1994). Because of their large size (much larger than wavelengths of visible light), they contribute significantly to scattering, and are very effective absorbers of
light due to their photosynthetic pigments.
Organic Detritus is produced by both the breakup of dead plankton and the waste
products of living plankton. Any pigments in these particles are quickly oxidized, changing their absorption characteristics from those of living phytoplankton.
Large Particles are an amalgation of particles larger than 100 1m. This includes
zooplankton and marine snow. The optical effects of these particles is largely unquantified because of the difficulty associated with such fragile, highly variable particles.
Physical, also called inorganic, particles are primarily the result of weathering of terrestrial rocks and sediments. These particles are then washed by rain or blown by wind into the marine environment. Once in a body of water, inorganic particles may settle and then be resuspended by bottom currents many times. The particles are removed by settling, aggregating, or dissolving. Inorganic particles tend to consist of finely ground quartz, clay, and metal oxides. These particles are the major cause of both temporal and spatial variability in absorption and scattering in more turbid coastal waters(Mobley, 1994). This can be contrasted with the importance of organic particles, such as phytoplankton, in clearer, oceanic waters.




3.3 Collection of Water Quality Data
Just as each of the monitoring studies measured light attenuation in slightly different ways, each study also gathered water quality data somewhat differently. All of water quality data, however, was collected at the same physical locations as the light data in the previous chapter'.
3.3.1 SERC Study
In the SERC study, data were collected over several days in December of 1992, March of 1993, and April of 1993. As such, there was no set frequency (monthly, weekly, etc.) to the sampling regime, but instantaneous samples were obtained. These water samples were collected according to Table 3.1.
Table 3.1: Water quality parameters collected in SERC study
Variable Collection Method Units Symbol
organic carbon (total) Niskin bottle mg/L TOC
organic carbon (particulate) Niskin bottle mg/L POC
organic carbon (dissolved) Niskin bottle mg/L DOC
phosphorus (total) Niskin bottle mg/L TP
pH Niskin bottle units pH
color Niskin bottle Pt. color
total suspended solids Niskin bottle mg/L TSS
mineral suspended solids Niskin bottle mg/L MSS
turbidity Niskin bottle NTU turb
chlorophyll a Niskin bottle pg/L chl
salinity Beckman RS 5-3 ppt sal
depth m depth
time HHMM time
salinity data was collected, but not released
Vertical salinity profiles were measured with a Beckman RS 5-3 induction salinometer. The vertically integrated water samples were collected in a 2 liter Labline Teflon bottle (a variation of the ubiquitous Niskin bottle). The bottle was lowered slowly and retrieved in less time than required to fill the bottle. Duplicate casts were
'Please refer again to Figure 2.1 for sampling locations.




made at one station per day. Field cleaning consisted of a preliminary sample for rinsing. The laboratory methods used to analyze the water samples can be found in (Gallegos, 1993a) and to a Research Quality Assurance Plan (RQAP) submitted to the FDEP.
3.3.2 HBOI Study
The HBOI data used in this study is divided into two portions. Year 1 data was collected from November of 1993 until November of 1994. Year 2 data picked up in December of 1994 and continued through November of 1995. Unlike the other studies, sampling of water quality variables was conducted at a weekly frequency.
Table 3.2: Water quality parameters collected in HBOI study
Variable Collection Method Units Symbol
temperature 'C temp
salinity Niskin bottle ppt salinity
nitrogen (total) Niskin bottle mg/L TN
nitrogen (soluble) Niskin bottle mg/L SN
phosphorus (total) Niskin bottle mg/L TP
phosphorus (soluble) Niskin bottle mg/L SP
color Niskin bottle Pt. color
total suspended solids Niskin bottle mg/L TSS
inorganic suspended solids Niskin bottle mg/L ISS organic suspended solids Niskin bottle mg/L OSS
turbidity Niskin bottle NTU turb
silicate Niskin bottle mg/L S
chlorophyll a Niskin bottle 1g/L chl
Table 3.2 shows the parameters collected, method of collection, and units used. Laboratory techniques used can be found in HBOI's FDEP approved Quality Assurance and Quality Control (QAQC) plan. It is important to note again that this water quality sampling was conducted at a much lower frequency than the light attenuation measurements (weekly versus daily). Light data that was taken more frequently than water quality data had to be discarded since the two types of data were not concurrent.




3.3.3 UF Study
The University of Florida study collected data through 12 synoptic measurements (Sheng, 1997, Melanson, 1997), so called because they gave a snapshot of the lagoon on a given day. These measurements began in April 1997 and were conducted approximately monthly. The sampling was completed in May of 1998. Only data from the first six sampling trips were available for this study.
Two different methods were used for sampling at each station. HydrolabTM data sondes were used to collect several parameters in situ. Water samples were also gathered at two depths using modified Niskin bottles (Melanson, 1997). These samples were then transported to a laboratory where they were examined for various parameters. Table 3.3 summarizes both the parameters measured and the method of collection.




Table 3.3: Water quality parameters collected in UF study

Variable Collection Method Units Symbol

depth
temperature conductivity salinity
dissolved oxygen pH
nitrogen (total) nitrogen (dissolved) nitrates and nitrites ammonia particulate organic nitrogen phosphorus (total) phosphorus (dissolved) ortho-phosphate particulate organic phosphorus total organic carbon color
chlorophyll dissolved silica total suspended solids location time

Data Sonde Data Sonde Data Sonde Data Sonde Data Sonde Data Sonde Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle Niskin bottle GPS
GPS

ft.
0C
E Cm
ppt
mg/L units mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L mg/L
Pt.
mg/m3
mg/L mg/L
lat/long
hours:minutes

depth temp cond salinity DO pH TN DN NO,
NH PON TP DP OP POP TOC color chl DS
TSS UTM time

location converted to UTM




CHAPTER 4
STATISTICAL MODEL
4.1 Data Set Characterization
Data from each study was first characterized using simple statistics, including
the mean, standard deviation, number of observations, and minimum and maximum
values. This was accomplished using the SAS version 6.11 statistical package of
software for UNIX TM (SAS Institute Inc., 1990).
These statistical characterizations are shown in in Table 4.1 for the Smithsonian Environmental Research Center. The values for the SERC, Harbor Branch
study and University of Florida studies are shown in Table 4.1, Table 4.2 and Table
4.3, and Table 4.4, respectively. These values can be used to compare the baseline
conditions for the three studies.
Table 4.1: Simple statistics for SERC study
Parameter Units N Mean Std Deviation Min Max depth m 78 2.04 1.90 0.10 8.20
ILO 69 0.87 0.08 0.69 1.00
color Pt. 85 20.55 23.51 0 94.00
chl pg/L 95 5.55 6.44 -0.12 32.14
turb NTU 91 2.94 1.70 0.04 6.40
TSS mg/L 95 11.90 8.46 0.13 45.80
MSS mg/L 95 8.79 6.94 -0.65 37.90
pH units 84 7.72 0.70 5.19 8.20
TOC mg/L 85 3.87 3.80 -0.68 16.19
DOC mg/L 85 3.10 3.59 -1.20 14.87
POC mg/L 85 0.78 0.56 -0.40 2.25
EXT40o 93 1.33 0.71 -0.04 3.05
KPAR m-1 59 1.28 0.44 0.55 2.47




Table 4.2: Simple statistics for HBOI study (Year 1)
Parameter Units N Mean Std Deviation Min Max KPAR m-1 296 1.97 1.44 0.04 6.89
temp C 296 26.44 4.79 13.80 34.90
salinity ppt 296 24.06 6.62 4.00 36.50
color Pt. 296 1.93 2.18 0.16 12.63
turb NTU 296 7.86 7.81 1.02 60.60
TSS mg/L 295 61.27 35.14 11.50 312.00
ISS mg/L 267 40.55 29.16 11.00 286.00
OSS mg/L 267 20.40 9.04 3.25 66.00
TN mg/L 296 0.74 0.42 0.01 2.40
SN mg/L 296 0.65 0.38 0.01 2.22
TP mg/L 296 0.07 0.04 0 0.19
SP mg/L 296 0.03 0.03 0 0.16
S mg/L 296 3.86 3.14 0 15.80
chl ,ag/L 296 14.07 11.60 0.95 96.22

4.2 Principal Component Analysis (PCA)
Principal component analysis (PCA) serves to derive the smallest number of linear combinations (referred to as principal components) from a set of variables that retains the most information from the original variables (SAS Institute Inc., 1990). By finding the smallest linear combination of variables, one can uncover linear dependencies within the variables themselves (Rao, 1964). This allows one to estimate how many truly orthogonal dimensions a data set contains. In addition to uncovering information about the n-space structure of a data set, the principal components (also called roots) themselves can be used in place of the original variables if desired.
PCA begins by representing one's data set as a matrix D.
dil d12 ...
D = d21 d22 ... (4.1)
Each row, d[i], represents one of m samples or observations. Every column, d[j], represents one of n variables.




