4 '
SPATIAL AND TEMPORAL DYNAMICS IN THE EVERGLADES ECOSYSTEM
WITH IMPLICATIONS FOR WATER DELIVERIES TO EVERGLADES
NATIONAL PARK
By
LANCE H. GUNDERSON
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1992


Copyright 1992
by
Lance H. Gunderson

Dedicated to Gene, Dorothy and Sara Gunderson
My immediate links with the past and the future

ACKNOWLEDGMENTS
The author is indebted to numerous individuals and agencies, without
whom this work would not have been completed. First and foremost, my
deepest thanks go to Buzz Holling, for his support and guidance in the midst of
shifting paradigms, but most of all for teaching me that it is important to have
fun in the endeavor of science. I am very grateful to J.J. Delfino, who has been
extremely supportive as chairman of the committee. Committee members
Warren Viessman, Ronnie Best and Dan Spangler all provided expert comments
and assistance. Clay Montague and H.T. Odum are acknowledged for their
input in the early stages of the work.
Friends, family and colleagues all assisted with various tasks. John
Stenberg is gratefully acknowledged for his help on tasks too numerous to list.
Dave Sikkema, George Schardt, and Bob Johnson provided data from Everglades
National Park. John Stenberg and Alan Herndon were integral parts of the
evapotranspiration studies. Steve Davis, John Richardson, and Jennifer Silviera
all provided maps used in the cross scale analyses of the vegetation. Steve Light
helped enlighten (groan) me on the theories and practice of public policy and
water resources. No thanks would be too much for Carl Walters. Candy Lane,
Toni Carter, Keiley and Kenny Pilotto all helped with tasks along the way.
Finally, I am grateful to Bev, for taking care of all the details that enabled me to
tackle this project, and everything else.
This work was supported by grants from the South Florida Water
Management District, the Division of Sponsored Research at the University of
Florida and funds from the Arthur R. Marshall, Jr. Chair in Ecological Sciences.
IV

TABLE OF CONTENTS
page
ACKNOWLEDGMENTS iv
LIST OF TABLES vii
LIST OF FIGURES viii
ABSTRACT xvi
CHAPTER I. INTRODUCTION TO THE EVERGLADES ECOSYSTEM 1
The Everglades Ecosystem 3
Hydrology 7
History of Human Use 10
Water Management 12
Water Deliveries to Everglades National Park 18
Managing Ecological Systems 23
Summary 25
CHAPTER 2. POSING THE QUESTIONS 26
Views of Ecosystem Structure and Function 27
Hypotheses 31
Water Deliveries to Everglades National Park - The First
Hypothesis Set 32
Cross-Scale Patterns In The Everglades Ecosystem - The
Second Hypothesis Set 33
Objectives 34
CHAPTER 3. MODELING THE "RIVER OF GRASS” 36
Background 38
Evapotranspiration in Wetlands 38
Measurements of Evapotranspiration in southern Florida 40
Transpiration from Three Everglades Plant Communities 43
Measurements of community evapotranspiration 46
Flow in Wetlands 51
Ecological Models and Scale 54
Model Description and Development 56
Hydrologic Components 56
Vegetation Components 59
v

Changes in Landscape Vegetation Types 62
Development of Flow Coefficients for Landscape Units 65
Development of Evapotranspiration Coefficients for Landscape
Units 67
Results 70
Sensitivity Analysis- Flow and Evapotranspiration 71
Agreement with Historic Data 73
Linkages between hydrology and vegetation 77
Flow and upstream area 84
Summary 89
CHAPTER 4. A CROSS SCALE EXPLORATION OF THE EVERGLADES
LANDSCAPE 93
Methodology 94
Methods to Detect Discontinuities 100
Methods to Analyze Patterns of Self-Similarity 103
Techniques of estimating fractal dimensions 107
Fourier analysis 112
Summary of Methodology 113
Data Sets Used In The Cross-Scale Analyses 116
Fire data 122
Hydrologic data sets 127
Evaporation Data 127
Sea Level Data 128
Results Of Cross-Scale Analyses 129
Topographic data 132
Vegetation Patterns 138
Fires 144
Rainfall 153
Water Levels 173
Water Flow 184
Fires 187
Sea Level 187
Temperature and Pan Evaporation 192
Discussion of Results 203
Summary 214
CHAPTER 5. AN END AND A BEGINNING 217
A Summary 217
Understanding Ecosystem Dynamics through Alternative
Paradigms 221
Prognosis for System Restoration 223
LITERATURE CITED 226
BIOGRAPHICAL SKETCH 239
vi

LIST OF TABLES
Table 1. History of major water management structures in the
Everglades ecosystem that influenced water deliveries to
Everglades National Park 14
Table 2. History of major water management policies that influenced
water deliveries to southern Everglades and Everglades
National Park 15
Table 3. Daily transpiration rates for three vegetation types in the
Everglades 45
Table 4. Description of vegetation categories (landscape units) used
in Everglades model 61
Table 5. Vegetation density and related flow coefficients as a function
of depth for sawgrass, tree island, wet and marl prairie
vegetation types 64
Table 6. Spatially weighted flow coefficients for each landscape unit
used in the Everglades Model 67
Table 7. Average daily and annual evapotranspiration for plant
communities used to develop evapotranspiration
coefficients for Everglades model 68
Table 8. Summary of data sets used in cross-scale analyses of
Everglades ecosystem 130
Table 9. Summary of cross-scale analyses of spatial data sets,
indicating break points detected by fractal and gap
analyses 131
Table 10. Summary of cross-scale analyses of temporal data sets,
indicating dominant frequencies found in each set 131
vii

LIST OF FIGURES
Figure 1. Location of the Kissimmee River, Lake Okeechobee and
Everglades Drainage Basin in Southern Florida 4
Figure 2. Current broad scale land-use designations in the historic
freshwater Everglades drainage basin 6
Figure 3. Mean daily transpiration rates from sawgrass, tree island
and marl prairie plant communities 47
Figure 4. Time course of mean daily evapotranspiration (cm/day) at
study sites P33 and P37 from February 1985 through
September 1986 49
Figure 5. Model grid used to depict hydrologic and vegetation
dynamics in Everglades ecosystem 57
Figure 6. Location of sample rain and stage gauges, flow sections and
pan evaporation sites within the Everglades region 60
Figure 7. Percent cover of sawgrass, wet prairie, and tree island in
various window sizes 63
Figure 8. Effects of doubling and halving flow coefficients on
simulated flow through Tamiami flow section 72
Figure 9. Effects of varying base evapotranspiration rates on
simulated flow through Tamiami flow section 74
Figure 10. Time series of simulated (solid lines) and actual (dashed
lines) stages at gauge P33 from 1960 to 1988 75
Figure 11. Time series of simulated (solid lines) and actual (dashed
lines) stages at gauge P35 from 1960 to 1988 76
Figure 12. Map codes for initial landscape vegetation types in the
Everglades model. Dominant code in the Everglades
proper is type 1. Cover types developed from Davis
(1943). Explanation of codes is found in Table 4 79
vm

Figure 13. Map codes of landscape vegetation types in grid cells of
Everglades model at end of 28 year simulation run. Note
presence of type 3 codes in right -central portion of array.
See Table 4 for explanation of codes 81
Figure 14. Results of changing vegetation patterns on simulated flow
through three flow sections in the southern Everglades 83
Figure 15. Difference in predicted stage between models with and
without vegetation linkages of succession,
evapotranspiration and flow. The model without
linkages tended to predict higher stages (less than 0.5 ft),
under both the natural and managed scenario 85
Figure 16. Three dimension plot showing increase in annual flow (z) as
upstream area is increased (y) over a 28 simulated year 87
Figure 17. Log-log plot of simulated flow versus upstream area. Scatter
due to differences in annual rainfall. Gray area
represents bounds of actual flow and equivalent area 90
Figure 18. Rank order plot, difference indices 1 and 2 for mock data set
designed to simulate continuous normal distribution.
Distribution has mean of 50. For smooth curves such as
this, no value of Dll is significant. No sequential values
of DI2 are significant 99
Figure 19. Rank order plot, difference indices 1 and 2 for mock data set
derived from uniform random distribution. Values of
both Dll and DI2 are significant, yet values between gaps
exhibit no pattern 100
Figure 20. Rank Order Plot, Difference Indices 1 and 2 for mock data
set designed to show gaps. Gaps are values of difference
indices (1 and 2) outside a 95% confidence interval.
Clumps are not evident, but indicated by a pattern of
uniformity small groups of difference indices 101
Figure 21. Sample Koch curves to show patterns of increasing fractal
dimension (1.5 -1.7), from Mandelbrot (1983) 108
Figure 22. Example of first four levels or divisions for rendering data
into a quadtree storage format Ill
IX

Figure 23. Log-log plots of tile size versus number of tiles for three
Koch Curves of known fractal dimension. Fractal
dimension is estimated by the negative slope of curves.
Actual fractal dimensions (D) of curves are A) D=1.5, B)
D=1.63, C) D=1.71, as shown in Figure 21 113
Figure 24. Fourier analysis of random mock time-series data, showing
time-series plot (top) and spectral plot (bottom). This
data set was created by taking 64 samples from a uniform
random number distribution. No peaks are significant in
the spectral plot 116
Figure 25. Fourier analysis of structured mock time series data,
showing time-series plot (top) and spectral plot (bottom).
This data set was created by combination of two sine
waves 117
Figure 26. Top transect maps 120
Figure 28. Sample vegetation map, showing patterns of sawgrass
within a 160 m window 125
Figure 29. Sample vegetation map, showing pattern of sawgrass within
a 1600 m sample window 126
Figure 30. Sample vegetation map, showing pattern of sawgrass within
a 16 km sample window 127
Figure 31. Location and size of sample window within which recent
fire histories were analyzed for spatial and temporal
patterns 128
Figure 32. Topographic surveys from transects 1 through 4 ( see Figure
4 for locations) showing elevational variation with east
west distance 135
Figure 33. Topographic surveys from transects 5 through 8 ( see Figure
4 for locations) showing elevational variation with east
west distance 136
Figure 34 Topographic surveys from transects 9 through 11 ( see
Figure 4 for locations) showing elevational variation with
east west distance 137
x

Figure 35.
Figure 36.
Figure 37.
Figure 38.
Figure 39.
Figure 40.
Figure 41.
Figure 42.
Figure 43.
Log-log plot of transect length versus step length (top plot)
used to estimate breaks in fractal dimension. Bottom plot
shows results of rolling regressions. Break in top plot is
indicated at point of maximum regression coefficient
(bottom plot) 138
Log-log plots of box size versus box count used to estimate
fractal dimensions of sawgrass vegetation within three
sample windows. Estimates of fractal dimension are
given by slope of regression. Data from three windows
are combined in lower right plot, and suggest a break in
the fractal dimension 141
Log-log plots of box size versus box count used to estimate
fractal dimensions of wet prairie vegetation within three
sample windows. Estimates of fractal dimension are
given by slope of regression. Data from three windows
are combined in lower right plot, and suggest a break in
the fractal dimension 142
Log-log plots of box size versus box count used to estimate
fractal dimensions of sawgrass vegetation within three
sample windows. Estimates of fractal dimension are
given by slope of regression. Data from three windows
are combined in lower right plot, and suggest a break in
the fractal dimension 143
Rank order plot (top plot) and difference indices (bottom
plot) for sawgrass patches sampled from 1600 m
windows 145
Rank order plot (top plot) and difference indices (bottom
plot) for wet prairie patches sampled from 1609 m
windows 147
Rank order plot (top plot) and difference indices (bottom
plot) for tree island patches sampled from 1609 m
windows 148
Rank order plot (top plot) and difference indices (bottom
plot) for sawgrass patches sampled from 16 km
windows 149
Rank order plot (top plot) and difference indices (bottom
plot) for wet prairie patches sampled from 16 km
windows 150
xi

Figure 44. Rank order plot (top plot) and difference indices (bottom
plot) for tree island patches sampled from 16 km
windows 151
Figure 45. Rank order plot of log fire sizes from Shark River Slough,
1958-1979 153
Figure 46. Difference Indices 1 and 2 used to determine gaps in fire
sizes, Shark River Slough, 1958-1979 154
Figure 47. Time series plot of daily rainfall data from Tamiami Ranger
Station, 1949 through 1977 156
Figure 48. Time series plot of daily rainfall data from Royal Palm
Station, 1949 through 1977 157
Figure 49. Spectral plots from Fourier analysis of daily rainfall from
Tamiami Ranger Station, indicating dominant annual and
monthly cvcles 158
Figure 50. Spectral plots from Fourier analysis of daily rainfall from
Royal Palm Station, indicating dominant annual and
monthly cycles 159
Figure 51. Rank order plots of daily rainfall data, Tamiami and Royal
Palm Stations 160
Figure 52. Difference index 2 versus rank order for daily rainfall data.
Bars represent value of index, gray areas represent mean
+ 95% C.1 161
Figure 53. Time series plot of monthly rainfall data from Royal Palm
and Tamiami Ranger Stations, 1949 through 1977 163
Figure 54. Spectral plots from Fourier analysis of monthly rainfall from
Tamiami Station, indicating dominant annual and
monthly cycles 164
Figure 55. Spectral plots from Fourier analysis of monthly rainfall from
Royal Palm Station, indicating dominant annual and
monthly cycles 165
Figure 56. Rank order plot and difference index 2 for monthly rainfall
data from Tamiami Ranger Station. Arrows locate
significant gaps 166
Xll

Figure 57. Rank order plot and difference index 2 for monthly rainfall
data from Royal Palm Station. Arrows locate significant
gaps 167
Figure 58. Time series of total annual rainfall at Tamiami and Royal
Palm Stations 168
Figure 59. Spectral plots from Fourier analysis of annual rainfall data
from Royal Palm and Tamiami Stations 170
Figure 60. Rank order plot and difference index 2 for monthly rainfall
data from Royal Palm Station. Arrows locate significant
gaps 171
Figure 61. Hierarchical Cluster Tree for annual rainfall at Royal Palm
Station 172
Figure 62. Rank order plot and difference index 2 for monthly rainfall
data from Tamiami Ranger Station. Arrows locate
significant gaps 173
Figure 63. Hierarchical Cluster Tree for annual rainfall at Tamiami
Ranger Station 174
Figure 64. Time series plots of monthly water levels at gauging stations
P33 and P38, from 1958-1979 176
Figure 65. Time series plots of monthly water levels at gauging stations
P35 and P37, from 1958-1979 177
Figure 66. Spectral plots from Fourier analysis of monthly water level
data from four P stations 178
Figure 67. Spectral plots from Fourier analysis of daily water level data
from four P stations 179
Figure 68. Rank order plots of daily water level data from stations P33
and P 35 180
Figure 69. Rank order plots of daily water level data from stations P37
and P 38 181
Figure 70. Rank order plot and difference index 1 for monthly water
level data at station P33 182
Figure 71. Rank order plot and difference index 1 for monthly water
Xlll

level data at station P35.
183
Figure 72. Rank order plot and difference index 1 for monthly water
level data at station P37 184
Figure 73. Rank order plot and difference index 1 for monthly water
level data at station P38 185
Figure 74. Time series plot of monthly water flow across Tamiami Trail
flow section 1940-1982 187
Figure 75. Spectral plots from Fourier analysis of monthly flow across
Tamiami Trail flow section 188
Figure 76. Rank order plot of monthly water flow across Tamiami flow
section 190
Figure 77. Difference indices 1 (top plot) and 2 (bottom plot) for
monthly flow data, Tamiami flow section 191
Figure 78. Time series plot of log fire sizes (top plot) from 1958-1979,
and spectral analysis (bottom plot) indicating dominant
cycles in fire data 192
Figure 79. Time series plots of mean monthly sea level elevation at Key
West, Miami, and Naples for the time period 1910
through 1990 193
Figure 80. Spectral plots from Fourier analysis of detrended sea level
data from Key West. Dominant cycle is the annual
period 195
Figure 81. Spectral plots from Fourier analysis of detrended sea level
data from Miami. Dominant cycle is the annual period 196
Figure 82. Spectral plots from Fourier analysis of detrended sea level
data from Naples. Dominant cycle is the annual period 197
Figure 83. Time series plot of mean monthly minimum and maximum
air temperatures from Belle Glade and Tamiami Ranger
Stations 198
Figure 84. Spectral plots from Fourier analyses of maximum and
minimum monthly temperature data from Belle Glade 199
Figure 85. Spectral plots from Fourier analyses of maximum and
xiv

minimum monthly temperature data from Tamiami
Ranger Station 200
Figure 86. Time series plots of monthly pan evaporation from Belle
Glade and Tamiami Ranger Stations, 1965 through 1991 201
Figure 87. Spectral plots from Fourier analyses of monthly pan
evaporation from Belle Glade and Tamiami Ranger
Stations, 1965 through 1991 202
Figure 88. Time series plots of daily evapotranspiration and pan
evaporation at site P33, January 1985 through October
1986 203
Figure 89. Time series plots of daily evapotranspiration and pan
evaporation at site P37, January 1985 through October
1986 204
Figure 90. Spectral plots from Fourier analyses of daily
evapotranspiration at sites P33 and P37. Bars represent
magnitude of cycle, gray 95% C.1 206
Figure 91. Spectral plots from Fourier analyses of daily pan
evaporation at sites P33 and P37. Bars represent
magnitude of cycle, gray 95% C.1 207
Figure 92. Results of mini-model , frequency of rain input (A), ET
outflow (B), and stage fluctuations (C). Note difference
in time range, stage plot covers 40 simulated years 211
Figure 93. Hydrologic hierarchies in the Everglades ecosystem,
showing scales of dominant frequencies in surface water
and atmospheric variation 213
Figure 94. Topographic hierarchies in the Everglades ecosystem,
indicating breaks between microtopographic and
macrotopographic features and processes 215
Figure 95. Vegetation hierarchies in the Everglades ecosystem, showing
scales of plant species, communities, landscape units and
the Everglades ecosystem as defined by breaks in the
fractal dimension 217
xv

Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
SPATIAL AND TEMPORAL DYNAMICS IN THE EVERGLADES ECOSYSTEM
WITH IMPLICATIONS FOR WATER DELIVERIES TO EVERGLADES
NATIONAL PARK
Lance H. Gunderson
December 1992
Chairman: Joseph J. Delfino
Cochairman: C.S. Holling
Major Department: Environmental Engineering Sciences
The Everglades is a unique wetland ecosystem. During this century, the
ecosystem has been partitioned for disparate uses of human habitation,
agriculture, water conservation and ecosystem conservation in a national park.
The sustainability of Everglades National Park is dependent upon upstream
water sources. Water management in the Everglades and water deliveries to the
Park are linked to human perceptions of ecosystem dynamics.
One line of inquiry used expansion of a state-of-the-art computer model to
examine the upstream area that once contributed water to the Park. Linkages
between vegetation and hydrology were added as vegetation mediation of
evapotranspiration and flow and hydrologically induced vegetation changes, but
neither addition appreciably improve understanding of hydrodynamics in the
Everglades system at the scale of the model. Prior to management, the entire
system, south of Lake Okeechobee, contributed flow to Everglades Park except
xvi

during dry years. Since the onset of intensive water management, an equivalent
area of only about one-third of the historic drainage basin has supplied water
into the Park. But these conclusions are dependent upon the assumptions made
to represent the system at a specific spatial-temporal scale in a model. At other
scales the conclusions could well be different. That led to the second major topic
of this thesis; that of cross-scale structure and dynamics.
A cross-scale mode of inquiry suggests that ecosystems exhibit
discontinuities in spatial structures and temporal patterns across time and space
due to the interaction of key processes operating over different scale ranges.
Spatial patterns in the topography, vegetation and fire data sets exhibited scale
regions of self-similarity separated by distinct breaks. Temporal patterns of
rainfall, stage, flow, evaporation and sea-level exhibited multiple cycles. These
analyses support the theory that ecosystems are structured around a few
keystone variables of mixed spatial and temporal dimensions. Dramatic
discontinuities appear in patterns as a result of the interactions of processes
operating at different space and time domains. This emerging viewpoint of
ecosystem structure and dynamics will hopefully provide a basis for new
understanding and hence improved management of this unique ecosystem.
xvi 1

CHAPTER 1.
INTRODUCTION TO THE EVERGLADES ECOSYSTEM
There are no other Everglades in the world.
-Marjory Stoneman Douglas
The Everglades is a wetland ecosystem unlike any other on Earth.
Situated in the subtropics of southern Florida, the unique combination of
physiography and biota blend into a landscape whose name is internationally
recognized. Undoubtedly some of the values and distinctions that the area now
holds are due to attributes of the natural system. During the twentieth century,
the human population in and around the Everglades ecosystem has increased
dramatically, resulting in a myriad of demands on and uses of a unique
ecosystem. Many of the current management problems are associated with the
historical spatial partitioning of resources within a once contiguous ecosystem.
The pattern unfolding throughout the past century is one of a transition of land
uses, from a pristine wetland with negligible human use to one dominated by a
variety of human uses each with characteristic spatial and temporal domain.
These varied land uses range from intensive agriculture in the northern
Everglades to Everglades National Park in the south.
The primary purpose of this work is to improve understanding of the
critical processes and factors in the Everglades ecosystem that influence water
deliveries to Everglades National Park. The issues surrounding water deliveries
to the park cannot be described from a single moment in history nor from a
spatial perspective of the current border of the park. Indeed, the water problems
l

2
of the park are woven throughout a rich tapestry extending back thousands of
years and covering the southern half of peninsular Florida. In order to make the
problem tractable, the dissertation is divided into five chapters. The introductory
chapter contains descriptions of the natural and human histories in the system
that lead to a conclusion that water management is fundamentally linked to
concepts of ecosystem dynamics. The second chapter in this work compares and
contrasts alternative concepts of ecosystem dynamics from which the hypotheses
and objectives of the dissertation are derived. The third chapter presents the
results of an attempt to invalidate the hypothesis that the entire Everglades
drainage basin contributed water to the park. The "upstream area" hypothesis
was tested using a state-of-the-art ecosystem model that couples vegetation and
hydrologic dynamics. The fourth chapter contains the results of analyses of a
series of data sets that are used to test the second hypothesis, based on an
alternative concept, and seeks to understand system dynamics based upon a
recognition of the role of discontinuities in both structure and processes . The
final chapter contains a summary that compares and contrasts the understanding
of system dynamics and water deliveries that were developed in chapters three
and four and presents implications of these results on water management and
policy.
This introductory chapter is devoted to describing both the natural and
human components in the Everglades ecosystem. First, the components and
processes of the pristine or natural Everglades ecosystem are described. The next
three sections are historical accounts, documenting the increasing human
involvement with the system. These historical accounts include a brief history of
relevant human activities, a review of how water management developed in
southern Florida, and finally, how the understanding and policies of water
deliveries to Everglades Park have changed. This chapter concludes with a

3
description of the linkages between management, policy and understanding of
system dynamics, and how these relationships have evolved in this complex
wetland system.
The Everglades Ecosystem
The Everglades is a distinct physiographic region located in southern
Florida, and its natural features have been described for over 100 years (Heilpren
1887, Willoughby 1898, Harshberger 1914, Harper 1927, Davis 1943, Craighead
1971, Gunderson and Loftus In Press). Prior to intervention by man, the
Everglades encompassed approximately 10,500 km^ of freshwater marshes,
sloughs and hardwood tree islands (Davis 1943). The system was approximately
210 km along the north-south axis, bordered by Lake Okeechobee on the north
and Florida Bay on the south. The widest east-west dimension was 77 km, from
the higher Atlantic coastal ridge on the east to the Big Cypress Swamp on the
west (Figure 1).
The wetland complex is a result of a large arcuate trough in the
underlying limestone bedrock. Three surficial formations are recognized, and all
were formed by shallow marine accumulations during the Pleistocene Era,
primarily the Sangamon interglacial stage (Parker and Cooke 1944). The Fort
Thompson formation underlies the northern Everglades, and is comprised of
marine and freshwater marls beds interleaved with limestone and sandstone.
The Anastasia formation is found in the northeastern Everglades, and is
characterized by sandy limestone, calcareous sandstone. The surficial feature of
the southern Everglades is Miami limestone, comprised of oolitic and bryozoan
facies (Hoffmeister 1974).

4
Figure 1.
Location of the Kissimmee River, Lake Okeechobee and Everglades
Drainage Basin in Southern Florida.

5
The wetland soils of the Everglades are Holocene sediments, categorized
as peats, mucks and marls, and are biogenic. The oldest soils in the Everglades
are approximately 5500 years old (Gleason et al. 1984), dating back to an
approximately 3 m transgression of sea level (Robbin 1984). Peats and mucks are
histosols, named by the dominant recognizable plant remains from which the
soils are derived, and accumulate under extended periods of inundation. The
marls are a calcitic mud, produced by reprecipitation of calcium carbonate from
saturated water during photosynthesis by blue-green algae (Gleason 1972).
The topography of both the bedrock and the soil surface is flat,
characterized by almost no relief with extremely low gradients. The maximum
elevations in the northern Everglades are approximately 5.3 m above the national
geodetic vertical datum (NGVD), and now occur in the Arthur R. Marshall
National Wildlife Refuge (Figure 2). The elevational gradient is mostly north to
south, with an average slope of 2.8 cm/km (Parker et al. 1955). The variation in
elevation is attributed to the underlying bedrock structure and accumulations of
organic sediments. The microtopographic variation is caused by and contributes
to differences in vegetation cover and type.
The vegetation of the Everglades region is a complex of gramineous and
woody wetland associations. The spatially dominant communities are sawgrass
marshes, wet prairies, and hardwood swamp forests (Davis 1943, Craighead
1971, Olmsted et al. 1980, Gunderson and Loftus In Press). Sawgrass marshes,
monotypic stands of sawgrass, Cladium jamaicensc found over peat and marl, are
the ubiquitous, characteristic association of the Everglades. Wet prairies over
peat are sparsely vegetated, generally dominated by either spikerush Eleocharis
cellulosa, or maidencane, Panicum hemitomon. Wet prairies on marl are diverse
association, dominated by sawgrass and muhly grass, Muh-lenbergia filipes, and
contain over a hundred other species (Olmsted et al. 1980).

6
Figure 2. Current broad scale land-use designations in the historic freshwater
Everglades drainage basin.

7
The hardwood swamp forests of the Everglades are called tree islands,
descriptive of the isolated clumps of trees surrounded by the lower stature
wetland grass communities. Dominant species in the tree islands are mostly bay
trees; swamp bay, Magnolia virginiana, red bay, Persea palustris, dahoon holly, Ilex
cassine, wax myrtle, Myrica cerífera.
The Everglades is a unique wetland due in part to the spatial and
temporal patterns of the components of the hydrologic regime. Year to year
variation in the hydrologic cycle results in oscillating periods of flood and
drought. The intra-annual variation is also great, characterized by wet summers
and dry winters. Rainfall and overland flow are the principal inputs, yet the
relative contribution of each to the hydrologic budget is debated. The magnitude
of direct rainfall contribution to the hydrologic regime of the Everglades
distinguishes it from other large freshwater wetland systems such as the Llanos
in Venezuela, the Okavango in Botswana or the Pantenal in Brazil where most of
the marsh water originates from rivers.
The climate of southern Florida is subtropical, classified by Hela (1952) as
a tropical savanna, with insufficient rainfall during the summer months to
compensate for a winter dry season. The area has also been classified as
subtropical moist forest type (Dohrenwend 1977, Greller 1980) due to the high
annual rainfall and moderate annual biotemperatures.
Rainfall over the Everglades exhibits both spatial and temporal variability.
Annual rainfall over the system averages 130 cm (Thomas 1970, Bradley 1972,
MacVicar and Lin 1984). Annual rainfall extremes for the period of record 1940
through 1980 range from low of 95 cm in 1961 to a high of 270 cm in 1947
(MacVicar and Lin 1984). Thomas (1970), using spectral analysis, found about a
seven year pattern within the record, indicative of a cyclical pattern with this
return interval. Rainfall patterns exhibit distinct seasonality; approximately 85%

8
of the annual average rain falls between May and October. Thomas (1970) found
that rain totals during the wet season were bimodally distributed, with peaks in
June and September. Spatial analysis of rainfall records indicate that the coastal
region receives on the average 30 to 35 cm more than the interior marshes. The
northern Everglades and southern Everglades receive more rainfall than the
central regions (MacVicar and Lin 1984).
The rainfall patterns can be related to different processes which influence
the timing and amount of precipitation. The summer rainy season is attributed
to convective thunderstorms, which are linked to mesoscale land-sea breeze
patterns. During the summer, insolation results in differential heating of the air
over the land mass compared to air over the water. The heated air over the land
rises, creating low pressure and establishing a pressure gradient along which
maritime air flows toward the center of the Florida peninsula. The moisture¬
laden air rises, cools adiabatically, condenses, and forms convective
thundershowers. This process has been described as the 'rain machine' (Pardue
1982, Yates 1982). Some authors suspect that rainfall totals have decreased
because drainage and development have altered the net radiation budget
(increased reflectance due to a higher albedo of developed areas) which in turn
decrease the rate of convection (Gannon 1978, Pardue 1982). Statistically higher
rain amounts measured during September have been explained by the greater
incidence of tropical cyclones during this month. Rain during the winter dry
season is associated with the passage of cold fronts that pass on the average
every seven days. Annual variations in frontal passage have been linked to jet
stream location.
Historically, surficial flow left the Everglades system through a number of
pathways. In the northeast, water moved through the cypress-dominated
Hungryland and Loxahatchee Sloughs. Major rivers that carried Everglades

9
waters through the coastal ridge include the New River, Little River and Miami
River. Surface water moved through the higher coastal ridge in a series of
transverse glades. Water flow in the southern Everglades occurred in the broad
shallow depressions of Taylor and Shark Sloughs, named for the rivers that
received the bulk of the flow.
Although the Everglades are recognized as a distinct physiographic
region, it is part of a much larger drainage system, containing a number of river
systems and Lake Okeechobee to the north (Figure 1). Prior to development,
hydrologic connections were traceable to central Florida where the Kissimmee
River originates. The Kissimmee is the largest of the rivers and other smaller
creeks and sloughs which empty water into Lake Okeechobee. Surface water
entered the Everglades from the southern boundary of the lake at two points
when stages exceeded 4.5 m NGVD, and a 52 km long spillway when stages
exceeded 5.6 m NGVD (Parker 1984). The entire system has been referred to as
the Kissimmee-Lake Okeechobee-Everglades (KLOE) system.
The hydrology of the historic Everglades ecosystem can be summarized as
follows. The system is a wide, shallow flat basin, with an overall small
topographic gradient. The primary hydrologic input is rainfall, and although
averages 1.3 m/yr, is characterized by wide spatial and temporal variability.
Other inputs occurred as surface and subsurface flow from Lake Okeechobee and
from wide sloughs in the Big Cypress Swamp. Evapotranspiration is the primary
avenue of water loss, estimated to be 80% of rainfall. Remaining water in the
system flows slowly to the south either to the east recharging the surficial aquifer
of the coastal ridge or the southwest entering the estuarine mangrove zone prior
to reaching Florida Bay. The seasonal patterns of rainfall and evapotranspiration
interact to yield distinct annual wet and dry periods as well as variations in
overland flow.

