• TABLE OF CONTENTS
HIDE
 Title Page
 Copyright
 Dedication
 Acknowledgement
 Table of Contents
 List of Tables
 List of Figures
 Abstract
 Introduction
 Light data
 Water quality data
 Statistical model
 PARPS numerical model
 Conclusion
 Reference
 Biographical sketch
 Signature page














Title: Photosynthetically active radiation in the Indian River Lagoon
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Permanent Link: http://ufdc.ufl.edu/UF00091384/00001
 Material Information
Title: Photosynthetically active radiation in the Indian River Lagoon
Series Title: Photosynthetically active radiation in the Indian River Lagoon
Physical Description: Book
Language: English
Creator: Kornick, Adam Marcus
Publisher: Coastal & Oceanographic Engineering Dept. of Civil & Coastal Engineering, University of Florida
Place of Publication: Gainesville, Fla.
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Bibliographic ID: UF00091384
Volume ID: VID00001
Source Institution: University of Florida
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Table of Contents
    Title Page
        Page i
    Copyright
        Page ii
    Dedication
        Page iii
    Acknowledgement
        Page iv
        Page v
    Table of Contents
        Page vi
        Page vii
        Page viii
    List of Tables
        Page ix
        Page x
    List of Figures
        Page xi
        Page xii
        Page xiii
        Page xiv
        Page xv
    Abstract
        Page xvi
        Page xvii
    Introduction
        Page 1
        Page 2
        Page 3
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    Light data
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
    Water quality data
        Page 33
        Page 34
        Page 35
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        Page 37
        Page 38
        Page 39
    Statistical model
        Page 40
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        Page 111
        Page 112
    PARPS numerical model
        Page 113
        Page 114
        Page 115
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    Conclusion
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    Reference
        Page 167
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        Page 169
        Page 170
        Page 171
    Biographical sketch
        Page 172
    Signature page
        Page 173
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, particu-

larly those who participated in the field work on the Indian River Lagoon, Justin

Davis, Joel Melanson, Peter Seidle, Matt Henderson, Hugo Rodriguez, William We-

ber, 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 Na-

tional 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

1 INTRODUCTION ................... .......... 1

1.1 Marine 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 Radiance . . . . . . . . . . . . . 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 r Sensors . . . . . . . . . . . .. . 28
2.1.3 Scalar Attenuation ...................... 29
2.1.4 4 -r 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 (Year2). ................. .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 0o . . . . . . . . . . . . . . . 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 (Year2) ........... 140
5.7.4 UF Data ... .... .... .. .. .. .. .. .. ... 142
5.8 Discussion of Numerical Model Results . . . . . ... 144
5.8.1 M odel vs. Data ....................... 148
5.8.2 Model vs. Model ....................... 149
5.8.3 Sources of Error ....................... 149

6 CONCLUSION ................... ......... 152

6.1 D ata . . . . . . . . . . . . .. . . . 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 W ork ................... .......... 163
6.4.1 Lab W ork ........................... 163
6.4.2 Integration . . . . . . . . . . . . . 164
6.4.3 Sediment Dynamics . . . . . . . . .. 164
6.4.4 Radiative Transfer Model . . . . . . . .... 164
6.4.5 Tree M odel .......................... 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 maritima ............................. 7

Sampling stations in the Indian River Lagoon . . . . . ... 27

2 x Sensor . .. . . . . ...... . . . . ...... 29

4 7r 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

. . . . 7 8

. . . . 78

. . . . 79

. . . . 8 0

. . . . 8 1

. . . . 8 1








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 po0

of P/o

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 c

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

lata . . . . . . 138

data. ...........139
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 statis-

tical 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 pre-

dict 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 estu-

arine 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 over-

all 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 (Virn-

stein 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
10km


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.









































SHOAr-GRASS


Figure 1.2: Halodule wrightii






























IrhitrgnadiIntjlifnrn
MANAGE IE-LCSS


Figure 1.3: Syringodium filiforme


SJ





I~ I:~ *18. .



