U.S. Department of the Interior

U.S. Geological Survey

Prepared as part of the U.S. Geological Survey Greater Everglades Priority Ecosystem Science

Hydrologic Record Extension of Water-Level Data in the 

Everglades Depth Estimation Network (EDEN), 1991–99

Scientific Investigations Report 2014–5226
Cover Design: Bar chart showing the number of Everglades Depth

Estimation Network (EDEN) stations in operation (fig. 6 in report) and 

data types for the 237 stations used in the study from 1990 to 2010 

(fig. 7 in report).

Predawn at Arthur R. Marshall Loxahatchee Wildlife Refuge, Boyton 

Beach, Florida, background image used courtesy of Charles O. Slavens.
Hydrologic Record Extension of WaterLevel Data in the Everglades Depth 

Estimation Network (EDEN), 1991−99

By Paul A. Conrads, Matthew D. Petkewich, Andrew M. O’Reilly, and 

Pamela A. Telis

Prepared as part of the U.S. Geological Survey Greater Everglades Priority 

Ecosystem Science

Scientific Investigations Report 2014–5226

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2014

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Conrads, P.A., Petkewich, M.D., O’Reilly, A.M., and Telis, P.A., 2014, Hydrologic record extension of water-level 

data in the Everglades Depth Estimation Network (EDEN), 1991–99: U.S. Geological Survey Scientific 

Investigations Report 2014–5226, 27 p., http://dx.doi.org/10.3133/sir20145226.

ISSN 2328-0328 (online)
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................6

Description of Study Area ...................................................................................................................6

Data-Collection Network.....................................................................................................................8

Previous Studies ...................................................................................................................................8

Approach................................................................................................................................................8

Limitation of the Datasets..................................................................................................................11

Estimating Water Levels .............................................................................................................................11

Time-Series Cluster Analysis............................................................................................................13

Empirical Estimation Models ............................................................................................................15

Linear Regression Models.................................................................................................................15

Artificial Neural Network Models....................................................................................................16

Decorrelation of Input Variables ......................................................................................................17

Statistical Measures of Water-Level Estimation Model Prediction Accuracy ........................18

Shifting Water-Level Estimates ........................................................................................................20

Evaluation of Hindcasts using Modeled Water-Level Surfaces ..........................................................21

Summary........................................................................................................................................................25

References Cited..........................................................................................................................................26

Figures

1–3. Maps showing: 

 1. Location of the water-level stations used in the Everglades Depth Estimation 

Network surface-water model to hindcast water surfaces...........................................3

 2. Example of the Everglades Depth Estimation Network water-surface 

map for a wet season day and a dry season day.............................................................4

 3. Location of the 106 stations in the Everglades Depth Estimation Network 

that were operating in 1990. ................................................................................................5

4. Vegetation map of southern Florida circa 1943 .......................................................................7

5. Plot showing an example of hindcasting a short-term dataset to a longer term 

dataset............................................................................................................................................9

6. Bar chart showing the number of Everglades Depth Estimation Network 

stations in operation for the years 1990 to 2010. ...................................................................10

7. Timeline from 1990 to 2010 showing data types for the 237 stations used in 

 the study......................................................................................................................................12

8. Map showing the time-series cluster analysis results for Water Conservation 

Area 3A ........................................................................................................................................14

9. Plot showing the 7-day average water levels for the Group 1, Group 2, and Group 3 

gages in Water Conservation Area 3A South for the period January 1, 2006 to 

December 31, 2009......................................................................................................................15

10. Multilayer perceptron artificial neural network architecture.............................................17
iv

11. Schematic showing the decorrelation of water levels for SITE_64, SITE_65, 

and SITE_69W.............................................................................................................................18

12. Graph showing frequency distribution of percent model error of the water-level 

estimation models.......................................................................................................................20

13. Graph showing example of measured, estimated, and shifted estimated data at 

NP46 over the period June 1993 to March 1994 ....................................................................21

14. Map showing example of 2-centimeter contour water-surface elevation maps 

for high-water conditions on September 26, 1995 used to evaluate the preliminary

hindcasted data ..........................................................................................................................23

15. Graph showing measured data for SITE_17 and hindcasted water-level data for 

EDEN_11, WC2AN1, and WC2AS1 for preliminary water-level estimation models 

and final water-level estimation models.................................................................................24

16. Map showing example of water-surface elevation maps for high water conditions 

using hindcasted data for September 26, 1995 and measured data for 

October 2, 2008............................................................................................................................25

Tables (Tables 1 and 3 are available at http://pubs.usgs.gov/sir/2014/5226/)