Table 4.3: Simple statistics for HBOI study (Year 2)

Parameter Units N Mean Std Deviation Min Max KPAR rn-1 503 1.78 1.12 0.09 6.59
temp oC 503 25.84 5.03 13.50 34.40
salinity ppt 503 21.15 7.69 0.90 37.00
color Pt. 503 1.97 2.38 0.34 16.37
turb NTU 503 8.17 5.74 1.34 47.60
TSS mg/L 503 69.73 24.51 24.00 159.30
ISS mg/L 503 43.18 17.95 13.00 104.00
OSS mg/L 503 26.59 8.80 8.00 84.50
TN mg/L 503 0.62 0.29 0.01 2.14
SN mg/L 503 0.51 0.26 0 1.53
TP mg/L 503 0.07 0.04 0 0.22
SP mg/L 503 0.04 0.03 0 0.14
S mg/L 503 4.45 2.68 0 13.74
chl pg/L 503 16.29 11.00 3.29 79.09
The n x n covariance matrix C is then calculated (Jackson, 1991), where

c[i,j] = cov(d[i],d[j]).

(4.2)

Next, the n eigenvectors', e[1] ... e[n] are calculated along with the corresponding n scalar eigenvalues2 A[1]...A[n] (Paige and Swift, 1961, Jolliffe, 1986), where

(4.3)

Ce[i] = A[i]e[i],

and

IC -AI = 0.

(4.4)

The eigenvectors can be determined by solving the following two equations (Jackson, 1991).
'Eigenvectors are also known as characteristic or latent vectors, but the German terminology is most common among engineers.
2Similarly, eigenvalues are also referred to as characteristic or latent roots.




Table 4.4: Simple statistics for UF study

(C A[i]i)t[i] = 0.

(4.5)

t[i] (4.6)
ei~i]t
Each eigenvector corresponds to the orthogonal dimension of one principal component. The contribution or importance of this component corresponds to the magnitude of A[i]. The trick then becomes to choose the right subset of e[1] ... e[n], to represent the data with p < n variables. Clearly, the larger p is, the better the PCA will account for data variability, but the smaller p is, the fewer variables required (Dunteman, 1989).
Many numerical significance tests exist to attempt to determine how many principal components should be included for a given data set (Jackson, 1991). Unfortunately, reduction of a data set through PCA requires knowledge about the variables and their relationships that only a scientist-not an algorithm-can currently provide.

Parameter Units N Mean Std Deviation Min Max
UTM m 270 3142083.02 27799.05 3089767.98 3180992.34
Julian Day 270 134.50 27.94 94.00 176.00
temp C 261 25.91 2.47 22.02 31.90
salinity ppt 261 25.26 6.50 14.65 40.45
DO mg/L 249 5.88 0.89 3.17 7.88
pH units 230 8.00 0.45 6.90 10.80
TP mg/L 264 0.05 0.02 0.02 0.20
TN mg/L 264 1.39 0.26 0.60 2.16
TSS mg/L 264 7.96 6.45 1.70 55.00
color mg/L 264 14.3712 3.18 5.00 26.00
DS mg/L 264 1.35 0.92 0.06 4.95
TOC mg/L 264 34.81 6.96 9.93 47.91
chl mg/m3 263 4.71 2.60 0.46 20.16
KPAR m-1 230 2.32 1.16 0.35 6.34




For this reason we will use the graphical SCREE3 method (Cattell, 1966). This method plots A[i] on the y axis and i on the x axis. By looking for changes in slope or other interesting phenomena one can decide how many principal components to retain. Additionally, the proportion of total variability explained by each eigenvector will also be examined to make decisions on the number of orthogonal dimensions present in each data set.
The next 3 sections show the results of principal component analysis for the three data sets within this study. Listed are the eigenvalue of each component, the difference between successive eigenvalues, the proportion of variation represented, and the cumulative proportion of the variation represented. A SCREE plot is also shown for each data set.
4.2.1 SERC PCA
Table 4.5: PCA for SERC data set
1 2 3 4 5
Eigenvalue 5.6367 3.8511 1.6710 1.3161 0.7147 Difference 1.7856 2.1801 0.3548 0.6014 0.0705 Proportion 0.3758 0.2567 0.1114 0.0877 0.0476 Cumulative 0.3758 0.6325 0.7439 0.8317 0.8793
6 7 8 9 10
Eigenvalue 0.6443 0.3813 0.2751 0.1651 0.1447 Difference 0.2629 0.1062 0.1100 0.0204 0.0496 Proportion 0.0430 0.0254 0.0183 0.0110 0.0096 Cumulative 0.9223 0.9477 0.9660 0.9770 0.9867 11 12 13 14 15
Eigenvalue 0.0951 0.0775 0.0261 0.0011 0.0000
Difference 0.0176 0.0514 0.0250 0.0011
Proportion 0.0063 0.0052 0.0017 0.0001 0.0000 Cumulative 0.9930 0.9982 0.9999 1.0000 1.0000
3The name SCREE comes from the debris which slides off an oceanside cliff as tree roots are exposed by weathering. Scree is the rubble at the bottom of a cliff, so that one is retaining good roots and discarding the scree.




The SCREE plot in figure 4.1 shows a sharp decline in eigenvalue after the second principal component. Examining Table 4.5 shows that these first two principal components explain 63 % of the variance in the SERC data set. The proportion that each root contributes drops significantly4 beyond the fourth root. This corresponds to the second large drop in eigenvalue on the SCREE plot. Both Table 4.5 and Figure 4.1 show very little influence for the fifth through fifteenth components. In fact, the final 5 roots contribute roughly 1 % of the cumulative variance for this data set.
Considering the observations made above, we can now guess as to the true dimensionality of this data set. It is most likely that there are between 2 and 4 truly orthogonal variables in this data set. Later analyses5 can be compared to this number as a second check on our PCA methods.
6i PCA o
5
4
0
2
0
0
0
2o
0o
0o
0o
0 I~ 0 i
0 2 4 6 8 10 12 14 16
root
Figure 4.1: SCREE plot for SERC data set




Table 4.6: PCA for HBOI Year 1 data set
1 2 3 4 5
Eigenvalue 4.4716 4.2315 1.9044 1.2621 0.7573 Difference 0.2401 2.3270 0.6424 0.5047 0.2188 Proportion 0.2981 0.2821 0.1270 0.0841 0.0505 Cumulative 0.2981 0.5802 0.7072 0.7913 0.8418
6 7 8 9 10
Eigenvalue 0.5385 0.4414 0.4230 0.2977 0.2523 Difference 0.0971 0.0184 0.1253 0.0454 0.1050 Proportion 0.0359 0.0294 0.0282 0.0198 0.0168 Cumulative 0.8777 0.9071 0.9353 0.9552 0.9720 11 12 13 14 15
Eigenvalue 0.1472 0.1255 0.0988 0.0487 0.0000
Difference 0.0217 0.0268 0.0501 0.0487
Proportion 0.0098 0.0084 0.0066 0.0032 0.0000 Cumulative 0.9818 0.9902 0.9968 1.0000 1.0000
4.2.2 HBOI PCA (Year 1)
Table 4.6 displays a similar trend to the one found in Table 4.5. By the fifth eigenvector, the individual contribution of that component has declined to less than 5 %. Likewise, figure 4.2 shows a very noticeable drop in eigenvalue beyond the second root. There is another change in the slope of the SCREE plot beyond the fourth root, but it is much smaller in magnitude.
Here again, the last few eigenvalues shown in Table 4.6 are relatively small. These observations lead us to a conclusion very similar to the one we reached for the SERC data set. It appears that there are between 2 and 4 truly orthogonal variables in this data set. The large difference beyond the second root suggests that these might be dimensions derived from very different parts of the environment. These two
'Each root contributes less than 5 % after the fourth.
5In particular, multiple regression tests will be sensitive to the number of principal components.




sources might well correspond to the system itself and instrumentation and/or other testing and measurement

to components representing variability (Jackson, 1991).