Ilalophrila enlrt~cnaitiz


Figure 1.4: Halophila engelmannii















<\ .' i. ->.\ ;,' ,.'



' I".( c ,i

(I(? ~ ICL
a. ffI i] Sl

1'- "1'i al .ssia te. srtdhiin ii
TURTLE-GRASS



Figure 1.5: Thalassia testudinum









.... -,. ,- : ^ "
-^-^ H^;!j

-1^* 2> 1$IJ
'/



" '., !'A OU 'L.tGI k1 'h


/


Figure 1.6: Halophila decipiens


NI


(-7>
I















II I .,t





Hdtophila joIhnsonil
JOHNSON'S SEAGIL-SS
Figure 1.7: Halophila johnsonii


Ruppia aritia .ma
AIvDGEO-N-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 pro-

duction 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 Uni-

versity 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 ra-

diometry, 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 direc-

tions. 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 Es
radiant energy joule q
thermal energy joule Q








energy per unit area of a sphere around the sun, or any light source, is inversely pro-

portional to R2. The integral solar radiance from photons at all wavelengths arriving

at the Earth's atmosphere, E,, is (Mobley, 1994),


E, = 1367Wm2. (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 = J (1.2)

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 im-

pact 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
S = (1.3)
9t c, m Ot








For this equation, T is temperature, t is time, c, is specific heat, m is the

mass, and 2 is heat absorbed or lost per unit time.
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-' K-l,. 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),



aT 1 (0.05)(400 J) 10
at (3900 J kg-1)(1025 kg) 1 s

Twelve hours of sunlight would result in the upper meter's temperature in-

creasing by

AT = (5 x 10-6)(12h)( 30 ) s 0.22 K. (1.5)

This temperature change is significant as a boundary condition for ocean cir-

culation 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 monochro-

matic average wavelength of 550 nm (Mobley, 1994),



Q A (400 J)(550 nm) 2
N = Q 1021 photons (1.6)
q hc= (6.63 x 10-34)(3 x 10 ms-1) photons

Mobley (1994) has also shown that the linear momentum of all these photons

is,
1Q is simply E times surface area.










p = Nh = 10216.63 10-34n 1.2 x 10-6 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 s-l1

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 quanta2. 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 C3 plants 3. 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 % x 400J = 8 28J (1.8)
2It should be noted, however, that quanta of different wavelengths will be absorbed preferentially
(Jerlov, 1976)
3All 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 28 J
28 = 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 = x = 240 kJ (1.11)
2.5 x 101quanta 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 CO2 to one mole of carbohydrate requires
4These absorbtion levels were observed in concentrations of 100 m








472 kJ. Therefore, the maximum possible theoretical efficiency for converting light

energy to chemical energy is


.472 MJ
efficiency = 2 MJ 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 photosyn-

thetically active radiation, EPAR, the sunlight available for photosynthesis by plants

(Kirk, 1983),

I700 nm A
EPAR -Eo(x, A)dA (photons s-1 m) (1.14)
J350 nm hc
EPAR can also be expressed in einst s-1 m-1, 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 10 350 nm hc
Eo 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(, t, A) (W m-2sr-nm-1). (1.16)
A t 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 irradi-

ance, which measures the energy absorbed over some constant solid angle, generally

a hemisphere or sphere. Examples of photometric instruments which measure irradi-

ance 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) cos 0 sin OdOd (W m-2sr-nm-1). (1.17)
Z=0 0=0
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, 0, A) cos 0s sin OdOd (W m-2srnm ). (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, 0, A) sin Od0df(W m-2sr-lnm-1). (1.19)
=0 0=0
Like plane irradiance scalar irradiance can also be used to measure upwelling

photons. This quantity is called the upward scalar irradiance, Eo, (Mobley, 1994),


/27r 0=r
Eo (x, t, ) L(x,t, 0, t, A)sinO dOdf (W m-sr-nm-1). (1.20)
J----0 J^

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 irradiance, Eo. This quantity is

simply the sum of the upward scalar irradiance and the downward scalar irradiance.