1. Everglades Depth Estimation Network station, map label number, type of station,

operating agency, location, and data estimation sorted by area........Microsoft Excel file

2. The number of stations by conservation area in the Everglades Depth Estimation 

Network Surface Water Model Version 2 in 1990 and 2000 ................................................10

3. Everglades Depth Estimation Network station, map label number, type of 

model, and input variables sorted by area ..............................................Microsoft Excel file

4. Summary of the performance statistics for the training and testing ANN models .........19

5. Minimum, median, and maximum values for the summary statistics for 

237 water-level estimation models ..........................................................................................20

Appendixes 1–2 (available at http://pubs.usgs.gov/sir/2014/5226/)

1–1. Input variables and description used in the water-level models.........Microsoft Excel file

1–2. Everglades Depth Estimation Network station, map label number, type

 of station, type of model, and model performance statistics for the 

water-level estimation models sorted by area .......................................Microsoft Excel file
v

SI to Inch/Pound

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch (in.)

millimeter (mm) 0.03937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) 0.6214 mile (mi)

Area

square meter (m2) 10.76 square foot (ft2) 

square kilometer (km2) 0.3861 square mile (mi2)

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the vertical datum.

Abbreviations

ADAM Automated Data Assurance and Management

ANN artificial neural network

BCNP Big Cypress National Preserve

BEP back error propagation

CERP Comprehensive Everglades Restoration Plan

EDEN Everglades Depth Estimation Network

EDENapps Everglades Depth Estimation Network applications

ENP Everglades National Park

GUI graphical user interface

HLN hidden layer neuron

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.5400 centimeter (cm)

foot (ft) 0.3048 meter (m).

mile (mi) 1.609 kilometer (km)

Hydraulic gradient

inch per mile (in/mi) 1.5783 centimeters per kilometer (cm/km)

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Area

square mile (mi2) 2.590 square kilometer (km2)
vi

ME mean error

MLP multilayer perceptron

MSE mean square error

NAVD 88 North American Vertical Datum of 1988

OLS ordinary least squares 

PME percent model error

R Pearson correlation coefficient

R2 coefficient of determination

RMSE root mean square error

SFWMD South Florida Water Management District

SISO Single Input Single Output

SOFIA South Florida Information Access

USGS U.S. Geological Survey

V2 EDEN Surface-Water Model Version 2

WCA Water Conservation Area

WL water level

Abstract

The real-time Everglades Depth Estimation Network 

(EDEN) has been established to support a variety of 

scientific and water management purposes. The expansiveness of the Everglades, limited number of gaging stations, 

and extreme sensitivity of the ecosystem to small changes 

in water depth have created a need for accurate water-level 

and water-depth maps. The EDEN water-surface elevation 

model uses data from approximately 240 gages in the 

Everglades to create daily continuous interpolations of the 

water-surface elevation and water depth for the freshwater 

portion of the Everglades from 2000 to the present (2014). 

These maps provide hydrologic data previously unavailable 

for assessing biological and ecological studies.

 Ecologists working in the Everglades expressed a 

need to the EDEN project team for daily EDEN water-level 

surfaces from 1990 to 1999. The additional 10 years of 

surfaces will provide ecologists and resource managers 

with two decades (1991–2011) of surfaces to analyze 

hydrologic dynamics. Before 2000, many of the EDEN 

gages used to generate water surfaces were not in operation. These datasets were extended to provide estimations 

of hydrologic time-series histories. The general approach to 

the record extension (hindcasts) was to (1) create a database 

of available data from 1990 to the present; (2) use dynamic 

cluster analysis to group stations with similar hydrologic 

behaviors for subareas of the Everglades with a large 

number of stations; (3) use results from the cluster analysis 

to select candidate explanatory variables; (4) develop linear 

regression or artificial neural network models to extend 

water-level records; and (5) evaluate record extensions 

by using model performance statistics and comparison 

of water-surface maps for similar hydrologic conditions 

for the hindcasted period (1991–99) and measured period 

(2000–11).

To hindcast and fill data records, 214 empirical models 

were developed—189 are linear regression models and 

25 are artificial neural network models. The coefficient 

of determination (R2) for 163 of the models is greater 

than 0.80 and the median percent model error (root mean 

square error divided by the range of the measured data) 

Hydrologic Record Extension of Water-Level Data in the 

Everglades Depth Estimation Network (EDEN), 1991–99

By Paul A. Conrads, Matthew D. Petkewich, Andrew M. O’Reilly, and Pamela A. Telis

is 5 percent. To evaluate the performance of the hindcast 

models as a group, contour maps of modeled water-level 

surfaces at 2-centimeter (cm) intervals were generated 

using the hindcasted data. The 2-cm contour maps were 

examined for selected days to verify that water surfaces 

from the EDEN model are consistent with the input data. 