45

0 2 4 6 8 10 12 14 16 root
Figure 4.2: SCREE plot for HBOI Year 1 data set

4.2.3 HBOI PCA (Year 2)

Table 4.7 displays a similar trend to the one found in Table 4.6. By the fifth eigenvector, the individual contribution of that component has again declined to nearly 5 %. However, figure 4.3 does not show as noticeable a decrease in eigenvalue beyond the second root. Instead the curve is much smoother, but still shows a significant decrease by the fourth root.
Here again, the last few eigenvalues shown in Table 4.7 are relatively small. Despite, the differences between SCREE plots of first and second year data, it appears that there are again between 2 and 4 truly orthogonal variables in this data set. It is interesting to note that we do not, however, find any evidence for a second source of variance beyond the second root as we did in Table 4.6.

0 PCA
0 o
0 o 0 0 o
II I I 0




Table 4.7: PCA for HBOJ Year 2 data set
1 2 3 4 5
Eigenvalue 4.9087 3.6263 2.6810 1.8435 1.3315 Difference 1.2824 0.9453 0.8375 0.5121 0.3637 Proportion 0.2584 0.1909 0.1411 0.0970 0.0701 Cumulative 0.2584 0.4492 0.5903 0.6873 0.7574
6 7 8 9 10
Bigenvalue 0.9677 0.8272 0.6772 0.4350 0.3911 Difference 0.1405 0.1500 .0.2422 0.0438 0.0664 Proportion 0.0509 0.0435 0.0356 0.0229 0.0206 Cumulative 0.8084 0.8519 0.8875 0.9104 0.9310 11 12 13 14 15
Eigenvalue 0.3248 0.3020 0.2414 0.1635 0.1237 Difference 0.0228 0.0605 0.0779 0.0398 0.0441 Proportion 0.0171 0.0159 0.0127 0.0086 0.0065 Cumulative 0.9481 0.9640 0.9767 0.9853 1.0000
4.2.4 UF PCA
Figure 4.4 shows a much smoother overall curvature for the SCREE plot of the UF data set. There are, however, noticeable breaks at 3 and 5 components, respectively. Table 4.8 likewise reaffirms that this data orthogonally occupies at most 5-space. The first 5 roots account for 71 % of the variance, while the last 5 account for only 4 %. We again should expect to see at most 5 and more likely 3 variables contributing significantly to this data set.
Nonetheless, this data set shows more principal components than the SERC and HBOJ data sets. The majority of the variance is still confined to approximately 3 components, but there are identifiable contributions all the way to component 15, something not found in the other data sets. It is possible that this again corresponds to components from two sources. If that is the case than the UF data set might be showing more response to sampling error and instrument fluctuations as a second source of error. We can return to this point when we perform later multiple variable




49
PCA
4.5
4
3.5
3
Caa
S 2.5
0)
2
1.5
Ia
0.5
0 2 4 6 8 10 12 14 16
root
Figure 4.3: SCREE plot for HBOJ Year 2 data set
analyses. If they show a contribution close to 4 or 5 components than we would expect that we are seeing a fundamental difference between the UF data set and the SERC and HBOI data sets. Otherwise, we can attribute the additional components to our earlier explanation of a response to a second system than the one being measured.
4.3 Pearson Correlation Coefficients
Once each data set had been characterized with simple statistics, it was next analyzed using correlation coefficients. Every variable was correlated with every other variable and the Pearson correlation coefficient, r, calculated. The Pearson's correlation coefficient varies between -1 and 1. A correlation of 0 indicates that neither of the two variables can be predicted from the other by using a linear equation. An r of 1 indicates that one variable can be predicted perfectly by a positive linear function of the other. If the sign of r changes to -r, then the variables still predict one another without error, but with a negative linear function. Pearson's correlation coefficient is strictly defined by the following equation (Weimer, 1987),




Table 4.8: PCA for UF data set
1 2 3 4 5
Eigenvalue 3.1103 2.4372 2.2527 1.5839 1.2951
Difference 0.6731 0.1846 0.6688 0.2887 0.4161 Proportion 0.2074 0.1625 0.1502 0.1056 0.0863 Cumulative 0.2074 0.3698 0.5200 0.6256 0.7119
6 7 8 9 10
Eigenvalue 0.8791 0.8247 0.7506 0.5112 0.4525 Difference 0.0544 0.0741 0.2394 0.0587 0.1380 Proportion 0.0586 0.0550 0.0500 0.0341 0.0302 Cumulative 0.7706 0.8255 0.8756 0.9097 0.9398 11 12 13 14 15
Eigenvalue 0.3145 0.2847 0.1855 0.0672 0.0507
Difference 0.0298 0.0992 0.1184 0.0164
Proportion 0.0210 0.0190 0.0124 0.0045 0.0034 Cumulative 0.9608 0.9798 0.9921 0.9966 1.0000
. x_ y (4.7)
Oax O'yj
In equation 4.7, x and y are the two variables being correlated, axy is the covariance of x and y, ax is the standard deviation of x, and aGy is the standard deviation of y. When two variables are independent aoy = 0 and r = 0.6
These correlation coefficients are listed in Table 4.9 and Table 4.10 for the SERC study. Table 4.11 and Table 4.12 lists the correlation coefficients for each parameter in the HBOI study, and Table 4.15 and Table 4.16 list the correlation coefficients for the University of Florida study.
4.4 Single Variable Regression
Having examined each parameter for correlations and distribution in each data set, it was possible to construct statistical models that explain the dependence of light on other parameters from each data set.
6The reverse, axy = 0 therefore two variables are independent does not hold true.




3.5 I
PCA o
3 2.5
0.5
00
01 22 0 1 4 1
roo
Fiur 4.:SREpo o0Fdt e
First 1.5 prmtrta hwe o esaitclad elwrdsgiiat
coreatonwthlihtateuaio asusd s h ideenet arabeina iml
linarreresin.Vaialeswee ls cosn f om knwnphsialreatonhi
exite btwenth praete ad igt ttnutin e~g cloopyl i kow t
to 2qato 4. an 8qu10io2 4116
Frle s t e parameyptei tha showced sn omelain a statistical adra ol significant. Correlation with lonihte atenuatio weas useld sgiane indis eedaricraleion aoefsiple existedlbewee the pramelterha and ligtsaenation (e tog.do chcalohllienont
195,anT nadutde2o coefficient of determination was tericalculul ote qaefPatedn' acordain toefieut.is seraon 4.9te and equnoation 4.10., 187




Table 4.9: Correlation between parameters in SERC study
depth time p0 color chl turb TSS depth 1.00 0.07 -0.06 -0.47 0.04 0.19 0.37 time 0.07 1.00 -0.28 0.03 -0.17 0.12 0.01
Po -0.06 -0.28 1.00 0.13 0.37 0.54 0.46
color -0.47 0.03 0.13 1.00 0.06 -0.05 -0.18 chl 0.04 -0.17 0.37 0.06 1.00 0.34 0.27
turb 0.19 0.12 0.54 -0.05 0.34 1.00 0.86
TSS 0.37 0.01 0.46 -0.18 0.27 0.86 1.00
MSS 0.39 0.02 0.40 -0.20 0.20 0.84 1.00
pH 0.21 0.01 0.01 0.13 0.36 0.63 0.50
TOC -0.44 0.07 0.07 0.97 0.09 -0.07 -0.18
DOC -0.43 0.08 0.03 0.96 -0.01 -0.14 -0.24
POC -0.23 -0.02 0.35 0.37 0.71 0.45 0.31
EXT400 -0.19 0.05 0.51 0.36 0.45 0.77 0.62 KPAR -0.48 -0.01 0.28 0.81 0.20 0.01 -0.12

F(df1,df2) SSR (4.8)
The degrees of freedom of the regression is dfl, df2 is the degrees of freedom of random error, SSR is the sum of square for the regression, and s,2 is the residual variance and provides an estimate of the error variance. If the two sums of squares are equivalent, F should be 1 or less. As the regression accounts for much more variance than random error, the F statistic grows large and allows us to reject the null hypothesis, H0, that the model does not predict the dependent variable (KPAR in our case).
n-i
adjusted r 2 = 1 ( l-,' ) (4.9)
"n l1
The number of observations in equation 4.9 is n, I is the number of parameters including the intercept (where 1 = 2 for a single variable regression), i = 1, again for this type of regression, and r2 is defined in equation 4.10.