Eo(x,t, A) ] L(x,t,O0,,A) sin OdOd (W m -2sr-lnm-l). (1.21)
=0 I
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 impor-

tant 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 attenu-

ation. 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 attenu-

ation 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 down-

welling irradiance in Chincoteague Bay and the Rhode River. His model was spec-

trally based, allowing calculation of both PAR and Photosynthetically Usable Radi-

ation (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 to-

tal 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 (multi-

annual) 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 signifi-

cantly 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 fresh-

water 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 coeffi-

cients 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 depths9 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'1. 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 aph 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.
9Photic depth is the depth to which biologically usable light penetrates.
1"In 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 (r2 < 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 tech-

niques 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 vari-

ability 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 SAV. 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)12

We also must examine research concerning the color of estuarine waters. Chap-

ter 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 g440. 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-9 is given by,


true color (Pt, m) = 18.216 x g440 0.209. (1.22)

At Ft. Pierce Inlet, regression analysis was used to find relationships be-

tween water quality and attenuation at 445 nm, 542 nm, and 630 nm. Scattering

by suspended particulate material was the primary mechanism controlling the at-

tenuation of downwelling 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 calcu-

lated 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 pro-

vide 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 Uni-

versity 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 KPAR

The most important difference between these studies lie in how they mea-

sure 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






27











SERC

HBOI

SUF

A, grid


A &
A
A

A

A







L









ArE


Figure 2.1: Sampling stations in the Indian River Lagoon








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 Kod,

depends how we choose to define the irradiance being attenuated in the water col-

umn. 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),

r0
Ed(z,A) = Ed(zo, A) exp -Kd(z',A)dz' (W m-2 nm1). (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, allow-

ing 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
1As 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 03 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 (-Kod(A) x z) (W m-2 nm-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 po denotes the cos
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 7 in both polar directions for a total of 4 r.
















S- Opique Shield
Filter
-- 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 2r Licor sensors to measure downwelling plane attenu-

ation 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 27r 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. Be-

cause 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 Quality

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 con-

tinuous 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 num)

(Henderson, 1997) all the way to organisms, such as manatees, 109 larger (1 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 dis-

solved, 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 subdivi-

sions:


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 backscat-

ter. 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 0.2ium to 1.0prm 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 200/m, 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 oxi-

dized, changing their absorption characteristics from those of living phytoplank-

ton.

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 vari-

able 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
1Please 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 pug/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 measure-

ments (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

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 Smith-

sonian 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
Po 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
EXT40 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 oC 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 ,pg/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.

dl 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 m-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 pig/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[l]...e[n] are calculated along with the corre-

sponding 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).
1Eigenvectors 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)


iit[i]
e[i] = (4.6)

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). Unfor-

tunately, 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.

6 I--- i ---i---- i --- --- i ---- i ------
o PCA o


5 -



4 -




o











root
S
2
0
0


0
0
0 0
0 0 *
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
4Each 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

A


to components representing

variability (Jackson, 1991).


45U


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.


o PCA o

















0 0
0 o
0 0 0 .
SI I I I 0








Table 4.7: PCA for HBOI 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
Eigenvalue 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 HBOI 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 o
4.5

4

3.5

3

> 2.5
0)
2

1.5

1 0
0
0
0.5 o
0 0
0
0 I --- i --- i --- i ---------- i ---- i ---
0 2 4 6 8 10 12 14 16
root

Figure 4.3: SCREE plot for HBOI 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




r = ax. (4.7)

In equation 4.7, x and y are the two variables being correlated, ax is the

covariance of x and y, ax is the standard deviation of x, and ay is the standard

deviation of y. When two variables are independent axy = 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




2.5









root
Ij 2 -
C
S 1.5

10

0
0

0.5 o
0

0 2 4 6 8 10 12 14 16
root

Figure 4.4: SCREE plot for UF data set




First, each parameter that showed some statistical and real world significant'

correlation with light attenuation was used as the independent variable in a simple

linear regression. Variables were also chosen if some known physical relationship

existed between the parameter and light attenuation (e.g. chlorophyll is known to

absorb PAR). The slope and intercept of each regression were calculated using the