The biweekly 2-cm contour maps did show a higher number 

of issues during days in 1990 as compared to days after 

1990. May 1990 had the lowest water levels in the Everglades of the 21-year dataset used for the hindcasting study. 

To hindcast these record low conditions in 1990, many of 

the hindcast models would require large extrapolations 

beyond the range of the predictive quality of the models. 

For these reasons, it was decided to limit the hindcasted 

data to the period January 1, 1991, to December 31, 1999. 

Overall, the hindcasted and gap-filled data are assumed to 

provide reasonable estimates of station-specific water-level 

data for an extended historical period to inform research 

and natural resource management in the Everglades.

Introduction

The Everglades Depth Estimation Network (EDEN) 

project was started to provide scientists working on the restoration of the Everglades with spatially continuous qualityassured and quality-controlled hydrologic data at any point 

within the freshwater part of the Greater Everglades (fig. 1). 

The Everglades Depth Estimation Network is a network of 

real-time water-level gaging stations, an integrated groundelevation model, and a water-surface elevation model that 

originally was designed to provide scientists, engineers, 

and water-resource managers with current water-level and 

water-depth information (2000–14) for the entire freshwater 

portion of the Greater Everglades (Telis, 2005, 2006; Telis 

and others, 2014). The Everglades Depth Estimation Network offers a consistent and documented dataset that can be 

used by scientists and water-resource managers to (1) guide 

large-scale field operations, (2) integrate hydrologic and 

ecological data and analysis, and (3) support biological and 

ecological restoration assessments that measure ecosystem 

responses to the Comprehensive Everglades Restoration 
2 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Plan (CERP; U.S. Army Corps of Engineers, 1999). In 

addition, EDEN, with the integration of real-time data and 

models, provides opportunities for real-time evaluation of 

water-level conditions and water-resource management 

practices.

The expansiveness of the Everglades, limited number 

of gaging stations, and sensitivity of the ecosystem to small 

changes in water depth have created a need for accurate 

water-level and water-depth maps (Pearlstine and others, 

2007). To create daily water-level surfaces for the 

Everglades, EDEN integrates data from a network of 

more than 250 water-level gages maintained by multiple 

agencies, including Big Cypress National Preserve (BCNP), 

Everglades National Park (ENP), South Florida Water 

Management District (SFWMD), and U.S. Geological 

Survey (USGS) (fig. 1). The EDEN surface-water model 

(Telis and others, 2014) generates daily water-level surfaces 

gridded to 400-square-meter cells for January 1, 2000, to 

the present (2014) by using the EDEN grid developed by 

Jones and Price (2007a). Examples of the daily water-level 

elevation are shown in figure 2. When these water-level 

surfaces are combined with EDEN’s digital elevation 

model for ground surface (Jones and Price, 2007b; Jones 

and others, 2012; Xie and others, 2011), daily surfaces of 

water depth can be generated. To assist users in applying 

the EDEN datasets to their needs, a series of tools, or 

applications (EDENapps), were developed to view, extract, 

plot, and manipulate EDEN data to create other derived 

hydrologic data (Telis and Henkel, 2009).

Scientists using EDEN data requested that daily EDEN 

water surfaces be created from 1990 to 2000, a period 

that did not previously have any surfaces. The extended 

period of hydrologic record would provide a longer time 

period for ecologists and scientists to evaluate the relation 

between hydrologic changes and ecological response, and 

ultimately, assist local, State, and Federal agencies in their 

efforts to restore the Everglades ecosystem. Unfortunately, 

before 2000, fewer EDEN gages used to generate water 

surfaces were in operation (fig. 3). To be able to generate 

water-surface maps for 1990 to 1999, water-level data for 

the EDEN stations that were not in operation needed to be 

extended back to 1990.
Introduction 3

Florida City

Canal

South New River Canal

Snapper

Creek Canal

Tamiami

Canal

L-2 Canal

Watson River

BROWARD

MIAMI-DADE

MONROE

PALM

BEACH

HENDRY

COLLIER

81°30' 81° 80°30'

26°30'

25°30'

25°

L-40 Canal

Base from Esri® data and maps, 2010 0 5 10 15 20 MILES

U.S. Geological Survey Everglades Depth Estimation Network, 2011

Universal Transverse Mercator projection, zone 17

"

"

"

"

"

"

"

"

"

"

"

"

"

"

""

"

"

"

"

"

"

"

"

"

""

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

""

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

!