Table 4.10: Additional correlation between parameters in SERC study
MSS pH TOC DOC POC EXT4oo KPAR
depth 0.39 0.21 -0.44 -0.43 -0.23 -0.19 -0.48
time 0.02 0.01 0.07 0.08 -0.02 0.05 -0.01
P0 0.40 0.01 0.07 0.03 0.35 0.51 0.28
color 0.20 0.13 1.00 0.96 0.37 0.36 0.81 chl 0.20 0.36 0.09 -0.01 0.71 0.45 0.20
turb 0.84 0.63 -0.07 -0.14 0.45 0.77 0.01
TSS 1.00 0.50 -0.18 -0.24 0.31 0.62 -0.12
MSS 1.00 0.47 -0.20 -0.24 0.25 0.58 -0.16
pH 0.47 1.00 0.11 0.05 0.44 0.60 -0.60
TOC -0.20 0.11 1.00 0.99 0.42 0.36 0.79
DOC -0.24 0.05 1.00 1.00 0.30 0.28 0.77
POC 0.25 0.44 0.42 0.30 1.00 0.71 0.39
EXT4oo 0.58 0.60 0.36 0.28 0.71 1.00 0.59 KPAR -0.16 -0.60 0.79 0.77 0.39 0.59 1.00

2 SSE (4.10)
SSE is the sum of squares due to errors and SST is is the total sum of squares corrected for the mean of the dependent variable (KPAR).
4.4.1 SERC Single Variable Regressions
For the SERC data set, depth, pH, TOC, DOC, Po, and chlorophyll, and color were examined in detail as single variable regression models.
First, let us examine depth, in meters. Equation 4.11 and Figure 4.5 display the relationship between depth and KPAR. The total water depth of the sampling site does have an appreciable affect on water clarity. Increasing water depth actually lowers KPAR. This is demonstrated by F(1, 52) = 15.14 with a p value of 0.0003 and an adjusted r2 = 0.21.
This decrease of KPAR could be related to the stratification of color (the primary light attenuator in the SERC data set). Most of the color observed was terrestrial in origin and occurred as a lense on the surface of the water. Light in deeper




Table 4.11: Correlation between parameters in HBOI (Year 1) study KPAR temp salinity color turb TSS ISS KPAR 1.00 0.05 -0.21 0.29 0.60 0.46 0.49
temp 0.05 1.00 -0.18 0.29 -0.24 -0.28 -0.36
salinity -0.21 0.18 1.00 -0.74 0.02 0.32 0.29 color 0.29 0.29 -0.74 1.00 -0.02 -0.29 -0.26
turb 0.59 -0.24 0.02 -0.02 1.00 0.83 0.83
TSS 0.46 -0.28 0.32 -0.29 0.83 1.00 0.98
ISS 0.49 -0.36 0.29 -0.26 0.83 0.98 1.00
OSS 0.42 -0.03 0.15 -0.15 0.73 0.75 0.60
TN -0.10 -0.00 -0.29 -0.11 -0.10 -0.11 -0.10
SN -0.11 -0.03 -0.27 0.13 -0.15 -0.17 -0.14
TP 0.47 0.18 -0.58 0.52 0.54 0.28 0.29
SP 0.11 0.33 -0.73 0.68 -0.00 -0.25 0.29
S 0.27 0.33 -0.70 0.48 0.13 -0.15 -0.17
chl 0.34 0.03 -0.32 -0.10 0.56 0.40 0.34
waters traveled through proportionally less colored water and the overall KPAR for the water column might therefore be lower.
pH, measured as log [molarity], has a relatively large (r2 = 0.38) determination coefficient with light attenuation. Its variation with KPAR is displayed in equation 4.12 and is shown graphically in Figure 4.6.
Statistical analysis of equation 4.12 yielded an F(1, 52) = 33.07 with a p value of 0.0001 and an adjusted r2 = 0.38. This is a somewhat puzzling result since pH has no known direct relationship with light attenuation. It is most likely that pH is controlling or being controlled by other factors, such as freshwater inflow, that are in turn directly influencing KPAR.
Color is clearly the best predictor of light attenuation for the SERC data set, as shown in Gallegos (1993a). Color, when measured in Pt. units, predicts KPAR as shown in equation 4.13. Equation 4.13 results in F(1, 52) = 123.68 with a significant p value of 0.0002 and an adjusted r2 = 0.70. The strong relationship between color and KPAR can be seen in Figure 4.7.




2.6
2.4
2.2
2 1.8 1.6 v 1.4
1.2
1 0.8
0.6
0.4
0
Figure

4.5:

0 data o
.0 model ..
-0
, ,0

1 2 3 4 5 6 7 8
Depth
Depth based statistical model for SERC KPAR = -0.12 x depth + 1.50

2.6
data o
2.4 model ----2.2
1.8 -- 0
,r 1.6 0 o a" -..,o
1.4
00 0
0.0
1.20 o
0
o 0
0.8 0
0.6
0.4
7.4 7.5 7.6 7.7 7.8 7.9 8 8.1 8.2
pH
Figure 4.6: pH based statistical model for SERC data
KPAR = -1.55 x pH + 13.64

9
data

(4.11)

(4.12)




2.6
data +
2.4 model
2.2 0
2 +
1.8 0
a 1.6 0 "
a- 0 *00
1.4
1.2 0 + 0
1 0.8
0.6
0.4
0 10 20 30 40 50 60 70 80 90 100 Color
Figure 4.7: Color based statistical model for SERC data
KPAR = 0.015 x color + 0.88

2.6
day 0
2.4 modl
2.2 0
20
1.8
1.6
1.4 0 0
1.2 0 0 .
0
0.8 .. 0
00
0.6
0.(
2 0 2 4 6 8 10 12 14 16 18 TOC
Figure 4.8: TOC based statistical model for SERC data
KPAR = 0.09 x TOC + 0.84

(4.13) (4.14)




Table 4.12: Additional correlation between parameters in HBOI (Year 1) study

The next two best predictors are DOC and TOC. Both dissolved and total organic carbon are strongly tied to measurements of color (Cuthbert and del Giorgio, 1992), so this is to be expected from our results with color.
TOC is in ', and yields F(1, 52) = 102.83 with a p value of 0.0001 and an adjusted r2 = 0.66. It is displayed in equation 4.14 and is shown graphically in Figure 4.8. DOC is likewise measured in m_. Statistical analysis results in F(1, 52) = 92.01 L"
with a p value of 0.0001 and an adjusted r2 = 0.63, shown in equation 4.15 and Figure 4.9.
One of the most commonly used methods for quantifying fulvic and humic acids-when carbon analysis is not used-is the measurement of color. This explains the high r2 for both forms of organic carbon as predictors of light attenuation. We should therefore expect that any explanation of color's relationship with light attenuation will also apply to organic carbon.
Variations in p0, the cosine of the zenith solar angle, appear to have very little to do with variations in light attenuation despite the theoretical relationship between