REG procedure (Fruend and Litell, 1981, SAS Institute Inc., 1990) in the previously

mentioned SAS statistical software. In addition, a p value 8 was calculated using

an F-test, as described in equation 4.8 (Weimer, 1987, Wonnacott and Wonnacott,

1985), and an adjusted r2 or coefficient of determination9 was calculated according

to equation 4.9 and equation 4.10.

'All analyses in this study were considered at an alpha level of 5 % (a = 0.05). Thus, if a p value
was less than a, the null hypothesis was rejected and the correlation was statistically significant.
A correlation was considered to have real world significance if its Pearsons's correlation coefficient
was 0.60 or higher
8a p value is the probability that an observation is due to random chance alone.
9The coefficient of determination is theoretically equal to the square of Pearson's correlation
coefficient. This is the reason for the r and r2 notation (Weimer, 1987)








Table 4.9: Correlation between parameters in SERC study

depth time Po 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


SSR
F(df, df2) = 2 (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, Ho, that the model does not predict the dependent variable (KPAR

in our case).

n-i
adjusted r2 = 1 ( l- ) (4.9)
n l
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 EXT400 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
EXT400 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


SSE
2 =1 SS (4.10)
SST
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 molarityy], has a relatively large (r2 = 0.38) determi-

nation 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

Y 1.4

1.2

1

0.8

0.6

0.4
0



Figure


4.5:


data o
- model ---






o
-0

-, 0



"--

o
O -----



1 2'45 6 7
^ ''~


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 0

2 '---.

1.8 --.

I 1.6 o '- 0o
- "--.. o o o o
1.4 --

1.2 o

So $ o
1 0 0
00 0
0.8
0 o
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 -

2 .-''

1.8 0


a o .-""
.. 1. o o /,+ 4 o-

l 1.4 o -


o 1



0.8
00
0.6 0
o

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
datI 0
2.4 0. mod|l ---
2.4

2.2 o

2 0

1.8


2 2. o. 0
c- 1.6 o 0.o ,






01.2
1 /* o o

0.8
oo
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 mg. Statistical analysis results in F(1, 52) = 92.01

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 atten-

uation will also apply to organic carbon.

Variations in po, 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 a
2.4 model--
2.4

2.2 .
-


2
1.8
0 -




a a +-
1. a%-' a0 0 a
00 0 0
1.2 o









2 0 2 4 6 8 10 12 14 16
DOC


Figure 4.9: DOC based statistical model for SERC data
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
Mu_zero


Figure 4.10: po based statistical model for SERC data


KPAR = 1.74 x /o 0.24


(4.15)


data o
model ---.

a a

o

0


0 0
8 .. a

a a a--
------ -"- a o




0 0
0


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. Po (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 (Mcpher-

son and Miller, 1994). In hindsight, this is to be expected in the more turbid coastal

waters10 of the Indian River Lagoon where attenuation is dominated by absorption

(Kirk, 1984). It is therefore most likely acceptable to neglect Po 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 .

10The TSS (a surrogate of turbidity) is high enough to easily be classified as turbid compared
to Tampa Bay, TSS a 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 through-

out 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 chloro-

phyll 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 o
2.4 model ---

2.2 0

2 -

1.8

rc 1.6 o
1 o - - ..--
1.4 o ... ..-- ------------------ --



00
1.2 .. -




0.8 -

0.6 -

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 -o o



4-



3 0

00 0
2 aAo a a'
S00 0 0 00
a a
$0000 % 0





0 2 4 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. Sta-

tistically, 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 e o
data o
o model ----
,o o
++ a
6 -



a-- o o-

5 *

o 1o 0 00 0 o









Figure 4.13: Chlorophyll based statistical model for HBOI year 1 data
R = 00 c + 1
2 0 a a










with F(1,265) = 45.28, ap value of 0.0001, and an adjusted 2 = 0.14.
o 0
0 10 20 30 40 50 60 70 80 90 100
Chlorophyll

Figure 4.13: Chlorophyll based statistical model for HBOI 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 4.13.chi is in a in 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 ----



6 0 50,0''

5- o oo o-
4 00 0
o o y\
4 0 0 0 -o
3 00 0W 0o
o 0 .