10
History of Human Use
Evidence of human inhabitance in southern Florida dates to well over
10,000 years. B.P. (Carr and Beriault 1984), prior to the existence of the vast
wetland ecosystem. Written accounts, which date back almost 500 years,
describe native humans using the resources of the wetland ecosystem. Nunez de
Cabeza (1514) relays descriptions of the fierce native Indian tribes that inhabited
the coastal portions of southern Florida and the peaceful Mayami tribes which
colonized the edge of Lake Okeechobee. These early Americans probably burned
the Everglades (Robertson 1954), and used the area for hunting and fishing
purposes.
The name Everglades first appeared on British maps in the early 1800s
(Vignoles 1823) probably a contraction of "Never a glade," descriptive of the large
treeless expanses. With the expansion of European derived settlers throughout
the southeastern coastal plain, native Americans translocated from the Carolinas
to southern Florida. The term "Seminole," which is the name for the major tribes
of current native populations that persist today, means "runaway." The Seminole
term for the area is "Pa-hay-okee", which loosely translates into "grassy lake",
again, descriptive of a non-forested wetland system. These native Americans
used the elevated tree islands for homesites and cultivation of crops, as well as
hunted and fished throughout the system. The United States fought a series of
wars with the Seminóles during the mid 1800s, restricting their territory to a few
reservations through south Florida. One remains within the Everglades proper,
where the Miccosukee Indians still retain land use rights.
The latter part of the nineteenth century marked the first influx of white
settlement and attempts at "reclamation" of the wasteland known as the
Everglades. Soon after Florida became a state in 1845, early settlers and their
governments embarked on programs to drain the Everglades for habitation and

11
agriculture. Buckingham Smith was commissioned by the U.S. Senate to
reconnoiter the Everglades for development potential (Smith 1848). In 1850,
under the Swamp and Overflowed Lands Act, the federal government deeded
7500 mi^ to the state, including the Everglades. The Florida legislature
established the Internal Improvement Fund, whose board was to sell and
improve these swamp lands through drainage. Attempts at manipulation of the
water were ineffective in the 1800s, as the magnitudes of the variations in
hydrology were far greater than the minor control structures could handle.
By 1900, initial colonization of the coastal regions east of the Everglades
was underway. The population of Palm Beach, Broward and Dade counties in
southern Florida in 1900 was 28,000 (U. S. Dept, of Commerce 1990). By 1920, the
major land uses now found in southern Florida had started. Urban development
was occurring along the railroad line down the east coast. Agriculture was
developing in the peat lands south of Lake Okeechobee. Conservation of the
natural resources had begun with the formation of Royal Palm State Park in 1917
in the southern Everglades.
During the period 1920 through 1990, the spatial extent of these land uses
grew, in large around these three general loci. In the 1940s, 283,000 ha of the
northern Everglades was designated as the Everglades Agricultural Area (EAA).
By the mid 1940s Water Conservation areas were designated in the central
regions of the glades to manage water resources for multiple purposes.
Conservationists work started during the 1920s came to fruition in 1935 with the
establishment of Everglades National Park in the southern Everglades, although
the park was not formally dedicated until 1947. The park area was increased in
1989 from 1.4 million to 1.6 million acres by the addition of Northeast Shark
Slough. Urban development along the east coast has followed the exponential
increase in population, and resulted in the drainage and colonization of former

12
wetland areas. As of 1990, 5.1 million people live within the confines of the
historic drainage basin (U. S. Dept of Commerce 1990). The current
configuration of the Everglades ecosystem depicting agricultural areas in the
north, water conservation areas in the central areas and Everglades National Park
in the south is shown in Figure 2.
Through the past century, the spatial extent of the historic Everglades
ecosystem has been slowly whittled away, to the degree that perhaps one-half of
the original system has been irrevocably converted to specific land uses. As of
1985 the historic Everglades ecosystem as defined by Davis (1943), was
partitioned into at least five major use types. Gunderson and Loftus (In Press),
estimate that 32% of the historic Everglades is in areas designated for water
management, 27% in agriculture, 17% for preservation of natural resources, 12%
has been developed for urban purposes, and 12% remains as drained,
undeveloped lands. Davis et al. (In Press), estimate that only half of the original
land area of the Everglades is still in native vegetation types, and that certain
landscape types, including a large pondapple forest in the north as well as
marshes and cypress forests in the east, are gone. The remaining natural areas
have probably been hydrologically altered, and their future viability is largely
dependent upon water management actions.
Water Management
Water management within the Everglades is accomplished by physical
structures and operational criteria. The physical structures consist of levees or
dikes, canals, water control gates (mainly weirs), and pumps. The operational
criteria are constructed around the multiple objectives of the system. The two
primary objectives are flood protection and water supply, having evolved with
the changes in land use within the system and the nature of the historical

13
ecosystem. The history of water management appears to be one where natural
events or crises precipitated plans and activities that resulted in more
infrastructure and attempts to control the variation in the natural system.
Reactions to natural crisis have resulted in changes and development of two
components of water management; the physical structures of water manipulation
(Table 1) and the policies and programs by which water is managed (Table 2).
Canal construction typified the earliest period of water management in the
Everglades. The first large canal in the system was completed in 1882, when
dredges excavated a channel between Lake Okeechobee and the Caloosahatchee
River. Water levels in the Lake were reported to have declined approximately 50
cm (Johnson 1958). During the next 45 years, canal construction proceeded
sporadically as a result of intermittent funding. By 1917, four major canals, the
Miami, North New River, Hillsboro and West Palm Beach had penetrated the
interior of the Everglades, probably resulting in some drainage of the wetland
system.
Hurricanes during the 1920s devastated human developments along the
east coast and south of Lake Okeechobee. Earthen dams which had been
constructed to exclude waters of the Lake were breached during the hurricane of
1928, resulting in extensive flooding and a loss of about 2400 lives (Blake 1980).
In response, the federal government funded the construction of the Hoover Dike
around the Lake, which was completed by 1938, in order to contain floodwaters.
During the 1940s, federal and state laws established the system of water
management as it now exists. Rainfall during this decade varied wildly, creating

14
Table 1.
History of major water management structures in the Everglades
ecosystem that influenced water deliveries to Everglades National
Park.
YEAR
STRUCTURE
RESULT
1917
Construction of Miami,
North New River, Hillsboro
and Palm Beach Canals
Drainage of coastal areas
and interior Everglades
wetlands
1924
Construction of
Caloosahatchee Canal
Lowering of water level in
Lake Okeechobee
1926 -
1938 -
Lake Okeechobee levees
Muck levee constructed
Hoover dike constructed
Impound water in Lake
Okeechobee, control water
movement to south
1928
Construction of Tamiami Trail
Alteration of flow patterns
channel through culverts
1959
Everglades Agricultural
Area levees completed
Control of water movement
in northern Everglades
1962
Water Conservation Areas
1,2, and 3 enclosed by levees
Control of water movement
in middle Everglades
1962
S-12 structures complete
Flow spatially constricted to
four flowways
1967
L-67 canal and levee
Canal to deliver water into
center of Shark Slough

15
Table 2. History of major water management policies that influenced water
deliveries to southern Everglades and ENP. (Blake 1980, Wagner
and Rosendahl 1985).
YEAR
POLICY
PURPOSE
1907
Everglades Drainage District
To drain Everglades for
agricultural and development
1948
Flood Control Act PL 80-858
Ameliorate flood effects by
construction of conservation
areas, levees
1962 -
1966
Deliver water from WCA 3A,
based upon stages
Store water in WCA 3A,
park to receive after
storage requirements met
1966 -
1970
Deliver water based upon
stage in Lake Okeechobee
Increase flow to park during
hurricane season, restrict
flow during drought
1970 -
1982
Minimum delivery schedule
(PL 91-282 guarantee park a
amount of water)
To assure ENP 260,000 acre-
feet/year, and share in certain
drought adversity
1982 -
1985
Flow through plan
(PL 98-181 allowed for
experimental deliveries)
Allow S-12 structures to
remain open, no regulation
schedule
1985 -
present
Rainfall plan
Deliver water based upon
upstream climatic conditions

16
conditions which prompted action The early 1940s were extremely dry,resulting
in saline intrusion into the freshwater aquifers of the coast and subsequent salt
dam construction. Extensive flooding occurred during 1947, following an
extremely wet summer and the passage of two cyclonic storms. Over 105 inches
(270 cm) of rain was reported to have fallen (MacVicar and Lin 1984) during
1947. This flood resulted in the passage of the federal Flood Control Act in June
1948 (PL 80-853). The act authorized the U.S. Army Corps of Engineers to
develop a plan known as the Central and Southern Florida Project for Flood
Control and Other Purposes, which would address the water management needs
of the area. The plan contained three basic elements: 1) designation of the EAA,
2) construction of water conservation areas in the central Everglades and 3)
construction of an eastern levee. The purposes of the water conservation areas
were to protect the east coast and agricultural areas from flooding, recharge
regional aquifers and prevent salt water intrusion. In 1949, the state legislature
created the Central and Southern Florida Flood Control District (FCD) to act as
local sponsors for the federal project. The FCD was renamed in 1977 as the South
Florida Water Management District, at which time an additional objective,
enhancing environmental resources, was added to the above mentioned
purposes.
Construction of the physical structures of the project began in the early
1950s and continues to be modified to date. Three water conservation areas
(WCA) were surrounded by levees (Figure 2). Water conservation area 1, was
also given designation as the Loxahatchee National Wildlife Refuge in 1951. (In
1984, the area was renamed the Arthur R. Marshall National Wildlife Refuge in
honor of an eminent ecologist). Water Conservation Areas 2 and 3 were divided
into subunits A and B, primarily to decrease infiltration losses in the southeastern
portions of these areas. By 1962, the conservation areas were closed in and

17
functionally intact. Canal construction to date has resulted in approximately
1400 miles of canals.
Operational criteria for water management in the southern Everglades
revolves around the stated regulation schedules for the water conservation areas.
The schedules are target stages which vary over the year, which tend to revolve
around two objectives: 1) minimizing flood risk during the hurricane season
(June-October) and 2) maximizing storage during the dry season (November-
May). When levels are below regulation schedule, water outflow is minimized to
allow stages to increase to the regulation level. When the schedule is exceeded,
water is released to lower levels. Modifications to these schedules have been
made during recent years. The schedule for WCA 3A has been modified to allow
zones around a certain stage value, within these zones water input and outflow
are moderated so that rapid movement of water is negated. The regulation
schedule of WCA 2 has been modified to allow periodic drydown (Worth 1987).
Currently, the schedule for the Marshall NWR (WCA1), is being evaluated for
changes that would improve wildlife habitat.
The water conservation areas are not only spatially central, but
functionally central to water management in the Everglades. These areas are
designed to be used for many purposes, primarily flood control and water
supply. These areas act as surge tanks in receiving water during flood periods.
Runoff from agricultural areas to the north is placed in these areas. Water in the
WCA's is also kept from flowing into areas to the east, in order to lessen flood
impacts. During dry periods, water is also stored in order to meet demands
along the coast and to the south, especially Everglades Park.

18
Water Deliveries to Everglades National Park
Estimates of pre-drainage water flow into the area now in Everglades park
are tenuous due to at least two reasons. No measurements of flow were made
prior to 1940 and by 1940 many upstream canals were in place and may have
siphoned upstream waters to the coast. The Miami Canal was cut through the
ridge as of 1917 (Blake 1980) thereby removing water from the area immediately
north and east of the park. Historic (pre-drainage) average annual flows to the
area of the park were calculated to be 2 to 2.5 million acre feet. (Parker 1984). The
U.S. Army Corps of Engineers (1968) calculated a smaller mean value,
approximately 1.25 million acre feet. These flows were estimated to be the
amount of overland flow into the southern Everglades. Smith et al. (1989) using
a correlation between freshwater flow and the annual band width of a coral in
Florida Bay, estimated that during the period 1881-1939 annual flow averaged
1.15 million acre feet (1.4 billion cubic meters), whereas flow during 1940-1986
was estimated to be 0.47 million acre feet (0.5 billion cubic meters). Dynamic
flow models (Walters et al. 1992) driven bv actual rainfall during the period 1960-
1987, predict flow to have varied between 0.5 and 2.5 million acre feet (0.62 and
3.1 billion cubic meters ), depending upon rainfall.
Overland flow has entered the area now in northern Everglades Park
(primarily Shark Slough) through man-made structures since about 1928 when a
series of round and square culverts were placed beneath the roadbed of Tamiami
Trail (US Highway 41). Most of these culverts are still in place and deliver water
to northeast Shark River slough. As part of the plan to enclose southern WCA
3A, a levee (named L-29) was constructed on the border between WCA 3A and
ENP. This effectively altered the distribution of flow through the western half of
the historic Shark Slough. Four sets of gates (designated S12A through S12D)
were placed in Levee-29 to allow water movement between the conservation area

19
and the park. Each of the four gates is comprised of six 25 foot wide vertical lift
gates. Each set of gates is designed for a maximum flow of 8000 cfs (226 m3/sec),
with a maximum headwater stage of 12.4 ft. and maximum tail water stage of 11.9
ft. (U.S. Army COE 1968). The L-29 borrow canal provides the headwater to the
gates. Other structures that were constructed for various reasons to direct flow
in the Shark Slough, but no longer used, include the L-67 extension canal, S-12-E,
S-12-F and S-14 (Wagner and Rosendahl 1982). The alignment of park boundary
also bisects the other main drainage basin (Taylor Slough) from its headwater.
The physical structures that deliver water at the boundary into Taylor Slough
include a pump station (S-175) that delivers water out of canal L-31 W .
There have been at least eight different time periods each with varying
hydrologic regimes under which water has flowed into the Shark Slough area of
the park. Prior to initiation of construction of L-29 and the S-12 structures, water
flow into the park was unregulated in the sense that water across the boundary
was dependent upon hydraulic gradients within the upstream marshes and only
restricted by the capacity of the culverts. Starting in 1961, overland flow was
entirely cut off to Shark Slough while construction was underway, marking the
second flow regime. From December of 1963 through March of 1965, water was
moved from WCA 3A only after regulation schedule was met, that is, the park
only received excess water after upstream storages were met (Wagner and
Rosendahl 1985). During 1965 and 1966, three zones within WCA 3A were used
to deliver a monthly amount of water. From the period of March 1966 through
September 1970, the stage in Lake Okeechobee was used to determine water
deliveries to the park, with totals scaled from no delivery if the stage was below
12.5 ft, 150 cfs if the stage was above 12.5 and below 13.5, and 1000 cfs if the stage
was greater than 13.5 ft. (Wagner and Rosendahl 1985).

20
During the 1960s the park experienced low rainfall years and was
concerned about the quantity of water it received in context of increasing urban
demands. Two studies defined the water needs of the park using existing flow
and stage data. Dunn (1960) analyzed data for the period 1947-1952 and found
that the median annual flow into the Shark Slough area was 273,000 acre feet
(3.36 x 10^ m^), a value that he recommended be adopted as the minimum flow
requirement. Hartwell et al. (1964) developed stage-duration curves for station
P-33 in the park and stage-discharge correlation between P-33 and flow into the
park, and used these relationships to determine an annual discharge requirement
of 243,000 ac. ft. (2.97 x 10^ m3). A crude average of these two figures was
incorporated into a congressional act in 1970 (PL 91-282) which guaranteed the
park an annual minimum delivery of 315,000 ac. ft. (3.85 x 10^ m3) or 16% of the
water in the system. These annual deliveries were to be partitioned into the three
flow sections into the park. Shark Slough was to receive a minimum of 260,000
ac. ft (3.18 x 108 m3) annually, 37,000 ac. ft.( 0.45 x 10^ m3) were to be delivered
into Taylor Slough, and 18,000 ac. ft. (0.22 x 10^ m3) into the eastern panhandle
area of the park (Wagner and Rosendahl 1985). This law established the legal
right of the park to a minimum amount of water and to share adversity
associated with periods of drought. During the 1970s the minimum delivery
concept was altered from a minimum threshold to one of a static portion of water
allocated to the park each year. The annual flows through the S-12s were
regulated tightly, and during the years 1970 through 1982, met minimum
delivery requirements, but tended to release water over the schedule during
summer months.
In 1983, following a wet year and changes in the operating criteria for
backpumping into Lake Okeechobee, the park service requested alterations to the
"minimum" delivery schedule. Fearing too much water would come into the

21
park, a number of alterations to the structures of the system were requested,
along with changes to methods of delivery. In order to remove water from
eastern and southern WCA 3A through pathways other than into the park,
culverts were placed in Levee 28 in order to allow water to flow into the Big
Cypress. Other outlets for WCA 3A were requested but not implemented. Water
was to be diverted into WCA 3B. In response to these requests, Congress passed
a law (PL 98-181) that allowed for experimental water deliveries to the park. For
the next two years (1983-1985), the S-12 structures were left entirely open, so that
water would enter the park as a function of hydraulic gradients between WCA
3A and the park. Although the flow-through plan may have achieved objectives
of restoring the natural timing of flow, the situation of leaving the gates open did
not bode well with water managers faced with the necessity of storing as much
water as possible in WCA 3A for meeting other needs on the coast.
The latest act in the unfolding play of water deliveries to the park was the
Rainfall plan developed by Tom MacVicar of the SFWMD and staff of the COE.
They analyzed rainfall-runoff data from the period 1940 through 1952, and
developed a statistical model which predicted weekly flow based upon net
rainfall (rainfall minus evapotranspiration) over WCA 3A from the previous ten
week period and the previous weeks' discharge. The model achieved two
objectives; the timing and quantities of deliveries were linked to upstream
weather conditions, and the flow would be re-distributed spatially as it was prior
to the construction of the water conservation area. The regulation schedule was
also modified to allow for variation in water level conditions within WCA 3A in
order to avoid the rapid releases of water into the park (MacVicar and VanLent
1984, MacVicar 1985, Neidrauer and Cooper 1988). In essence, the rainfall plan
limits the source basin of the park to WCA 3A by directly timing delivery to
rainfall over the area. Buried in this delivery plan is the unknown contribution

22
of other areas in the Everglades (and Lake Okeechobee) to water in WCA 3A and
eventually to the park. This is manifest in the supplemental deliveries, by which
more water than the rainfall formula predicts is delivered. The supplemental
deliveries are linked to a modified regulation schedule. The key elements of the
rainfall plan are 1) to link timing and quantity of baseline deliveries to upstream
rainfall, 2) to increase quantity of flow during periods of high water, 3) to
decrease quantity of insured deliveries during dry periods, and 4) to supplement
the baseline quantity of water depending upon a wider range of water depths
(regulation schedule) within WCA 3A.
Major determinants to the constantly changing methods and policies of
water delivery to the park have been the observed degradation of biological
resources in the southern Everglades and Everglades National Park. Dry years
and accompanying fires during 1962 and 1971 prompted the appeal for more
guaranteed water. Increased mortality of alligator young (Kushlan and Kushlan
1980) was attributed to rapid water level rises associated with regulatory releases
during the early dry season. Browder (1985) developed relationships between
flow into the estuary of Florida Bay and shrimp production. The most attention
has been drawn to a dramatic decline in the number of wading birds; nesting
success of wading birds has decreased by 95% of levels in 1930s (Robertson and
Kushlan 1984). Reasons for the declines have been intimately linked with
decreases in flow through the park (Ogden 1978, Ogden 1987, Powell et al. 1989,
Walters et al. 1992). Other authors believe that too much water in the Everglades
has contributed to the population decreases (Kushlan 1987) and that the park
should receive less water.
The preceding review of the Everglades ecosystem has followed two
separate paths: one recounts the natural history and the other the human

23
history. These histories intertwine, and are linked by the ways in which humans
perceive, understand and react to nature, the subject of the next section.
Managing Ecological Systems
One interpretation of the history of water management in the Everglades
is that it appears to follow a pattern of crisis and reconfiguration (Light et al, In
press). The crises arise from dramatically unexpected system behavior, such as
floods, droughts and fires. Crises in the past have appeared suddenly, as
surprises, and the subsequent responses have dramatically changed the way the
system has been managed (Table 1). The central reconfiguration occurred
following the flood of 1947, when the Central and Southern Florida Project was
spawned. Since then, other crises have occurred with subsequent changes in the
policy and practice of delivering water to the park. The reaction by humans to
these surprises takes the form of policies and management actions. The
responses are shaped by perceptions and interpretations of how nature operates.
At least two concepts are involved in the interpretation of nature that
create the basis of policy and management formulations. The first concept relates
to various views of system stability. The second concept deals with the assumed
or perceived uncertainties associated with either system understanding or
impacts of management actions. At least three views of system stability have
been abstracted: equilibrium, dynamic and evolutionary (Holling 1987). An
equilibrium view is defined as one dominated by the assumption that key
response variables always return to a point or set of points. The dynamic
perspective recognizes that system variation occurs within and between a range
of stability regions so that system behavior appears at times constant, other times
continuously changing, and at times jumping abruptly into another stability
regime. In the evolutionary view, the stability landscape can change, implying

24
fundamental structural and organizational changes in the system. Dealing with
the inherent and fundamental uncertainty associated with shifts within and
among these stability domains is at the heart of adaptive management (Holling
1978, Walters 1986). During the last decade both the policy and management
philosophy in the Everglades crossed thresholds involving both changes in views
of stability domains, and in strategies of management.
Policy in the Everglades is still largely rooted in the equilibrium-centered
perspective, although the dynamic view has been recognized and partially
incorporated into management schemes in the mid 1980s. Water movement is
largely determined by regulation schedules in the different components of the
system (Lake Okeechobee and the water conservation areas). These regulation
stages reflect an equilibrium view of water management, that is, it always returns
to an ideal stage within a retention pool. The modifications to WCA 3A schedule
associated with the rainfall delivery plan, however, indicate a shift to a dynamic
viewpoint, allowing variability in the managed system.
Water management in the southern Everglades during the last decade has
developed more attributes of adaptive environmental management (Holling
1978, Walters 1986). Within the last decade, programs such as the iterative
testing plan (Light et al. 1989) have been applied using the concept that water
management necessarily has some experimental attributes. This has even been
codified, by the adoption of PL 98-181 which allows for experimental deliveries
to the park. The rainfall plan can be classified as a passive adaptive technique
(Walters 1986), whereby historical data are used to construct a model that guides
management plans. Two problems with this technique are that 1) environmental
and management effects are confounded, and 2) little opportunity exists for
improving the model or testing new models (Walters 1986, Walters and Holling
1990).

25
Summary
In this chapter, the key pieces of the interplay between the natural and
human dimensions of the Everglades are described. The undisturbed Everglades
ecosystem can be characterized as an oligotrophic, sub-tropical wetland system
with high temporal variability in rainfall input. The landscape is flat, yet
supports a complex spatial mosaic of marsh and woody vegetation plant
associations. Humans have interacted with the system for as long as it has been a
wetland. Dramatic changes have occurred during this century, within which
time about half of the land area has been converted to agriculture and urban
development. Over the past 50 years, Everglades National Park has been
established, as has one of the largest water management infrastructures in the
world. Water management and deliveries to Everglades Park have undergone
dramatic, non-linear changes resulting from recurrent crises and surprises. The
foundations for policy and management development during these periods of
reconfiguration are intimately linked to and dependent upon our understanding
of ecosystem dynamics. Understanding ecosystem dynamics and the different
paradigms regarding system organization is the point at which the first chapter
ends and the second chapter begins.

CHAPTER 2.
POSING THE QUESTIONS
Using all the weapons of our logical, mathematical and technical armoury we try to prove
that our anticipations were false-in order to put forward, in their stead, new unjustified
and unjustifiable anticipations, new 'rash and premature prejudices' as Bacon derisively
called them
-K.R. Popper
As indicated in the preceding sections, the problem of water deliveries to
Everglades Park has many dimensions, including how ecosystems vary over
different time spans, and the subsequent reactions and adaptations of people to
these fluctuations in the system. Resource policy and management is
fundamentally related to how humans perceive and attempt to comprehend the
vagaries of nature. Even though institutional and human dynamics of the system
are important, they are fundamentally rooted in basic paradigms about how
ecosystems function. The study of ecosystems can be particularly difficult
because of the variety of components, processes and variables. Attempting to
incorporate all variables makes the problem overwhelmingly complex (Gallopin
1991). Simplifying assumptions allow for these studies to become tractable. The
remainder of this chapter will outline and contrast three existing approaches to
simplify understanding of ecosystem dynamics and a description of a new
emerging paradigm. Hopefully, this theoretical background will lay the
framework from which hypotheses and objectives of this work are derived in the
concluding sections of this chapter.
26

27
Views of Ecosystem Structure and Function
Understanding and interpreting ecosystem structure and function are
based upon underlying methodological assumptions and paradigms held by the
observer. At least three such concepts are recognized, while a new one is
emerging to account for the paradoxes that emerge from applying the first three.
These viewpoints can be characterized and contrasted by two components of the
paradigms: 1) the factors or variables that are important in the system and, more
fundamentally, 2) the manner in which these variables interact. The first
assumption is that variables interact in such a way that the strength or
significance of the interaction can be tested against a null model that is random.
The second paradigm is based upon a view that the world is structured in a
hierarchical manner, with distinct levels of causation defined by the observer.
The third view of ecosystem science is rooted in mathematical modeling, and
concentrates on system dynamics across a limited range of scales. The newest
belief, emerging because of limitations in the other views, is cross-scalar in scope
and implies a world of lumps and discontinuities in which a small number of key
processes determine function, each over its own range of scales. None of these
views are wrong; indeed, all represent partial truths and continue to thrive
because they are useful. Following a brief characterization of each existing
assumption and their limitations, the emergence of a new view will be presented.
Ecosystem science as practiced by the 'Stochastics' is characterized by
multi-variate statistical approaches. The implicit assumption is that the variables
are operating within similar domains in space and time and therefore have
correspondingly similar ranges of variation. Explicit assumptions include that
the variables are essentially derived from continuous distributions and therefore
have certain properties that can be estimated from sampling. In the extreme,
variation in response variables is partitioned to either the variation of other

28
variables or to a random error term. In all cases, the null hypothesis is a random
one; relationships can only be inferred by rejection of the null. Examples of work
in the Everglades ecosystem of this type include analyses by Smith et al. (1989)
and Browder (1985) in correlating freshwater flow in the system with biotic
responses in Florida Bay. Indeed, the current rainfall formula developed by
MacVicar (1985) is a statistical approach, whereby flow through the southern
Everglades is regressed against rainfall and stage. This approach is powerful,
because the tools are readily available, and only a statistically significant number
of samples are necessary for application.
The hierarchical view of ecosystems, on the other hand, while a powerful
concept, is still struggling for widespread application after being introduced at
least 50 years ago. The basic framework offered by hierarchists is one of
partitioning variables and interactions into distinct levels or "holons" (Allen and
Starr 1982). Variables that operate at similar scale ranges occupy the same level
within a hierarchy and interact more than with variables between levels. One
feature of hierarchies is dubbed as asymmetry, where the variables at slow levels
constrain the variables at fast levels. The underlying assumptions of variability
are similar to the random approach, in that the variables are assumed to have
continuous distributions and that these distributions are predictable. Another
common belief of hierarchists is that hierarchies are relatively stable, static and
operate near equilibrium. The most current view of hierarchists is that the world
should be partitioned into the appropriate hierarchical level such as landscape,
ecosystem, population, organism for study, analysis and understanding (Allen
and Hoekstra 1992). To my knowledge, no applications of this theory has been
applied to studies of the Everglades.
A tremendously rich understanding of ecosystem structure and function
has been achieved by modellers who apply the third aproach to explanation.

29
Although inductive, the approach can improve understanding by testing
dynamic interactions among variables. Assumptions regarding variables and
interactions can be clearly stated by mathematical formulae translated into
computer code. The utility or power of modeling also carries related costs.
Empirical rules such as "parsimony in the selection of variables" (Clark et al.
1979), the "power of two" (Walters 1986) or the optimum trade-off between
articulation and predictability (Costanza and Sklar 1985) all attest to constraints
on modeling.
The limitations imposed on each of these views has to do with issues of
scaling. All of these approaches to explanation treat both variables and
interactions as scale invariant. Scale invariant means that the behavior of
variables and the rules or properties of interaction do not change within the scale
limits imposed by the observer. The power of these approaches comes from the
knowledge of a rule set, and how far (over what range of scales) the rules apply.
Limitations related to scale are a result of underlying assumptions (stochastics),
theoretical frameworks (hierarchists) and of practical experience (modellers). For
variables to be analyzed, compared or contrasted using the available statistical
approaches, they must change within a similar manner. If there are dramatic
differences in the space or time dynamics of variables, then statistical methods
either give erroneous conclusions or, flat out, don't work. An example of this is
the rainfall formulation (MacVicar 1985) mentioned above, where the regression
analysis indicated that no statistical relationship existed between rainfall and
flow!
Similar problems of the mismatch between variable spatial or temporal
domain arise in hierarchical theories and in the application of modeling
techniques. The hierarchists (Allen and Starr 1982, O'Neill et al. 1986) recognize
that "slower" variables constrain "intermediate" variables while "faster" variables

30
are essentially meaningless, or noise. Little progress has been made with linking
these variables together other than in a conceptual or qualitative sense.
Modellers have come to essentially similar conclusions, as expressed in the
practical "Rule of Two". The empirical rule states that the best models never
extend more than two orders of magnitude in either space or time. The basic
approach of scaling in modeling, is to treat "slower" variables as constants, and to
treat "faster" variables as random or stochastic events. Existing space-time
models of hydrodynamics in the Everglades fall within this guideline and will be
described later in the modeling section. The result of limitations imposed by
these various approaches is the breakdown of understanding, as evidenced by
inherently unpredictable system behavior (Holling 1986). These limitations and
inevitable surprises helped prompt the development of a theory that attempts to
embrace the cross-scale dynamics of ecosystems.
This emerging cross-scale theory has roots in both the hierarchical and
modellers perspective and can be traced to a review and synthesis of the
dynamics of a number of ecosystems. Holling (1986) compared the dynamics of
23 ecosystems, and concluded that the essential behavior of the system could be
traced to three or four sets of variables, each of which operated at distinctly
different rates. The sample ecosystems were categorized into one of four classes
of systems: forest insects, forest fires, grazing in savannas and aquatic harvesting.
Models of the reviewed ecosystems all generated complex behavior in space and
time that qualitatively correlated with observations of the actual systems. The
essential dynamics of the systems could be attributed to a small number of
keystone variables. The speeds of each keystone variable differed from each
other by as much as an order of magnitude, so that the time constants were
discontinuous in distribution (the hierarchists would consider each keystone
variable as a part of different levels or holons) or as a small number of nested

31
cycles. The results of the review led to the hypothesis that ecosystem dynamics
are organized around the operation of a few key variables, each operating at
distinct speeds.
The next critical step in development of theory was the proposed
hypothesis that the system should be structured in such a way that the keystone
variables entrain other variables. The entrainment should occur in both spatial
and temporal dimensions creating structural features that exhibit distinct gaps
and lumps and temporal processes that exhibit distinct periodicities. An overt
manifestation of a lumpy, discontinuous world should be expressed by attributes
of the animals that live in these systems. This hypothesis was challenged by a
series of tests using data from three biomes (Holling 1992). The tests using adult
body mass of birds and mammals from the boreal forests, prairies and pelagic
ecosystems, indicated the presence of discrete gaps that defined groups (Holling
op cit.). Alternative hypotheses using developmental, historic or trophic
explanations for the groupings were all invalidated, leaving only the strong
inference that ecosystems (abiotic and biotic components) were similarly
organized (Holling op cit.) into discreet lumps.
Hypotheses
Two hypotheses are posed in this work and arise from two of the
approaches mentioned above. Both are aimed at improving understanding of the
structure and function of the Everglades ecosystem that specifically relates to
system dynamics and flow to Everglades Park. The first hypothesis derives from
the approaches that understanding complex system behavior can be induced
from modeling non-linear interactions among continuous keystone variables
within a constrained range of scales. The second hypothesis is developed from

32
the cross-scale arguments, and attempts to invalidate the lumpy, discontinuous
view of the world.
Water Deliveries to Everglades National Park - The First Hypothesis Set
A dynamic water budget approach is a powerful conceptual tool for
evaluation of the factors influencing deliveries to Everglades Park. The amount
of water in the southern Everglades at any time is a net result of changes between
inputs (rainfall and inflow), and outputs (outflow, evapotranspiration, and
groundwater infiltration). Theoretically, the rates of flow and evapotranspiration
are related to vegetation type and structure. Since Everglades National Park is
situated at the downstream end of the historic ecosystem, it is dependent upon
water from upstream sources. The water that enters the park comes from two
sources: rainfall over the park and overland flow from the north. Assuming that
local rainfall contributions to the park water budget are relatively unchanged, the
first hypothesis deals with the contribution of upstream sources to the water
requirements of the park.
Hypothesis: The effective drainage basin that supplied water to
Everglades Park was the entire Kissimmee, Lake Okeechobee and
historical Everglades ecosystem. Implicit in this hypothesis is that
overland flow is a dominant pathway of water movement, and that
hydrologic continuity throughout the historic system is crucial to
maintaining water supply to the park.
Corollary: In an area as flat as the Everglades, the vegetation and
hydrology are intimately coupled. The structure and type of vegetation
affect both evapotranspiration rates and resistance to overland flow.

33
Vegetation type and structure are in turn, affected by water depths and
hydroperiod. The coupling between hydrology and vegetation
determines the relationship between the amount of water that flows
through the system and the amount that evapotranspires to the
atmosphere.
Null: The effective drainage basin was a much smaller geographic area.
Overland flow into the park system originates from an effectively smaller
drainage basin. This is because evapotranspirative losses are high relative
to rainfall, therefore water would evaporate before moving very far
downstream. Other users in the system can remove water without major
disruption of the flow that entered the park historically.
Cross-Scale Patterns In The Everglades Ecosystem - The Second Hypothesis Set
The processes that influence flow to the southern Everglades cover a wide
range of space and time scales. Rainfall results from atmospheric processes,
ranging from meso-scale (Florida peninsula) to global dynamics. Vegetation
structure can be identified at scale ranges from parts of individual plants (stems,
leaves) to the organization of plant associations in the landscape. The combined
processes of evaporation and transpiration occur from the level of leaf stomata to
entire ecosystems. Other processes have similarly wide ranges of variation in
space and time.
In order to attempt to invalidate the first hypothesis, the methodology
requires that the world of the Everglades be "squeezed" into a framework of fixed
spatial and temporal domains. The second hypothesis is based upon the
emerging theory which suggests that across scale ranges, ecosystems are

34
organized in such a way so that dumps and gaps appear in structural features
while a small number of cycles and harmonics occur in temporal features.
Hypothesis: The Everglades ecosystem is structured by a small number of
processes, of which hydrology and vegetation are one set of keystone
variables. Over a range of scales, patterns produced by vegetative and
hydrologic processes should have a few characteristic domains in space or
time that are separated by discontinuities. Within the time domain, a few
dominant frequencies or cycles should emerge in the hydrologic processes
of rainfall, water level, flow and evapotranspiration. Within the spatial
domain, a few groupings of object size (such as vegetation patches), or
texture will emerge that correspond to levels in a spatial hierarchical
structure. Other ecosystem level processes, such as topography and fire,
will exhibit similar patterns.
Null: Over a range of scales, the temporal patterns of hydrology and
spatial patterns of vegetation in the Everglades will exhibit structures that
correspond to underlying continuous distributions . No dominant or
nested cycles will appear in the time patterns of hydrologic processes such
as rainfall, water level, flow or evapotranspiration. No breaks or
discontinuities in the spatial patterns will be found, and patterns will be
self-similar over a wide range of scales.
Objectives
The aim of this work is to develop new understanding of ecosystem
dynamics by testing hypotheses regarding water and vegetation dynamics that
are rooted in two different viewpoints. There are two main objectives: 1) use

35
"scale-bound" modeling techniques to help understand factors influencing water
deliveries to Everglades Park, and 2) apply cross-scale analyses to Everglades
data sets to test for breaks or discontinuities in patterns.
The first objective will involve the construction of a spatially and
temporally explicit model to capture the dynamics of the system in order to test
the first hypothesis. The model will couple dynamics of hydrology and
vegetation within a spatial domain of two orders of magnitude and a temporal
domain of almost three orders of magnitude. The model will be used to attempt
invalidation of the proposal that the entire basin contributed water to the
southern Everglades. This objective is the focus of Chapter 3.
The second objective will be to develop, test and apply a variety of cross¬
scale methods to identify patterns in keystone variables in the Everglades
ecosystem. Since the theory of cross-scale interactions is just emerging, a great
deal of this work has been devoted to the development of new methods and
methodology. Fortunately, this work was able to reap the benefit of data sets of
many variables that have been collected over the years on different portions of
the Everglades system. The methodology, and results of the cross-scale analyses
are the subject of Chapter 4.