!

!

!

!! !!

!

!

!

!

! !

!

!

!

!

!

!!

! ! !

!

!

!

!

!

!

! !

!

!

!

!

!

! ! !

!

!

!

!

!

!

! !

!

!

!

!!

! !

!

!

!

!

!

!

!!

!

!

#

#

# #

# # #

# #

# #

#

#

# #

# #

#

#

# #

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

#

# #

#

#

#

# #

#

#

# #

##

#

#

#

!

!

!

! !

!

!

!

!

!

!

!

! !

!

! !

!

!

0 5 10 15 20 KILOMETERS

GULF OF MEXICO

Lake Okeechobee

Florida Bay

WCA1

88

11

29

76

EXPLANATION

EDEN water-level gaging stations by operation agency

and index number (table 1)

! Big Cypress National Preserve 

Everglades National Park 

South Florida Water Management District 

U.S. Geological Survey

#

!

"

National park, National Preserve, and Water

 Conservation Areas (WCA) and name

EDEN model domain

WCA1

BIG CYPRESS

NATIONAL

PRESERVE

EVERGLADES

NATIONAL

PARK

WCA2A

WCA2B

WCA3A

WCA3B Pennsuco

wetlands

26°

229

1

2

3

4

5

6 7

8

9

10

11

12

13

14

15

16

17

18 19

20

21

22

23

24

25 26 27 28

29

30 31

32

33

34

35

36

38 37

39 40 41

42 43

44

45

46

47

48

49

50

51

52

53

54

55

56 57

58

59

60

61

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97 98

99

100

101

102 103

104

105

106

107

108

109

110

111

112

113

114 115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

134 133 135

136

137

138

139

140

141

142

143

144

145

146

147

148 149

150

151

152

153 154 155

156

157 158

159

160

161

162

163

164 165

166

167

168

169 170

171

172 173 174 175

176

177

179

180

181

182

183

184

185

186

187

188

189

190

191

192 193

194

195

196

197 198

199

200

201

202

203

204

205

206

207

208 209

210

211

212

213

214

215

216 217

218

219

220

221 222

223

224

L-67 Canal

225

226

229

230

233

234

235

236

237

Hillsboro

Bolles Canal

Canal

Area shown

GULF

OF

MEXICO

FLORIDA

ALABAMA GEORGIA

62

63

64

65 66

227 228

231

232

Area enlarged

to show labels

"

"

"

"

"

!

!

!!

Figure 1. Location of the water-level stations used in the Everglades Depth Estimation Network (EDEN) surface-water 

model to hindcast water surfaces
4 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

BROWARD

MIAMI-DADE

MONROE

PALM

BEACH

HENDRY

COLLIER

BROWARD

MIAMI-DADE

MONROE

PALM

BEACH

HENDRY

COLLIER

81°30' 81° 80°30'

26°30'

25°30'

25°

26°30'

25°30'

25°

81°30' 81° 80°30'

L-40 Canal

Base from Esri® Data & Maps, 2010 0 5 10 15 20 MILES

U.S. Geological Survey Everglades Depth Estimation Network, 2011

Universal Transverse Mercator projection, zone 17

EXPLANATION

Water-surface elevation,

in centimeters

High : 470

Low : –65

Canal/stream

A. November 1, 2011 B. April 30, 2011

0 5 10 15 20 KILOMETERS

GULF

OF MEXICO

Florida Bay

GULF

OF MEXICO

Florida Bay

26° 26°

Figure 2. Example of the Everglades Depth Estimation Network (EDEN) water-surface map for A, a wet season day and

B, a dry season day
Introduction 5

Florida City

Canal

South New River Canal

Snapper

Creek Canal

Tamiami

Canal

L-2 Canal

Watson River

BROWARD

MIAMI-DADE

MONROE

PALM

BEACH

HENDRY

COLLIER

LEE

81°30' 81° 80°30'

26°30'

25°30'

25°

L-40 Canal

Base from Esri® data and maps, 2010 0 5 10 15 20 MILES

U.S. Geological Survey Everglades Depth Estimation Network, 2011

Universal Transverse Mercator projection, zone 17

"

"

"

"

"

"

"

"

""

"

"

"

"

"

"

"

"

"

"

"

""

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

!

!! !!

!

! !

!

!

!

!

!

!

!

!

!

!

!

!

! !

!

!

!!

!

!

!

!

!

!

!

!

!