000


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 o
o / model ----
o so /
S 00
6



5 00
o

4 -
2 o/o o





1 "0 o0 0

3 0 0 00 --


2 0* 0 0
//" o








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
o modeF'--
o




0a 0

00 0





0 Of0 0 0 0
o o 0
o o







0 0
a O 0o
03eF


250 300






67


7 o'0o o
data 0
o model ----
6 0
6-

5 o0

5 o 0
4 0--





SC0 *
0 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 mea-

surement 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

1Phosphorus does not directly attenuate light itself any more than most particles.






68



data o
model ----
0 0



o.
6 -

5o o o

0 0 0 0
I0 000 ,-
S 0 0 0 0 0 0 0 0
000 *0 0 0
















KPAR = 19.20 x TP + 0.71 (4.24)
So oo o p m









to be laden with phosphoruS2





















4.4.3 HBOI Year 2 Single Variable Regressions


For the second year HBOI data set, color, turbidity, TSS, OSS, ISS, TP, and
0 o 0 0
-0 00

0 0.02 0.04 0.06 0.04 00.1 0.12 0.14 0.16 0.18 0.2
TOTTP





KPAR = 19.20 x TP + 0.71 (4.24)



that loads the water with chlorophyll, or phosphorus might be a simple tracer. Per-

haps the sediments best at attenuating sunlight (turbidity, TSS, ISS, &F OSS) happen





















4.25.
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 o00 00 -.
-0 00
3 _- w> ,o <,.+,+<+ = ,--"
AR 0.04 chl + 1.14 (4.26)
4- r 0 0%,0oo0*o
0 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 j. For the second year data much different results

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 ',

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 o
model ---
6 0






0* o
oa o















KPAR = 0.12 x turb .81
So ooo '
3 Ito 0 O -





0 5 10 15 20 25 30 35 40 45 50
Turbidity

Figure 4.21: Turbidity based statistical model for HBOI year 2 data


KPAR = 0.12 x turb + .81


(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 data -o
model----
6

00 0
0
5
000
0




S00 2 000 0 0





Or: o e o 00 s0o o
0 0 0
00 >0 0

0 --- --- -------------- ----------------------



0 10 20 30 40 50 60 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



o 5
0 00
l 0o 000 0
3
S000 00
0 *o




0
0.5 0 0.1 0.








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 'g. F(1, 501) was
found to be 100.36, resulting in ap value o 00001 and an adjusted 2 = 0.17. Despite









the still high T2, this represents a 10 % decrease from first year data. Equation 4.31
0 00 % o08 00 8000









shows the TP model, and it is shown graphically in Figure 4.25.
TOTTP










FigureTable 4.19 shows several of the bebased statist single variable models for the HBOI year 2 data
KPAR = 11.90 x TP + 0.92 (4.31)










2 data set for comparison. Four of the sevfficien of determination of any diret chemicals of

0.0001, measurement taken in the irrefutably stair 2 stically significant. It is interesting to note,501) was

that measurfound to be 100.36, resulting in a p value from highly significant in the year 1 data
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 HBOI year 2 study

Parameter N r2 p value
color 502 0.190 0.0001
turb 502 0.370 0.0001
TSS 502 0.002 0.8205
ISS 502 0.002 0.6787
OSS 502 0.002 0.8002
TP 502 0.170 0.0001
chl 502 0.150 0.0001



(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, TOC, and chlorophyll

were examined as single variable regression models.