OSS TN SN TP SP S chl
KPAR 0.42 -0.10 -0.11 0.47 0.11 0.27 0.34 temp -0.03 -0.00 -0.03 0.18 0.33 0.33 0.03 salinity 0.15 -0.29 -0.27 -0.58 -0.73 -0.70 -0.32
color -0.15 0.11 0.13 0.52 0.68 0.48 0.10 turb 0.73 -0.10 -0.15 0.54 -0.00 0.13 0.56 TSS 0.75 -0.11 -0.17 0.28 -0.25 -0.15 0.40
ISS 0.59 -0.10 -0.14 0.29 -0.29 -0.18 0.34
OSS 1.00 -0.09 -0.15 0.41 -0.01 0.01 0.44
TOTN -0.09 1.00 0.88 0.14 0.25 -0.00 0.08 SN -0.15 0.88 1.00 0.07 0.23 -0.04 -0.00
TP 0.41 0.14 0.07 1.00 0.75 0.50 0.56
SP -0.01 0.25 0.23 0.75 1.00 0.56 0.26
S 0.01 -0.00 -0.04 0.50 0.56 1.00 0.34
chl 0.44 0.08 -0.00 0.56 0.26 0.34 1.00




2.6
data + 2. 0 model--2.4 a
2.2 a0
1.8
1.6 + o ,-0 0
1.4 -+
1
1.2 0
0.8
00
06 +
0.4
2 0 2 4 6 8 10 12 14 16
DOC
Figure 4.9: DOC based statistical model for SERC data

KPAR = 0.09 x DOC + 0.90

0.7 0.75 0 8 0.85
Muzero

Figure 4.10: [o based statistical model for SERC data

KPAR = 1.74 x 0o 0.24

(4.15)

data a
model...
0
a$
. *_a.
0 a -- ------- ---------a----a~ 0
00
a' .... 4

0.9 0.95

(4.16)




Table 4.13: Correlation between parameters in HBOI (Year 2) study
KPAR temp salinity color turb TSS ISS KPAR 1.00 -0.19 -0.39 0.40 0.61 0.01 0.02
temp -0.19 1.00 -0.18 0.26 0.00 -0.17 0.27
salinity -0.39 0.26 1.00 -0.60 -0.17 0.69 0.71
color 0.40 0.00 -0.61 1.00 0.08 -0.38 -0.35
turb 0.61 -0.16 -0.17 0.08 1.00 0.40 0.38
TSS 0.01 0.26 0.69 -0.38 0.40 1.00 0.96
ISS 0.02 0.19 0.71 -0.37 0.38 0.96 1.00
OSS -0.01 0.34 0.46 -0.30 0.34 0.81 0.62
TN 0.06 -0.08 -0.52 0.10 0.05 -0.35 -0.37
SN 0.04 -0.07 -0.46 0.10 -0.05 -0.35 -0.36
TP 0.41 0.29 -0.22 0.45 0.36 0.04 0.01
SP 0.22 0.42 -0.20 0.65 -0.02 -0.13 -0.18
S 0.17 0.22 -0.39 0.34 0.04 -0.30 -0.28
chl 0.39 -0.08 -0.39 -0.14 0.50 -0.05 -0.11
the two variables. p0 (a dimensionless number) resulted in F(1, 52) = 4.591 with a p
value of 0.0368 and an adjusted r2 = 0.06. These results are illustrated in equation
4.16 and Figure 4.10.
This is counter to research on the west coast of Florida in Tampa Bay (Mcpherson and Miller, 1994). In hindsight, this is to be expected in the more turbid coastal
waters1 of the Indian River Lagoon where attenuation is dominated by absorption
(Kirk, 1984). It is therefore most likely acceptable to neglect P0 in the Indian River
Lagoon.
Both equation 4.17 and Figure 4.11 show that Chlorophyll performs very
poorly as a predictor of light attenuation in the SERC data set. This result is also
consistent with earlier work (Gallegos, 1993a). Chlorophyll is measured here in a L"
1The TSS (a surrogate of turbidity) is high enough to easily be classified as turbid compared to Tampa Bay, TSS P 10 (Mcpherson and Miller, 1987), in both HBOI data sets, but not in the UF data set. This is most likely because the UF sampling was generally conducted during mild, fair weather and therefore probably represents lower than average turbidities and TSS for stormy conditions at the same locations.




Table 4.14: Additional correlation between parameters in HBOI (Year 2) study

It is not relevant statistically or practically, with F(1, 52) = 2.152, a non-significant p value of 0.1484, and an adjusted r2 = 0.02.
It is possible that in the more nutrient poor southern reaches of the lagoon less plankton is present. Each unit of chlorophyll might attenuate equally throughout the lagoon, but in areas with less chlorophyll, light attenuation would tend to be controlled by other water quality parameters. Unfortunately, an examination of the correlation between chl and UTM in Table 4.16, shows a very small Pearson's correlation coefficient of -0.01. This makes it unlikely that chlorophyll is unimportant in some areas of the lagoon, but dominant in others. One might make the argument that seasonal variation in phytoplankton might cause these low correlations during some seasons of the year and not others. However, the SERC data was collected over winter and spring, the HBOI data over the entire annum, and the UF data over spring and summer, so it appears unlikely that any important seasonal affects would have

OSS TN SN TP SP S chl
KPAR -0.01 0.06 0.04 0.41 0.22 0.17 0.39 temp 0.34 -0.08 -0.07 0.29 0.42 0.22 -0.08 salinity 0.45 -0.52 -0.46 -0.22 -0.20 -0.39 -0.39
color -0.30 0.10 0.10 0.45 0.55 0.34 0.14 turb 0.34 0.05 -0.05 0.36 -0.02 0.04 0.49 TSS 0.81 -0.35 -0.35 0.04 -0.13 -0.29 -0.05
ISS 0.62 -0.37 -0.36 -0.01 -0.18 -0.28 -0.11
OSS 1.00 -0.21 -0.23 0.13 0.00 -0.24 0.10
TOTN -0.21 1.00 0.86 0.07 0.07 0.11 0.21 SN -0.23 0.86 1.00 0.02 0.08 0.09 0.11
TP 0.13 0.07 0.02 1.00 0.82 0.27 0.39
SP 0.00 0.07 0.08 0.82 1.00 0.25 0.12
S -0.24 0.11 0.09 0.27 0.25 1.00 0.19
chl 0.10 0.21 0.11 0.40 0.12 0.19 1.00




Table 4.15: Correlation between parameters in UF study

UTM Julian Day time temp salinity DO pH UTM 1.00 0.00 -0.06 -0.03 0.64 -0.40 0.27
Julian Day 0.00 1.00 -0.17 0.88 0.00 -0.33 0.01
time -0.06 -0.17 1.00 0.02 -0.30 0.36 0.00
temp -0.03 0.88 0.02 1.00 -0.18 -0.22 -0.07
salinity 0.64 0.00 -0.30 -0.18 1.00 -0.60 0.24
DO -0.40 -0.33 0.36 -0.21 -0.60 1.00 -0.13
pH 0.27 0.01 0.00 -0.07 0.24 -0.13 1.00
TP -0.06 0.03 0.07 0.06 -0.08 -0.13 0.01
TN 0.52 0.24 0.09 0.28 -0.05 -0.15 0.04
TSS 0.19 -0.31 -0.03 -0.30 0.36 -0.25 0.04
color 0.09 -0.05 0.01 0.15 -0.04 -0.05 0.05
DS -0.31 -0.09 -0.01 -0.09 -0.07 -0.18 -0.04
TOC 0.22 0.37 -0.04 0.15 0.05 0.02 0.21
chl -0.01 -0.04 0.06 0.08 -0.13 0.08 0.21
KPAR -0.30 -0.14 0.10 -0.10 -0.21 0.04 -0.24
been overlooked in such a broad range of data. This lack of spatial variation in chlorophyll combined with its poor performance as a predictor means that phytoplankton
blooms and die offs simply do not covary with changes in light attenuation.
In summary, table 4.17 shows several of the best models for the SERC data set.
Not all nine of the SERC models shown have p values of 0.0001. One, chlorophyll, is
not even statistically significant at the a 0.05 level.
TSS and turbidity are not shown graphically, but are summarized in Table
4.17. They are both very poor predictors of light attenuation in the SERC data
set. This is contradictory to much of the earlier work in predicting light attenuation
from both a theoretical (Thompson et al., 1979, Gallegos and Correll, 1990, Kirk,
1984) and experimental standpoint (Thompson et al., 1979). Both variables showed
such poor Pearson's coefficients in Table 4.10 that neither was used in section 4.4.1.
However, Table 4.17 shows both turbidity and TSS as linear, single variable models
for the purpose of comparison to other data sets and earlier studies.




