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 NonLinear 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 NonLinear 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 nonfactorial models . . ... 108
4.24 Approximate Indian River Lagoon segment boundaries . . ... 111
4.25 Ftest 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 nonlinear, 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.
SHOArGRASS
Figure 1.2: Halodule wrightii
IrhitrgnadiIntjlifnrn
MANAGE IELCSS
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
TURTLEGRASS
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 SEAGILSS
Figure 1.7: Halophila johnsonii
Ruppia aritia .ma
AIvDGEONGRASS
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 (manmade) 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 Wm2 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 m2 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 m2, so Q = 400 J1 for each square meter of the surface
and c, = 3900 J kg' Kl,. 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 kg1)(1025 kg) 1 s
Twelve hours of sunlight would result in the upper meter's temperature in
creasing by
AT = (5 x 106)(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 m2 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 1034)(3 x 10 ms1) 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 1034n 1.2 x 106 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 sl1
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 reemitted 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 reemitted 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 s1 m) (1.14)
J350 nm hc
EPAR can also be expressed in einst s1 m1, where one Einstein is one mole
of photons. Equation 1.14 is then simply,
1 p700 nm A
EPAR = 6.02 1023 Eo(x, A)dA (einst s1 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 m2srnm1). (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 m2srnm1). (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 m2srnm ). (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 m2srlnm1). (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 msrnm1). (1.20)
J0 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 2srlnml). (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 singlescattering 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 nonchlorophyll matter in attenuating
visible light. They found that in Charlotte Harbor nonchlorophyll 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 PtCo 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, I9 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 m2 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 m2 nm1). (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 m2 nm1). (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 m3 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 
1012m3. 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 53 ppt sal
depth m depth
time HHMM time
salinity data was collected, but not released
Vertical salinity profiles were measured with a Beckman RS 53 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)
orthophosphate
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 m1 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 m1 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 nspace 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 m1 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 scientistnot an algorithmcan 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 m1 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 5space. 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 Ftest, 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).
ni
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. modl 
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
acidswhen carbon analysis is not usedis 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 nonsignificant
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 nonchlorophyll 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 reexamine 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 105 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 104 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 Sg "
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 ..,.o0 ?" 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)