CHAPTER 3.
MODELING THE "RIVER OF GRASS"
When your only tool is a hammer, the answer to every problem is a nail.
-R. Yorque
Almost 50 years ago, Marjory Stoneman Douglas created a dramatic image
when she described the Everglades as a "River of Grass" (Douglas 1947).
Technically, neither of these terms are appropriate. The system is hardly a river
because there is no defined water course and water flows very slowly, only about
60 kilometers a year. The "grass" in the title refers to sawgrass, which is properly
classified as a sedge. However, the metaphor is still appropriate because it can
be interpreted to depict the coupling of the vegetation and hydrology in this
ecosystem that at one time, was a united ecosystem.
In this chapter, the test of the first hypothesis that the entire Everglades
system provided water to Everglades National Park and test of the corollary
hypothesis regarding the coupling of vegetation and hydrology, are presented.
These hypotheses were tested with a model that incorporates coupled vegetation
and hydrologic dynamics over time within an explicit spatial array. Hydrologic
models of the Everglades system have been used to evaluate management
options within the current system configuration (MacVicar 1985) or to create
views of the system prior to human intervention (Walters et al. 1992, Perkins and
MacVicar In prep.). Such models provide a robust methodology from which the
contributions of upstream areas to flow into the southern Everglades can be
36

37
evaluated. Key uncertainties in these models include information about
overland flow resistance and evapotranspiration and infiltration to groundwater.
In a system as flat as the Everglades, vegetation influences surficial
hydropatterns by mediating resistance to flow and controlling
evapotranspiration. Hydrologic regimes also influence the vegetation pattern
(Davis 1943, Craighead 1971, Gunderson 1989). The corollary hypothesis posits
that the interactions between hydropatterns and vegetation patterns are coupled
and create feedback loops. None of the previously developed hydrologic models
of the Everglades incorporate complete feedbacks between hydrology and
vegetation. The SFWMD models (MacVicar 1985, Perkins and MacVicar, In
prep.) vary flow and evapotranspiration by land cover types, but the land cover
types do not change as a function of hydrology. The model of Walters et al.
(1992) changes vegetation types as a function of hydrology and other factors, but
has spatially fixed flow and evapotranspiration rates. The approach in this work,
therefore, is to couple vegetation and hydrologic feedback dynamics in the
framework of existing models to test hypothesis about upstream area
contributions to the park.
This chapter is divided into four sections: background, model
development, results and summary. A fair portion of this chapter is devoted to
improving understanding of the interactions among evapotranspiration, flow
and vegetation since they are key uncertainties in the model. The background
section will develop a theoretical base for understanding these processes and the
results of studies that compares evapotranspiration rates among vegetation
communities of the Everglades in order provide a foundation for the linkages in
the model. Following the background section, the model is described including
components and their interactions. The section following the model description
presents the results of testing the upstream area hypothesis and the corollary

38
hypothesis regarding the coupling of vegetation and hydrologic processes. This
chapter is concluded with a summary of modeling the "River of Grass" and
implications of the results to policy and management.
Background
Evapotranspiration in Wetlands
Evapotranspiration is the combined processes of water flux into the
atmosphere by evaporation from water or soil surface and transpiration from
vegetation. In an area such as the Everglades, both processes are in effect, as
there are areas of relatively sparse vegetation (open water marshes), grassy
wetlands and forested wetland communities. In addition to the interaction
between evapotranspiration and vegetation, other physical variables influence
the rate of water flux. All of these variables, and measures of evapotranspiration,
appear to vary across scales of interest. Previous studies on evapotranspiration
in the Everglades have been made at different scales, and will be reviewed below
in relation to spatial and temporal groupings, but first a review of theoretical
background.
Evapotranspiration is a component of the energy budget. A general
formulation for steady state system at a specific location is shown in equation (1),
modified from Brutsaert (1984), and Viessman et al. (1989). The amount of net
solar radiation (ambient minus reflected) determines the amount of energy
available for other processes. The energy can be used to increase the
temperatures (sensible heat) of both the atmosphere and the soil substrate. Some
of the energy is used in photosynthesis, and some may be moved by advection
(wind) to other areas. The other energy is used for the phase transition of water
from liquid to vapor. Since the evaporative process requires energy for the phase
transition, the energy is not measurable or latent. The latent heat of evaporation

39
times the rate of evaporation describes the evaporation term in the energy budget
equation.
(1) Rn = LeE + H + G + P + A
Rn = specific flux of incoming net radiation
Le = latent heat of evaporation
E = rate of evaporation
H = specific flux of sensible heat into the atmosphere
G = specific flux of sensible heat into the ground
P = rate of energy used in photosynthesis
A = rate of lateral advection of energy
Due to difficulties in measurement of the latent heat of evaporation and
the confounding effects of vegetation influences on the processes, a number of
techniques have been developed to measure evapotranspiration. The techniques
fall into two categories, those that derive from energy budget, with certain
simplifying assumptions and those that are empirical. Penman (1948) derived a
formula that includes a wind (advection) term with assumptions of constant
Bowen ratio (ratio between sensible and latent heat) that allows for measurement
at one level. Other techniques derive from the Dalton formulation that estimates
a vapor gradient between the surface and the atmosphere. Empirical methods
include formulations by Blaney-Criddle (1950) who related evapotranspiration
with average temperature; Holdridge (1967) who related vegetation form to
temperature and potential evaporation and simple techniques such as pan
evaporation or lysimetry.

40
Evapotranspiration is influenced by a mixture of processes that occur at
different scales in space and time. Solar insolation at a spot on the earth
fluctuates on daily, annual and multiple year cycles. The solar radiation is also
influenced by fast (on the scale of minutes) fluctuations in processes, such as
cloud cover. Vegetation both directly and indirectly influences the
evapotranspirative processes. The fastest controls vegetation occur at the level
of the stomata, where water flux is linked to photosynthesis (Jarvis and
McNaughton 1986). Individual plant species' genetic composition and
adaptations influence the size and density of stoma, leaf orientation, responses
to various changes in insolation, wind, humidity and temperature (Jarvis and
McNaughton 1986). The composite architecture of the canopy in wetlands can
influence the reflectance of both short and long wave radiation, with implications
to net energy and water use (Odum 1984, McClanahan and Odum 1991). At the
landscape or regional level, the vegetation cover type influences the reflectance
or albedo.
The preceding paragraphs gave a brief review of evapotranspiration
theory to provide a basis for understanding the various approaches and
techniques for measurement of this complex process. The following section will
present the results of previous investigations and present published
measurements of rates of evapotranspiration at different spatial and temporal
scales.
Measurements of Evapotranspiration in southern Florida
Measures of evapotranspiration in southern Florida have also been made
at different scales ranging from local up to the entire peninsula. For convenience,
these can be grouped for discussion into broad-scale measures that include the
region and basins, medium scale measures (less than 10 m on a side) typified by

41
lysimeters, and evaporation pans and small scale measures that examine losses
from leaf surfaces.
For the region, Dohrenwend (1977) used an empirical formula developed
by Holdridge (1967) that related evaporation and mean annual biotemperature to
calculate an annual evapotranspiration of about 1000 mm. Input-output analyses
of basins in and around the Everglades calculate a range of values of
evapotranspiration that are similar. Allen et al. (1982) estimated annual
evapotranspirative losses from 890 to 1040 mm from Taylor Creek basin north of
Lake Okeechobee. Leach et al. (1971) estimated evapotranspiration from the
Water Conservation Areas at 965 mm/yr. Shih et al. (1983) estimated water
losses from the Everglades Agricultural area at 1018 mm/yr using a water
budget approach and also compared a number of other techniques and found
annual means ranging from 1018 to 1035 mm.
Most of the smaller scale investigations involve the use of lysimeters
(tanks with planted vegetation), evaporation pans or shallow wells to derive
monthly and annual estimates of evapotranspiration. Clayton et al. (1949)
planted sawgrass in lysimeters and found monthly ranges of 78 to 208 mm and
mean annual losses of 1735 mm. Parker et al. (1955) estimated
evapotranspiration from pan evaporation and reported annual values from 1016
to 1143 mm. The Army Corps of Engineers (1968) reported monthly values from
63 to 135 mm. Shih (1981) compared average monthly and annual
evapotranspiration among sugarcane, alfalfa, and bahiagrass plants planted in
lysimeters with data from Clayton (1949). Shih (1981) found a range of monthly
values from 35 mm to 212 mm for sugarcane. Other crops were within these
monthly averages, and had lower annual totals. Carter et al. (1973) derived
annual estimates of 1100 mm for the Big Cypress Swamp area, immediately west
of the Everglades.

42
A number of studies attempted to develop relationships between
evapotranspiration (from lysimeters) and climatological data. Most assume
constant Bowen ratio; that is, a constant proportion between the sensible heat
flux and the evapotranspiration. Stephens and Stewart (1963) found that best
approximation to lysimeter values of potential evapotranspiration were based
upon a fraction of ambient radiation. Shih (1981) found good correlation
between lysimeter losses and monthly temperature corrected for cloudy days, a
modification of the Blaney-Criddle technique. Stewart and Mills (1967) and Shih
(1983) both measured decreasing evapotranspiration rates with declining,
subsurface water levels.
Perhaps the fewest studies have been done at the level of the individual or
on a daily basis. Brown (1981) studied pondcypress in southern Florida, and
measured average daily losses at 1.3 mm/day. Dolan et al. (1984) working to the
north measured daily marsh evapotranspiration from 0.5 to 10 mm/day. One
small scale study (Alexander et al. 1976) compared evapotranspiration rates of
potted seedlings of sawgrass and Melaleuca..
Different variables operating at different space and time scales have been
shown to influence evapotranspiration. Some variables, such as radiation are
spatially global; that is, they remain the important input to the process across all
scales. Other variables, such as leaf stomata, dictate fine scale (leaf level) control,
but cease to be important at the regional scale (Jarvis and McNaughton 1986).
More work has been done on scaling measures of evapotranspiration over the
time domain by increasing the extent or window (day to month to year).
Authors working in southern Florida (Stephens and Stewart 1963, Shih 1981, and
Carter et al. 1971) all recognized a decrease in variation as the time unit is
increased.
i

43
In reviewing the available literature, few measurements of evaporation or
transpiration from the native plant communities in the Everglades have been
published. In order to incorporate community level measures into the model, a
series of studies were done to develop measures of water loss by community
type. The studies were important for two reasons, 1) to establish that
evapotranspiration rates varied among the major vegetation communities, and 2)
to estimate the magnitude of any differences. If there was no difference among
the vegetation types, then evapotranspiration could be modeled by a variable
that only changed in time and not over space. If there was a difference in water
loss rates among the vegetation communities, then maps of vegetation
communities could be used to develop spatial patterns of evapotranspiration.
The next section of this chapter reports on the summary of two studies
using two different methods to calculate rates of evapotranspiration among the
dominant native plant communities. The first study uses transpiration rates
reported in Herndon and Gunderson (1989), and, with a few assumptions,
attempts to aggregate from the leaf level to the community. The second study
uses data reported by Gunderson and Stenberg (1990) on evapotranspiration
from two wet prairie sites. The measures reported in these two studies will be
summarized for use in the model.
Transpiration from Three Everglades Plant Communities
The rates of water flux from the leaves of dominant species in three
community types; sawgrass, tree island and marl prairie, (wet prairies had no
macrophytes) were measured. The measurements of leaf transpiration were
multiplied by the leaf area per vegetation type to yield community estimates.
Water flux rates (millimoles/cm2/sec) from the leaf surfaces were measured
using a steady state porometer (Li-Cor Model 1600). During the period from

44
December 1984 through February 1986, measures were made at 10 am, 12 pm
and 2 pm local time during one day every other month. At each sample period a
total of thirty measurements were made at random locations within the
community. The thirty measurements were combined to give an average flux for
each period. The rates of water loss were integrated over the day in order to
yield a water loss per day. To translate or scale these measures to a community
level, estimates of leaf surface area were made for each community type. All
leaves within a one meter square area were counted and leaf areas measured to
yield a leaf area/ m2.
Transpiration rates did not vary much among the vegetation types
sampled. Mean and range of water fluxes (transpiration) from the leaf surface
were determined from the field measures. Sawgrass transpiration ranged from a
low of 0.9 mmol m2-sec'1 during December 1985 to a high of 3.2 mmol-m^sec'1 in
July of 1985 (Table 3). Muhly grass, Muhlenbcrgia filipes, the co-dominant species
in the marl prairie, had similar rates, ranging from 1.6 to 2.4 mmol-m2-sec'1 (Table
3). The swamp forest species showed similar transpiration, with values ranging
from 1.8 to 3.0 mmol-m2-sec'1 (Table 3). A one-way analysis of variance was
performed, and indicated no significant difference in daily transpiration among
vegetation type. A second analysis of covariance that removed the seasonal
trend in the data, also indicated no significant difference in transpiration rates
among the species monitored.
Daily water losses per community type were estimated by first calculating
daily transpiration and multiplying by leaf area per community type. Daily
transpiration was calculated by multiplying a six hour day length times the leaf
transpiration rates. A six hour day was thought to reflect an average period of
daily metabolic activity through out the year and probably underestimates daily
transpiration in the summer and overestimates wintertime values. Estimates of

Table 3.
Daily transpiration rates for three vegetation types in the Everglades.
VEGETATION
TYPE
DATE
TRANSPIRATION RATE
Mean High Low
mmol/m2 LA/sec
DAY
LENGTH
(sec/day)
DAILY TRANSPIRATION
Mean High Low
cc/m2LA/day
LEAF AREA
m2 LA/
m2 g
WATER LOSS
Mean High Low
cm/day cm/day cm/day
Sawgrass
Jan-85
1.4
1.5
0.8
21600
544
583
311
2.44
0.13
0.14
0.08
Mar-85
2.1
2.4
1.9
21600
816
933
739
2.44
0.20
0.23
0.18
May-85
2.4
2.8
1.9
21600
933
1089
739
2.44
0.23
0.27
0.18
Aug-85
2.0
2.1
1.7
21600
778
816
661
2.44
0.19
0.20
0.16
Oct-85
1.7
1.7
1.2
21600
661
661
467
2.44
0.16
0.16
0.11
Dec-85
0.9
1.2
0.2
21600
350
467
78
2.44
0.09
0.11
0.02
Sawgrass
Dec-84
1.9
2.1
1.1
21600
739
816
428
0.67
0.05
0.05
0.03
Feb-85
1.1
1.2
1.0
21600
428
467
389
0.67
0.03
0.03
0.03
Apr-85
2.0
2.2
1.9
21600
778
855
739
0.67
0.05
0.06
0.05
Jul-85
3.2
4.0
2.2
21600
1244
1555
855
0.67
0.08
0.10
0.06
Sep-85
1.7
2.1
1.5
21600
661
816
583
0.67
0.04
0.05
0.04
Dec-85
1.0
1.8
0.2
21600
389
700
78
0.67
0.03
0.05
0.01
Marl Prairie
Feb-85
1.8
2.4
1.4
21600
700
933
544
0.22
0.02
0.02
0.01
(muhly grass)
Apr-85
2.4
2.6
1.2
21600
933
1011
467
0.22
0.02
0.02
0.01
Jul-85
2.0
2.1
1.9
21600
778
816
739
0.22
0.02
0.02
0.02
Sep-85
1.6
1.9
1.0
21600
622
739
389
0.22
0.01
0.02
0.01
Dec-85
1.6
2.1
0.6
21600
622
816
233
0.22
0.01
0.02
0.01
Swamp Forest
Jan-85
1.8
3.2
1.5
21600
700
1244
583
5.00
0.35
0.62
0.29
Mar-85
2.5
3.2
1.2
21600
972
1244
467
5.00
0.49
0.62
0.23
Jun-85
3.0
4.8
1.5
21600
1166
1866
583
5.00
0.58
0.93
0.29
Jul-85
2.8
3.5
1.8
21600
1089
1361
700
5.00
0.54
0.68
0.35
Oct-85
2.0
2.5
1.5
21600
778
972
583
5.00
0.39
0.49
0.29
Jan-86
1.8
2.2
1.4
21600
700
855
544
5.00
0.35
0.43
0.27

46
leaf area per m2 of ground area were multiplied times the daily transpiration to
yield a community water loss.
Seasonal trends in community transpiration among the three types were
most evident in the swamp forest (Figure 3), and less evident in the marl prairie.
Transpiration was measured from all three vegetation types throughout the year,
indicating year round metabolic activity and no dormant period.
Analyses indicated a significant difference in water loss among the
vegetation types, due to differences in leaf area. A one-way analysis of variance
and one-way analysis of covariance (removing seasonal trend) both indicated a
significant difference in daily water loss among the three vegetation types.
Water loss rates from the marl prairie vegetation was the lowest, with an annual
mean of 0.016 cm/day. Average loss from the sawgrass marsh was 0.16 cm/day
and from the swamp forest 0.45 cm/day. Posteriori contrasts indicated that these
three types were significantly different.
In summary, estimates of water loss using the technique of scaling from
small scale transpiration to community values are dependent upon the
vegetation structure more than the flux rates. The water flux from the leaf
surfaces tend to vary seasonally, and do not exhibit differences among vegetation
type. Significant differences in water loss do appear to exist among community
types and appear to be related to the amount of leaf area present.
Measurements of community evapotranspiration
Other estimates of community evapotranspiration were made using
recorded tracings of water levels in shallow wells at two sites in Everglades
National Park. One well is designated P33 and is surrounded by wet prairie on
peat vegetation type. The other well is designated P37 and is situated in a wet
prairie on marl.

47
Hj Sawgrass
m Tree Island
■ Marl Prairie
MONTH
Figure 3.
Mean daily transpiration rates from sawgrass, tree island and marl
prairie plant communities.

48
Evapotranspiration was estimated by comparing nighttime water losses
with daytime water losses, similar to the technique reported by Dolan et al,
(1984). The method is based upon the assumption that the only difference
between daytime and nighttime recession rates is due to evapotranspiration. The
technique is not useful on days with rain.
Rates of community evapotranspiration were different between the wet
prairie on peat and marl prairie sites. Mean daily water loss rates from the marl
prairie, calculated for each month of available data, ranged from a low of 0.10
cm/day during December to a high of 0.28 cm/day during June (Figure 4). This
translates to a mean annual total water loss of about 77 cm at the marl prairie
site. Daily rates were higher at the peat site. Anomalously high rates were
observed during June 1985, when the mean daily rate was 1.15 cm/day. This
occurred during a period of high temperatures, little rainfall and low ambient
water levels. Annual water loss at the peat wet prairie site was about 114 cm.
The mean difference between sites was 0.10 cm/day, (significant at P = 0.001),
indicating dramatically higher water loss rates at the peat site than at the marl
prairie site.
Mean daily evapotranspiration rates at the marl prairie (P37) followed a
smooth sinuous pattern over the time course of a year (Figure 4), whereas the
peat prairie site had dramatic anomalies during the early part of the summer.
The variation over time was summarized as percentages of annual water loss for
each month for use in the modeling section.
Summarization of Evapotranspiration Studies
The transpiration studies indicate that a difference in community
transpiration exists among the types studied, that comprise a hierarchy of water

Mean daily evapotranspiration (cm/day)
Feb-1985 May-1985 Aug-1985 Nov-1985 Feb-1986 May-1986 .Aug-1986
Month
Figure 4.
Time course of mean daily evapotranspiration (cm/day) at study
sites P33 and P37 from February 1985 through September 1986

50
use in the landscape. The variation in community rates is due to dramatic
differences in leaf area among the vegetation types, more than losses per leaf
area. The marl prairie has low rates of transpiration, has a small total leaf area
per unit ground area, and is the most oligotrophic of the sites. The sawgrass sites
on peat have higher leaf area and community transpiration rates. The highest
transpirative water loss is from the tree island/swamp forest community, due to
higher rates and highest leaf areas. The swamp forest appears to be the most
eutrophic of the sites.
The studies of community evapotranspiration, indicate that differences
among types exist, the components of evaporation and transpiration vary among
the types. The transpiration and community evapotranspiration data both
indicate the fluctuation in rates over an annual cycle. Even though the rates
fluctuate seasonally, a mean daily rate will be used as the basis of comparison
among types and pathways of water loss. The P37 site is the only one of the sites
to have both transpiration and community estimates. The transpiration estimates
(0.02 cm/da) were about an order of magnitude lower than the community
estimates (0.2 cm/day), indicating that transpiration is not a large pathway of
water loss. The wet prairie on peat site (P33) had a higher daily rate (0.3
cm/day) than the marl prairie. The wet prairie rates were higher than the daily
transpiration rates in the sawgrass and lower than the transpiration rates at the
tree island site.
Evapotranspiration is one major pathway of water flow out of wetland
ecosystems. The other major outflow is via overland flow. The theoretical and
practical work studying this process will be reviewed in the next section.

51
Flow in Wetlands
Surface water flow in wetland ecosystems has been studied using
principles of applied hydraulics. The theoretical foundations for flow arise from
hydraulic principles, although there appears to be disagreement in the literature
as to the fundamental nature of flow regimes. A unique functional feature of
wetland systems is the periodic flooding and flow followed by periods of no
flow. This periodicity involves transitions among flow regimes from no flow to
laminar flow to turbulent flow. Most studies of wetland flow (Ree 1949, Petryk
and Bosmajian 1975, Lin and Shih 1979, Rosendahl and Probst 1980, Rosendahl
1981, Shih and Rahi 1982) assume a turbulent flow regime and utilize Manning's
formula (Manning 1890). Kadlec (1990) argues that laminar flow is dominant in
wetlands due to the low energy gradients and suggests a formulation such as the
one given in Equation (2) be used. Wetland flow is of the magnitude that
momentum terms in flow equations are usually ignored (Kadlec 1990, Hammer
and Kadlec 1992). The disagreement involving flow regimes can be partially
resolved as one of parameter values, as shown in Equation (2). Equation (2) is a
generalization of the Manning equation relating flow velocity as a function of
hydraulic radius and hydraulic slope. The critical parameters are a and P and
are assigned values of a = 0.5 and p = 0.67 in the Manning formula. Kadlec
(1990) reports values of a range from 0.4 to 1.0 and p from 2.5 to 3.75 for laminar
flow in wetlands.
(2) V = K * Sa * Rhc
V = velocity
K = general resistance coefficient
= Hydraulic slope (difference in elevation potential)
S

52
Rh = Hydraulic radius (Cross-sectional area/wetted perimeter: Note
for very wide channels, Rh is approximated by water depth)
a = slope exponent
P = hydraulic radius exponent
In Manning's formula, K is represented by 1/n in SI units (1.49/n in
English units), and n is referred to as a roughness coefficient or as Manning's n.
Assuming turbulent regimes, most prior work on wetland flow has
attempted to develop better estimates of Manning’s n, and particularly how this
coefficient varies with factors of water depth and vegetation density. The earliest
work relates n with water depth (Ree 1949) and the product of velocity and water
depth (Palmer 1945). Ree worked with flow in short grasses and found an
increase in n with depths up to the height of the grass, then a decrease, similar to
Palmer. Petryk and Bosmajian (1975) laid much conceptual framework, and
related n as a function of vegetation characteristics (primarily vegetation
density), boundary roughness and hydraulic radius. Petryk and Bosmajian
(1975) thought that vegetation resistance was much greater than boundary
roughness, and hence related n to vegetation density and inversely to hydraulic
radius; for n to remain constant vegetation density had to decrease if depth (Rh)
increased. Shih and Rahi (1982) using principles of Petryk and Bosmajian (1975),
developed estimates of n from 0.16 to 0.55 for marshes in the Kissimmee basin,
where n varied with seasonal changes in vegetation density.
Studies of flow in the marshes of the Everglades date back to the 1940s,
with the earliest work (Parker et al. 1944) measuring decreased flow in canals
resulting from infestations of water hyacinths. The U.S. Army Corps of
Engineers developed estimates of Manning's n in design memoranda for the
C&SF project, that averaged 0.035 and ranged inversely with water depth (U.S.

53
Army 1954). Leach et al. (1971) investigated data from a series of years and
found maximum flow rates of 1600 ft/day (0.6 cm/sec), which translate to a
cumulative annual distance of 50 miles (81 km). Rosendahl and Probst (1980)
and Rosendahl and Rose (1981) measured flow rates and resistance coefficients in
sawgrass and open marshes in Everglades National Park and reported greater
flow rates; from 0 to 0.022 ft/sec ( 0.67 cm/s) in dense sawgrass strands and
from 0 to 0.034 ft/sec (1.0 cm/s) in open marshes. Rosendahl (1981) calculated a
range of values of Manning's n between 0.4 and 2.4, with a mean of 0.99 and
found little correlation with depth.
Most of the models of water flow in the Everglades marshes use
Manning's equation and with varying reports as to the sensitivity of model
output to variations in the roughness coefficient. Lin and Shih (1979) used values
of n between 0.4 and 1.2, with an inverse relationship between n and depth. Lin
and Shih (1979) found that seasonal variation in n was necessary to achieve
model calibration, with lower values in the dry season and higher values in the
wet season. MacVicar et al. (1983) relate flow coefficients as a function of land
cover type, with values ranging from 0.1 to 2. Perkins and MacVicar (In press)
did a sensitivity analysis using very low value of n (0.05) and very high (2.0) and
found more effect on flow volume than stage, recommending development of
better coefficients with vegetation type. Walters et al. (1992) developed a
coefficient of flow equivalent to K in equation 2, of 2, which translates to a
Manning’s n of 0.75.
A review of previous studies involving flow in wetland systems can be
summarized as follows. Although there is still uncertainty regarding the nature
of the flow regime, a generalized form of Manning's equation can be used. The
equation equates flow velocity as a function of water depth, hydraulic slope, and
a resistance coefficient, such as Manning's n. The flow coefficient can be

54
estimated from vegetation density, defined as the total cross-sectional area of
vegetation per unit length of flow (Petryk and Bosmajian 1975)
In the preceding sections, the processes influencing the measures of
evapotranspiration in south Florida and flow relationships in wetlands were
discussed in context of scale. The way in which these processes are incorporated
into a landscape model is primarily a scaling issue. The details of how this
scaling process was done is described below in the section on modeling
methodology. A brief review of some general concepts and approaches to
scaling in ecological models is included as a final piece in this background
section.
Ecological Models and Scale
Most descriptive landscape or ecosystem models have explicit domains in
space and time. Temporal domains are defined at the small end by the time step
and at the large end by the time horizon. Similarly, spatial grain is defined by
the size of grid cell and extent by the number of grid cells. Bounding the model
along spatial and temporal dimensions, defines what is inside and outside the
model domain in terms of scale. The empirical rule of thumb is that models
cover no more than two to three orders of magnitude in either space or time. The
rule is probably not related to technical constraints such as computer processing
power (Costanza and Maxwell 1992). The scale restriction may be related to
practical factors, such as debugging problems, validation criteria (Clark et al.
1979 ), or understanding the model (Costanza and Sklar 1985).
By using an ecological model with a fixed domain, decisions must be
made about what to do about processes that occur at different scale ranges. The
common approach in model construction is to treat processes that occur at slower
speeds and over broader ranges as constants. For example, if a model is

55
constructed to examine seasonal dynamics in sea level, then the global processes
that created a dramatic sea level rise between 5 and 10 thousand years ago, are
assumed to not change much over the course of a few years and therefore are
treated as constant. Faster processes are generally treated as noise or random
fluctuations within the system and can be averaged. Using the same example,
tidal influences on sea level occur over a short term and therefore can be treated
as noise over time spans of a year. The short term (daily) influences are averaged
to study seasonal or annual dynamics.
Components both inside and outside model structures are dealt with by
processes of aggregation and disaggregation. The simplest form of aggregation
is linear scaling. Scaling is defined as the translation of units based upon a fixed
relationship or ratio among metrics used in measurement. For example,
temporal metrics of minutes, hours, and days have a fixed relationship, therefore
one can trivially determine that one day is equal to 1440 minutes. Broadly, the
issue of aggregation has been dealt with either in terms of applying standard
statistical methods to derive "best" estimates and minimize error (O’Neill et al.
1986, Gardener et al. 1982), or by assuming linear aggregations among complex
variable sets (Iwasa et al. 1986, 1989). Basically, aggregation works if the
assumptions and rules used remain valid over the scales of translation.
Incorporation of evapotranspiration, flow and vegetation dynamics into a
spatially and temporally explicit hydrologic model of the Everglades involves
"fitting" these into a model with explicit bounds in time and space. The next
section describes the structure and development of the model used to investigate
hydrodynamics in the system.

56
Model Description and Development
The framework for the model was developed during a series of
workshops held between 1989 and 1990. The initial objective of the model was to
improve communication among scientists, engineers and practitioners in order to
discuss issues related to Everglades restoration. The model resisted a series of
attempts at invalidation (Walters et al. 1992, Richardson et al. 1990) and hence
has become a credible tool for examination of movement of water across the
landscape. The model framework depicts the time dynamics of the hydrology
within approximately 800 4 x 4 km grid cells (Figure 5) that cover the historic
Everglades ecosystem and surrounding areas. The model is bounded by Lake
Okeechobee to the north, the Atlantic coastal ridge to the east, Florida Bay to the
south and the Big Cypress National Preserve to the West (Figure 5). The basic
framework reported by Walters et al. (1992) was modified to include coupling of
vegetation and hydrology. The hydrology and vegetation components of the
model are described in the next two sections, followed by the development of
subroutines of evapotranspiration and flow that link the hydrologic and
vegetation components.
Hydrologic Components
Water depths within a cell change over time due to inflow associated with
rainfall, losses via evapotranspiration, net flux associated with overland runoff
from adjacent cells and net flux of water into or out of canals. The model is
driven by historic rainfall data, covering the period from January 1960 through
December 1988. Input data are of total monthly rainfall, averaged over the entire
basin area. Even though spatial gradients exist in the system (MacVicar and Lin
1984) equal amounts are added to each cell at the beginning of each simulated
month. Annual rainfall during the model time period ranges from 100 to 150

Figure 5.
Model grid used to depict hydrologic and vegetation dynamics
Everglades ecosystem.

58
cm/yr. The input to a cell is actually as net rainfall; that is, the recorded rain
total minus evapotranspiration.
Water is moved to adjacent cells based upon the Manning formula, where
velocity is a function of hydraulic slope, water depth and a resistance coefficient
(Equation 2). The alpha and beta values from equation 2 are 0.5 and 0.67.
Hydraulic slope is determined by difference between adjacent cells in the sum of
ground elevation and water depth. Levees in the model stop flow movement.
Water management is incorporated in the model by a series of water
management schedules within each conservation area and rules of water
movement around the schedules. If water levels at index cells are above the
monthly schedule, then water is removed from certain output cells. If water
levels are below scheduled levels, then water is retained. Water is diverted to
coastal areas by removal from key index cells to simulate removal via canals.
Target diversion rates are a function of maximum diversion (flow allowed in a
canal) and water depth.
Only surface water movement is calculated; no losses to groundwater are
included. In the peat areas of the system, with high infiltration resistance, this is
not considered to be a major source of error. In the transitional, sandy and marl
areas, movement from surface to groundwater is considerable, resulting in
overestimates of water depths.
The modeled area exchanges water with the surrounding areas. Water is
input from Lake Okeechobee, based upon decision rules and schedules within
the Lake. The Big Cypress regions to the west receives the same rainfall inputs as
areas over the Everglades proper. Water exchange with this area is only
constrained by structures in the model. No exchange (other than management
diversion) is made with the east, even though under historic conditions water
moved through the coastal ridge through a number of rivers, sloughs and finger

59
glades. Boundary conditions at Florida Bay vary seasonally from a low value in
winter to a high value in late fall, to reflect the annual dynamics of sea level.
Information on water depth and flow over time can be output for each
grid cell. Target cells that correspond to the locations of sites P33, P35, P37 and
P38 (Figure 6) were used as key indicators of model results. Cumulative annual
flow amounts were determined for three flow sections. One is for the set of cells
that coincide with the Tamiami Trail Flow section (Figure 6). The other sections
are at the boundary cells at the mouth of Shark River Slough, and at the mouth of
Taylor Slough.
The preceding paragraphs summarized the hydrologic variables and
interactions within the model framework. The next section deals with the
structure of the vegetation component of the model.
Vegetation Components
A total of 26 cover types were created to capture the variety of vegetation
patterns in the landscape of the model area (Table 4). The types were based upon
combinations of plant associations, as a grid cell of four kilometers generally
covers a non-homogeneous combination of plant communities. Some of the
vegetation types, such as sawgrass, can be the only type within some grid cells.
Other types, such as sloughs and tree islands are always smaller than the grid
cells. To determine the percent cover of vegetation communities within the
dominant landscape types, and how robust the measures of percent cover were
with a change in scale, the following exercise was done.
Vegetation cover was measured in a series of subsamples from the two
classified sixteen kilometer SPOT satellite scenes used in the vegetation map
section above. A total of thirty two samples were made (sixteen from each
scene), for window sizes of 500, 1000, 2000 and 4000 m. Percent cover was

60
Figure 6. Location of sample rain and stage gauges, flow sections and pan
evaporation sites within the Everglades region.