Table 4.16: Additional correlations between parameters in UF study
TP TN TSS color S TOC chl KPAR
UTM -0.06 0.52 0.19 0.09 -0.31 0.22 -0.01 -0.30
Julian Day 0.02 0.03 0.24 -0.05 -0.09 0.37 -0.04 -0.14
time 0.07 0.09 -0.03 0.01 -0.01 -0.04 0.06 0.10
temp 0.06 0.28 -0.30 0.15 -0.09 0.15 0.08 -0.10
salinity -0.08 -0.05 0.36 -0.04 0.07 0.05 -0.14 -0.21
DO -0.13 -0.15 -0.25 -0.05 -0.18 0.02 0.08 0.04
pH 0.01 0.04 0.04 0.05 -0.04 0.21 -0.05 -0.24
TP 1.00 0.26 0.24 -0.05 0.10 -0.05 0.33 0.27
TN 0.26 1.00 0.04 0.12 -0.12 0.26 0.36 0.07
TSS 0.24 0.04 1.00 0.01 0.00 -0.35 0.23 0.48
color -0.05 0.12 0.01 1.00 0.29 -0.07 0.16 -0.02
DS 0.10 -0.12 0.00 0.29 1.00 -0.16 -0.02 0.20
TOC -0.05 0.26 -0.35 -0.07 -0.16 1.00 -0.05 -0.21
chl 0.33 0.36 0.23 0.16 -0.02 -0.05 1.00 0.39
KPAR 0.27 0.07 0.48 -0.02 0.20 -0.21 0.39 1.00
Table 4.17: Comparison of single variable models for SERC study

4.4.2 HBOI Year 1 Single Variable Regressions

For the first year HBOI data set, color, turbidity, TSS, OSS, ISS, TP, and chlorophyll were examined as single variable regression models. These results are expressed numerically in equations 4.18 4.19, and graphically in Figures 4.12 -

4.18.

Parameter N r2 p value depth 78 0.21 0.0003
P0 69 0.06 0.0368
color 85 0.70 0.0002
chl 95 0.02 0.1484
turb 91 0.00 0.0001
TSS 95 0.01 0.0001
pH 84 0.38 0.0001
TOC 85 0.66 0.0001
DOC 85 0.63 0.0001




63
2.6
data + 2.4 < model
2.2
2
1.8
a 1.6 +
1. a a a-------- ------------------1.2 ----- .
0 0 0. . . .
0.8
0.6 a<
0.4
0 5 10 15 20 25 30 35
Chlorophyll
Figure 4.11: Chlorophyll based statistical model for SERC data
KPAR = 0.01 x chl + 1.18 (4.17)
data o a model --6
5 aa
o + ++
4
0 ^0<
0 ~~~ 20% 1 2 1
N 0
* a *
0 0
0 6 8 10 12 14
Color
Figure 4.12: Color based statistical model for HBOI year 1 data
KPAR = 0.34 x color + 1.41 (4.18)




Figure 4.18 shows the color based statistical model for the first year HBOI data. Equation 4.18 shows the derived regression, where color is in Pt. units. Statistically, F(1, 265) was found to be 44.05 with a p value of 0.0001 and an adjusted r2 = 0.14. Thus, color is significant in the first year HBOI, data but apparently not as much as in the SERC data.
7 0 ,
data o
a model ---6 0 0
50 0
a- 0000 o o
/ aea~o --o
a, 3
% a 0 o
wit 1,65 =4528a p vau af a.0 anda dutdr .4
00
0 10 20 30 40 50 60 70 80 90 100 Chlorophyll
Figure 4.13: Chlorophyll based statistical model for HBOJ year 1 data
KPAR =0.05 x chi + 1.28 (4.19)
The results of a statistical model based on chlorophyll are shown in equation 4.19 and Figure 4.13Ach is in ain equation 4.19. This model was also significant, with F(1, 265) = 45.28, a p value of 0.0001, and an adjusted r2 = 0. 14.
So, measurements of color and chlorophyll explain less data variance for the HBOI data set, but still vary with light attenuation (r2 = 0.14 for both). Color's significant but small role in estuarine light transmission has been shown in prior studies that found non-chlorophyll matter accounted for over 72 % of the variation in light attenuation (Mcpherson and Miller, 1987).




65
data o
.Model ---8
(Loo 00
4 0 4.,
400 0 0O
I
: o 0 0
0 10 20 30 40 50 60 70
Turbidity
Figure 4.14: Turbidity based statistical model for HBOI year 1 data
KPAR = 0.12 x turb + 1.08 (4.20)
Turbidity is a very good predictor for the HBOI data set. When measured in NTU, a regression yields F(1, 265) = 168.61 with a p value of 0.0001 and an adjusted r2 = 0.39. This regression is represented in equation 4.20 and Figure 4.14.
The turbidity model explains much more of the data variance than any other model presented for the first year HBOI data. This is consistent with much of the work reviewed in section 1.5 (Mcpherson and Miller, 1987, Hogan, 1983, Gallegos, 1993a, Thompson et al., 1979). In fact, it has been shown that in shallow waters subject to wave and current induced resuspension, TP shows good correlation with TSS when particulate phosphorus is the major constituent of TP (Sheng, 1993).
TSS is also a statistically significant predictor of light attenuation. Equation 4.4.2 (TSS in 7) shows the regression plotted in Figure 4.15. For this regression, F(1, 265) = 95.52, p = 0.0001, and r2 = 0.26.
Similarly, the regression for ISS is shown in symbolically in equation 4.22 and graphically in Figure 4.16. ISS is in units of L. Equation 4.22 resulted in F(1, 265) = 85.17 with a p value of 0.0001 and an adjusted r2 = 0.24.




,'data + S/ model ---0 00
6
5 00
o
0 0 0
0 00 0
4
I*0
* 00 0
1 -
00 *0
3
0
0 50 100 150 200 250 300 350
Total Suspended Solids
Figure 4.15: Total suspended solids based statistical model for HBOI year 1 data
KPAR = 0.02 x TSS + 0.66 (4.21)

0 50 100 150 200
Inorganic Suspended Solids

Figure 4.16: Inorganic suspended solids based statistical model for HBOI year 1 data KPAR = 0.07 x ISS + 0.58 (4.22)

data p 0 modef-00 *
o o00
/
00 00
0 00
00
00* 0 0 V1000 0
o
0 0
000
0 ,0 0

250 300




67
70 0'00 0
data 0
a model ----6 0
5 0
am
0 o 0
2 0 0
00
** 0 00 0
::-. 0
00 eO 11
$- 0
0~ 0
0 10 20 30 40 50 60 70
Organic Suspended Solids
Figure 4.17: Organic suspended solids based statistical model for HBOI year 1 data KPAR = 0.02 x OSS + 0.96 (4.23)
The final measurement of suspended solids, OSS, was also measured in 'L"
It was found to be significant with F(1, 265) = 56.07, p = 0.0001, and an adjusted r2 = 0.17. Equation 4.17 and Figure 4.17 show OSS as a predictor of KPAR.
Measures of suspended solids, including TSS, ISS, and OSS, also have some of the higher coefficients of determination (r2). One would expect this, since suspended solids are the primary cause of turbidity and should therefore explain a comparable amount of variance in light attenuation as turbidity.
TP, in 'g, resulted in F(1, 265) = 93.83 with a p value of 0.0001 and an adjusted r2 = 0.26. This is displayed in equation 4.24 and Figure 4.18.
TP shows the highest coefficient of determination of any direct chemical measurement taken in the first year of the HBOI study. TP's relationship with light attenuation is an indirect one11. Increased phosphorus might spark an algal bloom "Phosphorus does not directly attenuate light itself any more than most particles.