#

# # #

#

#

# #

#

#

#

#

#

#

#

#

#

#

#

#

#

# #

#

#

#

# #

#

#

# #

#

#

!

!

!

0 5 10 15 20 KILOMETERS

GULF OF MEXICO

Lake Okeechobee

Florida Bay

WCA1

88

11

29

76

EXPLANATION

EDEN water-level stations by operating agency

and index number (table 1)

! Big Cypress National Preserve 

# Everglades National Park

! South Florida Water Management District 

"

U.S. Geological Survey

EDEN model domain

National Park, National Preserve, and

 Water Conservation Areas (WCA)

 and name

WCA1

BIG CYPRESS

NATIONAL

PRESERVE

EVERGLADES

NATIONAL

PARK

WCA2A

WCA2B

WCA3A

WCA3B Pennsuco

Wetlands

26°

10

11

12

23

24

25 26 27

29

34

36

40 39

41

44

49

50

51

52

56 57

58

60

61

70

76

77

78

79

81

82

83

84

85

86

87

88

89

90

91

96

97 98

99

100

101

102

103

104

105

106

107

108 109

110

112

113

121

122

125

126

134 133 135

136

137

138

139

140

143

147

148 149

150

151

152

156

157

167 158

176 180

181

182

183 184

185

186

187

189 191

197 193 198

199

200

201

202

203 204

205

206

207

208

210

211

212

215

216 217

218

219 221

225

231

232

233

236

Hillsboro

Bolles Canal

Canal

L-67 Canal

Figure 3. Location of the 106 stations in the Everglades Depth Estimation Network (EDEN) that were operating in 1990.
6 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Purpose and Scope 

This report documents the water-level record extensions 

(hindcasts) of 237 stations in the freshwater portion of the 

Everglades. The geographical extent of the hindcasts includes 

gaging stations in Water Conservation Area (WCA) 1, 

WCA2A, WCA2B, WCA3A, WCA3B, Pennsuco Wetlands, 

BCNP, and the ENP (fig. 1). An important part of the USGS 

mission is to provide scientific information for the effective 

water-resources management of the Nation. To assess the 

quantity and quality of the Nation’s surface water, the USGS 

collects hydrologic and water-quality data from rivers, lakes, 

estuaries, and wetlands using standardized methods, and 

maintains the data from these stations in a national database. 

One of the critical directions outlined in the USGS science 

strategy for 2007–17 (U.S. Geological Survey, 2007) is to 

provide scientific information for understanding ecosystems 

and predicting ecosystem change. To study the causes and 

consequences of ecological change, the USGS collects 

hydrological, biological, and other data using standardized 

methods, and interprets these data for policymakers to indicate 

how changes will potentially affect natural resources and the 

public. The techniques presented in this report demonstrate 

how valuable information can be extracted from existing 

USGS databases, integrated with other agencies’ data networks, and extended back in time (hindcasted) to evaluate the 

linkage between hydrology and ecological response. 

Description of Study Area 

The Everglades is a vast wetland consisting of 

approximately 2.9 million acres covering much of southern 

Florida. The Everglades primarily consists of peat soils and 

tall sawgrass that are interspersed with slightly raised tree 

islands covered by shrubs and woody vegetation (McPherson 

and others, 1995). Historically, the Everglades was an uninterrupted wetland that extended from Lake Okeechobee and 

flowed to the southwestern tip of Florida (fig. 4; Richardson 

and others, 1990). The annual rainfall in the Everglades 

generally is between 50 and 60 inches (in.), depending on 

location, with substantially more rainfall along the eastern 

edge (Lodge, 1994). The rainfall has a distinct seasonal pattern, with a wet season from May or June through September 

or October that accounts for about 75 percent of the annual 

total. Water depths in the freshwater marshes range from 0 to 3 

feet (ft) during the wet season. During the annual wet season, 

water levels rise and inundate most of the land, producing 

seasonal flows into the Florida Bay and the Gulf of Mexico 

(fig. 1). Heavy rainfall associated with tropical depressions, 

storms, and hurricanes have a large effect on water levels. A 

single such event can increase water levels by 1 ft or more 

over large parts of the Everglades, and because of the slow 

runoff rates, this can effect water levels for months (German, 

2000). Minimum seasonal water levels generally happen in 

May before the onset of the wet season. In contrast, during the 

dry season, water levels decline to near land surface (McPherson and others, 1995). In particularly dry years, large portions 

of the Everglades may become dry and are subject to wildfires. 

This hydrologic pattern of wet and dry seasons helped produce 

and sustain the unique ecosystem of the Everglades.