61
Table 4. Description of vegetation categories (landscape units) used in
Everglades model.
Map
No.
LANDSCAPE UNIT
Description of Components
1
sawgrass, slough, tree island
2
sawgrass/slough
3
slough, with periphyton
4
slough, no periphyton
5
sawgrass marsh
6
sawgrass with woody invasion
7
sawgrass,cattail
8
wet prairie, on peat, tree islands
9
wet prairie, on peat, native woody plants
10
wet prairie, on peat, exotics
11
wet prairie, on marl and tree islands
12
wet prairie, on marl, muhly grass
13
wet prairie, on marl,native woody plants
14
wet prairie, on marl, exotics
15
Pine, hammock
16
Pine, hardwood
17
Pine, prairie
18
Upland hardwood scrub
19
tall mangrove forest
20
short mangrove forest
21
mangrove prairie
22
dwarf cypress
23
cypress dome
24
cypress hardwood
25
agriculture
26
no ve£etation__

62
calculated from each sample for each of the three major vegetation types;
sawgrass, tree island and wet prairie. The percent cover of sawgrass, wet prairie
and tree island communities in the southern Everglades did not vary over the
sampled window sizes. For windows sizes from 500 through 4000 m, the cover
of each of the three types was relatively constant (Figure 7). The mean cover was
about 66% for sawgrass, 21% for wet prairie and 13% for tree island. A two-way
analysis of variance indicated no significant difference in cover among the
window sizes. Although variances tended to decrease with window size, the
differences were not enough to violate assumptions of homoscedasticitv. These
results indicate that using the percent cover of plant communities to describe the
landscape units is very robust to changes in the cell size of the landscape units.
A map editor is established in the model to allow for creating the initial or
starting vegetation array within the active cells. The map editor creates an array
that consists of a vegetation type code for each cell that can be addressed and
updated during the simulation. The rules in the model for changing the
vegetation types are the subject of the next section.
Changes in Landscape Vegetation Types
The vegetation change module of the model is set up to switch among
vegetation types, based upon rules relating to hvdroperiod, nutrient
concentration and fire. At the end of each year of simulation, the hydroperiod
(number of months per year that a site is wet) and soil nutrient concentration are
calculated for each grid cell. The annual hydroperiod value is used to update a
running average hvdroperiod for each cell. Fire is a stochastic event, with
probability related inversely to the annual hydroperiod value. If a random
number is less than the assigned probability for the hydroperiod value, then a
fire event is said to have burned the cell. The average hydroperiod, soil nutrient

Percent Cover Percent Cover Percent Cover
63
100
80
60
40
20
0
100
80
60
40
20
0
1000 2000 4000
Window Size (m)
WET PRAIRIE
1000 2000 4000
Window Size (m)
Figure 7.
Percent cover of sawgrass, wet prairie, and tree island in various
window sizes.

64
concentration and a fire event are all used as critical values to make changes
among vegetation types. If average hydroperiods are wetter or drier than a
certain threshold value, or if the soil nutrient concentration exceeds a critical
value, or if a fire occurs in the cell, then the vegetation cover type for that cell
changes. The threshold values of hydroperiods and target transition types are
user defined.
The transitions among vegetation types were determined using
information derived from a combination of sources, namely, literature and field
experience. The transitions involve the loss or gain of certain community types
within a cover type. The primary cover in the peat portions of the Everglades
system is a mosaic of sawgrass, slough and tree islands, designated as type one.
The hydroperiod ranges from 9 to 11 months in this type. If hydroperiods exceed
11 months, then the tree island and sawgrass types disappear, leaving only
slough (Craighead 1971, Worth 1987). If hydroperiods are less than 9 months,
then woody plants invade the sawgrass and slough (Craighead 1971, Gunderson
and Loftus In Press) resulting in a change to type 9. The other dominant peat
landscape type was a monospecific stand of sawgrass in the area now known as
the EAA (Davis 1943). If the sawgrass burns or dries out, woody plants invade,
(.Wade 1980) resulting in type 6. The vegetation dynamics associated with a
change in nutrient status include a loss of periphyton in a slough system (Swift
1984), and a transition from sawgrass to cattail (Davis 1989).
The preceding paragraphs describe the "landscape" vegetation units used
in the model. These units are comprised of combinations of identifiable plant
communities. The transitions among landscape types involve the addition or
replacement of plant communities within each landscape unit. Since the plant
communities provide the "building blocks" for each landscape unit, they will be
used as the basis of relating flow and evapotranspiration.

o5
Development of Flow Coefficients tor Landscape Units
Two steps were involved in the determination of flow coefficients by
landscape unit. The first step related estimates of vegetation density for each of
the dominant plant communities to flow coefficients. The second step used the
percent cover relationships within a landscape type to develop a spatially
weighted flow coefficient.
To develop relationships between vegetation type and flow regimes,
estimates of vegetation density were derived. Vegetation densities were then
translated to Manning's flow coefficients using relationships developed by
Petryk and Bosmajian (1975) and Shih and Rahi (1982). Vegetation density was
determined for four vegetation types: sawgrass marsh, wet prairie over peat,
marl prairie and tree island. The literature was surveyed for measured values of
stem density for the gramineous vegetation types (marsh and prairie) and for
values of basal area for the forest type (tree island). Average stem densities in
the graminoid vegetation types were multiplied by the average stem size to yield
an average cross sectional area per length of flow. Total basal area was divided
by the stem density to yield an average tree size, then average cross sectional
area was determined per unit of flow length. The values of vegetation density
were then correlated to a Manning's n value based upon data compiled by Petryk
and Bosmajian (1975).
Stem density varied from a low value in the wet prairie (0.05 / m2)
to the highest (42/m2) in the marl prairie (Table 5). Even though the marl prairie
had the highest stem density, the sawgrass had the highest vegetation density.
The cross-sectional area of the plants comprising the marl prairie were much
smaller than sawgrass. The vegetation density reflects the total cross-sectional
area (m2) per ground area in the direction of flow (m3), and is in units of nr1.
The vegetation densities were highest in the sawgrass areas (0.15 nr1),

66
Table 5. Vegetation density and related flow coefficients as a function of
depth for sawgrass, tree island, wet and marl prairie vegetation
types.
Vegetation Type
Sawgrass
Wet Prairie
Tree Island
Marl Prairie
Stem Density
(#/m2)
28
*0) 3 *(2)
0.6 *(3)
42 *(4)
(#/ft2)
8.5
0.9
0.2
12.8
Stem Size
(ft)
0.08
0.03
0.30
0.02
Stem Area
(ft2/ft2)
0.71
0.03
0.05
0.27
Depth
Vegetation
(ft)
Density
0.5
1.42
0.06
0.11
0.53
(ft2/ft3)
1
0.71
0.03
0.05
0.27
1.5
0.47
0.02
0.04
0.18
2
0.36
0.01
0.03
0.13
2.5
0.28
0.01
0.02
0.11
3
0.24
0.01
0.02
0.09
3.5
0.20
0.01
0.02
0.08
Mannings
*(5)
0.5
1.12
0.22
0.31
0.68
n *
1
1.26
0.25
0.35
0.77
1.5
1.35
0.27
0.37
0.82
2
1.41
0.28
0.39
0.87
2.5
1.47
0.29
0.41
0.90
3
1.51
0.30
0.42
0.93
3.5
1.55
0.31
0.43
0.95
Model Flow
*(6)
0.5
1.3
6.7
4.8
2.2
Coefficient
1
1.2
5.9
4.3
1.9
K
1.5
1.1
5.5
4.0
1.8
2
1.1
5.3
3.8
1.7
2.5
1.0
5.1
3.7
1.7
3
1.0
4.9
3.5
1.6
3.5
1.0
4.8
3.5
1.6
REFERENCES
*0) Herndon et al. 1991
*(2) Goodrick 1984
*(3) Gunderson 1982
*(4) Olmsted et al. 1980
*(5) Petryk and Bosmajian, 1975
*(6) Walters et al., 1992
n = (depth)A0.67*(veg density)A0.5
K = 1.49/n

67
intermediate in the marl prairie (0.06 m*1) and tree islands (0.05 m*1), and lowest
in the wet prairie (0.01m*1). The estimated flow coefficients for sawgrass was
about twice that of tree island and wet prairie, and substantially greater than in
the wet prairie.
A spatially weighted average flow coefficient was determined for each
landscape unit. First, a mean flow coefficient was calculated over a range of
depths for each plant community type. The percent cover of each plant
community in a landscape unit was used as the weighting factor. For example,
in landscape unit 1, sawgrass covers on the average 66% of a cell, wet prairie
covers 22%, and tree islands cover 12%. The depth averaged flow coefficient for
these three types are 1.09, 5.44 and 3.93, respectively. The flow coefficient for this
landscape unit is (0.66*1.09+.22*5.44+.12*3.93) = 2.4. The spatially weighted
coefficients are given in Table 6. Even though the values vary among plant
community types, the spatially weighted averages are similar among the
landscape units
Development of Evapotranspiration Coefficients for Landscape Units
A spatially weighted average evapotranspiration rate was also calculated
for each landscape unit. The plant community rates were derived from average
daily rates calculated from the evapotranspiration data. The values ranged from
a low of 0.22 cm/day in the marl prairie to 0.4 cm/day in the swamp forest
(Table 7). The values for cattail and melaleuca were estimated from other
sources (Koch, unpub. data; Woodall 1980). The calculation of annual totals is
extremely sensitive to the daily rates, a difference of 0.1 cm in the daily rates
results in an annual difference of 36 cm. The spatially weighted mean annual
evapotranspiration values ranged from 95 cm (marl prairie, type 11) to 159 cm for
the unit of exotic trees on peat (Table 7). Annual totals for each landscape type

68
Table 6. Spatially weighted flow coefficients for each landscape unit used in
the Everglades Model.
Spatially
Map LANDSCAPE UNIT
Spatial %
Weighted
No. Description of Components
Components
Average K
1 sawgrass, slough, tree island
66-22-12
2.4
2 sawgrass/slough
78-22
2.0
3 slough, with periphyton
100
5.4
4 slough, no periphyton
100
5.4
5 sawgrass marsh
100
1.1
6 sawgrass with woody invasion
88-12
1.4
7 sawgrass,cattail
50-50
1.3
8 wet prairie, on peat, tree islands
80-20
5.1
9 wet prairie, on peat, native woody plants
60-40
4.8
10 wet prairie, on peat, exotics
20-80
4.2
11 wet prairie, on marl and tree islands
80-20
2.2
12 wet prairie, on marl, muhly grass
80-20
2.2
13 wet prairie, on marl,native woody plants
60-40
2.6
14 wet prairie, on marl, exotics
40-60
2.6
15 Pine, hammock
100
1.8
16 Pine, hardwood
100
1.8
17 Pine, prairie
100
1.8
18 Upland hardwood scrub
100
1.8
19 tall mangrove forest
100
10.0
20 short mangrove forest
100
10.0
21 mangrove prairie
100
10.0
22 dwarf cypress
100
2.0
23 cypress dome
100
2.0
24 cypress hardwood
100
2.0
25 agriculture
100
2.0
26 no vegetation
100
2.0

Table 7.
Average daily and annual evapotranspiration for plant
communities used to develop evapotranspiration coefficients for
Everglades model.
69
Plant Community
Daily ET
(cm)
Annual ET
(cm)
Annual ET
(in)
Sawgrass
0.33
120
47
Wet Prairie/Slough
0.26
95
37
Tree island
0.42
153
60
Marl Prairie
0.22
80
32
Exotic-Melaleuca
0.48
175
69
Map
No.
LANDSCAPE UNIT
Description of Components
%
Spatial
Components
Spatially
Weighted
Annual ET
(cm)
Relative
Annual Rate
X/114 cm
1
sawgrass, slough, tree island
66-22-12
119
1.04
2
sawgrass/slough
78-22
115
1.01
3
slough, with periphyton
100
95
0.83
4
slough, no periphyton
100
95
0.83
5
sawgrass marsh
100
120
1.06
6
sawgrass with woody invasion
88-12
123
1.08
7
sawgrass,cattail
50-50
145
1.27
8
wet prairie, on peat, tree islands
80-20
107
0.93
9
wet prairie, on peat, native woody plants
60-40
118
1.04
10
wet prairie, on peat, exotics
20-80
159
1.40
11
wet prairie, on marl and tree islands
80-20
95
0.83
12
wet prairie, on marl, muhly grass
80-20
95
0.83
13
wet prairie, on marl,native woody plants
60-40
110
0.96
14
wet prairie, on marl, exotics
40-60
118
1.04
15
Pine, hammock
100
114
1.00
16
Pine, hardwood
100
114
1.00
17
Pine, prairie
100
114
1.00
18
Upland hardwood scrub
100
114
1.00
19
tall mangrove forest
100
114
1.00
20
short mangrove forest
100
114
1.00
21
mangrove prairie
100
114
1.00
22
dwarf cypress
100
114
1.00
23
cypress dome
100
114
1.00
24
cypress hardwood
100
114
1.00
25
agriculture
100
114
1.00
26
no vegetation
100
114
1.00

70
were expressed as a ratio of 114 cm/yr, the fixed coefficient for the model. As
with the flow values, there appears to be some spatial convergence of averages.
That is, a relatively constant percentage of plant community types within a
landscape unit combined with a difference in rates among plant communities,
appears to result in a global average for a grid cell.
The preceding section of this chapter described the hydrologic
components, vegetation components and linkages of flow and
evapotranspiration in the model. Water depths within each grid cell change
monthly as a function of historic rainfall, net flow, and evapotranspiration. At
the scale of the model, 26 landscape types comprised of plant communities, are
used to describe vegetation patterns. Flow and evapotranspiration rates are
linked to the "landscape" type. This linkage was done through two steps: first to
determine coefficients for the dominant vegetation communities, then to develop
a spatially weighted average coefficient for each landscape unit based upon the
percent cover of vegetation types within the landscape unit. The transitions
among the landscape units are a function of cumulative water depths
(hydroperiod), fire and nutrient concentration. The next section of the chapter
presents the results of sensitivity analyses and testing the hypotheses.
Results
The results section has three parts. The first part assesses the sensitivity of
key parameters to flow calculations and compares model output with historic
data. The second part presents attempts to invalidate the linkages between
vegetation and hydrology. The third portion of this section reviews the tests of
the upstream area hypothesis.

71
Sensitivity Analysis- Flow and Evapotranspiration
Tests were done to explore the sensitivity of the model output (primarily
flow) to uncertainties in parameters associated with flow and evapotranspiration.
The sensitivity analyses of flow coefficients were done by doubling and halving
all coefficients calculated in the above paragraphs, running the model for a full
28 year scenario under natural conditions (no water control structures in the
system). The sensitivity to evapotranspiration was tested by running a full 28
year natural scenario with the annual evapotranspiration rate set at 89,102,107,
and 114 cm (35,40,42 and 45 inches).
Doubling and halving the flow coefficients did not appear to have an
appreciable affect on flow through the Tamiami flow section (Figure 8). The
largest deviations among the three sets of coefficients occurred during wet years
(model simulation years 1967, 1969, 1970; Figure 8). During these periods, the
flow differed by about 500 x 106 m3/yr between either of the runs with adjusted
coefficients and the unadjusted coefficients. This difference during wet years,
between the adjusted coefficient flows and the unadjusted flow, was about 12%
of the unadjusted flow. Differences during dry years were much less. There was
no evidence that changes in vegetation landscape types during any of these runs
altered or confounded the flow relationship among the adjusted coefficients. The
flow results from the unadjusted run were always intermediate between the
higher flows calculated by doubling the flow coefficients, and the lower flows
associated with halving the flow coefficients.
The results of varying base evapotranspiration indicate counter-intuitive
effects on rates of annual flow through the Tamiami flowsection. The results are
unexpected because there is not a constant relationship between the
evapotranspiration rate and amount of flow. The lower evapotranspiration rates
should generate higher stages and higher flow. The simulated flow data start out

72
FLOW COEFFICIENT *1/2
FLOW COEFFICIENT * 2
A- NATURAL
Figure 8. Effects of doubling and halving flow coefficients on simulated flow
through Tamiami flow section.

73
with this relationship, but the relationship changes through the time course of
the model run (Figure 9). These discrepancies are the result of the linkages
between hydrologic conditions and the vegetation landscape conditions. If the
system gets too dry, such as the scenario of higher base annual
evapotranspiration (114 cm/yr), then woody species invade the landscape,
increasing the evapotranspirative loss and lowering flow rates. The system
appears to entrain flows at lower levels of evapotranspiration. The lower
evapotranspiration maintains "wetter" landscape types that result in higher flow
rates.
Even with these interesting and counter-intuitive effects of vegetation-
hydrology-evapotranspiration linkages on flow, the model is apparently more
sensitive to changes in evapotranspiration than to variations in flow coefficients.
Changing the base transpiration rate only 25 cm/yr, results in a variation of
annual flow on the order of 500 x 106 m3/yr (Figure 9). A similar effect was
achieved by doubling and halving the flow coefficients. After establishing the
sensitivity of changing the base settings on flow regimes, model output using the
base settings will be compared to historic data.
Agreement with Historic Data
The model output, both stage and flow, indicates periods of agreement
and divergence with measured data. The actual stage at P33 and P35 and flow
through Tamiami tend to be lower than the model output during the period from
1961 through 1965 (Figures 10 and 11). This is probably due to the management
policy in effect during this period, when little or no flow was delivered to the
park (Wagner and Rosendahl 1985, Gunderson 1989). During other years, the
actual and modeled stage data tend to qualitatively agree. Since there was no
groundwater component to the model, agreement was only possible with surface

74
89 -o- 102 -4— 107 —o— 114
Annual Base Evapotranspiration (cm)
Figure 9.
Effects of varying base evapotranspiration rates on simulated flow
through Tamiami flow section.

75
MANAGED ACTUAL
-80 t
1960 62 64 66 68 70 72 74 76 78 80 82 84 86
Year
Figure 10.
Time series of simulated (solid lines) and actual (dashed lines)
stages at gauge P33 from 1960 to 1988.

76
MANAGED
ACTUAL
Year
Figure 11. Time series of simulated (solid lines) and actual (dashed lines)
stages at gauge P35 from 1960 to 1988.

77
water conditions. The modeled flow through Tamiami trail also agreed fairly
well with measured flow in periods other than the early 1960s and early 1970s.
The vegetation patterns at the end of the simulation period of the natural
scenario appear to agree with early descriptions of vegetation in the Everglades.
The initial array of landscape units in the model grid consisted of a sawgrass
plain south of Lake Okeechobee, the tree island/sawgrass mosaic in the central
core of the system, and marl prairies units in the south. (Figure 12). At the end of
the run, the sawgrass plain and marl prairie units had persisted (Figure 13). The
tree island/sawgrass mosaic had changed to a sawgrass/slough type in the area
of the persistent pool described in the paragraph above. Davis (1943) and Jones
(1948) observed and mapped similar patterns; the tree island/sawgrass mosaic
was only mapped in the northeast and southwest portions of the central
Everglades and a tree-less marsh was in the topographically lower southeast
region. The tree-less sawgrass/slough vegetation type is also captured in the
native Americans description of the system as "Pa-hay-okee", which loosely
translates to a grassy lake (Douglas 1947).
The output from the model agrees fairly well with historic hydrologic and
vegetation information. Even with uncertainties and sensitivities to
understanding flow and evapotranspiration processes, the model captures key
aspects of hydrologic and vegetation dynamics of the system. The next section
puts the model at risk, and attempts to determine the bounds of the relationships
between the hydrology and vegetation.
Linkages between hydrology and vegetation
Since the model output agreed fairly well with historic data sets, a test was
developed to determine the limits of the influence of vegetation dynamics on the
relationship between rainfall and runoff. The test consisted of a series of model

78
5
5
5
5
5
5
5
5
5
5
5
5
5
1
*
5
5
5
5
5
5
5
5
5
5
5
5
5
1
1
.
.
5
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
5
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
•
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
i
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
23 23 23 23
9 23 23
24
23
23
22
23 23 22
22 22
5
5
5
5
5
5
5
5
5
1
1
1
1
1
1
23 23 23
9 24 24 24
24
24
23
23
23 22 11
22
5
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23 24
23 24
24 23 24
23
23
22
23
23
22 11
22
22
23
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23 24 23 24 24 23 23
23
22
23
23
23
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
17 17 23 23
23
23
23
23
23
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
11
22 17
11
17
22
22
22
22
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
11
11 17 17
17
17
17
17
22
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
23 11
11 17
17
17
17
17
17
17
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
11
9 22
17
17
17
17
17
22
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
11
24 24
23
11
17
17
17
17
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
11
11
24 24 23
17
11
17
17
22
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
21
11 23 23
11
23
23
11
22
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
20 11 11
11
23
23
23
23
22
22 22
22
22
22
1
1
1
1
1
1
1
1
1
1
1
1
1
1
20 21
20 21
11
11
23
23
23
22
22 22
22
22
22
2
1
1
1
1
1
1
1
1
1
1
1
1
1
21 20 20 21
11
23
23
17
22
22 11
11
11
11
11
1
1
1
1
1
1
1
1
1
1
1
1
21 21
20
21
11
11
17
22
11 11
11
11
11
1
1
1
1
1
1
1
1
1
1
1
1
1
21 19
20
20
21
17
17
11
11 11
11
11
13
1
1
1
1
1
11
1
1
1
1
1
1
1
. 21
21
19
21
21
11
11
11 11
13
13
1
1
1
1
1
11
13 13
11
1
1
1
1
. 19
21
21
19
21
21
11
11 11
13
13
1
1
1
1
11 11 13
13 11
11
11
11
11
. 19
19
21
19
19
21
11
11 13
1
1
1
1
1
11
11
13 13 13 11
11
11
11
11
21
21
19
21
19
20
11 1
1
1
1
1
11
11
12 13 13
13
11
11
11
11
19
19
19
21
21
20 1
1
1
1
11
17
11
11
13 11
11
11
11
11
11
19
19
19
21
19
20 1
1
1
22 17
15 15 13 11
11
11
8
11
11
19
21
21
19
20 1
1
1
17
17
18 18
17
11
11
8
8
11
11
.
19
19
19
19
19 20
1
17
22
13 13 13 13 11
11
8
11
11
19
19
19
19
19
19 19 21
11
11
22 22 22
8
11
11
8
11
11
19
21
19
19
19
19 19 19
21
21
13 22
8 11 13 11
8 11
11
19
21
19
19
19
19 19 19
19
21 21
11
9 20 20 20 20 21
21
19
21
21
19
19
19 21
19
19
19 19 20 20 19 19 19 20 20 20
.
21
21
21
21
19 19
19
19
19 19 19 19 19 19 19
21
21
21
19 19
.
.
19
19
.
.
.
19
19 .
Figure 12. Map codes for initial landscape vegetation types in the Everglades
model. Dominant code in the Everglades proper is type 1. Cover
types developed from Davis (1943). Explanation of codes is found
in Table 4.

79
Figure 13. Map codes of landscape vegetation types in grid cells of Everglades
model at end of 28 year simulation run. Note presence of type 3
codes in right -central portion of array. See Table 4 for explanation
of codes.

80
runs For each run, a set amount of rain was delivered each year of a 20 year
simulation. The rain varied seasonally, as modeled by composite sine waves to
emulate the natural annual pattern, but remove any interannual variation. Four
runs were made, ranging from a very dry year to a very wet year. The model
inputs were equivalent to annual totals of 105,118,142 and 176 cm (36,46,56 and
68 inches).
The relationships between rain and runoff appears constant over a wide
range of rainfall inputs, then dramatically shifts if the system becomes very wet.
The flow and stages at key stations all reached a seasonally oscillating
equilibrium with rainfall inputs less than 142 cm. At steady rainfall up to 142
cm, the landscape vegetation types remained constant, and hence, the
relationship between rainfall and runoff was linear. At an annual input of 176
cm, a dramatic shift occurred around year 6, when the landscape units shifted to
a treeless wet prairie. Without tree islands or sawgrass, the overland flow rates
were greatly increased, resulting in a new equilibrium of flow coming through
the Tamiami flow section (Figure 14). No such vegetation shifts occurred in the
mangrove areas and hence, no dramatic change in the flow relationships in either
the Shark Slough or Taylor Slough flow sections.
These results indicate that the vegetation-hydrology linkages can be
invalidated at an extreme. The key point is that the vegetation array is fairly
stable with constant levels of average rainfall input and the relationship between
rainfall-runoff is constant. However, if the system has a prolonged (at least five
year period) of surplus rainfall, then the vegetation structure is destroyed and a
different equilibrium in the rainfall-runoff relationship occurs. Since the
vegetation units are fairly stable with constant levels of average rainfall, the
relationship between rainfall and runoff may not be dramatically influenced by
the coupling of landscape vegetation dynamics with the hydrology.

Annual Flow (10E6 m3/yr)
81
TAMIAMI
SHARK SLOUGH
TAYLOR
SLOUGH
Figure 14.
Results of changing vegetation patterns on simulated flow through
three flowsections in the southern Everglades.

82
The output of two models, one with and one without coupled vegetation-
hydrologic dynamics, was compared to see if addition of the linkages changed
the predicted hydropatterns. The output of the model with linkages qualitatively
agrees with the models without linkages (Walters et al. 1992, Perkins and
MacVicar In press) All models predict a persistent pool of water north and east
of Tamiami Trail in the area now known as the Pennsuco wetlands. Flow and
stage results are similar between the model with and without linkages (Figure
15). Key uncertainties to these results are in assumptions about the amount of
water that moved surficially and as groundwater into the coastal ridge, and
contributions from Lake Okeechobee.
The results in the preceding paragraphs lead to the conclusion that the
addition of the vegetation and hydrologic dynamics does not improve the
models' ability to predict stage and flow. Dramatic changes in rain and runoff
relationship occurs only after persistent wet conditions. Model output of flow
and stage is not different between models with and without vegetation linkages.
One of the reasons may be that the dominant influence on surficial hvdropatterns
is the rainfall. Certainly this is partially true. Other reasons are related to
problems of scaling. The landscape units are composites of vegetation
communities. There is good evidence for dramatic differences in evapo-
transpiration rates and flow resistance coefficients among the vegetation
communities. However, when composite values are calculated at the landscape
levels, the differences are spatially homogenized and converge towards singular
coefficients. The net result of modeling at the landscape scale is that the addition
of more complexity at "smaller” scales does not dramatically improve accuracy of
the model to predict surficial hvdropatterns. The failure to improve model
accuracy by the addition of complexity agrees with previous workers (Walters
1986, Clark et al. 1979, Costanza and Sklar 1985). In spite of these limitations, the

83
Simulated Year
<u
CJQ
S 0.8
1
cd
3 0.6
£
'S3
■s 04
o
a
£
£ 0.2
5
o
60 62 64 66 68 70 72 74 76 78 80 82 85 87
Simulated Year
Figure 15. Difference in predicted stage between models with and without
vegetation linkages of succession, evapotranspiration and flow.
The model without linkages tended to predict higher stages (less
than 0.5 ft), under both the natural and managed scenario.

84
model can be used to test the hypothesis regarding contribution of upstream area
to flow in the Park.
Flow and upstream area
The hypothesis of upstream area contributions to Everglades Park was
tested with a series of simulations. All simulations were done using the same
rainfall input (28 years of historic data) and none of the current control
structures. Each successive scenario increased the upstream area that
contributed flow to the park by creating a levee that contained and diverted flow
to the north of the levee, allowing only the area south of the levee to generate
flow into the park. The contributing area was systematically increased, in
increments of two rows of cells across the system. Annual flow across Tamiami
Trail was tallied during each scenario for comparison to annual rainfall and
upstream area. For each scenario, the parameter settings represented a pristine
system, with historic topographic data, an outlet at the Miami River, and no
diversion of water to the coast. A schedule was developed so that Lake
Okeechobee contributed water only after stages exceeded 20 ft, which is similar
to values reported by Parker (1984).
Increasing the upstream area both increases the flow at Tamiami Trail and
magnifies the amount of interannual variation. The flow appears to increase in a
logarithmic profile as area contributing to the flow is increased (Figure 16). The
effects are variable with rainfall; wetter years generate substantially more flow
per upstream area than drier years with large upstream area. Another way of
stating this is that the amount of area upstream appears to amplify variations in
annual rainfall.

85
Figure 16. Three dimension plot showing increase in annual flow (z) as
upstream area is increased (y) over a 28 simulated year.
Row at Tamiami (10E6 m3)

86
The relationship between upstream area and flow has been shown
empirically to follow a logarithmic profile of the form shown in equation (3)
(Viessman et al. 1989). A constant exponent in the equation is evidence that a
constant relationship exists between flow and upstream area. The test of
constancy of the exponent was done using regression analysis of a log-log plot
between upstream area and flow (Figure 17). In the log transformation, r is the
slope of the regression line and K is the intercept on the dependent axis. The
straight line in the log-log plot indicates that the relationship between flow and
upstream area is constant. A rolling regression analysis was done and no breaks
were found in the relationship.
(3) Q
Q
Q
K
A
K*A r
5.2 * A0-63
annual flow
coefficient
upstream area
exponent
The significance of the exponential parameter in equations such as the above, is
uncertain. Perhaps the parameter is just an empirical or model artifact. Some
authors indicate that parameter is indicative of an underlying system property.
In similar hydrologic work, Hack (1959) found a constant exponential parameter
(equal to 0.6) in relating streamlength to drainage area. Mandelbrot (1983) and
Feder (1988) interpret this as evidence of a fractal relationship between
streamlength and drainage area. The exponent has also been described as a

87
scaling parameter (Mandelbrot 1983, Feder 1988) and indicates a fractal or self¬
similar relationship between flow and area. The parameter may be related to
some geomorphologic attribute of the system. If the scaling exponent has a value
of one, then a linear relationship would exist between flow and upstream area. A
fractal dimension between 1 and 2 is indicative of a structure that fills more
surface than a line and less than a plane. A fractal dimension of less than one can
be represented by "dust"; something less than a line that indicates perhaps a
"patchy" relationship. One explanation then, is that as area contributing to flow
increases, the flow increases in a non-linear or "spattering" manner perhaps
because water has other pathways (evapotranspiration or infiltration) and does
not end up as overland flow. Another possibility is that the "patchiness" in the
spatial dimension may be a reflection of variation in the temporal domain. The
variation of rainfall inputs may be somehow creating a non-linear variation in
system flow as upstream area is increased.
The analysis so far has examined how flow varied solely as a function of
upstream area. Interannual variation in rainfall appears to confound the
relationship between flow and area. The variation in the plot of flow versus
upstream area is due to annual variation in rainfall (Figure 17). The variation
increases as the area contributing flow increases, as would be expected if area
and rain are confounded. During years of low rainfall, the relationship between
area and flow appears to reach a plateau (bottom points, Figure 17) indicating
that increasing the upstream area does not increase flow. During dry years,
smaller upstream areas contributed flow to the park. The remaining years, the
relationship is not confounded and it appears that the entire freshwater system
(south of the Lake ) contributed flow.
Lake Okeechobee does not appear to directly contribute flow to the
southern Everglades. A series of model runs were made; changing the regulation

88
Upstream Area (Log km2)
Figure 17. Log-log plot of simulated flow versus upstream area. Scatter due to
differences in annual rainfall. Gray area represents bounds of
actual flow and equivalent area.

89
schedule of the Lake and monitoring flow to the Park. The amount of flow into
the southern Everglades did not significantly change with changes in Lake
schedules from 20 to 22 ft. above sea level. Water from the Lake would enter the
marsh system, flow south and contribute to a pool in the topographic low areas
of the Pennsuco wetlands, north of the Park.
The Park is at the downstream end of the historic ecosystem. Since the
early part of this century, upstream water has been diverted for other use. Even
so, water continued to flow into the park. The effective upstream area that has
been used to deliver water to the Park was estimated with the empirical equation
(3). This was done by translating the range of actual flows into equivalent
upstream area. The lowest and highest measured annual flows during the period
1960-1987 were approximately 50 and 2000 x 106 m3. These flows translate into
equivalent upstream areas of between 140 and 3500 km2 (Figure 17). These
results are consistent with the deliveries in the early 1960s, when the S-12
structures were closed and little upstream water was let into the park. The
largest upstream equivalent area is slightly more than a third of the Everglades
ecosystem, or about the size of the three water conservation areas. Since the
completion of the Central and Southern Florida Flood Control Project, it appears
that, at the maximum, only about one third of the historic freshwater wetland
system has contributed flow to Everglades Park.
Summary
The vegetation-hydrologic interaction is an example of feedback dynamics
operating at distinct spatial and temporal scales. The vegetation responds to
longer term variations in hydrologic patterns (depth and flow); if water depths
are too deep for long periods, the system looses the tree island and sawgrass
communities (Worth 1987, Craighead 1971). If the system dries over multiple

90
years, woody species invade and dominate the marshes The resultant
vegetation patterns appear stable for over time frames of multiple decades, if not
longer,(Alexander and Crook 1975, Davis et al. In Press, Gleason 1984). The
vegetation patterns set the conditions for the "faster" dynamics of stage and flow
by influencing flow coefficients and evapotranspiration rates. In the context of
hierarchy theory, the vegetation can be thought of as a "slow" variable, that
entrains the behavior of more rapid hydrologic dynamics. The model
incorporates the feedback dynamics by summarizing hydrologic conditions over
periods of times that are used to change the "slower" variable of vegetation
pattern.
Coupling the dynamics in the model framework does not appear to
appreciably improve understanding of hydrodynamics because of two reasons.
The feedback dynamics described in the above paragraph occur on a smaller
spatial scale. Aggregation of these processes was done based upon spatial cover
of plant communities in the landscape. The spatial averaging tended to
homogenize the differences among the communities, which led to a convergence
of parameter values. The second reason, is that the landscape vegetation
categories appear to be relatively stable in a system without human intervention
even with high variation in rainfall.
There is good evidence that the entire freshwater system, south of Lake
Okeechobee, contributed water that flowed into Everglades Park except during
extremely dry years. The relationship between upstream area and flow appears
to be fractal or spatially self-similar. As the upstream area is changed, the flow is
changed in a similar amount. The scale invariance of this relationship may be a
property of hydrologic systems within a drainage basin. The management
implications of these results are that since the early 1960s, when the construction
of the Central and Southern Florida Flood Control Project was essentially

91
finished, the equivalent contributing areas to flow into Everglades Park have
been the Water Conservation Areas. Under pre-management conditions, the
entire basin contributed to flow into the southern Everglades. The evidence that
the southern Everglades received more water and hence had a greater upstream
area agrees with previous work by Smith (1989), Powell (1989) and Walters et al.
(1992).
The conclusions reached in this chapter are based upon the results of a
model with fixed and limited scales in space and time. The model includes the
interactions of variables operating across two orders of magnitude in space and
three orders of magnitude in time. The spatial grain of the model is 4 km, with a
spatial extent of 160 km or about two orders of magnitude. The temporal grain
(time step) is about one week, and the temporal extent almost three decades or
about three orders of magnitude greater. The model can be both powerful and
limited. The power arises from the ability to interact across these distinct
regimes, and understand system dynamics over longer time scales. The model is
limited, in that longer and broader dynamics (such as sea level or climate
change), are excluded. The dynamics of processes occurring at other spatial or
temporal scales can be accounted for in the model as long the scaling
relationships are invariant. The limitations therefore are not due to bounding the
problem within a model, but in the translation across scales of important
processes. Since processes occur at a variety of scales in the real world, and their
translations or rules of scaling are not invariant, inevitable surprises will occur
with the use of scale bound models.
Understanding of critical ecosystem processes and structures will be both
advanced and limited using the precepts of scale limited modeling. An
alternative theory base is emerging that recognizes fundamental discontinuities
across scales and attempts to determine how processes and structures change

92
with scale. Data sets from the Everglades will be used to test a hypothesis of
ecosystem structure and function based upon this discontinuous hypothesis. The
methodology and results of these tests are the subject of the next chapter.