Location within the lagoon has a modestly large (for this data set) r2. 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 a
model --
6 -


5
a 0


4 a a




10
3 --.--- --- --- o

o - ... -.. o
8" 0 a 0 a
*a a 0a g a


2 a a
0 a a a a
a a


0
.0 0


0 s s A e 1 0 ole
3.08e+063.09e+063.1e+063.11e+ a3.12e+06B.13e+06.14e+063.15e+063.16e+063.17e+063.18e+f0 .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 a
model --.

6










-.- --- -- --- -- -- -- -- -- --





a00
S0 0 0






o0 100 11 2 120 130 140 150 160 170 180
3 a











Julian Day


Figure 4.27: Julian day based statistical model for UF data

KPAR = -0.005 x Julian day + 2.98 (4.33)
90 10 1 10 10 4 10 16 7 180
2~ tJulian Day

Figur 4.7 Juindybsdsaitia oe o Fdt

KPA = 005xJla a .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 o




4 0
0

4 0 0 0 0
Tim0
0 o 00 -----oo 0 0
3 0- o --

KPAR = 41 10 time + 1.45 (4.34)


So a s l n o
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

r2 = 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 o
model ----




5
o

0 0
0 o
.oo
2 A2
----------------- --- ----- .----
3 o o o -

O O
ao a o- o a



a1 0 0
o 0 o o
0
o




0 1 2 3 4 5 6 7 8
DO


Figure 4.30: Dissolved oxygen based statistical model for UF data


KPAR = 0.04 x DO + 2.13


(4.35)


(4.36)





























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 r2 = 0.08. These results are derived from equation 4.32 and Figure 4.32.

pH has a small (r2 = 0.04) but significant (p = 0.0020) relationship with

KPAR. Salinity also explains a somewhat large amount of variability (r2 = 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 o $/ ''
7 -





o % ,i P --"""
6 0 o
5

4 0 -0

3 -




0
0 0.02 0.04 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

KPAR = 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 r2 = 0.18. Equation 4.39 shows this





80


regression with TP in units of '-. The same model is shown graphically in Figure

4.33.
7
data a
model ---


5



0













KPAR = 0.22 x TN + 2.02 (4.40)


with a3p value of 0.0001 and adjusted 2 = 0.13.
.. ----_------- o-- S|g "
2 ------------------- ---^ $




0 o.5 1 1.5 2 2.5





KPAR = 0.22 x TN-+ 2.02 (4.40)





F(1, 198) = 1.530 with ap value of 0.45492175 and an adjusted 2 = 0.00. The model is shown graphically in

Figure 4.34

TSS is one of the better predictors of KPAR (r2 = 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 !a, was found to be significant with F(1, 198) = 29.715

with a p value of 0.0001 and an adjusted r2 = 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 ---




5
0 ..''


4o o

am odea o" "


3 o o ?-"

0 400 "a 0

25
2 o .O o







04
Co

0 10 20 30 40 50 60
TSS


Figure 4.35: TSS based statistical model for UF data



KPAR = 0.07 x TSS + 1.81 (4.41)










7
data o
model --
o
6 -00 a


5
0.0








3 0 a a
-a--- --------------------- aa a a-
a.. -------- _* ---- -

2 a a Ia4 a 0-----------
too



O0 0 a00

0 5 10 15 20 25 30
Color


Figure 4.36: Color based statistical model for UF data



KPAR = -0.03 X color + 2.78 (4.42)
Fiue .6 Clr ae saisia mode o Fdt

KPA -00 oo .8(.2















5 2 0 0 35 0
KPAR = -02 TOC + 3.12 (4.43)
equan 4.43 *d F e
3 ----- ------------------- ---
2o .












an adjusted 22 = 0.05. This regression is shown in equation 4.44 and Figure 4.38.
S10 15 20 25 30 35 0 1 a
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 intme, F(,t198) = 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 o
model -----
o
00 % a




0 a a
o o


o a 0aa of -------------
r o ..,.-o-0- ?" o
-a a 0 a a


"0 a 0a a 0


0.5 1 1.5 2 2.5 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)




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