The Everglades contains several types of environments, 

including freshwater marshes, tree islands, pinelands, mangrove swamps, and shallow coastal marine waters. The EDEN 

project is concerned with freshwater marshes, the predominant 

Everglades ecosystem. These marshes are characterized by 

sawgrass stands of varying density and height, ranging from 

2 to 3 ft above land surface to 9 ft in some northern areas. 

Other common emergent plants in the freshwater marshes 

include spike rush, muhly grass, and, in some areas, cattails. 

Typical topographic and vegetative features include ridge and 

slough, tree islands, wet prairie, sawgrass, and marl prairie 

(German, 2000).

From the mid-1800s to the late 1900s, the flow patterns, and thus the ecosystem, of the Everglades have been 

substantially altered. Beginning in the mid-1800s, wetlands 

began to be drained and used for agricultural purposes and 

urban development such that by the early 1990s, about 

50 percent of the historic Everglades had been drained 

(McPherson and others, 1995). With population growth and 

increased agricultural production, flood mitigation and water 

use in South Florida became prominent concerns. To address 

those concerns, WCA1, WCA2, and WCA3 (fig. 1) were 

constructed by the U.S. Army Corps of Engineers in the 1940s 

with the goal of regulating water through an extensive series 

of levees and canals. In general, the WCAs store water during 

the wet season and supply water during the dry season. The 

combined effect of drained wetlands and water regulation 

introduced during the 1800s and 1900s diverts an estimated 40 

percent of the water originally flowing through the Everglades 

(McPherson and others, 1995). The substantial changes in land 

use and flow patterns within the Everglades have had adverse 

environmental effects on the hydrology, water quality, and 

native plant and animal communities (McPherson and others, 

1995). Since the late 1990s, through the collaboration of 

Federal, State, and private agencies, substantial focus has been 

given to mitigate these adverse effects and, where possible, to 

begin restoration of the ecosystem and ecological communities 

of the Everglades.

The study area is the freshwater portion of the greater 

Everglades area, which extends from south of Lake 

Okeechobee to the southern part of the ENP (fig. 1). This area 

is a wetlands system that is about 50 miles (mi) wide and 

about 100 mi long. The Everglades is regarded as unique in 

the world because it is not primarily associated with a natural 

river system but is itself a wide and shallow “river” that 

transports water by sheet flow from Lake Okeechobee to the 

Gulf of Mexico. The land slopes within this shallow “river” 

generally are less than about 0.2 foot per mile (ft/mi; German, 

2000).
Introduction 7

Lake

Okeechobee

Palm

Beach

Fort

Lauderdale

Miami

Ten

Thousand

Islands

Jupiter

Inlet

GULF OF

MEXICO

ATLANTIC

OCEAN

Bay

Florida

FLORIDA

Map

area

Base modified from U.S. Geological Survey State base, 1933

Originally printed 1943, 1:400,000

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

EXPLANATION

General vegetation

Scrub forest

Hammock forest

Bay tree forest

Inland swamp

Cypress forest

Cypress heads or

domes

Pine flatwood forest

High pine forest

Miami Rockland

pine forest

Miami open pine forest

Mangrove swamp

Mangrove swamp and

saltwater marsh

Saltwater marsh

Salt Prairie (Cape Sable area)

Freshwater marsh

(outside of E.)

Wet prairies

Saw palmetto or Dry Prairies

Southern coast marsh prairie

Coastal beach and

dune vegetation 

Saw-grass marsh (medium dense

to sparse) 

Saw-grass marsh (dense)

Saw-grass marsh (with wax-myrtle

thickets) 

Willow and elderberry zone

(mostly cultivated) 

Custard-apple zone (mostly

cultivated) 

Saw-grass marsh (with

abundant ferns and cattails) 

Tree island, bay tree forest

Tree island, hammock forest

Marsh prairie, southern E.

Slough, pond, and lake (with

aquatic plants)

Main Everglades (E.) vegetation

Figure 4. Vegetation map of southern Florida circa 1943 (modified from Davis, 1943).
8 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Data-Collection Network 

The EDEN database (2014) is composed of hourly waterlevel data from 312 gaging stations and includes marsh, river, 

canal, and control structure stations operated by the BCNP, 

ENP, SFWMD, and the USGS in the freshwater and coastal 

waters. Water monitoring networks typically are established 

to meet the mission of the agency, be it regulatory compliance 

requirements, scientific investigation, or other reasons. The 

configuration of networks often changes to meet changing 

agency objectives and funding levels. As with many monitoring networks, the total number of EDEN gages may change 

from year to year because of funding levels, agency mandates, 

and gaging logistics. For any given year, the number of input 

stations used in the EDEN surface-water model may change 

the network configuration. Of the 312 EDEN stations, 237 are 

used in the EDEN Surface-Water Version 2 Model (referred 

to in this report as the “V2 model”; Telis and others, 2014) to 

generate daily water-surface maps for the year 2000 (table 1). 