CHAPTER 4.
A CROSS SCALE EXPLORATION OF THE EVERGLADES LANDSCAPE
Toto, 1 don't think we're in Kansas anymore
-Dorothy in the Wizard of Oz
The intertwined natural and management history of the Everglades
ecosystem was described in the first chapter to establish a linkage between
management and precepts of nature. Alternative concepts that guide modes of
inquiry were set forth in the second chapter and formed the basis for two
hypotheses. The first hypothesis was tested using the methods of mathematical
modeling. The critical hydrologic and vegetation processes were combined in a
model framework that covered about two orders of magnitude in space and time.
Processes operating at different scales could be aggregated because the scaling
rules were assumed to be invariant. As a consequence policy surprises are
inevitable because of the unpredictable interactions of processes operating at
scales outside the model domain. Whereas the method in the previous chapter
involved the "compression" of variables into a bounded range of scales for
analysis of keystone processes and structures, the work presented in this chapter
is developed from a cross-scale paradigm.
The cross-scale exploration begins at this point. The word exploration was
chosen to describe the contents of this chapter for the following reasons. The
theory and tools to test the theory are in an early stage of development. One of
the objectives of this dissertation is to develop and test methods further as well as
to advance the theory. The work does not attempt to reject hypotheses based
93

94
upon well accepted and proven methods. No single method or technique has the
appropriate sensitivity and power to be robust. Therefore, the approach is to
compare the results from a variety of techniques. Due to these uncertainties in
the methods, therefore, this work should be viewed as more of an exploration
into the emerging cross scale theory than rigorous hypothesis testing.
In spite of methodological shortcomings, a hypothesis is posed and tested
in this chapter. The theory base presented in Chapter 2 infers that keystone
ecological processes operate across space or time scales in a discontinuous
manner. The hypothesis is posited that these discontinuous patterns of keystone
variables should be manifest as breaks in structural features, and a few reasonant
frequencies in temporal processes. The hypothesis is put at risk using a series of
data sets from the Everglades ecosystem. Data on structural features of the
system including soil surface topography, vegetation maps and fire size were
analyzed. Time series data on various aspects of the hydrologic regime were
analyzed for temporal patterns.
The remainder of this chapter has four sections. The first section is on
methodology used in the cross-scale analyses. The data sets used to test the
hypothesis are described in the second section of this chapter. The results of the
cross-scale analyses are presented in the third section of the chapter. An
intrepretation of the analyses comparing methods and data sets is the subject of
the final section of this chapter.
Methodology
The purpose of this section is to present a suite of methods used to discern
whether discontinuities and gaps exist in patterns of keystone ecosystem
variables across time and space scales. No one method can be used with
sufficient reliability, so a group of methods are necessary. Some methods

95
measure discontinuities in distributions while other methods analyze patterns
across scale ranges. Two mock distributions, one highly structured and one
random, will be used to illustrate what can be distinguished by each method .
The rationale for grouping methods is presented below, but first, terms necessary
for describing aspects of scale are defined.
Scale is a term associated with measurement. One meaning of scale is the
unit of measurement. For example, both a meter and a foot are scales, measures
of objects are made using multiples or fractions of these units. Data sets used in
cross-scale analysis require definition of two terms: grain and extent (O'Neill et
al. 1986). These terms can be applied along either temporal or spatial
dimensions. The grain is defined as the unit of the smallest resolution within a
data set and thus is equivalent in meaning to scale as described above. In one
dimensional spatial data, such as a transect, the grain is the unit of measure or
step length. In two dimensional spatial data, such as a map, a pixel or grid cell
size is the grain of the data set. In temporal data, the grain is usually defined as
the minimum time unit, such as minute, day, or year. The extent of a data set
defines the bounds in space or time. For one dimensional spatial data, the extent
could be the length of a transect. For two dimensional spatial data the extent is
defined as the window of the map. For temporal data, the window is the period
of record used in analysis. Therefore, for the remainder of this chapter, scale is
defined by two components; the grain and extent. Both components of scale can
describe not only data, but also discern among types of methods.
Two groups of methods are described below; 1) methods that discern
discontinuties in data sets and, 2) methods that measure patterns across a range
of scales. The extent and grain of data sets is one way of distinguishing between
these groups. The methods that determine discontinuities utilize data sets with a
fixed grain and a fixed window. The second group of methods (fractal and

96
Fourier techniques) utilize a fixed window data set, but vary grain m the
analysis. Before the methods aimed at detecting patterns and breaks across scale
ranges are discussed, a brief review of problems derived from assumptions of
underlying distributions to the interpretation of frequency histograms or rank
order distributions.
Frequency histograms are frequently used to portray patterns of sampled
data sets, primarily for comparison with distributions of known statistical
properties. The pattern portrayed by a histogram is very dependent upon the
size or width of the bin used to tally occurrences. The technique tends to mask
differences between sets of points within the distribution. Hence, differences
within data set that are derived from two distinct distributions, may be smoothed
over in histogram analyses
Rank order plots are an alternative method of exploring the distribution of
samples. They are derived bv sorting a data set and plotting the magnitude of
sequential observations. Three examples are presented to contrast the differences
in rank order plots derived from a continuous distribution, a random distribution
and a clumped distribution (Figures 18-20). The continuous example is relatively
smooth, with few bumps (Figure 18). The random distribution is more jagged,
with a few jumps between successive observations (Figure 19). The structured
distribution (Figure 20) looks like a staircase; dramatic jumps (risers) followed by
flat spots (runs). The jumps represent gaps in the distribution, and the flat spots
represent clumps. A rank order plot of a data set derived from a discontinuous
distribution, therefore, should exhibit a pattern of rises and runs.
A number of theories have been proposed to explain rank order
distributions. Although some of these theories are derived for species abundance
and niche space, the conceptual underpinnings are similar. The arguments

97
Figure 18. Rank order plot, difference indices 1 and 2 for mock data set
designed to simulate continuous normal distribution. Distribution
has mean of 50. For smooth curves such as this, no value of Dll is
significant. No sequential values of DI2 are significant.

98
Rank Order
A
95%
C.I.
V
1
0.8
0.6
Ol
■§ 0.4
■S °-2
0
2 -0.2
-0.4
-0.6
Rank Order
Figure 19. Rank order plot, difference indices 1 and 2 for mock data set
derived from uniform random distribution. Values of both Dll and
DI2 are significant, yet values between gaps exhibit no pattern.

99
90 p
IS
11 16
21 26 31
Rank Order
36 41 46
95 %
C.I.
1.5
<N
1
X
nj
■8 0.5
c
OJ
r »
0
w
C
oi
V-.
<U
-0.5
o
-1
-1.5
n i r| i ill
I
1
i
:inimii
in 1111111
1 1 I II MI 1
LLLLLl II ll
lililí 11 1
rr
I
Tl 1!|II 11
I
B
A
V
95%
C.I.
11 16 21 26 31
Rank Order
36 41 46
Figure 20. Rank order plot, difference indices 1 and 2 for mock data set
designed to show gaps. Gaps are values of difference indices (1
and 2) outside a 95% confidence interval. Clumps are not evident,
but indicated by a pattern of uniformity small groups of difference
indices.

100
contain both random and deterministic elements. MacArthur (1957) , and
Hutchinson and MacArthur (1959) proposed the "broken-stick" model to explain
observed abundance distributions. The model conceptualizes that random
partitioning (breaking) of resources space (stick) yields observed patterns of few
large pieces, and sequentially more little pieces. Odum (1983) relates that rank
order patterns are a result of the energy required to support and maintain
structure. Holling (1992) building on earlier work (Holling 1986) argues that the
hierarchy of structures are the result of causal variables operating at
characteristically different domains in space and time.
To determine if patterns in rank order distributions are derived from
underlying multiple scale processes, and hence exhibit discontinuities, the
patterns are compared against a null random distribution. Both the size and
patterns of gaps are compared between these two distributions. The methods or
techniques to quantify gaps in distributions are the subjects of the next section.
Methods to Detect Discontinuties
Two methods have been used to measure gaps. Both methods calculate a
relative distance between successive points in a rank order distribution. The
magnitude of the statistic in both methods is related to the size of the gap (or rise)
in the distribution.
The simpler index, called difference index one (Dll), calculates a relative
difference between a point and the next highest point as shown in equation (3)
and was developed by Holling (1992). A mean difference index (and variance)
was calculated for each data set. A 95% confidence interval was calculated for
each set of difference indices and any value greater than this was thought to
represent a significant gap in the distribution.

101
(3) Difference Index One
S
Dili
DI
(Si+i - Si)/S,r
relative change index
value of variable
r
position in rank order
exponential parameter
Difference index one as given in equation (3) has a number of difficulties.
One is that the index tends to emphasis differences at the low end of the value
scale, that is small absolute changes can be large relative changes. For example,
an increase from 0.5 to 1.0 is an absolute change of 0.5, but a relative change of 1.
This is corrected by the parameter r, however, r must be estimated. This was
done so that the values of the difference index at the low end of the distribution
were approximately the same magnitude as those at the high end of the
distribution. Another problem with this formulation is the population of index
values do not have a normal distribution, and appear to follow a chi-square
distribution. The non-normality may change the value of the confidence level
used to determine the statistical significance of a measured gap size. Therefore,
another difference index was used, and was called difference index two.
The formulation is shown in equation (4), and uses a three position or
window reference frame. The difference statistic DI2, has been shown to have a
mean of zero, and a normal distribution (Silverman 1986) and was developed for
"bump hunting" in probability distributions.
(4) Difference Index Two
DI2j
(Si+i - 2S¡ + Si_i)/((2(Si+i +Si + Sm#5)

102
Both difference indices are used in the analyses, although difference index
one tends to be a little more difficult to use, in that it requires determination of
the exponent parameter r. Both indices applied to the same data set indicate
significant gaps in similar locations. Difference index one is always positive,
difference index two is both positive and negative. The next paragraph discusses
how the magnitude and pattern of these indices can be used to interpret gaps
and lumps in data sets.
Each of the difference indices were calculated for the three rank order
distributions presented above (Figure 18-20). No pattern was apparent from the
difference indices calculated for the continuous distribution. The difference
indices indicate significant gaps in the random distribution. Difference indices
for the structured mock data set exhibit a pattern of high magnitude (detecting
the jump or rise), followed by a sequence of low values (Figure 20).
Two criteria are important in the detection of gaps and lumps. The first is
the presence of a significant gap. Significant gaps can be determined by
calculating a 95% confidence interval about a mean gap size. A significant gap is
any gap with a value greater than the value defined by the 95% confidence
interval. The second criteria is the pattern of difference indices that define a
clump. A series of gradually smaller gaps that converge to a small value and
then gradually increase indicate a clump or flat spot in the rank order
distribution. Both of these criteria; a significant gap followed by a clear
convergence or clump, in the difference indices are necessary to detect lumpiness
of a rank order distribution.
The pattern of difference indices or gap detectors can be used to determine
the texture or structure of a data set. Structure can also be analyzed using a
hierarchical clustering techniques.

103
Hierarchical cluster analyses
Hierarchical cluster analysis is a technique for identifying at structure and
similarities in a data set and was used as a corollary to the rank order/gap
assessment. In this work, all data sets are univariate. The technique utilizes two
components, one is the calculation of distance between data points and the other
is a grouping of all data points into levels of a hierarchy, based upon the
calculated distances. Each observation in a data set is set into an individual
cluster. Clusters are merged based upon the calculated distance between it and
other clusters. The process is continued until all groups are joined into one
cluster. The average linkage method was used, the mean value of a cluster is
used to calculate distances to other clusters. A pseudo-t2 distribution can be
generated from the distance measures, and was used as a measure of significance
of a cluster level. All data were analyzed using the CLUSTER routine in SAS/PC
version 6.03 (SAS 1990).
The techniques listed above can be used to analyze pattern in data sets
with a fixed extent and fixed grain. Discontinuites and clumps in a data set are
based upon relationships defined by a fixed grain size. The techniques that
follow take a different approach, and can be used examine how patterns or
structure of the data vary by systematically changing the size the grain.
Methods to Analyze Patterns of Self-Similarity
The next set of methods are used to analyze for patterns of self-similarity
across scale ranges. Self-similarity can be defined as the property of retaining
similar structure or pattern with a change in grain size. Although the size of the
grain changes, the grain retains a similar shape. For example, Fourier analysis is
described as decomposition of a signal into a series of progressively smaller sine
waves. The sine waves have similar shape, but differ in size (wavelength or

104
frequency). These techniques incorporate an approach of analysis based upon a
fixed window, then determining how patterns change with a systematic variation
of grain size.
Two primary methods have been developed to examine patterns of self¬
similarity of data sets. Spatial patterns can be studied using techniques derived
from fractal geometry (Mandelbrot 1983). Temporal patterns can be analyzed
using Fourier techniques applied to time series ecological data. A more detailed
description of each method is presented next, starting with fractals.
What is a fractal dimension?
Fractal geometry (Mandelbrot 1983) provides a basis for describing how
structure of an object varies with spatial scale. To define a fractal dimension, first
a formal method for measurement of any object is described by equation (5)
following derivations presented in Mandelbrot (1983), Burrough (1981), and
Morse et al. (1985). In this equation, the total measure (length, area, volume) of
an object is determined by the count (K) of number of unit lengths (r), raised to a
scaling parameter. The exponential parameter (D) is related to the number of
dimensions to be described in space. In Euclidean geometry, the exponential
parameter D is one for one dimensional objects (lines) two for two-dimensional
objects (planes) and three for three dimensional objects (cubes). Mandelbrot
(1983), and others realized that the scaling parameter did not have to be an
integer, but indeed a fractional (abbreviated as fractal) value appeared to better
describe many natural objects.
(5) L(r) = K*r<D)
L = Total object measure
r = unit of measure
K = number of units

105
D = exponential parameter or fractal dimension
Attempting to understand the meaning of a fractal dimension tugs at deep
rooted concepts and intuition. The integer values of the exponent D, may not be
recognized as such, but form the basis of learned models of perception.
Traditionally, objects are measured in terms of length (D=l), area (D=2), or
volume (D=3). Most measurements are done using a fixed scale (grain size or
unit of measure ) and assume integer values of the parameter D. This leads to a
problem in the measurement of most irregular objects; total measure (length,
area, etc) is dependent upon the unit used to make the measurement!
Geographers (Richardson 1961) noted this in attempting to answer the question;
How long is the coast of Britain? The solution proposed by Mandelbrot (1983),
is that the relationship between total measure and unit of measure can be
constant over wide ranges of units and measures. If this relationship is constant,
then the exponent D or fractal dimension is constant and the pattern exhibits a
property of self-similarity. But what does a fractal dimension of 1.2 mean and
how is it different from 1.5? Irregular objects on a page have a fractal dimension
between one (a line) and two (a solid plane). Generally, a fractal dimension
closer to one exhibits more linearity As the fractal dimension increases between
one and two an object becomes more articulated, and fills up a greater percentage
of space intermediate between a line (D=l) and a solid plane (D=2). Three curves
with increasing fractal dimensions between one and two are shown in Figure 21.
The fractal dimension has been used in the ecological literature to
determine changes in structure or patterns with scale (both grain and window).
Breaks in fractal dimension can define the scale that separates ranges where
different processes affect patterns. Within the ranges that the fractal dimension is
constant, a structure or object exhibits a pattern of self-similarity. For example,

106
D- 1.61
D - 1.73
Figure 21. Sample Koch curves to show patterns of increasing fractal
dimension (1.5 -1.7), from Mandelbrot (1983).

107
Bradbury et al. (1983, 1984) found three regions of self-similarity on a coral reef
that were defined by abrupt changes in the fractal dimension. The fractal
dimension (D=1.13) at the smallest step length was attributed to the structure
associated with individual corals. The next scale range had lower fractal
dimensions (D=1.05) and was associated with the processes of coral colonies.
The fractal dimension (D=1.17) at the largest step length was related to geologic
processes. Kent and Wong (1982) measured the fractal dimension of the littoral
zone of a lake in Canada, found a change in the fractal dimension at a step length
of 350 m. They (op. cit.) found a higher fractal dimension (D=1.44) for longer
step lengths and attributed the pattern to broad scale geologic processes and and
a smaller dimension (D=1.14) at shorter step lengths which they attributed to
processes of shoreline erosion such as wind and waves. Although the measures
of fractal dimension are of interest, the utility appears to be in the separation of
regions of scale invariance. Each of these regions of self-similarity appear to be
associated with different structuring processes, that operate at characteristically
different domains in space and time.
The two previous paragraphs describe the conceptual underpinnings of
fractal geometry and how these concept have been interpreted by ecologists. The
next section describes how a fractal dimension can be measured using one¬
dimensional or two-dimensional data.
Techniques of estimating fractal dimensions
A fractal dimension is estimated by repeated measures of an object using
different grain sizes or units of measure within a fixed window. The fractal
dimension is the relationship between changes in total object measure and the
units of measure. The relationship of general measurement (equation 5) can be
made linear by a log transformation, resulting in equation (6). The fractal

108
dimension (D) can be estimated from regression analysis of the slope of a log-log
plot of total object measure versus the size of the unit of measures.
(6) log L(r) = D log (r) + log K
The technique is applicable for one or two dimensions. In one-dimension
(such as a topographic transect), the total object measure is total length and the
unit of measure is called the step length. The fractal dimension for one
dimensional data is estimated by the slope of a log-log plot of total length versus
step length. For data of two-dimensions (such as maps), the total object measure
is area, and the unit of measure is the box or tile size. Similarly, the fractal
dimension is estimated from the slope of a log-log plot of total area versus box
size (Morse et al. 1985, Milne 1988). The slope of the line is estimated using
regression analysis.
A technique was developed to calculate the fractal dimension of spatial
patterns such as vegetation maps. The maps or figures were scanned to render
the patterns into a spatial array. The spatial arrays were translated into a quad¬
tree data format using custom software. A quad-tree format is created by
successive quartering of an image in the manner of a nested hierarchy (Figure
22). The method is similar to one used in legal description of land parcels, for
example, the northwest quarter of the southeast quarter of section. The recursive
divisions render units (boxes or tiles) that range from the size of the map, (the tile
size equals the window size) to one that has been subdivided nine times (the tile
size equals the scanned pixel size). For each layer (or level in the hierarchy), all
sample pixels are compared to the patterns at the finest scale, and the pixels are
determined to contain either something (covering a piece of the mapped
vegetation pattern) or nothing. The number of pixels which cover the

109
First Level
Division,
■f'liif*
4 Squares
Second Level
Division,
16 Squares
Third Level
Division,
pill
64 Squares
Fourth Level
Division,
256 Squares
Figure 22. Example of first four levels or divisions for rendering data into a
quadtree storage format.

110
mapped pattern for each layer are summed. The fractal dimension is determined
by regressing the log of the number of pixels with something in them versus the
log of the size of the sample pixels. Examples of log-log plots of box size
versus number of boxes are shown in Figure 23. Although nine divisions are
possible in the quad-tree, only six are used. The first three divisions of an area
(total tiles = 1,4,16) do not contribute information and are not included in the
plot.
The accuracy of this technique was assessed by measurement of fractal
dimensions of patterns with known dimension. A group of Koch curves (Figure
21) with fractal dimensions from 1.5 to 1.76 were analyzed using the methods
listed in the preceeding paragraph (Figure 23). The results indicate that the
technique is accurate for curves with fractal dimensions up to 1.61, but
underestimated the fractal dimension of the most intricate (highest fractal
dimension) pattern.
The description of fractal methods to this point have all been based upon
techniques that utilize a fixed window, variable grain approach. In order to
expand the analysis across space, data from multiple, overlapping windows are
analyzed. First, the patterns within each window are analyzed, then the sets of
points from each window are combined to cover a broader window range. The
box counts in one data sets are adjusted by the relative difference in window size
between two data sets. For example, if window A is 10 x 10 m, and window B is
1000 x 1000 m, the box counts of data in window B are increased by 100 times.
The final technique used in the fractal analysis is the determination of
breaks in the fractal dimension. Breaks in the fractal dimension of structural
features appear to be related to a change in the processes affecting the structure.
Any breaks in structural processes would fail to invalidate the hypothesis tested

Ill
Figure 23. Log-log plots of tile size versus number of tiles for three Koch
Curves of known fractal dimension. Fractal dimension is estimated
by the negative slope of curves. Actual fractal dimensions (D) of
curves are A) D=1.5, B) D=1.63, C) D=1.71, as shown in Figure 21.

112
in this chapter. Breaks or inflection points in the log-log plots were assessed
using a technique named "rolling regression". The technique involves
partitioning the entire data set into a smaller set of points and calculating a
regression coefficient. Data points are systematically added to the analysis and a
series of regression coefficients are calculated. An increase in the regression
coefficient to a maximum value, followed by a decrease can be interpreted as a
break in the slope or an inflection point.
Fractal geometry provides the basis for measuring techniques that
quantify changes in spatial patterns across scales. The techniques examine how
patterns change with respect to changing grain size. The shape of the grain size
is determined by the number of dimensions in the spatial data set. For one¬
dimensional data, the grain shape is a line. For two-dimensional data, the grain
shape is a tile or box. Similar techniques using wave-forms as the grain shape or
unit of resolution have been developed to decipher patterns or signals in the time
domain, and are grouped under the general heading of Fourier analysis.
Fourier analysis
Fourier analyses were developed to study harmonics or components of
complex waveforms. The Fourier analysis utilizes a fixed window (extent of data
in time or space) and a variable grain to discern component patterns. The
technique utilizes a set of discrete values at equally spaced intervals (in time or
space) and fits a series of sine waves of increasing frequency to the data. The fast
Fourier technique is a modification that utilizes data sets with windows that are
2n units. The essence of the Fourier analysis is in the transform, whereby the
discrete data points are transformed from a time domain to a frequency domain.
The amplitude is calculated for each frequency ranging from intervals of the
entire data set (one sine wave fit to the entire set) to a frequency of one half the

113
number of data points (wavelength every two data points). Frequencies that
correlate to a large number of data points have high magnitude values. The
magnitudes represent the amound of variance explained by the corresponding
frequency. Statistics of mean and variance can be calculated from the magnitude
values and represent the amount of noise or random behavior in the data.
Dominant frequencies in the data set have high magnitude values.
The analyses were done with the fast Fourier algorithm in the SYSTAT
software for the Macintosh. For each data set the mean was subtracted from
every value and the data detrended, so that the values varied above and below
zero with no overall change or trend in the mean. Missing data were coded at
the mean value, so that they would appear at zero in the transformed data set.
Two mock data sets were developed to illustrate the techniques used to
recognize dominant frequencies. Both mock data sets had 64 observations over
time, and amplitude ranges from 0 to 100. The first data set was derived from a
uniform random number generator and presumeably, no periodicity (Figure 24).
The second mock data set was developed by adding two sine waves of different
frequency, one had a wavelength of 32 time units and the other of 6 time units.
The results of the analysis of structured pattern data sets is shown in Figure 25 .
Summary of Methodology
The rather lengthy description of methods presented in the section above
indicates a variety of techniques can be used to analyze data for patterns across
scale ranges. The three primary techniques used in the following applications
are summarized below.

114
Time Units
Wavelength (time units)
Fourier analysis of random mock time-series data, showing time-
series plot (top) and spectral plot (bottom). This data set was
created by taking 64 samples from a uniform random number
distribution. No peaks are significant in the spectral plot.
Figure 24.

115
95%
C.I.
Wavelength (time units)
Figure 25. Fourier analysis of structured mock time series data, showing time-
series plot (top) and spectral plot (bottom). This data set was
created by combination of two sine waves; one 32 time units long,
the other 6 time units long. Two peaks occur in the spectral plot,
one at equivalent wavelengths of 32 and 6 time units.

lib
•Discontmuites within rank order distributions can be determined by the
pattern of difference indices; a signficantly large index value followed by
a convergence towards a small values is indicative of a gap followed by
a lump.
•Fractal dimensions can be estimated for one or two-dimensional data sets
from fixed or nested window sizes. Breaks in the fractal dimension
indicate changes in structural properties and can be detected by changes
in the linearity of relationship between log of total measure and log of
step length.
•Dominant frequencies can be determined by statistically significant
peaks in spectral plots from Fourier analysis.
The next section describes the derivation of the data sets used to test for
discontinuties in the spatial components and reasonanat frequencies in the
temporal components of keystone features of the Everglades ecosystem.
Data Sets Used In The Cross-Scale Analyses
Two types of data were used in the cross-scale analyses; spatial and
temporal. The spatial data are from key structural features of the Everglades.
Some of the temporal data sets include measures of key aspects of the hydrologic
regime, such as rainfall, stage, flow and evaporation. The details of the spatial
data sets are presented first, followed by a description of temporal data sets.
Three data sets were analyzed to test for changes in spatial pattern across
scale ranges. Two keystone features in the Everglades system are the soil surface
topography and the vegetation. Ground elevation data along transects were

117
analyzed using one-dimensional fractal methods and using Fourier techniques.
Patterns from vegetation maps were analyzed using two dimensional fractal
methods and for discontinuities in patch size distribution. Data on fire sizes
were analyzed for discontinuities.
Seven time-series data sets were obtained. The data sets on rainfall, stage,
flow, evaporation, and fire all represent a keystone process, whereas the data on
air temperature and sea-level do not. All were analyzed using the Fourier
technique to test for the presence of a few characteristic frequencies. Some of the
temporal data sets were analyzed using the rank order/gap assessement as
described above, or hierarchical cluster analyses.
Descriptions and origins of the nine data sets are presented in the
following order of groups; topography, vegetation, fire, hydrology, evaporation
and sea-level.
Topographic data
Elevational data from the everglades ecosystem were analyzed using two
different techniques to compare topographic variation with scale. Data were
obtained from Everglades National Park, and included coordinates on easting
(x), northing (y) and elevation (z) from eleven surveyed east-west transects
across Shark Slough (Figure 26). Elevation measures were made at
approximately 100 m intervals along each east-west transect. The transects were
spaced at about 2 km intervals from north to south. A program was written to
estimate fractal dimension of each of the transects. The program calculated the
length of the total transect by using the smallest step lengths (distance between
survey points), then increased step length geometrically until the total distance of
the transect equalled the step length. Slopes of the lines in a log-log plot of

Figure 26. Location of topographic transects in the southern Everglades.

119
distance versus step length were used as estimates of fractal dimension
^Mandelbrot 1983, Feder 1988)
Vegetation maps
Plant communities were mapped within three different windows of
coverage, each an order of magnitude smaller in the linear dimension. The linear
dimension of the three overlapping square windows were 16 kilometers, 1609
meters (one mile), and approximately 160 meters. The resolution of each map is
defined by the size of the picture element (pixel). The relationship between pixel
and window sizes were approximately constant for all three maps; the pixel size
of the 16 km was 20 x 20 m; the 1609 m map was 2 x 2 m and the resolution of the
160 m map was 20 x 20 cm. The maps made in each window were derived from
a different source.
The largest window and grain vegetation maps used data from the French
SPOT satellite. The satellite carries a multi-spectral scanner, which measures
scaled reflectance values within three wave-length bands (centered on 0.55, 0.65
and 0.80 mm). The spectral data were classified using parallel-piped clustering
routing within the GRASS® software package at Everglades National Park as
part of vegetation mapping activities within the park. The classification rendered
a park vegetation map at the pixel resolution of 20 x 20 m, containing sixteen
cover type classes. Two 16 x 16 km (800 x 800 pixels) scenes within Shark River
Slough were obtained from the National Park Service. One scene included the
Shark Valley Loop Road area and was designated as the Loop Road, the other
scene designated as Panther Mound (Figure 27). The sixteen cover class
categories were combined to create three classes of vegetation; sawgrass, wet
prairie and swamp hardwood (tree islands).

120
Figure 27. Location of 16 kilometer and 1609 m windows throughout the
Everglades ecosystem within which vegetation communities were
mapped for analyses.

121
The second largest vegetation maps were made within 25 square-mile
windows located throughout the Everglades ecosystem (Figure 27). The maps
were made by tracing vegetation patterns apparent on aerial photographs taken
in 1987 onto transparent overlays. The maps used in this study were a subset of
maps used to evaluate vegetation changes in the Everglades ecosystem (Davis et
al, In prep). The one-square mile boundary was determined by using the scale of
the imagery to calculate the appropriate box dimensions. The scale of the
imagery ranged from 1:10,000 to 1:12,000, resulting in maps with dimensions of
5.4 x 5.4 in. to 6.4 x 6.4 in. Distinguishable vegetation units were outlined using a
fine-tipped (00) pen. The maps were ground-truthed during the summer of 1989
using helicopter overflights. The composite vegetation maps were traced in
order to produce a separate map for each vegetation type. Although many
vegetation classes were mapped, only the three spatially dominant classes
(sawgrass, tree island and wet prairie) categories were used in the cross windows
comparisons.
The third and smallest window vegetation maps were made from 35 mm
color slides taken from a helicopter during June, 1989. Attempts were made to
keep the camera at right angle to the ground, in order to minimize distortion of
patterns. Since the altitude was variable, the window size varied as well, from
about 50 to 250 m. The photographs were made at sites in Shark Slough,
Everglades Park where markers of known spacing were included in the
photographs. The distance between the markers were used to calculate the
window size and scale of each of the slides. The slides were projected onto a
wall, where the vegetation patterns were traced onto letter size white paper. The
vegetation patterns were truncated at the borders of the square plot.
The small and medium window tracings were scanned using an Apple
Scanner at a resolution of 150 dots/inch. The scanned images were edited to

122
remove irregularities introduced by the scanning process. The outlined areas
were closed and filled. Typical maps of sawgrass in each window are shown in
Figures 28, 29 and 30. The black and white maps are a bit map, or a raster image
about 900 x 900 cells, with the bit in each cell being either on (black) or off
(white). The bit map files were then transported to other programs for analyses
of spatial patterns.
The sizes of each patch or clump of each vegetation type were analyzed
within the two largest windows. A patch was defined as a group of pixels or
cells that were isolated by a distance equal to at least one pixel. A routine from
ERDAS® software was used to clump contiguous pixels at a search radius of 1.5
pixels. The output from this package rendered a pixel count for each patch. The
pixel count was multiplied times the area per pixel to give the patch size in
square meters. Each patch area was transformed to logio- The transformed
series were sorted in rank order, from largest to smallest patch.
Fire data
Data on fire size were extracted from records compiled for Everglades
National Park by Taylor (1979) for the time period 1948-1979, the available period
of record. Fire ignition location was reported in terms of Township, Range and
Section. Areas burned were tallied within a window of three townships (55-57
South) and three ranges (35-37 East) (324 mi2 or 840 km2 located over northern
Shark Slough (Figure 31). Fire data were analyzed using the rank order/gap
assessement.
A time series of fire data were analyzed for cross-scale temporal patterns.
The origin of the data is described above. For the time series analysis, the time
period of 256 months betweeen 1958 and 1979 was used, because the fast Fourier
technique requires 2n data points. Total area burned was tallied for each month.

123
Figure 28. Sample vegetation map, showing patterns of sawgrass within a 160
m window.

Figure 29. Sample vegetation map, showing pattern of sawgrass within a 1600
m sample window.