68
7i
' data o
model ----6
5.
00 0 0
0 000
EL
3
000 0- ~ 0 D 0 0
- 0"
^ o" o 0 0
000 -- 0 0%0
2 0 00 0 0 0.12 0
I 0 0 0 oo
0 0 0 0 0 0. 0 .0 p0
0 000
0 0 00
0
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 TOTTP
Figure 4.18: TP based statistical model for HBOI year 1 data
KPAR = 19.20 x TP + 0.71 (4.24)
that loads the water with chlorophyll, or phosphorus might be a simple tracer. Perhaps the sediments best at attenuating sunlight (turbidity, TSS, ISS, & OSS) happen
to be laden with phosphorus12.
Table 4.18 shows several of the best single variable models for the first year of
HBOI data for comparison. All seven of the models shown have p values of 0.0001,
and are therefore irrefutably statistically significant.
4.4.3 HBOI Year 2 Single Variable Regressions
For the second year HBOI data set, color, turbidity, TSS, OSS, ISS, TP, and
chlorophyll were again examined as single variable regression models. These results
are expressed numerically in equations 4.25 4.26, and graphically in Figures 4.19
4.25.
2Because both phosphorus and all four measurements of sediment have positive correlations with light attenuation, phosphorus and these measures must have positive correlations with each other for this theory to be true. Tables 4.11 and 4.12 show that TP is in fact positively correlated with all four.




Table 4.18: Comparison of single variable models for HBOI year 1 study
Parameter N r2 p value color 296 0.14 0.0001
turb 296 0.39 0.0001
TSS 295 0.26 0.0001
ISS 267 0.24 0.0001
OSS 267 0.17 0.0001
TP 296 0.26 0.0001
chl 296 0.14 0.0001

Color
Figure 4.19: Color based statistical model for HBOI year 2 data
KPAR = 0.19 x color + 1.41

(4.25)

Again, color, in Pt. units, is examined as a predictor. This results in equation 4.25 and Figure 4.19. F(1,501) was found to be 95.109, resulting in a p value of
0.0001 and an adjusted r2 = 0.16.
Chlorophyll is shown as a predictor of KPAR in Figure 4.20 and equation 4.26. It is measured in L-. The results were F(1, 501) = 88.572 with a p value of 0.0001 and an adjusted r2 = 0.14.




0,00 0 0...
0
0 0 0 3I *0
*00
00
0.
0 10 20 30 40 50 60 70 80 Chlorophyll
Figure 4.20: Chlorophyll based statistical model for HBOI year 2 data
KPAR = 0.04 x chi + 1. 14 (4.26)
Color and chlorophyll for the second year HBOI data vary in their coefficients (as will always be the case with empirical models), but are virtually identical to the first year in terms of variance explained.
The turbidity model is again the best single variable model for the HBOI data. Equation 4.27 shows this regression with turb in NTU. F(1, 501) was found to be 232.27, resulting in a p value of 0.0001 and an adjusted r2 = 0.37.
TSS was again analyzed in 'g. For the second year data much different results L"
were obtained (F(1, 501) = 0.052, p = 0.0001, and an adjusted r2 = 0.002). This is a very large change from the first year data. Equation 4.4.3 is shown graphically in Figure 4.22.
ISS, again, exhibits a very large change from the first year data.ISS, in '-L with F(1, 501) = 0.172, a p value of 0.6787, and an adjusted r2 = 0.002 is displayed in equation 4.29 and Figure 4.23.




e data +
model,--6
3t Io 1 Ob*I *
0 00
5
0 5 1~0 15,I 20 0 25 3 35 4 45 0
a u
Figure 4.21: ~~~~~~~~Turbidity bsdsaitclmdlfrHO er2dt
KPAR = 0.12 x turb + .81
g AR0$~0 a .2tr 8

(4.27)

20 40 60 80 100 120 140 160
Total Suspended Solids
Figure 4.22: Total suspended solids based statistical model for HBOI year 2 data KPAR = 0.0005 x TSS + 1.75 (4.28)




Figure 4.23: Inorganic suspended solids based statistical model for HBOI year 2 data

KPAR = 0.07 x ISS + 0.58

(4.29)

0 0 data -o 00 0>0<> model---600
6
0000
0
00 0
40
* O *e00
300 000 0 3 0000 00
0 ,% 00 00
0:o 00 0
9 0 0 0
0
0 ~* 10 20 30 4 0 60 7 0 9
r S o
0 10 20 30 40 50 0 70 80 9
Organic Suspended Solids

Figure 4.24: Organic suspended solids based statistical model for HBOI year 2 data KPAR = -0.001 x OSS + 1.81 (4.30)




Our final measure of suspended solids also shows a very large change from year
1 to year 2. OSS, in g, is shown in equation 4.24 and Figure 4.24. Statistical analysis
yielded F(1, 501) = 0.064 with a p value of 0.0001 and an adjusted r2 = 0.002.
Measures of suspended solids, including TSS, ISS, and OSS, had very high
coefficients of determination (r2) for the first year data, but not for the second year
data. We will examine possible explanations for this change in the summary.
7
0 data 0
model6
* 0>
5
0
0 0 00 00
4 0 0
c0 0 tol 0
040
0 01 0
*to0~ 0' 0
2 0: 0 C
0-% ov 00 0
1pAR--11.0 P 0.43
7 N o0 0 0 0
0*o 0 0%o 08 11~ 80*0 0
0
0 0.05 0 .1 0.15 0.2 0 25
TOTTP
Figure 4.25: TP based statistical model for HBOI year 2 data
KPAR = 11.90 x TP + 0.92 (4.31)
TP again shows the highest coefficient of determination of any direct chemical
measurement taken in the HBOI year 2 study. TP is in units of m_. F(1,501) was L"
found to be 100.36, resulting in a p value of 0.0001 and an adjusted r2 = 0.17. Despite
the still high r2, this represents a 10 % decrease from first year data. Equation 4.31
shows the TP model, and it is shown graphically in Figure 4.25.
Table 4.19 shows several of the best single variable models for the HBOI year
2 data set for comparison. Four of the seven of the models shown have p values of
0.0001, and are therefore irrefutably statistically significant. It is interesting to note
that measures of suspended solids change from highly significant in the year 1 data




Table 4.19: Comparison of single variable models for HBOJ year 2 study Parameter N r p value
color 502 0.190 0.0001
turb 502 0.370 0.0001
TSS 502 0.002 0.8205
155 502 0.002 0.6787
ass 502 0.002 0.8002
TP 502 0.170 0.0001
chi 502 0.150 10.0001
(Table 4.18 ) to not significant at all in the second year. It is impossible to know the exact reason for this change, but two possibilities present them self. The first would have to be experimental error on a massive scale from year 1 to year 2. The second is a change in how suspended solids are resulting in turbidity, the true optical measure of their effect. Unfortunately, neither of these can be verified from available data, but it might be worthwhile to attempt to re-examine any samples remaining from the HBOI study to attempt to ascertain if any analysis error was made.
4.4.4 UF Single Variable Regressions
For the UF data set, location, Julian day, time of day, temperature, salinity, dissolved oxygen, pH, phosphorus, nitrogen, TSS, color, silica, TOG, and chlorophyll were examined as single variable regression models.
Location within the lagoon has a modestly large (for this data set) T 2. Here we find F(1, 198) =29.37 with a p value of 0.0001 and an adjusted r2 = 0. 12. This is displayed in equation 4.32 and Figure 4.26 with UTM is in meters.
This lends some credence to those who postulate that a body of water as large and biologically diverse as the Indian River Lagoon will be limited by different water quality constituents in different regions.
Day of the year appears to be completely insignificant as predictor of KPAR. This conclusion was reached from equation 4.33 and Figure 4.27, where Julian day is