These 237 stations are the subset of EDEN gages that are used 

to create the hindcasted water-level surfaces for this study. 

The other stations in the EDEN database are used to evaluate 

coastal conditions of the Everglades, estimate missing data for 

the stations in the water-surface model, or are discontinued 

EDEN stations. In this report, the names of the stations follow 

the naming convention used by EDEN and are similar to the 

names used by the agency that maintains the gage. 

Previous Studies 

The EDEN project has used various techniques for 

hindcasting data for stations added to the gaging network to 

provide a concurrent period of water-level data records for the 

water-surface model and for estimating missing data. Soon 

after the initiation of the EDEN project and the development 

of the water-surface model in 2006, 25 real-time water-level 

gaging stations were added to the original EDEN network of 

253 established water-level gaging stations. These stations 

did not have data back to 2000, the original beginning of the 

EDEN database. To incorporate the data from the added stations to the 7-year EDEN database in the greater Everglades, 

the short-term water-level records (generally less than 1 year) 

needed to be hindcasted to be concurrent with data from the 

established gaging stations in the database. Conrads and Roehl 

(2007) used a three-step modeling approach using artificial 

neural network (ANN) models to estimate the water levels at 

the new stations. The ANN models used static variables that 

represent the gaging station location and percent vegetation 

in addition to dynamic variables that represent water-level 

data from the established EDEN gaging stations. The final 

step of the modeling approach was to simulate the computed 

error of the initial estimate to increase the accuracy of the final 

water-level estimate by incorporating the computed error term. 

The three-step modeling approach for estimating water 

levels at the new EDEN gaging stations produced satisfactory 

results. The coefficients of determination (R2) for 21 of the 

25 estimates were greater than 0.95, and all of the estimates 

were greater than 0.82. The model estimates indicated good 

agreement with the measured data. For some new EDEN 

stations with limited measured data, the hindcasts included 

periods beyond the range of the data used to train the ANN 

models. The comparison of the hindcasts with long-term 

water-level data proximal to the new EDEN gaging stations 

indicated that the water-level estimates were reasonable. The 

percent model error (root mean square error divided by the 

range of the measured data) was less than 6 percent, and for 

most of the stations (20 of 25), the percent model error was 

less than 1 percent.

To increase the accuracy of the EDEN daily water-level 

surfaces, water-level estimation equations were developed 

to fill missing data for every EDEN station (Conrads and 

Petkewich, 2009; Petkewich and Conrads; 2013). To minimize 

the inability of estimating data because of missing data for an 

input station, a minimum of three linear regression equations 

were developed for each station using different input stations. 

Of the 667 water-level estimation equations developed to 

fill missing data at 223 stations, more than 72 percent of the 

equations had an R2 greater than 0.90, and 97 percent have an 

R2 greater than 0.70. The estimation equations recently were 

recomputed to accommodate change in the gaging network 

and further understanding of the hydrologic response of the 

system (Petkewich and Conrads, 2013).

Daamen and others (2010) developed the Automated 

Data Assurance and Management (ADAM) software to allow 

quick and accurate quality-assurance review of the EDEN 

data. The ADAM software utilizes user-defined filter settings, 

linear regression equations (documented in Petkewich and 

Conrads, 2013), and multivariate regression equations to 

estimate missing data and quality assure real-time data. The 

automation process is used to efficiently identify erroneous 

data and provide accurate replacement estimates. In addition, 

the tool can be used to manually review previously processed 

results and modify the estimates, if necessary.