125
Figure 30.
Sample vegetation map, showing pattern of sawgrass within a 16
km sample window.

Figure 31. Location and size of sample window within which recent fire
histories were analyzed for spatial and temporal patterns.
ro
O'

127
The fire sizes were log transformed (months with no fires were assigned values
of zero) for Fourier and hierarchical cluster analyses.
Hydrologic data sets
Three types of hydrologic data were analyzed for temporal patterns;
rainfall, stage (water level), and surface flow. For each data set, Fourier analyses
were done, using the period of record (fixed window) and variable time units
(days, months and years). Rank order/gap analyses and hierarchical cluster
analyses were also used to determine hierarchical structure in most of the data
sets.
Two data sets were used in the analysis of temporal rainfall patterns.
Daily rainfall totals from May 1948 through December 1989 were obtained for
Tamiami Ranger Station and Royal Palm Station (Figure 6). The daily data were
totaled to yield monthly and annual amounts for the period of record.
Daily water levels were obtained from sites designated P33, P35, P37 and
P38 (Figure 6). Daily and monthly summaries covering the time period January
1954 through December 1975 (256 months) were used in the Fourier analysis of
stage data. Since the stations were established in 1953, these years represent the
longest available set of monthly data for that is an even power of two.
Total monthly flow data from the Tamiami Trail flow section (Figure 6)
were analyzed. The data span the time period October 1939 through 1983 for a
total of 512 months.
Evaporation Data
Since evaporation is a large pathway of water flow in the wetlands of the
Everglades, temperature and pan evaporation data sets were analyzed for
temporal patterns. Temperature and pan evaporation are analogous metrics of

128
evaporation, in that sensible heat flux is related to temperature patterns and pan
evaporation is a physical model of combined factors that influences evaporation
rates (Brutsaert 1984).
Monthly pan evaporation totals from sites at Tamiami Ranger Station and
Belle Glade Experimental Station (Figure 6) were obtained from National
Climatic Data Center for the time period 1965 through 1990. Data on mean
monthly minimum and mean monthly maximum air temperature were obtained
from the same source for Belle Glade (1931-1991) and Tamiami Ranger Station
(1940-1991). Fourier analyses were done on each of these data sets to identify
dominant time cycles.
Daily measures of pan evaporation and community evapotranspiration
were obtained from work of Gunderson and Stenberg (Gunderson and Stenberg
1990). Study sites were established at P33, an Eleocharis marsh over peat in
Shark Slough, and P37, a sawgrass/muhly grass marsh over marl in Taylor
Slough (Figure 6). At each site, a standard Class A evaporation pan with a
recorder was installed and daily pan evaporation measured between February
1985 and September 1986. During the same time period, daily estimates of
community evapotranspiration were derived from daily tracings of water levels
following techniques of Dolan et al. (1984), with modifications related to
differences between surface and ground water conditions. Fourier analyses were
done on all daily data evaporation sets.
Sea Level Data
Another variable that influences stage and flow dynamics in such a flat
system as the Everglades is the height of sea level. To compare temporal patterns
of the freshwater system with patterns in the surrounding saline systems, data on
monthly sea level were obtained for three south Florida sites. Data from Key

129
West were recorded and obtained tor the time period 1912 through 1991, from
Miami 1932 through 1982 and at Naples from 1965 through 1991. All three data
sets were detrended, to remove an obvious increase in sea level through the
period of record. Fourier analyses were done on all three sets to determine
dominant time cycles
A summary of the variety of data sets is presented in Table 8. The type of
data (spatial or temporal), type of analyses used, grain and extent and number of
replicates are presented for each of the data sets. This summary is useful as a
prelude to the results of all of these data sets and the various analyses. The
results of all of these analyses are the subject of the next section in this chapter.
Results Of Cross-Scale Analyses
Analyses of the data sets on the keystone structural features and processes
suggest that the discontinuous hypothesis cannot be invalidated. Examination of
the structual features across scales (grain and extent), imply the occurrence of
breaks that separate regions of self-similarity. As the window of examination
changed, regions of similar patterns would abruptly change to another region
that exhibited a different pattern. Only a few frequencies were noted in the
temporal fluctuations of key processes in the system. Repeated analyses that
varied window and grain of the temporal data sets, still generated results with
only a few reasonant frequencies.
Evidence of breaks in the structual features is shown from a summary of
analyses of spatial data sets. The topographic data has two scales of variation,
defined by a break in the fractal dimension at a step length of about 1.5
kilometers (Table 9). The changes in vegetation patterns over scale ranges, are
suggested by the fractal analyses, but appear at more definite resolution using

Table 8.
Summary of data sets used in cross-scale analyses of Everglades
ecosystem.
130
Variable
Space/Time Analysis
Grain
Unit
Window
Unit
Replicates
Vegetation
Sawgrass
Space
Fractal
0.5
m
150
m
12
2
m
1600
m
25
10
m
16
km
2
Tree Island
Space
Fractal
0.5
m
150
m
2
2
m
1600
m
25
10
m
16
km
2
Wet Prairie
Space
Fractal
0.5
m
150
m
9
2
m
1600
m
25
10
m
16
km
2
Sawgrass
Space
Rank Order/
2
m
loOO
m
25
Gap
10
m
16
km
2
Tree Island
Space
Rank Order/
2
m
1600
m
25
Gap
10
m
16
km
2
Wet Prairie
Space
Rank Order/
2
m
1600
m
25
Gap
10
m
16
km
2
Topography
Space
Fourier
100
m
32
km
5
Fractal
100
m
32
km
11
Water Flow
Time
Fourier
1
mo
44
F
1
Rank Order/
1
mo
44
yr
1
Rainfall
Time
Fourier
1
F
44
yr
2
1
mo
39
yr
2
1
day
39
yr
2
Rank Order/
1
F
44
yr
2
Gap
1
mo
39
yr
2
1
day
39
yr
2
Water Stage
Time
Fourier
1
mo
22
yr
4
1
mo
22
yr
4
Rank Order/
1
mo
22
yr
4
Gap
1
mo
22
yr
4
Fire
Time
Fourier
1
mo
22
yr
2
Space
Rank Order/
1
mo
22
yr
2
Gap
Sea Level
Time
Fourier
1
mo
88
yr
3
Temperature
Time
Fourier
1
mo
22
yr
2
Fourier
1
mo
22
yr
2
Pan Evaporation
Time
Fourier
1
mo
22
yr
2
Fourier
1
day
22
mo
2

131
Table 9. Summary of cross-scale analyses of spatial data sets, indicating
break points detected by fractal and gap analyses.
SPATIAL
DATA
SET
Type
Analysis
Window
SIZE
(km)
Break Points
Small
Step Length
log 10 (m)
Large
Step Length
log 10 (m)
Sawgrass
Fractal
16
2.2
158
-
-
Wet Prairie
Fractal
16
1.8
63
-
-
Tree Island
Fractal
16
2.4
251
-
-
Sawgrass
Gap
1.6
2.4
251
2.75
562
Wet Prairie
Gap
1.6
2.5
316
2.95
891
Tree Island
Gap
1.6
2.1
126
2.3
200
Sawgrass
Gap
16
-
-
3
1000
Wet Prairie
Gap
16
-
-
3.05
1122
Tree Island
Gap
16
-
-
3.05
1122
Topography
Fractal
30
-
-
3.2
1585
Fire
Gap
10
1.9
79
3.5
3162
Table 10. Summary of cross-scale analyses of temporal data sets, indicating
dominant frequencies found in each set.
TEMPORAL
DATA SET
WINDOW
GRAIN
FREQUENCIES (YEARS)
Primary Secondary Tertiary
Rainfall
39
y
day
1
0.25
0.3
39
yr
month
1
0.25
0.3
44
y
year
6
8
11
Stage
22
y
day
1
7
3
month
11
1
3
Flow
44
yr
month
1
8
22
Pan Evaporation
22
yr
month
1
11
5
Sea Level
88
yr
month
1
11
0.5
Temperature
22
yr
month
1
0.5
-
Fire
22
yr
month
11
1
-

132
the gap detection method. Changes in the fractal dimensions of the vegetation
types are suggested at step lengths of 60-250 m. Gaps in rank order distributions
of patch sizes appear at a similar range(100-300 m) and again at step lengths of
about 1 km. Although the measured values of breakpoints differ, all of the data
sets appear to exhibit some sort of breaks in key structural features.
The dominant frequency in the temporal patterns was the annual cycle
(Table 10). Other frequencies were significant in all of the analyzed data sets.
Multiple year patterns of 11 years were dominant in the stage and fire data sets.
Secondary frequencies of 8 to 11 years were noted in fluctuations of annual
rainfall, stage, flow, pan evaporation and sea level data sets. Cycles of 3 to 6
months were noted in the rainfall and air temperature data sets. Cycles of
multiple frequencies were apparent in all of the analyzed data sets, supportive of
the hypotheses.
The details of the multiple analyses are presented next, grouped by the
data set analyzed. The results of the spatial features of topography, vegetation
maps and fires are presented first, followed by the results using the time series
data on rainfall, stage, flow, fires, evaporation, air temperature and sea level.
The detailed interpretations of data sets are summarized in Tables 9 and 10.
Topographic data
The topography of the soil surface in the southern Everglades appears to
vary at two different spatial scales. The plots of surveyed elevation versus
horizontal distance for each of the transects (Figures 32, 33 and 34: A-D), depict
both the broad level changes in topography, and finer scale variation within the
broader pattern.
The fractal analyses suggests the presence of two regimes of topographic
variation. The plot of logio transect length vs logio step length (Figure 35 )

Elevation (m-msl) Elevation (m) msl
160000 170000 180000 190000 200000 210000
Distance (m) spe
Distance (m-spc)
160000 170000 180000 190000 200000 210000
E
É
C
O
LU
2.5
2.0
IS
1.0
150000 160000 170000 180000 190000 200000 210000
Distance (m-spc)
Distance (m-spc)
Figure 32.
Topographic surveys from transects 1 through 4 ( see figure 26 for locations) showing elevational variation
with east west distance.
OJ

Elevation (m-msl) Elevation (m-msl)
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
150000 160000 170000 180000 190000 200000 210000
Distance (m-spc)
Distance (m-spc)
150000 160000 170000 180000 190000 200000
Distance (m-spc)
Distance (m-spc)
Figure 33. Topographic surveys from transects 5 through 8 ( see figure 26 for locations) showing elevational variation
with east west distance.
•—*
£

Elevation (m-msl) Elevation (m-msl)
2.50
2.25
2.00
1.75
1.50
125
1.00
0.75
0.50
0515
0.00
150000 160000 170000 180000 190000 200000
Distance (m-spc)
2.50
2.25
2.00
S 1-75
| 1.50
'Z 1-25
1 1-00
0.50
0.25
0.00
150000 160000 170000 180000 190000 200000
Distance (m-spc)
Distance (m-spc)
Figure 34. Topographic surveys from transects 9 through 11 ( see figure 26 for locations) showing elevational variation
with east west distance. G
Ol

Log Transect Length tmeters)
136
5.6
5.4
5.2
5.0
4.8
4.6
4.4
Range of Points with
Maximum Correlation
//
2.0 2.5 3.0 3.5 4.0 45 5.0
Log Step Length (m)
1.00
0.95
0.90
™ 0.85
0.80
0.75
0.70
2.0 2.5 3.0 3.5 4.0 4.5 5.0
Log Step Length (m)
Figure 35. Log-log plot of transect length versus step length (top plot) used to
estimate breaks in fractal dimension. Bottom plot shows results of
rolling regressions. Break in top plot is indicated at point of
maximum regression coefficient (bottom plot).

137
indicates a change in the slope (fractal dimension) at a horizontal step length of
between 1 and 3.2 km (logio 3 and 3.5). The break in the fractal dimension was
further defined by using a rolling regression technique. The technique used a
linear regression approach and subsequently added data points. A break in the
linearity of the relationship is evident by an increase in the regression coefficient
to a maximum value, then a subsequent decrease. The maximum regression
coefficient was obtained using values up to logio 3-25 (Figure 35). The best
estimate, therefore, is that a break in the fractal dimension occurs at a step length
of about 1.5 km. For smaller step lengths, the topography is reasonably self
similar, with a fractal dimension of approximately 1.6. The fractal or scaling
dimension can be used to estimate the length of a transect as a function of step
length (between 0.1 and 1.5 km) by formula (8).
(8) L = 6.5 * 11-62
L= transect length
1 = step length
The cross-scale structure of soil surface elevation appears to change at step
lengths of about a little more than a kilometer. The measure of the breakpoint is
subjective and dependent upon interpretation of a pattern of two lines within a
set of points. Alternative explanations may be that the relationship between
length and unit of measure changes gradually, approaching some asymptotic
level. In either case, the fractal analysis suggests a change in pattern with scale,
and a similarity of pattern at the small step lengths. As an alternative approach,
the Fourier technique was applied to five of the data sets to see if multiple
"wavelengths" could be interpreted as evidence of multiple scales of variation.
The Fourier analysis did indicate multiple sets of waves, but emphasized the

138
long or broad wavelengths apparent in the data sets Whereas the fractal
analysis appear to emphasize the small scale variation, the Fourier analysis
appears to emphasize the broad scale variation.
It is not the result from either, but the combined results from both
techiques that indicate the presence of both a fine scale (small step length) and a
broad scale (longer step length) pattern. The broad pattern reflects the basin
morphometry associated with the surficial geologic features of the Everglades.
At the broad scale, the elevation varies on the order of one/half meter over
horizontal distances of of 20 km. The finer scale variation reflects changes of 20
cm over horizontal distances of less than 1 km. The finer scale variation reflects
microtopographic processes such as dissolution of bedrock and peat accretion.
The apparent changes in scales of the topography qualitatively agree with
spatial scale of processes creating the pattern. To determine if similar breaks are
manifest in other ecosystem variables, the results of cross-scale analyses of
vegetation patterns are presented next.
Vegetation Patterns
The spatial patterns of three dominant vegetation communities (sawgrass,
wet prairie and tree island) appear to have breaks and discontinuities at different
scale ranges. Gaps appear in the rank order plots of patch size and breaks are
suggested by the fractal analysis. First, the results from the fractal analysis.
Discerning breaks in the fractal dimension proved to be problematic. The
fractal dimensions of all three vegetation communities appeared to increase with
the window size. The dimensions of all three vegetation types ranged from 1.01
to 1.19 in the small window, 1.23 to 1.40 in the intermediate sized window and
from 1.77 to 1.89 in the large window (Figures 108-110 ). There is little evidence
of a break or change in the fractal dimension within the single window plots. A

139
160 Meter Window
1600 Meter Window
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0
Log Step Length (m)
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0
Log Step Length (m)
16000 Meter Window
All Three Windows
-2.0 -1.0 0.0 1.0 2.0 3.0
Log Step Length (m)
4.0
Log Step Length (m)
A)
Y = -1.01X + 2.51
r2 = 0.78
B)
Y = -1.36X + 2.65
r2 = 0.77
C)
Y = -1.89X + 8.07
r2 = 0.98
Figure 36. Log-log plots of box size versus box count used to estimate fractal
dimensions of sawgrass vegetation within three sample windows.
Estimates of fractal dimension are given by slope of regression.
Data from three windows are combined in lower right plot, and
suggest a break in the fractal dimension.

140
160 Meter Window
1600 Meter Window
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0
Log Step Length (m) Log Step Length (m)
16000 Meter Window
All Three Windows
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0
Log Step Length (m)
-2.0 -1.0 0.0 1.0 2.0 3.0 4.0
Log Step Length (m)
A
Y =-1.06 X+2.46
r2 = 0.82
B
Y = -1.40 X +4.95
r2 = 0.96
C
Y =-1.77 X+7.64
r2 = 0.99
Figure 37. Log-log plots of box size versus box count used to estimate fractal
dimensions of wet prairie vegetation within three sample
windows. Estimates of fractal dimension are given by slope of
regression. Data from three windows are combined in lower right
plot, and suggest a break in the fractal dimension.

141
160 Meter Window
1600 Meter Window
16000 Meter Window
All Three Windows
A)
Y = -1.19X + 2.97
r2 = 0.98
B)
Y = -1.23X + 3.59
r2 = 0.52
C)
Y = -1.73X + 7.54
r2 = 0.99
Figure 38.
Log-log plots of box size versus box count used to estimate fractal
dimensions of sSwgras's Vegetation within three sample windows.
Estimates of fractal dimension are given by slope of regression.
Data from three windows are combined in lower right plot, and
suggest a break in the fractal dimension.

142
break, if any, could be hidden by the scatter within the window. One approach
examined the correlation coefficients of the individual windows. If the small and
large windows had high correlation coefficients, and the intermediate window a
low coefficient, then perhaps a change in the relationship would be indicated by
the lower correlation coefficient. This approach proved unworkable, due to the
confounding effects of different numbers of sample among the windows. As a
final step, the mean number of boxes were calculated for each measured step
length. The plots of average box count versus average box size suggest that a
change or break in the relationships do occur (Bottom right plot-Figures 36-38).
The "break" only becomes apparent when the averages from the intermediate
combined with the data from smaller and larger windows. These plots suggest a
change in the fractal dimension at step lengths of about logio 1.8 (60 m) for wet
prairie (Figure 37), logio 2.2 (160 m) for sawgrass (Figure 36) and login 2.4 (250 m)
for tree islands (Figure 38). In spite of these apparent breaks, the method appears
insensitive when applied to the variation encountered in real data sets. Part of
the insensitivity is due to the magnitudes of the parameters, within maps, the
values only range from one to two. Since the methods are insensitive and the
variation in the estimated parameter large, a conclusion as to presence of these
changes or breaks cannot be reliably made. To determine if the "breaks" are
indicative of a change in underlying process, another technique was used, the
analysis of gaps in the distributions of vegetation patch sizes.
The analyses of patch sizes from the 1600 m window indicate the presence
of three clumps in the sawgrass and wet prairie vegetation types and two in the
tree island type. Although significant gaps occur at the beginning of all of the
distribution in all vegetation types, none of these are counted. Significant gaps,
followed by small index values occur in the distribution of sawgrass patch sizes

Difference Index 2 Log Patch Size (m2)
143
Log Patch Size (m2)
Figure 39. Rank order plot (top plot) and difference indices (bottom plot) for
sawgrass patches sampled from 1600 m windows.

144
at two points (Figure 39). The first dump indudes all patch sizes less than about
logio 4.8 (63,000 m2). The second clump is defined by points greater than logio
4.8 and less than logio 5-6 (316,000 m2). Significant gaps in the distribution of wet
prairie patch sizes occur at logio 5.4 and logio 5.9 (Figure 40). Similar gaps occur
in the tree island distributions at logio 4.2 (Figure 41).
The analyses using data from the larger window (16 km) indicated the
presence of one significant gap in rank order distributions of the three vegetation
types (Figures 42-44). The gaps appeared at the upper end of the spectrum, and
all occurred at patch sizes of about logio6, or a million square meters. These gaps
appear as breaks or jumps in the rank order distributions.
Both the gap and fractal analyses indicate similar properties of the
vegetation patterns displayed in maps. The gaps in the rank order distributions
seem to occur at patch sizes not very different from those inferred from the
fractal analyses. All three vegetation types exhibited a gap or change in the
fractal dimension at step lengths between about 50 and 300 m (Table 9). Another
break appears at a step length of about 1000 m (Table 9). Although none of the
results alone provide irrefutable proof, together they provide evidence that
supports the hypothesis that the system is structured in a series of lumps and
gaps. To see if this pattern continues, the results of the analyses of the fire data
are presented next.
Fires
During the 31 year period between 1948 and 1979, the 132 fires in Shark
slough ranged in size between 300 m2 to more than 133 km2. At least three size
classes are apparent in the data. The class with the largest fires, had two fires
(122 and 133 km2 ). The majority of fires (126) were between 4000 m2 and 34

Difference Index 2 Log patch Size (m2)
145
1.000 2.000 3.000 4.000 5.000 6.000 7.000
Log Patch Size (m2)
Figure 40. Rank order plot (top plot) and difference indices (bottom plot) for
wet prairie patches sampled from 1609 m windows.

Difference Index 2 Log Fateh Size (m2)
146
0.200
0.150
0.100
0.050
0.000
-0.050
-0.100
-0.150
0.0 1.0 2.0 3.0 4.0 5.0 6.0
Log Patch Size (m2)
Figure 41. Rank order plot (top plot) and difference indices (bottom plot) for
tree island patches sampled from 1609 m windows.

Difference Index 2
147
Log Patch Size (m2)
Figure 42. Rank order plot (top plot) and difference indices (bottom plot) for
sawgrass patches sampled from 16 km windows.

Difference Index 2 Log patch size (m2)
148
0.300
0.200
0.100
0.000
0.100
-0.200
-0.300
2 3 4 5 6 7 8
Rank Order
Figure 43.
Rank order plot (top plot) and difference indices (bottom plot) for
wet prairie patches sampled from 16 km windows.

Difference Index 2 Log Patch Size (m2)
149
Log Patch Size (m2)
Figure 44. Rank order plot (top plot) and difference indices (bottom plot) for
tree island patches sampled from 16 km windows.

150
km2. The class of smallest fire sizes was defined by fires less than 2500 m2.
These classes are evident in the rank order plot (Figure 45). The two difference
indices, both indicate at least two significant gaps in the rank order distribution
(Figure 46). The first gap appears at fire size of 103 m2' and the other significant
gap occurs around 107-5 m2 (Figure 45).
Even though the analyses indicate three classes, the smallest group of fires
is probably an artifact of the data collecting technique. During the early years of
the data set, the reporting of small fires in remote areas was sporadic and done
by estimating the fire sizes from airplane (Taylor 1980) The data set contains a
number of observations of 100 acre fires, indicating how fire sizes were
estimated. The break in the small class sizes therefore, are within the error
associated with estimating fire sizes.
The larger fires sizes represent a different type of fire, one probably
associated with a different set of processes that determine fire type. Once fires
reach a certain size, the fire can generate conditions that produce positive
feedbacks (autocatalytic) that dramatically increase fire size. Among the
feedbacks include, convective circulation associated with the rapidly rising
heated air, the drying of soil, and fuel near the fire. Distinctions in fire size and
processes affecting size have been reported by Craighead (1971) and Wade et al,
(1980).
The analyses of the spatial data sets (topography, vegetation and fires) all
indicate the presence of breaks or changes in the patterns of structure. A change
in the scale of variation appears in the topographic data. Changes in the
distribution of sizes of vegetation patches and fires are also noted. To see if the
keystone processes in the system exhibit a few, distinct frequencies, the results of
analyses of the temporal data are presented next, starting with rainfall data.

Log Fire Size (m2)
151
Rank Order
Figure 45. Rank order plot of log fire sizes from Shark River Slough, 1958-
1070

Difference Index 2
251 3.61 3.78 4.08 4.31 4.61 5.08 5.39 5.78 6.01 6.28 6.65 6.96 8.09
aj .-5
Log Fire Size (m2)
0.050
0.040
0.030
0.020
0.010
0.000
-0.010
-0.020
-0.030
-0.040
-0.050
-0.060
2.51
3.61
3.78
4.08
4.31
4 61
5.08
5.39
5.78 6.01
6.28 6.65
6.96
8.09
Log Fire Size (m2)
Figure 46. Difference Indices 1 and 2 used to determine gaps in fire sizes,
Shark River Slough, 1958-1979.

153
Rainfall
Rainfall data were analyzed over the same time window (January 1949
through December 1988), using three different grain sizes; daily, monthly and
annual. The monthly and annual values were derived by summing daily
amounts over each of these time intervals. Two types of analyses were done on
each of the three data sets; a fast Fourier transform to examine for cyclical or
sinusoidal patterns and a rank order/gap analysis to test for entrainment of
temporal patterns. The results are presented in the following paragraphs by
examination of how patterns change with the increasing grain size, first with
daily rainfall, then monthly, then annual summaries.
Daily patterns.
The temporal patterns of daily rainfall follows the typical annual cycle of a
summer wet season and winter dry season (Hela 1952, Thomas 1970, MacVicar
and Lin 1984). The measured daily amounts range from zero to 17 cm at
Tamiami Station (Figure 47) and zero to 23 cm at Royal Palm (Figure 48).
Although time series of daily rain exhibit much variation, only three significant
cycles appear in the data (Figures 49, 50). The dominant cycle for data from both
sites is the annual cycle, as indicated above. Significant cycling periods of three
and four months were also apparent in the data. No long term (multiple year)
cycles were observed from these data sets. The rank order analyses indicated a
few gaps in the distribution, at the high end of the rainfall spectrum. The gaps
started appearing at daily rainfall totals of 10 cm at both sites (Figure 51). The
only significant gaps were among the highest totals (Figure 52). The gaps may be
a function of the infrequent occurrence of high rainfall events such as tropical
storms and hurricanes.

18
16
14
12
10
8
6
4
2
0
Jan
1,49 Jan 1,53 Jan 1,57 Jan 1,61 Jan 1,65 Jan 1,69 Jan 1,73 Jan 1,77
DATE
£
Figure 47.
Time series plot of daily rainfall data from Tamiami Ranger Station
1949 through 1977.

25
20
5
0
Jan
DATE
Figure 48. Time series plot of daily rainfall data from Royal Palm Station, 1949
through 1977.

Magnitude^ Magnitude^
156
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00
Wavelength (YR)
0 5 10 15 20 25 30 35 40 45
Wavelength (YR)
Figure 49. Spectral plots from Fourier analysis of daily rainfall from Tamiami
Ranger Station, indicating dominant annual and monthly cycles.

Magni tude^
157
0 12 3
Frequency (yr-1)
i ■ r"-1 1 1 ■
0 10 20 30 40 50
Frequency (yr-1)
Figure 50. Spectral plots from Fourier analysis of daily rainfall from Royal
Palm Station, indicating dominant annual and monthly cycles.

Rainfall (cm/day) Rainfall (cm/day)
158
Rank Order
Rank Order
Figure 51.
Rank order plots of daily rainfall data, Tamiami and Royal Palm
Stations.

Difference Index 2 Difference Index 2
159
0.60
0.50
0.40
0.30
0.20
0.10
0.00
-0.10
-0.20
-0.30
-0.40
1 1001 2001 3001 4001 5001
Rank Order
Royal Palm Ranger Station
0.20
0.15
0.10
0.05
0.00
-0.05
-0.10
1 1001 2001 3001 4001 5001
Rank Order
Figure 52. Difference index 2 versus rank order for daily rainfall data. Bars
represent value of index, gray areas represent mean + 95% C.I.

16Ü
Monthly patterns.
As with the daily data, the monthly rainfall data sets indicate the strong
annual cycle and a weaker monthly cycle. At both sites, the monthly rainfall
ranged from zero to 60+ cm (Figure 53). The annual pattern of a wet summer
and dry winter are visible in the time series plots of monthly rainfall (Figure 53 ).
The dominant frequency in the signal is again the annual cycle, with significant
peaks at three and four months (Figures 54 and 55). No multiple year cycle is
signifcant in either data set.
Some hierarchical structure appears in the monthly rainfall data sets. The
data from Tamiami exhibits at least four gaps that separate groupings of rainfall.
Two gaps are at the extreme ends of the distribution, indicating low frequency
events (Figure 56). Significant gaps in the rank order distribution at about 10 cm
and 23 cm (Figure 56). These break points define three groups. The lowest
group , with monthly rainfall values less than 10 cm, represent the winter or dry
season months. The second grouping , defined by rainfall between 10 to 23
cm/month appears to reflect maximum rainfall during "drier" years. The third
group, (23 to 50 cm/month rainfall) includes the maximum rainfall values in
"wetter" years. Similar groupings are visible, but not significant at the Royal
Palm Site, due to the high variation caused by larger individual rainfall events
(Figure 57).
Annual patterns.
The annual rainfall totals for the two stations indicate the presence of
longer term cycles. Both sites exhibited similar patterns, although totals were
different between the sites. Annual total rainfall at Royal Palm ranged from a
low of 73 cm in 1956 to a high of 217 cm in 1968 (Figure 58). Annual rainfall was

Monthly Rainfall (cm) Monthly Rainfall (cm)
70
60
50
40
30
20
10
0
May-49 May-53 May-57 May-61 May-65 May-69 May-73 May-77 May-81 May-85
DATE
60
50
40
30
20
10
0
May-49 May-53 May-57 May-61 May-65 May-69 May-73 May-77 May-81 May-85
DATE
Figure 53. Time series plot of monthly rainfall data from Royal Palm and
Tamiami Ranger Stations, 1949 through 1977.

162
S, 8000
c3
2 6000
0.0
10.0 20.0
Wavelength (years)
30.0
40.0
Wavelength (years)
Figure 54. Spectral plots from Fourier analysis of monthly rainfall from
Tamiami Station, indicating dominant annual and monthly cycles.

Magnitudes Magnitudes
163
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0.0 10.0 20.0 30.0 40.0
Wavelength (years)
Royal Palm Station
Figure 55. Spectral plots from Fourier analysis of monthly rainfall from Royal
Palm Station, indicating dominant annual and monthly cycles.

Difference Index 2
164
Tamiami Ranger Station
Rank Order
Figure 56. Rank order plot and difference index 2 for monthly rainfall data
from Tamiami Ranger Station. Arrows locate significant gaps.

Difference Index 2 Monthly Rainfall (cm)
165
Royal Palm Station
70
Rank Order
Figure 57. Rank order plot and difference index 2 for monthly rainfall data
from Royal Palm Station. Arrows locate significant gaps.

Annual Rainfall (cm/yr)
166
Year
Year
Figure 58. Time series of total annual rainfall at Tamiami and Royal Palm
Stations.

167
less variable at Tamiami, ranging from a low of 97 cm in 1985 to a high of 177 in
1988 (Figure 58). Even though totals varied, cycling frequencies were similar
between the sites. Both sites had significant peaks of approximately 11 ,5 and 3
years (Figure 59), similar to the dominant frequencies reported for south Florida
by Thomas (1970)and Isaacs (1980).
Hierarchical analyses can be used to define rainfall years, as dry,
intermediate or wet. Gaps or breaks in rank order plots appear in data from both
sites, and define the limits of these groupings. Annual rainfall at Royal Palm
shows gaps at 73 and 163 cm defined by the difference index (Figure 60). A
hierarchical cluster analysis indicates similar groupings, with three groups
defined by breaks at annual totals of 102 and 163 cm (Figure 61). Annual rainfall
at Tamiami also exhibits three groups, but defined at different values. The rank
order, difference index indicates gaps at 110 and 165 cm (Figure 62). The
hierarchical cluster analysis indicated four signifcant groups with breaks at 110,
139, and 165 cm (Figure 63). The gaps and groupings at both sites are significant
at the 95% confidence interval, defined by psuedo t statistics. A bootstrap
simulation was done using a uniform random distribution that was scaled
between 100 and 180 and from which 39 samples were drawn, indicated that
three significant gaps occurred only five out of 100 times.
The analyses of the rainfall data produce different patterns at different
grains. The daily and monthly data exhibit only an annual and monthly pattern.
Multiple year periodicity is not evident in these data sets. The annual data sets
exhibit periodicities of about 6, 8 and 11 years. It is not clear why the smaller
grain data sets would not show similar patterns. Perhaps the higher variation in
the smaller grain data masks the longer term patterns. Another explanation is
that the summation of rainfall to yearly totals may exaggerate a pattern that is

MagnitudeA2 Magnitude A2
168
Figure 59.
Spectral plots from Fourier analysis of annual rainfall data from
Royal Palm and Tamiami Stations.

Difference Index 2 Annual Rainfall (cm)
169
Royal Palm Station
Rank Order
Figure 60. Rank order plot and difference index 2 for monthly rainfall data
from Royal Palm Station. Arrows locate significant gaps.

170
Hierarchical Cluster Tree Diagram
Euclidean Distance Metric
Average Linkage Method
Royal Palm
Annual
Rainfall
0.00
211
--
213
—
1
♦ —
195
1
1
.......
1
189
1
♦ — |
187
i-i i i
185
1+ 1 1
185
1- 1 1
♦ —
179
l- l
4-~
179
1-
163
| -
♦ -
162
l-l
«
159
1— 1
--
154
1 — 1
1
1
152
1— 1 1
1
♦ • I
l
147
1- 1 1 1
1
♦ - - - | I
|
146
| ♦ ||
1
146
1
♦ ---
1
142
1 1
1
1
139
l-l 1 1
1
♦“1 1
1
136
l-l t
1
136
1- 1
1
— 1
|
136
l-l 1
1
♦ -
1
133
1 —
1
4
130
1 -
1
1
1
|
129
l-l
l
1
♦ «
1
1
127
1 —1
1
1
♦ ---
1
I
124
l-l 1
1
1
124
| 4 | |
1
1
123
| + | |
1
1
♦ - | |
1
1
123
l-l 1 1
1
1
♦ - 1
1
1
120
1 — 1
l
1
1
117
1 - 1
1
1
117
l-l 1
1
I
115
1— 1 1
1
♦ —
1
110
|
1
102
1
1
1
95
l— 1
1
1
1
l
93
1 —
1
1
— - ——
73
1
■*i
SO.00
Figure 61. Hierarchical Cluster Tree for annual rainfall at Royal Palm Station

Difference Index 2 Annual Rainfall (cm)
171
Taniiami Ranger Station
Rank Order
Figure 62. Rank order plot and difference index 2 for monthly rainfall data
from Tamiami Ranger Station. Arrows locate significant gaps.

172
Hierarchical Cluster Tree Diagram
Euclidean Distance Metric
Average Linkage Method
Tamiami
Annual
Rainfall
Rain
(cm)
177
175
175
172
165
157
157
156
152
151
149
148
147
145
145
139
136
135
133
131
129
127
127
127
127
124
121
120
116
110
109
107
106
106
106
104
99
99
97
0.00
-DISTANCES-
20.00
Figure 63. Hierarchical Cluster Tree for annual rainfall at Tamiami Ranger
Station.

173
imperceptible in the other data sets. I'll revisit this anomoly later, but first the
results of analyzing the stage data from the system.
Water Levels
The stage data from four stations in the southern Everglades all exhibit
patterns of multiple cycles. The data were analyzed over a 22 year period, using
two levels of resolution; daily and monthly. The time series plots of mean
monthly stage data (Figures 64 and 65) suggest both annual variation and multi¬
year fluctuations. The data tend to be exaggerated when water levels go below
ground, as indicated by the sharp downward spikes in Figures 64 and 65. The
spectral analysis of the monthly data shows the presence of three cycles at all
four sites (Figure 66). The strongest cycle is a wavelength of approximately 11
years, with other peaks at frequencies of 1 and 3 years. The daily data also
exhibit three peaks in the Fourier analysis, but at slightly different wavelengths
than the monthly data set. The peaks in the spectral plots using the daily data
occured at wavelengths of one year, three years and 7-8 years (Figure 67).
The rank order curves of the daily data all had two deflection points
(Figures 68 and 69). The lower deflection point occurs near the soil surface,
where the stage readings shift from surface to ground water. This change reflects
a difference in the relationships between volume of water and the vertical
measure of stage. The upper deflection point in the stage data occured at about
40 to 60 cm above ground level. These fewer, higher stages correlate to
infrequent flooding events that are apparent in the Fourier analyses. The
monthly rank order curves (Figures 70 to 73) have similar shapes, but the
averaging process appears to have smoothed the curves, removing some of the
upper and lower limbs.