7
data +
mode -6 *
o
5
K A =.. -. 0 0
0
a0 a
adata0
o o 'v"P"-'c ..model<
2 0 0 0
0 0 2a 1 1 10 1 a0 a o
2 o oa .
3.08e+063.09e+063.1e+063.11e+06B.12e+06B.13e+063.14e+063.15e+063.16e+063.17e+0( l.18e+C Bl.19e+06
UTM
Figure 4.26: UTM based statistical model for UF data
KPAR = -1.4 x 10-5 x UTM + 47.00 (4.32)
data
model...
a o a
60
5o
4o
- ------ -- - - -- -
go 031 e 1 1 3 1 13o0 1403 150. 1 6'0 170 180 Figure 4.2: JuTMn a based statistical model for UF data
KPAR = -.40 x Julia daUT + 4.00 (4.32)
6 a
0 I 0 a
80 10 11 2 13 14 10 0 7 0 18
JulanDa
Figur 4.27 Julin d8 bae ttsia oe o Fdt
Kp* 0.0 a Jlan da .8(.3




76
in days, This resulted in F(1, 198) 2.923 with a p value of 0.0889 and an adjusted r2 -0.01.
7
data a
model ----6 o 0
5 0
4 0
4 0 0
0
0 0
0-- 0 000 0
0~e0.
---------------- - -0O
2. - ... -%
:/ o:: o: 0 1~o ooo0 oo0 -.
0
0 200 400 600 800 1000 1200 1400 1600 1800
Time
Figure 4.28: Time based statistical model for UF data
KPAR = 4.1 X 10-4 X time + 1.45 (4.34)
Time of day is likewise insignificant. Time is measured here in hours, minutes, seconds. F(1, 198) was found to be 3.531 with a p value of 0.0617 and an adjusted r2 = 0.01. Equation 4.4.4, which shows time, is shown graphically in Figure 4.28.
Temperature, equation 4.35 and Figure 4.29, is also insignificant. Temperature was measured in C, and resulted in F(1, 198) = 2.584 with a p value of 0.1095 and an adjusted r2 = 0.01.
Biological activity, as measured by DO, is also insignificant, where DO is in .Equation 4.36 yielded F(1, 198) = 0.170 with a p value of 0.6806 and an adjusted r = 0.00.
pH was somewhat significant for the UF data set. F(1, 198) = 9.829 with a p value of 0.0020 and an adjusted r2 = 0.04 were the statistical results. The regression itself is shown in equation 4.37 and is displayed graphically in Figure 4.31.




Figure 4.29: Temperature based statistical model for UF data
KPAR = -0.04 x temp + 3.57

7
data + model ---6
5
oo
4 o
a
0 + +
4 ODO
---- ------- ---- -----3 a 0a
a 0 .. a a 8* a 1
%0 00 *0a
000
KPAR = 0.04 x DO + 2.13

(4.35)

(4.36)




2
04
0 2 4 6 8 10 1
pH
Figure 4.31: pH based statistical model for UF data
KPAR = -0.50 x pH + 6.38

0 5 10 15 20 25 30 35 40 45
Salinity
Figure 4.32: Salinity based statistical model for UF data
KPAR = -0.05 x salinity + 3.55

(4.37)

(4.38)




79
Salinity, in ppt, resulted in F(1, 198) = 17.18 with a p value of 0.0001 and an adjusted r 2 =0.08. These results are derived from equation 4.32 and Figure 4.32.
pH has a small (r 2 = 0.04) but significant (p = 0.0020) relationship with KPAR. Salinity also explains a somewhat large amount of variability (r 2 = 0.08). These relationships are surprising not because they explain more variability than most other models, but because there is no known direct relationship between salinity and light transmission through salt water or between pH and light transmission.
The most plausible explanation that occurs to the author is that salinity and/or pH are acting as surrogates for freshwater inflow, which brings many of the other chemicals into the lagoon through runoff. It is important to note, however, that salinity can also be heavily influenced by evaporation, diminishing somewhat this explanation of the role of salinity as a surrogate parameter (but not that of pH).
8
data o
model -'
7
0
6 0
5
CC 0*8~
9 4 0 0
0
0%
0 0.02 004 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 TP
Figure 4.33: Total phosphorus based statistical model for UF data
KEAR = 34.08 x TP + 0.80 (4.39)
TP is relatively important as a predictor of KPAR, with F(1, 198) = 45.365 with a p value of 0.0001 and an adjusted r 2 =0.18. Equation 4.39 shows this




80
regression with TP in units of 'g. The same model is shown graphically in Figure L"
4.33.
7
data
model6 00
5
a a
a 0* 0
000 0aa00: 0
2 -- - - - -
1 0 &0 a %
00
0 0.5 1 1.5 2 2.5
TN
Figure 4.34: Total nitrogen based statistical model for UF data
KPAR = 0.22 x TN + 2.02 (4.40)
TN was measured in 'g. Equation 4.40 resulted in F(1, 198) = 0.561 with a p value of 0.4549 and an adjusted r2 =0.00. The model is shown graphically in Figure 4.34
TSS is one of the better predictors of KPAR (r 2 = 0.13) in the UF data set. Again this is to be expected from both earlier previous studies (Mcpherson and Miller, 1987, Hogan, 1983, Gallegos, 1993a, Thompson et al., 1979) and from three of the other four data sets. TSS, in was found to be significant with F(1, 198) = 29.715 with a p value of 0.0001 and an adjusted r 2 = 0.13.
Color is not statistically significant (p = 0.2175) in the UF data set. Color, in Pt. units, is displayed in Figure 4.36 and equation 4.42. This regression found F(1, 198) = 1.530 with a p value of 0.2175 and an adjusted r2 = 0.00. This is quite a difference from the SERC data set where color was fundamental in explaining light attenuation.




81
7
data a
model
3 ?
5
o 100 20o30.0 50 6
KPA = 0.7xTS+.1(.1
00
data+
model-6 -0 + a +5
4
rl 5 10 15$00203
aKARa -0.0 xaoo .8(.2
0 a0
00
0 10 20 30 40 5 60
Figure 4.35: TSSo based statistical model for UF data
KPAR = -0.07 x TSSo 1.8 (4.41)
7 m
" # dataoa
modlooo
6 a :
adaaaa
aodel.a.a
4o
ao
oOa
a o Ooa-o
a a $* a$ aa a
0a 1 a5 20 a53
a oo
KpAR = --0.03 X colo .8(.2




0 0 0 0
0 0 0 **t*
000 *
3 - 0
0 *0 0 0
00
1 10 15 20 25 30 35 40 45 50 TOC
Figure 4.37: Total carbon based statistical model for UF data
KPAR = -.02 x TOC 3.12 (4.43)
TOC, already an established surrogate for color, is also much less important in the UF study than in the SERC study. When measured inH-2, F(1,198) = 3.540 with a p value of 0.0011 and an adjusted r2 = 0.05. These results were derived from equation 4.43 and Figure 4.37.
DS, in --, was found to have F(1, 198) = 10.984 with a p value of 0.0011 and an adjusted r2 = 0.05. This regression is shown in equation 4.44 and Figure 4.38.
Chlorophyll was found to be marginally important, in units of -. Statistical analysis resulted in F(1, 198) = 18.344 with a p value of 0.0001 and an adjusted r2 = 0.08. Equation 4.45, which displays the regression, is shown graphically in Figure 4.39.
Table 4.20 shows several of the models for the UF data set. Not all of the UF models shown have p values of 0.0001. Several (Julian day, time, temperature, DO, TN, and color) are not even statistically significant at the a = 0.05 level. The best single variable model is TP, which was also an effective predictor for the HBOI data set (which the UF data set most closely resembles). In the next section, we shall




data a
model ----0
0 0
*0* 0 %a
a
a a
Olt a a. 0 0 0 0
* 0 aaa aa
<>o a) a a Oa 0a a aa oo a
a. aao\...a...a.
o 15 2 2.5 3---3.5

0 0.5 1 5 2 25 3 3.5 Silica
Figure 4.38: Silica based statistical model
KPAR = 0.26 x DS + 2.00

4 4.5 5 for UF data

(4.44)

0 5 10 15 20 25
Chlorophyll
Figure 4.39: Chlorophyll based statistical model for UF data
KPAR = 0.12 x chl + 1.77

(4.45)