Water Level (m) above msl Water Level (m) above msl
174
v ■ i i i 1 1 1 r—
1958 1963 1968 1973 1978
Year
Figure 64. Time series plots of monthly water levels at gauging stations P33
and P38, from 1958-1979.

Water Level (m) above msl Water Level (m) above msl
175
0.8
-0.6 H 1 i * " i 1 i ■ i
1958 1963 1968 1973 1978
Year
Figure 65. Time series plots of monthly water levels at gauging stations P35
and P37, from 1958-1979.

Magnitude A2
176
Spectral Analysis, Shark Slough Water Levels
1954-1975
Time (years)
O— P33
— P35
*— P37
-9— P38
Figure 66. Spectral plots from Fourier analysis of monthly water level data
from four P stations.

MagnitudeA2
177
O 2 4 6 8 10 12 14 16 18 20 22
Wavelength (yr)
CN
1
a
■a
to
(4
s
0 12 3
P33
—♦—
P35
—■—
P37
0
p38
Wavelength (yr)
Figure 67. Spectral plots from Fourier analysis of daily water level data from
four P stations.

Water Level (m-msl) Water Level (m-msl)
178
Rank Order
Rank Order
Rank order plots of daily water level data from stations P33 and P
35.
Figure 68.

Water Level (m-msl) Water ^vcl <m-msI)
179
Rank Order
0 1000 2000 3000 4000 5000 6000 7000
Rank Order
Figure 69. Rank order plots of daily water level data from stations P37 and P
38.

: difference index
(Ri-R)/R Water Level (m-msl)
180
V
a
0.04
0.03 -
0.02 -
0.01 -
0.00
1.2
1.4
□
B ID □ Q
03 □ Q CJ □
mnnna tzzo fr^nTno
i'WTTTTn <<n
1.6 1.8 2.0 2.2
2.4
Water Level (m-msl)
Figure 70. Rank order plot and difference index 1 for monthly water level data
at station P33.

Simple Difference Index Water Level (m-msl)
(Ri - R)/R
181
0.2 0.4 0.6 0.8 1.0
Water Level (m-msl)
Figure 71. Rank order plot and difference index 1 for monthly water level data
at station P35.

Difference Index Water Level (m-msl)
182
Rank Order
0.0 0.2 0.4 0.6 0.8
Water Level (m-msl)
Figure 72. Rank order plot and difference index 1 for monthly water level data
at station P37.

lie Difference Index Water Level (m-msl)
(Ri - R)/R
183
Rank Order
0.0 0.2 0.4 0.6 0.8
Water Level (m-msl)
Figure 73. Rank order plot and difference index 1 for monthly water level data
at station P38.

184
The rank order analyses of stage indicated few discontinuities in the daily
data, however, a few gaps did appear in the monthly data sets. No gaps were
measured in the daily data sets, due to the large number of observations.
With over 13,000 observations in each of the daily data sets, the only
differences between sequentially ranked observations were those associated with
the precision of measure of water level. Gaps appeared at the low and high ends
of the distributions in the monthly data sets. These are probably an artifact of the
averaging process, where extreme daily data points during a month were
removed, creating gaps.
As with the rainfall data, the dominant frequency in the stage data is the
annual cycle, although the presence of a multi-year cycle appears in both the
daily and monthly stage data. To see if the pattern of annual and multiple year
frequencies occur in other patterns of surface water, the results of analyses of the
flow are presented next.
Water Flow
As with the water levels, the flow through the southern Everglades also
exhibits multiple cycles or periodicities. The monthly flow data vary from zero
flow to more than 4.2 x 108 m3/mo which occurred during the wet year of 1947
(Figure 74). Notable peak flows occurred during 1947, 1961, 1967, and 1969-70.
The spectral analysis indicated the largest frequencies of 1 and 9 years, with
minor frequencies at 3, 5, and 22 years (Figure 75). The effects of water
management are included in this analysis, and can be seen in Figure 74. The
period in the early 1960's of extremely low flow is when the Tamiami Trail was
closed while the S-12 structures were completed. The period of regularity in the
1970's through early 1980's is when the minimum flow regime was in effect.

WATER FLOW (m3/mo)
Flow Across Tamiami Trail
(L-30-40 mile bend) 1940-1982
1940 1950 1960 1970 1980
Year
Time series plot of monthly water flow across Tamiami Trail flow
section 1940-1982.
Figure 74.

Magnitude^ Magnitud* *2
186
4.00ei-14
3.00e+14
2.00 e+14
1.00e+14
0.00e+0
0 5 10 15 20 25 30 35 40 45
Wavelength (yrs)
0123456789 10
Wavelength (yrs)
Figure 75. Spectral plots from Fourier analysis of monthly flow across
Tamiami Trail flow section.

187
The large variation in monthly flow creates a lumps and gaps in the rank
order distribution. The lumps are apparent as steps or risers in the rank order
plot (Figure 76 ). At least five significant (> 95% confidence level) gaps occur at
flows of 0.8,1.5,2.3,3.2 and 3.8 x 108 m3/mo. (Figure 77). The gaps can be used
to define breaks among flow groupings that correlate with the periodicities listed
above. Monthly flows greater than 3 x 108 m3/mo occur on the long term
frequencies (22+ years). The 3.2 x 108 m3/mo break seems to correlate with the 9
year return interval. The 2.3 x 108 m3/mo break is roughly observed on the 5
year cycle, the 1.5 x 108 m3/mo the three year cycle and the smallest break seems
to correlate with an annual cycle. These correlations are approximate, certainly
high flows don't occur every 9-10 years. The data indicate distinct periodicities,
with dramatic annual and decadal cycles, that appear to correlate with distinct
volumetric groupings.
Fires
Fire size data from Shark Slough indicate similar periodicities as the water
data sets. Fire sizes during the 22 year period from 1958 though 1980 ranged
from 102 to 108 m2 (Figure 46). Significant spectral peaks were measured at
return intervals of 11 and 1 years with minor peaks at a 5-6 year interval (Figure
78). Although the periodicities of fires are similar to the flow and stage the
phases are different. The years of high fire activitivy and size (early 1960's and
early 1970's) are years of low stage and low flow.
Sea Level
Multiple cycles are apparent in all three data sets (Figure 79). The
dominant cycle is the annual cycle and is probably associated with the thermal

(oui/tui) mo y
188
5.00e+8
4.00e+8
3.00e+8
2.00e+8
1.00e+8
0.00e+0
Figure 76.
Flow Tamiami Section 1949-1982
50 100 150 200 250 300 350 400 450 500
Rank Order
Rank order plot of monthly water flow across Tamiami flow
section.
550

Difference Index 2 Simple Difference Index (Ri-R)/R
189
Rank Order
Figure 77. Difference indices 1 (top plot) and 2 (bottom plot) for monthly flow
data, Tamiami flow section.

Log Fire Size (m2)
190
Fire Size by Month
Shark Slough (T 55-57, R 35-37)
Year
Spectral Analysis, Shark Slough Fires
1958-1979
Frequency (years)
Figure 78. Time series plot of log fire sizes (top plot) from 1958-1979, and
spectral analysis (bottom plot) indicating dominant cycles in fire
data.

Mean MomhJy Sea l,evel Mean Monthly Sea l-evel Mean monthly sea level
(cm NTDE) (cm NTDE) (cm-NTDE)
191
30
20
10
0
-10
-20
-30
lyio 1920 1930 1940 1950 1960 1970 1980 1990
Year
Figure 79. Time series plots of mean monthly sea level elevation at Key West,
Miami, and Naples for the time period 1910 through 1990.

192
expansion resulting from annual variation in solar insolation. Other significant
cycles occur at return intervals of 0.5 (6 months),4, 5, 6,12 and 22 years and are
most apparent in the Key West data (Figure 80). Significant cycles at Miami and
Naples also occur on a six month, 5.5 year, 13 and 23 year interval (Figures 81
and 82).
Temperature and Pan Evaporation
Minimum and maximum temperatures at both sites exhibit a regular,
annual cyclical pattern (Figure 83). The data tend to fluctuate more in the
minimum temperatures than in the maximum temperatures. The largest cycle
appears to be the the annual pattern. A significant cycle appears to be at a
frequency on the order of 5-6 months in both max and minimum temperature.
Only the minimum temperatures at Tamiami exhibited a multi-annual
periodicity; with a cycle of about 5-6 years (Figure 84 and 85). None of the other
sites or temperatures had a discernable multi-year pattern.
In contrast to the regularity of the temperature data, the pan evaporation
at both sites appears to vary at multiple cycles. The monthly values appear to
vary between 5 and 20 cm of water loss (Figure 86). The most significant
periodicity in both data sets was the annual cycle. Signficant multi-year periods
of 11 and 5.5 years were also observed in both data sets (Figure 87) although the
peaks were not as significant as the annual cycle. Periods of 4-6 months also
were significant. Again, just as the flow, stage, fire and sea level data, in
addition to the annual cycles, all these data sets exhibit significant cycles of 8 -11
year period and a 4-6 month period.
Daily evapotranspiration exhibits a seasonal pattern of fluctuation, with
much variation in magnitude between the two sites. Daily evapotranspiration
rates range from zero to almost 2 cm/day at site P33 (Figure 88). Rates at P37

Magnitude^ Magnitude^ MagnitudcA2
193
Wavelength (yra)
10000
8000
6000
4000
2000
0
0 24 6 8 10 12 14 16 18 20
Wavelength (yra)
0 1 2 3 4 J
Wavelength (yn)
Figure 80. Spectral plots from Fourier analysis of detrended sea level data
from Key West. Dominant cycle is the annual period.

194
O 4 8 12 16 20 24 28 32 36 40 44
Wavelength (years)
Figure 81. Spectral plots from Fourier analysis of detrended sea level data
from Miami. Dominant cycle is the annual period.

Magnitude^
195
O 2 4 6 8 10 12 14 16 18 20 22
Wavelength (years)
0 1 2 3 4 5
Wavelength (years)
Figure 82. Spectral plots from Fourier analysis of detrended sea level data
from Naples. Dominant cycle is the annual period.

TEMPERATURE oC TEMPERATURE oC
Belle Glade
0 I I 1 I 1 U
1931 1941 1951 1961 1971 1981 1991
YEAR
Figure 83. Time series plot of mean monthly minimum and maximum air
temperatures from Belle Glade and Tamiami Ranger Stations.

197
|
'§
2
0123456789 10
Wavelength (yens)
<N
%
3
'5
tf
2
500
400
300
200
100
0
0 J 10 15 20 25 30 35 40
Wavelength (years)
Minimum Tern peramre
Belle Glade
§5^23
• 95% Cl-
=to
Figure 84. Spectral plots from Fourier analyses of maximum and minimum
monthly temperature data from Belle Glade.

Magnitude^ Magnitude^
198
0 4 8 121620 24 283236 4044
Wavelength (years)
Wavelength (years)
500
400
Maximum temperature
Tamiami
? 300
O
I 200
. 1
i
2 100
\ 95% Cl
0
bi
0123456789 10
Wavelength (years)
0123456789 10
Wavelength (years)
Figure 85.
Spectral plots from Fourier analyses of maximum and minimum
monthly temperature data from Tamiami Ranger Station.

Monthly Pin Evaporation (cm) Monthly Pan Evaporation (cm)
199
Year
25
20
15
10
5 -
TAMIAMI RANGER STATION
1965
1970
1975
1980
1985
1990
Year
Figure 86. Time series plots of monthly pan evaporation from Belle Glade and
Tamiami Ranger Stations, 1965 through 1991.

200
Wavelength (years)
Wavelength (years)
Figure 87. Spectral plots from Fourier analyses of monthly pan evaporation
from Belle Glade and Tamiami Ranger Stations, 1965 through 1991.

Water Loss (cm/day) Water Loss (cm/day)
2
1.8
1.6
1.4
1.2
1
3.8
3.6
3.4
0.2
0
Jan-1985 Mar-1985 May-1985 Jul-1985 Sep-1985 Nov-1985 Jan-1986 Mar-1986 May-1986 JuI-1986 Sep-1986
Figure 88. Time series plots of daily evapotranspiration and pan evaporation
at site P33, January 1985 through October 1986.

Water Loss (cm/day) Water Loss (cm/day)
Jan-1985 Mar-1985 May-1985 JuI-1985 Sep-1985 Nov-1985 Jan-1986 Mar-1986 May-1986 Jul-1986 Sep-1986
Date
Figure 89. Time series plots of daily evapotranspiration and pan evaporation
at site P37, January 1985 through October 1986.

203
were much lower, ranging between zero and Ü.6 cm/day (Figure 89). Daily pan
evaporation also varies seasonally. Both evapotranspiration and pan
evaporation data exhibit sinusoidal patterns, with peak values during the period
of May through July and lowest values during January and February (Figures 88
and 89).
Spectral analysis of daily evapotranspiration and pan evaporation data
agree with the short term cycles found in the monthly pan evaporation data. The
significant cycles for daily evapotranspiration were at return periods of 4, 6, 8
and 17 months at both sites (Figure 90). The dominant cycles in the daily pan
evaporation data were at 6, 8 and 17 months (Figure 91).
All of the temporal data sets appear to exhibit multiple cycles. An annual
cycle is present in all of the data sets with grains less than one year. An eleven
year cycle is dominant in two of the data sets; i.e., monthly stage and the monthly
fires. Monthly cycles are apparent in the rainfall data sets. An interpretation of
these results is in the final section of this chapter.
Discussion of Results
Hydrology—Rainfall
The dominant cycles in the rainfall data appear to be related to
fluctuations in the spatial and temporal domains of the processes that generate
rainfall. The dominant cycle evident in both the daily and monthly data is the
annual cycle, with peak rainfall during the summer and lower rainfall during the
winter. Summer rainfall is mainly a result of convective thunderstorms
associated with the daily sea and land breeze cycle (Hela 1952, Bradley 1972,
MacVicar and Lin 1984). The generation of convective thunderstorms is related
to the annual variation in heat budget association with the earth orbit. During
the fall, winter, and spring months (November through April), rainfall is

MagnitudeA2 MagnitudeA2
204
0 100 200 300 400 500 600
Wavelength (days)
Figure 90.
Spectral plots from Fourier analyses of daily evapotranspiration at
sites P33 and P37. Bars represent magnitude of cycle, gray 95% C.I.

205
2
CN
<
O
•o
3
4—»
• F4
C
M
s
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
Pan P33
i
BA 1
BhiI 11 ■
mmmi
-•'V-: - -:.• . >
.< l. .. :• .V .•• -■
piiSillSiv
r-vox-: V .:
<<■>:«.<« pAm'XW/tvxil-'AtWt' f
v- - / £
0 100 200 300 400 500 600
Wavelength (days)
Figure 91. Spectral plots from Fourier analyses of daily pan evaporation at
sites P33 and P37. Bars represent magnitude of cycle, gray 95% C.I.

206
associated primarily with the passage of cold fronts (Hela 1952, Bradley 1972,
MacVicar and Lin 1984). The fronts pass at approximately weekly intervals and
do not produce much rainfall.
The three to four month cycle evident in the data is less well understood
or explained. This cycle is evident as the bimodal summer peaks of rainfall.
Some authors (Thomas 1970, MacVicar 1983) attribute the summer depression to
a combination of two processes. During the late summer months, convective
activity may decrease or level due to feedback dynamics of changing albedo,
lapse rates and heat budget after the freshwater system is full of water (Gannon
1978). The latter peak may also be a result of the increased frequency of tropical
storms and hurricanes in August and September that add to rain during these
months (Gentry 1984).
There is a paradox in the analyses of rainfall data as the grain or resolution
changes. The dominant cycles in both the daily and monthly grain data sets are
the annual and monthly frequencies. No multiple year cycle emerges from
analyses using these data sets. The interannual or multiple year cycles are only
significant in the Fourier analysis of annual rain totals. There are a number of
explanations for these results. The first is that the multiple year cycles may be in
the smaller resolution data sets, but there is so much variations that the signals
are masked by all of the data. Attempts were made to mask seasonal and annual
variation, and the interannual patterns were still not significant. Another
explanation may be that the multiple year patterns are an artifact of the totaling
process over a years time, in that they tend to exaggerate patterns. A number of
authors (Thomas, 1970, Isaacs, 1980) report multiple year cycling in annual
rainfall. Annual variations have been attributed to the degree of tropical storm
activity (MacVicar 1983). Other phenomena such as the southern ocean
oscillation (El Niño) contributes to increased rainfall over the southeast United

2U 7
States (Rasmussen 1985, Ropelewski and Halpert 1987). The presence of these
longer term, broader scale processes such as El Niño and tropical storm
frequency, seem to account for the interannual variation in rainfall but also that
these effects are probably more evident in rainfall totals summed over an annual
time period.
The multiple cycles in the rainfall data appear to be related to the
processes that generate rain. The next section discusses the implications of this
temporal variation in input on two response variables in the system; stage and
flow.
Hydrology—Stage and Flow
A significant cycle in both the stage and flow data is a multi-year (between
eight and eleven) periodicity. This result was surprising, given that it is almost
an order of magnitude more than the periodicity of the dominant input signal. A
number of alternative explanations may account for this result.
One idea was that the basin morphometry might be creating the longer
term pattern. That is, small variations in the rainfall interact with the slow flow
and basin morphometry in such a way to create longer term patterns in the
surface water variables. This idea was tested with the model presented in
Chapter 3. The test involved inputting a regular, annually varying wave to see
if a longer term wave would emerge. The input signal has a dominant annual
cycle and a shorter three month cycle. The magnitude of the rainfall (mean total
input) was set at one value for a 28 year simulation period at an average rainfall
amount. The resulting depths and flows were analyzed using Fourier
techniques, and no long term cycles were evident. These results indicate that a
combination of slow flow and basin morphometry probably does not explain the
longer time patterns in the surface water or flow data.

208
Another explanation is that the major outflow pathways, such as
evapotranspiration and sea level, vary over the longer term. There is evidence to
support this, since both sea level and evaporation have strong multiple year
cycles on the order of the eight to eleven year cycle. To test this idea, a simple
mini model was created using the ithink® modeling software. The model had
one state variable (water), one input (rain), and two outflows (ET and flow). The
input to the water was modeled as a sine wave with a frequency of one year. The
evapotranspiration (ET) pathway was modeled as a sine wave, with a frequency
of 10 years. The flow pathway was calculated as one-tenth times the amount in
the water tank. The results indicate that the overlay of input and output sine
waves creates both a short term (annual) and a long term (10 year) cycle in the
state variable-water (Figure 92). This lends credence to the idea that the long
term fluctuations in the stage and flow data in the Everglades may not be solely
due to fluctuations in the input (rainfall), but can be caused by longer term cycles
evident in the patterns of outflow. An anecdotal correlation is that the dominant
cycles for evapo-transpiration and sea levels seem to be at the same frequency of
sun-spot cycles.
The multiple-year cycles evident in the stage and flow data are probably a
result of variations of both input and output operating at different time intervals.
One way of depicting these cross scale interactions is the use of spatio-temporal
diagrams as demonstrated bv Steele (1985), Clark (1985), and 1 lolling (1992). The
diagrams are logarithmic scales over space (abscissa) and time (ordinant) that
cover ranges of about six orders of magnitude. Entities within the diagram are
defined by grain and window; in spatial terms grain is the smallest resolution
that defines the entity and window is the extent. In temporal terms, the grain is
the minimum resolution needed to define a pattern and the window is the
longevity of the entity. Breaks in the fractal dimension of

Simulated Rainfall
209
Figure 92.
Results of mini-model, frequency of rain input (A), ET outflow (B),
and stage fluctuations (C). Note difference in time range, stage plot
covers 40 simulated years.

21Ü
spatial patterns can be used to define breaks between entities in the spatial
dimension. Similarly, dominant frequencies appear to differentiate temporal
entities or levels. Surface water within the Everglades appears to fluctuate on at
least three dominant frequencies (daily, annually and decadal), as shown in
Figure 93. The daily and annual fluctuations in stage appear as a result of nested
fluctuations of land/sea breeze interactions that produce convective
thunderstorms on a daily and seasonal basis. The longer term fluctuations
appear to coincide with long wave influencing evapotranspiration and ,to a less
evident degree, decadal fluctuations in El Niño that vary rainfall. The
atmospheric dynamics are all lower and to the right in the diagram, reflecting the
faster dynamics over broad areas, whereas the surface water dynamics are
slower and occur over smaller areas.
Fires
Fire patterns indicate at least two classes of fires occur in Shark Slough;
more frequent smaller fires and less frequent large fires. The break between the
small and large fires occurs at a window length of about 5600 m. Fires above this
size, may be a result of many factors, including inability of humans to control or
contain fires over a given size, or perhaps a less frequent combination of climatic
conditions that would support the fire to burn over a broad area and longer time
frame. The larger fires burn over longer time periods than the smaller ones. The
periodicity of all fires exhibit the same multi year frequency (eight to eleven
years) as the stage and flow data. An attempt at regression between fire size and
water levels yielded no statistical correlation between these variables. Other
factors such as wind speed and direction, time since last fire as influencing fuel
loads and changes in ignition events all would tend to mask the relationship
between fire and water levels. Even though a statistical correlation does not

211
HYDROLOGIC HIERARCHIES
1
m
10
100
1
10
100
1000
m
m
km
km
km
km
10,000
years
century
year
day
hour
minute
Space (log meters)
Surface Water
Rainfall
Figure 93. Hydrologic hierarchies in the Everglades ecosystem, showing scales
of dominant frequencies in surface water and atmospheric
variation.

212
exist, there appears to be some association in that the fires occur during periods
of low water levels.
Topography
At least two regions of scale are evident in the topographic data and
appear to correlate with the processes that create the structure. A change in the
fractal dimension occurs at a step length of about 1.5 km, which defines a change
between the macro and micro topographic features (Figure 94). The fine scale
variations (measured by step lengths of less that the fractal break) that comprise
the small scale topography are related to processes that can increase or decrease
the soil surface elevation. Soil formation occurs in the areas of longer
hydroperiod, as decomposition is slow, resulting in peat accretion. Organic soils
can be rapidly oxidized if long-term droughts occur, or if the soil burns during
severe dry periods. Marl is formed on shorter hydroperiod sites, a result of
precipitation of calcium carbonate by blue green algae (Gleason 1972). Over
longer term periods solution of the limestone bedrock can create small scale
depressions (Hoffmeister 1974). The macro topography is associated with the
geologic features of the Everglades. The geologic features are associated with
broad landscape regions, defined by Jones (1948) and Davis et al. (In Press) and
are the result of broad scale processes of ocean currents. Another theory (Petuch
1985, Petuch 1987) is that the gross morphometry of the Everglades basin was
caused by a meteroite impact during the Eocene.
Vegetation
The observed breaks in vegetation patterns are puzzling. No plausible
explanation can suitably account for the patterns. The breaks do not occur in the

213
TOPOGRAPHY
micro
macro
rs
<V
t>C
O
OJ
£
H
4
2.
0
-2-
-4
-6.
10 1
cm m
10 100
m
m
1
km
10
km
100
km
i i f i i i i
Organic Processes
./X;VV--.;V'-. Marl and Peat
Formation, 'y-y-y-y/-'
■■■■fyfy'fy- Solution A;VvVvVv'A
%ÍÍÍÍÍCÍ¿Í¿ÍÍÍv'l
Geologic Í
■W Land forms £
« «*■ «*• «*.•**
S'S'N'S'V'S'S'S*
I'.'yyyyyy.s
10,000
years
century
year
day
hour
minute
Space (log meters)
Figure 94. Topographic hierarchies in the Everglades ecosystem, indicating
breaks between microtopographic and macrotopographic features
and processes.

214
smallest windows (< 160 m), and therefore do not represent the edge profiles of
communities. The breaks occur in the larger windows and appear around step
lengths of 300 m and about 1 km. The break at the largest scale may be related to
the topographic features, although it occurs at a smaller step length than the
change in the topographic fractal dimension. The breaks appear at about the
same scale grain across all three vegetation types. This suggests that perhaps
some meso-scale process such as fire or water flow might be influencing the
pattern rather than some biologic process such as spatial expansion of the
community size. Nothing in the analysis of fire patterns appears to correspond
with these scale ranges. The breaks are included in a space/time plot of
vegetation features (Figure 95) even though they don't appear to correspond with
any logical groupings in a vegetation hierarchy. In spite of the lack of reasons for
the observed patterns, the discontinuities appear to exist in the spatial patterns of
vegetation.
Summary
The analysis of existing data sets from the Everglades ecosystem fail to
invalidate the hypothesis that spatial patterns should exhibit breaks and
temporal patterns a few cycles. No one test is singularly convincing.
Comparison of results across methods seem to corroborate findings. Spatial
patterns exhibit scale regions of self-similarity separated by distinct breaks. The
soil surface topography appears to vary at two distinct spatial scales, the broad
scale is apparently a result of geologic features and the small scale appear related
to the processes or organic soil accretion and removal. Breaks in the size of fires
may be related to the approximately decadal time period between large burns.
The vegetation patterns exhibit breaks between regions of self-similarity

215
VEGETATION HIERARCHIES
to
hi
ftJ
cu
bO
O
D
g
P
4
2-
0-1
-2-
-4
-6-
10 1
cm m
10 100
m m
1
km
10 100
km km
t i i t j I j
Peat/Marl'.
Units
III
Fractal Breaks
I
4
1"
5
10,000
years
century
year
day
hour
minute
Space (log meters)
Plant
Species
Freshwater
Plant Landscape Everglades
Communities Units Ecosystem
Figure 95. Vegetation hierarchies in the Everglades ecosystem, showing scales
of plant species, communities, landscape units and the Everglades
ecosystem as defined by breaks in the fractal dimension.

216
although the reasons are unclear. Temporal patterns in the stage, flow reflect
dominant frequencies in the interplay between the faster dynamics of the
atmopshere, the intermediate speeds of the surface water (stage and flow) and
the longer term variations in vegetation, climate and sea level.
These analyses support the theory that ecosystems are structured around a
few keystone variables of mixed spatial and temporal dimensions. Dramatic
discontinuites patterns appear as a result of the interactions within and between
hierarchical levels in space and time which in turn create non-linearities in
system dynamics. The emerging viewpoint of ecosystem structure and dynamics
will hopefully provide a basis for understanding and hence meeting multiple
management objectives in this unique ecosystem. Failing to invalidate the cross¬
scale hypothesis, provides an alternative paradigm upon which ecosystem
understanding and management are based. A comparison and discussion of
system understanding and management based upon alternative concepts are the
subjects of the next and final chapter.

CHAPTER 5.
AN END AND A BEGINNING
The only things that can be universal, in a sense, are scaling things
-Mitchell Feigenbaum
This chapter is both an end and a beginning. The dissertation ends with a
summary of the first four chapters, followed by a comparison of two approaches
to understanding ecosytem dynamics. The final section of the chapter casts the
conclusions of this work in context of ongoing management issues of ecosystem
restoration and, perhaps, a beginning of new understanding.
A Summary
The first chapter recounted the history of the Everglades, both natural and
recent human experiences. The human response to environmental "crises" over
the last century has determined the water management infrastructure and
policies that are in place today (Light et al. In Prep) and dramatically
transformed the landscape (Davis et al. In Press, Gunderson and Loftus In
Press). During this century, crises have largely been the result of recurring
natural phenomena, characteristic of variation in broader spatial-temporal
region, but perceived as local surprises. The floods of the early 1900's coupled
with the desire to cultivate the seemingly rich muck soils, prompted the creation
of the Everglades Drainage District. The drainage district initiated construction
of four major canals, the Miami, New River, Hillsboro and Palm Beach, that are
central to the water management infrastructure today. A hurricane in 1928
217

218
caused massive human mortality, as a result of the breakage of an earthen dam
around Lake Okeechobee. The response witnessed the involvement of the
federal government who funded, constructed and continues to maintain the
Hoover Dike around the Lake. The next crises occurred in 1947, an extremely
wet year, and precipitated (sic) the Central and Southern Florida Flood Control
Project. The Central and Southern Florida Flood Control Project was a joint
federal and state effort that created much of the system of levees, canals and
structures that are in use today. Another crises was the drought of the early
1960's, that coincided with the final phases of construction of the C&S F Project.
The drought prompted the studies and political action that resulted in PL 91-282
that guaranteed Everglades National Park a piece of the water resources in the
system. A drought in 1971, coincident with a growing environmental awareness,
resulted in the transformation of the Flood Control District to a Water
Management District. A wet year in 1983, led to a request from the Park Service
seeking relief from release of flood water into the park, and for a revision in
water delivery policy. The resulting adaptation was the development of the
rainfall formula for calculating water deliveries to the park. This condensed
history of water management in the Everglades obviously does not do justice to a
rich, complex set of interacting events and people that have experienced and
influenced the time course of management. I lowever, it does support the idea
that the response to crises and subsequent adaptations are strongly correlated to
the way in ecosystem dynamics are perceived and understood.
Alternative concepts used to understand ecosystem structure and function
were the subjects of the second chapter. Existing concepts attempt to explain the
dynamics of complex systems, bv either statistical approaches, mathematical
representation of the interaction of variables, or hierarchical partitioning of
variable interactions. A new and emerging theory provides a basis for exploring

219
interactions across a range of spatial and temporal scales. Two hypotheses were
posed from these theoretical bases. The first hypothesis was posited that the
entire ecosystem, including the Kissimmee, Lake Okeechobee and historic
Everglades wetlands contributed flow to Everglades Park. The other hypotheses
stated that the cross-scale interaction of variables that influence ecosystem
structure and function would be manifest as breaks between regions of
similiarity in the spatial features and nested or reasonant frequencies in temporal
processes.
A model of the space-time dynamics of the vegetation and hydrology in
the Everglades was developed to test the first hypothesis. Vegetation influences
on pathways of water movement were linked in the model framework;
vegetation structure influenced flow resistence and vegetation type mediated
evapotranspiration rates. Hydrologic influences on vegetation succession
provided the link to couple these two key ecosystem components. At the scale of
the model framework, differences in flow and evaptranspiration parameters
among plant communities were averaged out and the vegetation types were
relatively stable. Both of these factors contributed to the conclusion that the
linkages between vegetation and hydrology did not substantially alter the
explanation of hydrodynamics in the system, at the scale chosen for the model.
At finer scales, the vegetation and hydrology clearly do interact.
The results indicate that except for extremely dry years, the entire
Everglades wetlands contributed flow to Everglades Park. The relationship
between flow and upstream area appeared to be "fractal" or self similar. As the
upstream area is changed, the flow is changed in a similar amount. The
management implications of these results are that since the early 1960's, when the
construction of the Central and Southern Florida Flood Control Project was
essentially finished, the equivalent contributing areas to flow into Everglades

220
Park have been the Water Conservation Areas. Under pre-management
conditions, the entire basin (and sometimes Lake Okeechobee) contributed to
flow into the southern Everglades. The evidence that the southern Everglades
received more water and hence had a greater upstream area agrees with a
growing body of evidence presented by Smith (1989), Powell (1989), and Walters
et al. (1992).
Nine data sets representing key structures and processes in Everglades
ecosystem were analyzed for cross-scale patterns using a variety of methods.
The analysis failed to invalidate the proposed hypothesis. The findings were
derived from a comparison of results using a variety of methods. Spatial
patterns exhibit scale regions of self-similarity separated by distinct breaks. The
soil surface topography appears to vary at two distinct spatial scales, the broad
scale is apparently a result of geologic features and the small scale appear related
to the processes or organic soil accretion and removal. Breaks in the size of fires
may be related to the approximately decadal time period between large burns.
The vegetation patterns exhibit breaks between regions of self-similarity
although the reasons are unclear. Temporal patterns in the stage, flow reflect
dominant frequencies in the interplay between the faster dynamics of the
atmopshere, the intermediate speeds of the surface water (stage and flow) and
the longer term variations in vegetation, climate and sea level. These analyses
support the theory that ecosystems are structured around a few keystone
variables of mixed spatial and temporal dimensions. Dramatic discontinuites
patterns appear as a result of the interactions within and between hierarchical
levels in space and time which in turn create non-linearities in system dynamics.
The next section compares these cross-scale conclusions with the results of the
modeling work, to provide a contrast between alternative ways of understanding
the complex interactions in the "River of Grass".

221
Understanding Ecosystem Dynamics through Alternative Paradigms.
The surface water conditions, stage and flow, in the southern Everglades
are linked to a variety of processes outside the boundaries of the Park, including
rainfall and the complex factors that influence overland runoff. Some of these
processes operate at numerous scales in space and time, parts of which can be
captured within the framework of a model. Processes operating at scale regions
outside the model cannot always be scaled into the model. The fundamental
issues of scaling both empower and limit the predictability of models.
Fortunately, the rules of hydrologic and atmospheric processes can be scaled to
apply over a wide range of spatial and temporal domains. Part of this is due to
the relatively long history that has gone into our understanding of hydrology
(Viessman et al. 1989), and perhaps part is due to the nature of the medium.
Unfortunately, the scaling involved with the biologic components of an
ecosystem is less well understood. Scaling processes of complex components
into a model is contingent upon assumptions of scale variance. In other words,
the nature of the relationships can be aggregated or decomposed in a predictable
manner. These scaling issues limit the ability to link hydrologic conditions in the
Park with processes going on at different scale regimes. As a probe into these
scaling issues, the influences of processes interacting across spatial and temporal
domains on rainfall patterns are discussed next.
Rainfall over the park is influenced by processes that cover large spatial
and temporal domains. The processes cover spatial scales ranging from the
peninsula of Florida, to the planet. The meso-scale, land-sea breeze interaction
generates rain from convective thunderstorms and has a temporal cycle of about
one year. Planetary cycles, such as the southern ocean oscillation (El Niño)
appears to influence rainfall at approximately 11 year periods. Less obvious
linkages, such as the 'rain machine' or other hypotheses that purport feedback

222
dynamics between land use conversion influences and rainfall, may exist, but are
still largely speculative. The net result of all of these interacting processes can be
captured in the model by the use of historical rainfall data that includes these
periods of variation. The model does indicate that the temporal variation in the
rainfall heavily influences the surface water conditions, but in a manner that may
be much more subtle and complex than can be captured with our existing tools.
Although the dominant input to the Everglades system is rainfall,
difficulties arise in correlations between rain and other hydrologic variables
(stage and flow) perhaps because cross-scale interactions may somehow
transform the relationship. Analysis of rainfall, stage and flow patterns indicate
different temporal regimes. The rainfall patterns emerge at time scales of months
and years; stage and flow at multiple year cycles. The implications are that the
combination of little topography, vegetation influences on flow and
evapotranspiration transform the "faster" rainfall inputs in such a way that
"slower" stage and flow patterns emerge. This has been noted before; MacVicar
(1985) in developing a statistical regression between flow at the Tamiami
flowsection and net rainfall found that the rainfall term was statistically
insignificant. The correlation of stage and flow is possible, because the two
variables operate within similar temporal domains, wheras rainfall does not. The
net result is that patterns of flow and stage emerge at distinct scale regimes. The
model does such a transformation, in that the historic surface water patterns can
be recreated by using the historic input data on rainfall.
Other factors at different spatial and temporal scales complicate the
relationship between rainfall and flow to the Park prior to human intervention.
The entire Everglades area upstream of the park, during extremely high water
conditions, appears to have contributed water to the Park. During drier times,
less of the system contributed water. These relationships are modified by the

223
vegetation, although the influence appear to be related to the scale of
investigation. At scales below the model grid size, the flow and
evapotranspiration relationships appear to be mediated by the vegetation. At the
model scale (grain of 4 km) and larger, these finer grain influences of vegetation
appear less important. These are two examples of scaling issues. The
relationship between upstream area and flow appears scale invariant (at least up
to the Lake), while the vegetation mediation dynamics are not. The cross-scale
analyses indicate the property of breaks in vegetation and topographic structure
across scale-ranges. The applied techniques of aggregation don't appear to
capture subtle translations across scale regimes, and hence inevitably lead to
surprises in system behavior.
Most of the preceeding discussion has dealt with attempting to
understand the dynamics of the relatively ''natural" parts of the system.
However, the system however has dramatically changed due to human
intervention. Water delivered to the park is routed through canals. Water
upstream of the park is diverted to urban areas to support millions of residents.
Agricultural inputs are affecting water quality, in a way that causes dramatic
changes in the ecosystem. Alien plant populations are expanding. All of these
factors suggest that the current notion of a natural Everglades landscape may be
in for a dramatic transformation. The last section of this chapter examines these
possibilities in context of ecosystem restoration.
Prognosis for System Restoration
The restoration of the Everglades has been underway for over half a
century. The initial survey of the biotic resources of Everglades National Park
was done in the 1930’s (Beard 1938). The conclusions at the time were that the
park was not in good shape, but that perhaps a few decades of wise management

224
would restore this unique system to it's previous splendor for the enjoyment of
future generations. Three generations later, the restoration has not materialized.
Many fine attempts have occurred at approximately decadal intervals. The
floods of 1947 coincided with the formation of the national park, but spawned
events that would create the massive system of levees and canals. The 1960's
witnessed the park being cut-off from upstream flow, that was diverted to the
coast to deal with salt-water intrusion problems. The pleas from the park were
heard, and Congress assured the park it's piece of the water pie. This policy was
conceptually transformed from an assurance of a minimum percentage to a
consistent minimum amount. Voices such as Art Marshall and H.T. Odum,
calling for ecosystem perspectives of problems and solutions, were largely
ignored during the 1970’s. The 1980's witnessed an onslaught of water supply,
eutrophication, and flood control issues, as latent pathologies in the system
design and operation became manifest. Positive signs of restoration began with
the first adaptive policies in the rainfall delivery formula (Light et al. 1989).
Other events such as the 1989 symposium (Davis and Ogden In Prep) provided
the focus for new understandings and directions for management of which this
work is an offshoot.
The state-of-the-art hydrologic models provide perhaps the best available
tool for the adaptive probes into new techniques of water delivery to the park.
The models provide partial truths that can combine rules across two to three
orders of magnitude along space or time domains. The models also provide a
framework for combining process that transform variables in ways that statistical
approaches such as the rainfall formula cannot. In any case, the models should
always be subjected to critical invalidation, for adaptation to changing or
evolving conditions in understanding and management institutions.

225
An understanding appears to be emerging that ecosystems are organized
and structured through a few keystone processes operating at distinct spatial and
temporal scales. Data from the Everglades indicates that such patterns exist in
the system. Understanding not only the obvious, but also the subtle ways in
which the complex of processes affecting flow interact across space and time are
necessary for system restoration. The cross-scale dimensions of the hydrologic
processes, and the other portions of the Everglades ecosystem are just beginning
to be unraveled through a combination of new methodologies and modeling
approaches. The presence of cross-scale interactions both in natural and human
systems, as documented in this work, will hopefully provide a foundation, and
hence a beginning, for positive efforts towards true restoration of this unique,
treasured ecosystem.

LITERATURE cited
Alexander, T. R. and A. G. Crook. 1975. Recent and long-term vegetation
changes and patterns in South Florida, Part II. Final Report, South Florida
Ecological Study, 827 p. University of Miami, Coral Gables, Florida.
Alexander, T. R. , R. H. Hofstetter and F. Parsons. 1975. Comparison of
Transpiration of Cajeput, Melaleuca quinquenervia, and Saw-Grass, Cladium
jamaicense. Proceedings of the Florida Academy Science 39th Annual
Meeting, Lakeland, Florida,
Allen, L. H. J., W. G. Knisel Jr. and P. Yates. 1982. Evapotranspiration, rainfall
and water yield in south Florida research watersheds. Proc. Soil Crop Soc.
Florida 41 :127-139.
Allen, T. F. H. and T.W. Hoekstra. 1992. Toward a Unified Ecology. Columbia
University Press, New York, New York.
Allen, T. F. H. and T. B. Starr. 1982. Hierarchy: Perspectives for Ecological
Complexity. University of Chicago Press, Chicago, Illinois.
Beard, D. B. 1938. Wildlife Reconnaissance of the Everglades National Park. US
Department of Interior, Washington, D.C.
Blake, N. 1980. Land Into Water - Water Into Land: A History of Water
Management in Florida (Everglades). University Presses of Florida,
Gainesville, Florida.
Blaney, H. F. and W. D. Criddle. 1950. Determining water requirements iin
irrigated areas from climatological and irrigation data. U.S. Department
of Agriculture Soil Conservation Service.
Bradbury, R. H. and R. E. Reichelt. 1983. Fractal dimension of a coral reef at
ecological scales. Marine Ecology 10 :169-171.
Bradbury, R. H., R. E. Reichelt and D. G. Green. 1984. Fractals in ecology:
methods and interpretation. Marine Ecology 14:295-296.
Bradley, J. T. 1972. Climate of Florida. Climate of the States, Environmental
Data Service, Silver Springs, MD.
226

227
Browder, J. A. 1985. Freshwater and the estuary: the Everglades National Park
story. Bulletin of Marine Science 15 (4): 20.
Brown, S. 1981. A comparison of the structure, primary productivity and
transpiration of cypress ecosystems in Florida. Ecological Monographs 51
(4): 403-427.
Brutsaert, W. 1984. Evaporation into the Atmosphere. Environmental Fluid
Mechanics, D.Reidel Publishing Company, Dordrecht/Boston.
Burrough, P. A. 1981. Fractal dimensions of landscapes and other
environmental data. Nature 294 : 240-242.
Carr, R. S. and J. S. Beriault. 1984. Prehistoric man in southern Florida, in
Environments of South Florida, Past and Present II, P. J. Gleason, editor.
Miami Geological Society, Coral Gables, Florida.
Carter, M., L. A. Burns, T. R. Cavinder, K. R. Dugger, P. L. Fore, D. L. Hicks, H. L.
Revells and T. W. Schmidt. 1973. Ecosystem Analysis of the Big Cypress
Swamp and Estuaries. U.S. Environmental Protection Agency, Region IV,
Atlanta, Georgia.
Clark, W. C. 1985. Scales of climate impacts. Climate Change. 7:5-27.
Clark, W. C, D. D. Jones and C. S. Holling. 1979. Lessons for ecological policy
design: A case study of ecosystems management. Ecological Modelling
7:1-53.
Clayton, B. S. 1949. Water control investigation, report of progress. University
of Florida, Agricultural Research and Education Center, Belle Glade,
Florida.
Costanza, R. and T. Maxwell. 1991. Spatial ecosystem modeling using parallel
processors. Ecological Modelling 58:159-183.
Costanza, R., F. Sklar, and M. White. 1990. Modeling coastal landscape
dynamics. BioScience 40:91-107.
Craighead, F. C, Sr. 1971. The Trees of South Florida. Vol. I. The Natural
Environments and Their Succession. University of Miami Press, Coral
Gables, Florida.
Davis, J. H., Jr. 1943. The Natural Features of Southern Florida, Especially the
Vegetation, and the Everglades. Florida Geological Survey, Tallahassee,
Florida.

228
Davis, S. M 1989. Sawgrass and Cattail Production in Relation to Nutrient
Supply in the Everglades. Fresh Water Wetlands & Wildlife, 9th Annual
Symposium, Savannah River Ecology Laboratory, 24-27 March, 1986,
Charleston, South Carolina, U.S. Dept, of Energy.
Davis, S. M., L. H. Gunderson, W. Park, J. Richardson and J. Mattson. In Prep.
Landscape dimension, composition and function in a changing Everglades
ecosystem, in The Everglades, Spatial and Temporal Patterns for
Ecosystem Restoration, S. M. Davis and J. C. Ogden, ed. Florida.
Davis, S. M. and J. C. Ogden, Editors. . In Prep. The Everglades; Spatial and
Temporal Patterns as Guidelines for Ecosystem Restoration.
Dohrenwend, R. E. 1977. Evapotranspiration patterns in Florida. Florida
Scientist 40:184-192.
Dolan, T. J., A. J. Hermann, S. E. Bayley and J. Zoltek. 1984. Evapotranspiration
of a Florida, U.S. A., freshwater wetland. Journal of Hydrology 74:355-371.
Douglas, M. S. 1947. The Everglades River of Grass. Mockingbird Books, St.
Simons, Georgia.
Dunn, A. V. 1960. Required Minimum Discharges to Everglades National Park
from Central and Southern Florida Flood Control District. U.S.
Department of Interior, National Park Service, Washington D.C.
Feder, J. 1988. Fractals. Plenum Press, New York, New York.
Gallopin, G. 1991. Human dimensions of global change: Linking the global and
the local processes. International Social Sciences Journal 130 : 707-719.
Gannon, P. T. 1978. Influence of Earth Surface and Cloud Properties on South
Florida Sea Breeze. NOAA Technical Report ERL 402-NHELM2.
Washington, D.C.
Gardner, R.H., W.G. Cale and R. V. O'Neill. 1982. Robust analysis of
aggregation error. Ecology 63:1771-1779.
Gentry, R. C. 1984. Hurricanes in South Florida, pages. 510-517 i_n
Environments of South Florida: Present and Past II: Memoir 2, P. J.
Gleason, editor. Miami Geological Society, Coral Gables, Florida.
Gleason, P. J. 1972. The Origin, Sedimentation and Stratigraphy of a Calcitic
Mud Located in the Southern Freshwater Everglades. Pennsylvania State
University. PhD Thesis.

m
Gleason, P.J., A. D. Cohen, P. Stone, W. G. Smith, H. K. Brooks, R, Goodrick and
W Spackman Jr. 1984. The Environmental Significance of Holocene
Sediments from the Everglades and Saline Tidal Plains, pages 287-341, in
Environments of South Florida: Present and Past II: Memoir 2, P. J.
Gleason,editor. Miami Geological Society, Coral Gables, Florida.
Goodrick, R. 1984. The wet prairies of the northern Everglades, pages 185-190
in Environments of South Florida: Present and Past II: Memoir 2, P. J.
Gleason, editor. Miami Geological Society, Coral Gables, Florida.
Greller, A. M. 1980. Correlation of some climatic statistics with distribution of
broad-leaved forest zones in Florida, U.S.A. Bulletin of the Torrey
Botanical Club 107:189-219.
Gunderson, L. H. 1989. Historical Hydropatterns in Vegetation Communities of
Everglades National Park. Fresh Water Wetlands & Wildlife, 9th Annual
Symposium, Savannah River Ecology Laboratory, 24-27 March, 1986,
Charleston, South Carolina, U.S. Department of Energy.
Gunderson, L. H. and W. F. Loftus. In Press. The Everglades: Competing Land
Uses Imperil the Biotic Communities of a Vast Wetland, in Biotic Diversity
of the Southeastern United States, S. C. Boyce, W. H. Martin and A. C
Echternacht, ed. John Wiley and Sons. New York, New York.
Gunderson, L.H. and L.L. Loope. 1982. An Inventory of the plant communities
in the L-28 Area, Big Cypress National Preserve. Report T-664, South
Florida Research Center, Everglades National Park, Homestead Florida.
38 p. +map.
Gunderson, L. H. and J. R. Stenberg. 1990. Pan evaporation and community
evapotranspiration from two wetland sites in Everglades National Park.
Report, South Florida Research Center, Everglades National Park,
Homestead, Florida.
Hack, J. T. 1959. Studies of Longitudional Stream Profiles of Small Watersheds.
Columbia University, Dept of Geology.
Hammer, D. E. and R. H. Kadlec. 1986. A model for wetland surface water
dynamics. Water Resources Research 22:1951-1958.
Harper, R. M. 1927. Natural Resources of Southern Florida. Florida Geological
Survey, Tallahassee, Florida.
Harshberger, J. W. 1914. The Vegetation of South Florida, South of 27 degrees
30' North, Exclusive of the Florida Keys. Transactions of the Wagner Free
Institute of Science. 7:49-189.

230
Hartwell, J. H., H. Klein, B.F. Joyner 1964. Preliminary Evaluation of Hydrologic
Situation in Everglades National Park, Florida. Open-File Report FL-
63001. U.S. Department of Interior, Geological Survey, Miami, Florida .
Heilpren, A. 1887. Explorations of the West Coast of Florida and in the
Okeechobee Wilderness. Transaction of Wagner Free Institute of Science,
Philadelphia, Pennsylvania.
Hela, I. 1952. Remarks on the climate of South Florida. Bulletin of Marine
Science 2 (2):438-447.
Herndon, A. and L. Gunderson. 1990. Patterns of transpiration from wetland
species in Everglades National Park. Report. South Florida Research
Center, Everglades National Park, Homestead, Florida.
Herndon, A., L. Gunderson and J. Stenberg. 1991. Sawgrass, Cladium jamaicense,
survival in a regime of fire and flooding. Wetlands 11:17-27.
Hoffmeister, J. E. 1974. Land from the Sea. University of Miami Press, Coral
Gables, Florida.
Holdridge, L. R. 1967. Life Zone Ecology. Tropical Science Center, San Jose,
Costa Rica.
Holling, C. S. 1978. Adaptive Environmental Assessment and Management.
John Wiley and Sons, London.
Holling, C. S. 1986. The Resilience of Ecosystems; Local Surprise and Global
Change, pages 292-317 in Sustainable Development of the Biosphere, W.
C. Clark and R. E. Munn, editors. Cambridge University Press,
Cambridge.
Holling, C. S. 1987. Simplifying the Complex; The paradigms of ecological
function and structure. European Journal of Operational Research 30:139-
146.
Holling, C. S. 1992. Cross-Scale Morphology, Geometry and Dynamics of
Ecosystems. Ecological Monographs 62(4):447-502.
Hutchinson, G. E. and R. MacArthur. 1959. A theoretical ecological model of
size distributions among species of animals. American Naturalist 93:117-
126.
Isaacs, J. A. 1980. Precipitation Regimes of Florida: Spatial Analyses and Time
Series. University of Florida. Master of Science Thesis.

231
Iwasa, Y., V. Andreasen, and S. Levin. 1987. Aggregation in model ecosystems.
I. Perfect Aggregation. Ecological Modelling 37:287-302.
Iwasa, Y., S. Levin, and V. Andreasen. 1989. Aggregation in model ecosystems.
II. Approximate Aggregation. Journal of Mathematics Applied in
Medicine and Biology 6:1-23.
Jarvis, P. G. and K. G. McNaughton. 1986. Stomatal control of transpiration:
scaling up from leaf to region. Advances in Ecological Research 15 :l-49.
Johnson, L. 1958. A Survey of Water Resources of Everglades National Park,
Florida. Unpublished Mimeo. Report to the Superintendent, Everglades
National Park and National Park Service, Homestead, Florida
Johnson, L. 1974. Beyond the Fourth Generation. University of Miami Press,
Coral Gables, Florida.
Jones, L. A. 1948. Soils, Geology, and Water Control in the Everglades Region.
University of Florida Agricultural Experiment Station, Belle Glade,
Florida.
Kadlec, R. H. 1990. Overland flow in wetlands: vegetation resistance. Journal of
Hydraulic Engineering 116:691-706.
Kent, C. and J. Wong. 1982. An index of littoral zone complexity and its
measurement. Canadian Journal of Fisheries and Aquatic Sciences
39:847-853.
Kushlan, J. A. 1987. External Threats and Internal Management: The Hydrologic
Regulation of the Everglades, Florida, USA. Environmental Management
11 (1):109-119.
Kushlan, J. A. and M. S. Kushlan. 1980. Water Levels and Alligator Nesting in
the Everglades. In: Proceedings of 2nd Conference on Scientific Research
in National Parks, J. Gouge, editor. San Francisco, California
Leach, S. D., H. Klein and E. R. Hampton. 1971. Hydrologic Effects of Water
Control and Management of Southeastern Florida. US Geological Survey ,
Coral Gables, Florida.
Light, S. S., L. H. Gunderson and C. S. Holling. In Prep. The Everglades;
Evolution of Management in a Turbulent Environment, in Barriers and
Bridges to the Renewal of Ecosystems, C. S. Holling, S. S. Light and L. H.
Gunderson, editors.

232
Light, S. S., J. R. Wodraska and S. Joe. 1989. The southern Everglades-evolution
oí water management. National Forum 69(1):11-14.
Lin, S. T. and S. F. Shih. 1979. Modified Water Quantity Receiving Model for
Florida Conservation Areas. Water Resources Bulletin 15 (1):155-166.
MacArthur, R. H. 1957. On the relative abundance of bird species. Proceedings
National Academy of Sciences, Washington, D.C. 54:293-295.
MacVicar, T. K. 1983. Rainfall Averages and Selected Extremes for Central and
South Florida. South Florida Water Management District Resource
Planning Department, Technical Publication No. 83-2. West Palm Beach,
Florida.
MacVicar, T. K. 1985. A Wet Season Field Test of Experimental Water Deliveries
to Northeast Shark River Slough. Technical Report, South Florida Water
Management District, West Palm Beach, Florida.
MacVicar, T. K. and S. S. T. Lin. 1984. Historical Rainfall Activity in Central and
Southern Florida: Average, Return Period Estimates and Selected
Extremes, in Environments of South Florida: Present and Past II:, P. J.
Gleason, editor Miami Geological Society. Coral Gables, Florida.
MacVicar, T. K. and T. VanLent. 1984. Evaluation Report-A Thirty Day Field
Experiment of Water Deliveries to Northeast Shark River Slough (April-
May 1984). Technical Report, South Florida Water Management District,
West Palm Beach, Florida.
MacVicar, T. K., T. VanLent and A. Castro. 1983. South Florida Water
Management Model - Documentation Report. Technical Report South
Florida Water Management District, West Palm Beach, Florida.
Mandelbrot, B. 1983. The Fractal Geometry of Nature. W. H. Freeman and
Company, New York, New York
Manning, R. 1890. Flow of water in open channels and pipes. Trans. Inst. Civil
Engrs. (Ireland).
McClanahan, T. R. and H. T. Odum. 1991. Infrared Reflectance and water
budgets of vegetation in reclamation after phosphate mining. Florida
Institute of Phosphate Research, and Center for Wetlands, University of
Florida.
Milne, B., T. 1988. Measuring the fractal geometry of landscapes. Applied Math,
and Computation 27:67-79.

233
Morse, D. R., J. H. Lawton and M. M. Dodson 1985 Fractal dimension of
vegetation and the distribution of arthropod body lengths. Nature
314:731-733.
Neidrauer, C. J. and R. M. Cooper. 1988. A Two-Year Field Test of the Rainfall
Plan. South Florida Water Management District Technical Publication 88-
2. West Palm Beach, Florida.
Nunez Cabeza de Vaca, Alvar. 1514. Observations on the Americas. Rio Grande
Press, Chicago, Illinois.
O'Neill, R. V., D. L. DeAngelis, J. B. Waide and T. F. H. Allen. 1986. A
Hierarchical Concept of Ecosystems. Monographs in Population Biology,
23, R. H. May,editor. Princeton University Press, Princeton, New Jersey.
Odum, H. T. 1983. Systems Ecology: An Introduction. John Wiley and Sons,
New York.
Odum, H. T. 1984. Cypress Swamps and their regional role, in Cypress Swamps,
K. C. Ewel and H. T. Odum, editors. University Presses of Florida,
Gainesville, Florida.
Ogden, J. C. 1978. Recent Population Trends of Colonial Wading Birds on the
Atlantic and Gulf Coastal Plains. In: Wading Birds Sprunt, Ogden and
Winckler, editors, Research Report No. 7, National Audubon Society, New
York, New York
Ogden, J. C, D. A. McCrimmon, G.T. Bancroft, B.W. Patty. 1987. Breeding
populations of the wood stork in the southeastern US. Condor 89:752-759.
Olmsted, I. C., L. L. Loope and R. E. Rintz. 1980. A Survey and Baseline Analysis
of Aspects of the Vegetation of Taylor Slough, Everglades National Park.
Report T-586. U.S. Department of Interior, National Park Service, South
Florida Research Center, Homestead, Florida
Palmer, V. J. 1945. A method for designing vegetated waterways. Agricultural
Engineering 26 (12):516-520.
Pardue, L., J. Freeling, L.J. Greenfield, P. T. Gannon, Sr. 1982. Who Knows the
Rain? Nature and Origin of Rainfall in South Florida. Friends of the
Everglades, Coconut Grove, Florida.
Parker, G. G. 1984. Hydrology of the pre-drainage system of the Everglades in
Southern Florida, in Environments of South Florida: Present and Past II, P.
J. Gleason, editor. Miami Geological Society. Coral Gables, Florida.

234
Parker, G. G. and C. W. Cooke. 1944. Late Cenozoic Geology of Southern
Florida, with a Discussion of the Ground Water. Report of the Florida
Geological Survey, Tallahassee, Florida
Parker, G. G., G. E. Ferguson and S. K. Love. 1955. Water Resources of
Southeastern Florida with Special Reference to Geology and Groundwater
of the Miami Area. US Geological Survey, Washington, D.C.
Parker, G. G., G. E. Ferguson, and S.K. Love. 1944. Interim Report on the
Investigations of Water Resources in Southeastern Florida with Special
Reference to the Miami Area in Dade County, Florida. Florida Geological
Survey Report of Investigation 439, Florida Geological Survey,
Tallahassee, Florida
Penman, H. L. 1948. Natural evaporation from open water, bare soil, and grass.
Proceedings Royal Society of London 193:120-146.
Perkins, W. A. and T. K. MacVicar. In prep. A computer model to simulate
natural south Florida hydrology, in The Everglades, Spatial and Temporal
Patterns as Guidelines for Ecosystem Restoration, S. Davis and J.C. Ogden,
editors.
Petryk, S. and G. Bosmajian. 1975. Analysis of flow through vegetation. Journal
Hydraulic. Division, ASCE 101:871-884.
Petuch, E. J. 1985. An Eocene Asteroid Impact in Southern Florida and the
Origin of the Everglades. Geological Society of America, 98th Annual
Meeting, Orlando, Florida, November 28-31,17(7):688,
Petuch, E. J. 1987. The Florida Everglades: A buried psuedoatoll? Journal of
Coastal Research 9:189-200,
Powell, G. V. N j R. D. Bjork, J. C. Ogden, R. T. Paul, A. H. Powell and W. B.
Robertson. 1989. Population trends in some Florida Bay wading birds.
Wilson Bulletin 101:436-457.
Rasmussen, E. M. 1985. El Niño and variations in climate. American Scientist
73:168-177.
Ree, W. O. 1949. Hydraulic characteristics of vegetation for vegetated
waterways. Agricultural Engineering 30:184-187.
Richardson, L. F. 1961. The problem of contiguity: An appendix of statistics of
deadly quarrels. General Systems Yearbook 6:139-187.

235
Richardson, J. R., W.L. Bryant, W.M. Kitchens, J.E. Mattson, and K.R. Pope. 1990.
An evaluation of refuge habitats, and relationships to water quality,
quantity and hydroperiod. Florida Cooperative Fish and Wildlife Unit,
University of Florida, Gainesville, Florida.
Robbin, D. M. 1984. A new holocene sea level curve for the Upper Florida Keys
and Florida Reef Tract, pages 437-458, in. Environments of South Florida:
Present and Past II, P.J. Gleason, editor. Miami Geological Society, Coral
Gables, Florida,
Robertson, W. B., Jr. 1954. Everglades Fires - past, present and future.
Everglades Natural History Magazine. 3:11-16.
Robertson, W. B., Jr. 1955. An Analysis of the Breeding-Bird Population of
Tropical Florida in Relation to the Vegetation. University of Illinois,
Urbana. PhD Thesis.
Robertson, W. B., Jr. and J. A. Kushlan. 1984. The Southern Florida Avifauna,
pages 219-257, in Environments of South Florida: Present And Past:
Memoir II, P. J. Gleason, ed. Miami Geological Society. Coral Gables,
Florida.
Ropelewski, C. F. and M. S. Halpert. 1987. Global and regional scale
precipitation patterns associated with the El Nino/Southern Oscillation.
Monthly Weather Review 115:1606-1626.
Rosendahl, P. C. 1981. Determination of Manning's Roughness and
Longitudinal Dispersion Coefficients in the Everglades Marsh.
Proceedings of Symposium on Progress in Wetlands Utilization and
Management, June 1981, Orlando, Florida.
Rosendahl, P. C. and R. J. Probst. 1980. Freshwater Flow Determination Within
the Shark River Slough, Everglades National Park. Proceedings of 2nd
Conference on Scientific Research in the National Parks, J. Gouge, Editor,
San Francisco, California.
Rosendahl, P. C. and P. W. Rose. 1981. Freshwater Flow Rates and Distribution
Within the Everglades Marsh. Proceedings of National Symposium on
Freshwater Inflow To Estuaries, San Antonio, Texas, October 9-11, 1980;
Fish & Wildlife Service, Office Of Biological Services Report FWS/OBS-
81/04.
SAS. 1990. SAS-PC Users Guide. SAS Institute, North Carolina.
Shih, S. F. 1981. Evapotranspiration as related to climatic factors in southern
Florida. Florida Scientist. 44:109-118.

236
Shih, S. F. 1983. Soil surface evaporation and water table depths. Journal of
Irrigation and Drainage Engineering 109 (4):366-367.
Shih, S. F., L. H. Allen, L. C. Hammond, J. W. Jones, J. S. Rogers and A. G.
Smajstrla. 1983. Basin water requirement estimation in southern Florida.
Transactions of the ASAE 26 (3):760-766.
Shih, S. F. and G. S. Rahi. 1982. Seasonal variations of Mannings roughness
coefficient in a subtropical marsh. Transactions of the ASAE 25 (1):116-
119.
Silverman, B. W. 1986. Density Estimation for Statistics and Data Analysis.
Monographs on Statistics and Applied Probability, D. R. Cox, D.V.
Hinckley, D. Rubin and B.W. Silverman, editors. Chapman and Hall,
London.
Smith, B. 1848. Report on Reconnaissance of the Everglades. Report Made to the
Secretary of the Treasury, Washington D.C.
Smith, T. J., Ill, H. Hudson, G. V. N. Powell, M. B. Robblee and P. J. Isdale. 1989.
Freshwater flow from the Everglades to Florida Bay: An historical
reconstruction based on fluorescent banding in the coral Solenastrea
bournorti. Bulletin Marine Science 44:274-282.
Steele, J. H. 1985. A comparison of terrestrial and marine svstems. Nature
313:355-358.
Stephens, J. C. and E. H. Stewart. 1963. A comparison of procedures for
computing evaporation and evapotranspiration. I.A.S.H. Committe for
Evaporation. Florida Agricultural Experiment Station.
Stewart, E. H. and W. C. Mills. 1967. Effect of depth to water table and plant
density on evapotranspiration rate in southern Florida. Transactions of
the ASAE 10:746-747.
Swift, D. R. 1984. Periphyton and Water Quality Relationships in the Everglades
Water Conservation Areas Florida USA. pages 97-117, in Environments
of South Florida: Present and Past II, P. J. Gleason,ed. Miami Geological
Society. Coral Gables, Florida.
Taylor, D. L. 1980. Summary of Fires in Everglades National Park and Big
Cypress National Preserve, 1979. Technical Report, US Department of
Interior, National Park Service, South Florida Research Center,
Homestead, Florida.

237
Thomas, T. M. 1970. A Detailed Analysis of Climatological and Hydrological
Records of South Florida with Reference to Man's Influence Upon
Ecosystem Evolution. University of Miami, Coral Gables, Florida.
U. S. Department of Commerce. 1990. Census of Population, 1990. Census
Bureau, Washington, D.C.
U. S. Army Corps Engineers. 1954. Central and Southern Florida Project, Part
VI; General studies and reports, Interim report on evaluation of Mannings
"n" in vegetated areas. Jacksonville, Florida.
U. S. Army Corps of Engineers. 1968. Water Resources for Central and Southern
Florida. US Army Corps of Engineers, Survey Review Report.
Viessman, W., G. L. Lewis and J. W. Knapp. 1989. Introduction to Hydrology.
Harper and Row, New York, New York.
Vignoles, C. B. 1823. Observations upon Floridas. Bliss and E.White, New York,
New York.
Wade, D. D., J. J. Ewel and R. Hofstetter 1980. Fire in South Florida Ecosystems.
US Department of Agriculture, Forest Service, General Technical Report
SE-17, SE Forest Experimental Station, Asheville, North Carolina.
Wagner, J. I. and P. C. Rosendahl. 1982. Structure S-12 Water Distribution to
Everglades National Park. Report T-650. US Department of Interior,
National Park Service, South Florida Research Center, Homestead,
Florida.
Wagner, J. I. and P. C. Rosendahl. 1985. History and Development of Water
Delivery Schedules for Everglades National Park Through 1982. Mimeo
Report. US Department of Interior, National Park Service, South Florida
Research Center, Homestead, Florida.
Walters, C. J. 1986. Adaptive Management of Renewable Resources. McGraw
Hill, New York, New York.
Walters, C. J., L. H. Gunderson and C. S. Holling. 1992. Experimental policies for
water management in the Everglades. Ecological Applications 2(2):189-
202.
Walters, C. J. and C. S. Holling. 1990. Large scale management experiments and
learning by doing. Ecology 71(6):2060-2068.
Willoughby, H. L. 1898. Across the Everglades. Philadelphia, Pennsylvania.

238
Woodall, S. 1980. Evapotranspiration and Melaleuca. Proceedings of Melaleuca
Symposium, Ft. Myers, Florida, Florida Division of Forestry, Tallahassee,
Florida.
Worth, D. 1987. Environmental Responses of Water Conservation Area 2A to
Reduction in Regulation Schedule and Marsh Drawdown. Technical
Report, South Florida Water Management District, West Palm Beach,
Florida.
Yates, S. 1982. Florida's broken rain machine. Amicus Journal 4(2):48.

BIOGRAPHICAL SKETCH
Lance Gunderson was born in Miami, Florida, on 7 December 1952. He
attended public schools in Fort Myers, Florida and, received both bachelor and
master’s degrees from the University of Florida, majoring in botany. Upon
completion of the master's degree, he worked for National Audubon Society for a
year as a research associate. He was then hired as a botanist for the National
Park Service from 1979 through 1991, working in both the Big Cypress National
Preserve and Everglades National Park. In 1988, he returned to the University of
Florida to pursue a doctoral degree in environmental engineering sciences.
239

I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctar-eiPhilosopl
íseph J. Delfino, ^airman
''Professor of Enviromental
Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy,
C.S. Holling, Cochaijmtan
Arthur R. Marshall, Jr., Professor
of Ecological Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philqsophy.
Warren Viessman
Professor of Enviromental
Engineering Sciences
I certify that I have read this study and that in my opinion it conforms to
acceptable standards of scholarly presentation and is fully adequate, in scope and
quality, as a dissertation for the degree of Doctor of Philosophy.
G. Ronnie Best
Scientist of Enviromental
Engineering Sciences
I certify that I have read this study and that in my opinion it coni
acceptable standards of scholarly presenJatkrcrancUs fully adequa
quality, as a dissertation for the degree of Doctor of Philosoph
is to
scope
Daniel P. Spangler^
Associate Professor of1
iology

This dissertation was submitted to the Graduate Faculty of the College of
Engineering and to the Graduate School and was accepted as partial fulfillment
of the requirements for the degree of Doctor of Phüj
December 1992
^ Winfred M. Phillips
Dean, College of Engineering
Madelyn M. Lockhart
Dean, Graduate School