Approach 

The general approach for hindcasting water-level data 

back to 1990 is to identify long-term datasets (measured data 

back to 1990) that are correlated to the short-term datasets 

(measured data beginning after 1990). An empirical model is 

developed that uses the long-term dataset for the explanatory 

(input) variable to estimate (hindcast) the short-term dataset 

back to 1990. An example of a hindcasted dataset is shown 

in figure 5. The measured data for station W14 in WCA3A 

(map label 224, fig. 1) began operation on January 25, 2006 

(table 1). To extend the record to 1990, the long-term station 

SITE_64 located to the north (map label 218, fig. 1) was used 

as input to an empirical model (in this case a linear regression 

model) to estimate the water level for W14 for the period 

January 1, 1990, to January 24, 2006. It is important to note 
Introduction 9

12

11

10

9

8

7

6

5

4

Water level, in feet above NAVD 88

SITE_64

W14

W14 hindcast

W14 minimum value

W14 maximum value

W14 hindcast minimum value

W14 hindcast maximum value

Jan. 1990

Jan. 1991

Jan. 1992

Jan. 1993

Jan. 1994

Jan. 1995

Jan. 1996

Jan. 1997

Jan. 1998

Jan. 1999

Jan. 1990

Jan. 2000

Jan. 2001

Jan. 2002

Jan. 2003

Jan. 2004

Jan. 2005

Jan. 2006

Jan. 2007

Jan. 2008

Jan. 2009

Jan. 2010

Jan. 2011

Jan. 2012

Hindcast data Measured data

Figure 5. Plot showing an example of hindcasting a short-term dataset (W14) to a longer term dataset

(W14 Hindcast).

the range of the measured and estimated data. Models, both 

empirical and mechanistic, are more accurate when interpolating 

within the historical range of the data used to develop the model 

(for W14, 7.01 to 10.31 ft, fig. 5) than extrapolating beyond 

the range of the data used to develop the model (for W14 on 

fig. 5., extrapolation below 7.01 ft to 5.03 and above 10.31 ft 

to 11.45 ft). Within the range of measured data, the model is 

interpolating from conditions exhibited in the historical data. 

Models are less reliable when estimating outside of the range of 

the data used to develop the model. Under these conditions, the 

models have to extrapolate to conditions that are not exhibited 

in the data. To make these extrapolations, the model assumes 

that the relation between input and output variables remain 

constant between the measured conditions and the extrapolated 

conditions. The models do not take into account changes in flowregulation schedules or meteorological conditions. Depending 

on the dynamics of the system being modeled, this assumption 

may or may not be valid. For the example of hindcasting site 

W14, the model had to extrapolate a little more than 1 ft for 

high-water conditions and almost 2 ft for low-water conditions. 

Limited extrapolation often is appropriate. In a shallow wetland 

system like the Everglades, high-water extrapolations are not 

as problematic as the low-water extrapolation. During highwater conditions, there is extensive ponding in the WCAs and 

high-water extrapolation probably increases the extent of the 

ponding. During low-water conditions, areas of the Everglades 

can become dry and surface water becomes shallow groundwater 

or discontinuous shallow pools or ponds. Because of microtopographic features, small decreases in surface-water elevations 

may translate to extensive dry areas. As discussed in the “Evaluation of Hindcasts using Modeled Water-Level Surfaces” section 

later in the report, extrapolating to the extreme low-water level in 

May 1990 was not appropriate.

The estimation of water levels for EDEN in previous studies 

relied on the configuration of the water-level station network (fig. 

1), which has fairly even spatial distributions of gaging stations. 

For most of the stations in the network, there are proximal 

stations that are well correlated to generate accurate water-level 

data estimates. The spatial distribution of the EDEN stations in 

1990 (fig. 3) is uneven and there are large areas without a gage. 

In 1990, 106 of the EDEN stations used in the V2 model were 

in operation (table 2 and figs. 3 and 6). From 1990 to 1996, 

that number grew to 177 stations. Between 1997 and 2001, 27 

stations were added to the network, between 2005 and 2006, 

31 stations were added to the network, and two stations in 2009 

(fig. 6). The most significant increases in stations occurred in 

WCA2B and BCNP where there was a 1,100- and 460-percent 

increase in gages, respectively between 1990 and 2000 (table 2).
10 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Table 2. The number of stations by conservation 

area in the Everglade Depth Estimation Network 

(EDEN) Surface Water Model Version 2 in 1990 and 

2000.

Area 1990 2000

Big Cypress National Preserve 7 32

Everglades National Park 47 92

Pennsuco Wetlands 2 6

Water Conservation Area 1 8 12

Water Conservation Area 2A 9 25

Water Conservation Area 2B 1 11

Water Conservation Area 3A 28 48

Water Conservation Area 3B 4 11

Total 106 237

0

50

100

150

200

250

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Number of active EDEN stations

Year

Figure 6. Bar chart showing the number of Everglades Depth Estimation Network (EDEN) stations in operation for the 

years 1990 to 2010.
Estimating Water Levels 11

For this study, hindcasts are considered estimated record 

prior to a gage being in operation and estimates are values to 

fill data gaps in the operational data record. Of the 237 stations 

needed for the EDEN V2 model, only 23 of the stations had 

complete records without any data gaps, 46 stations had data 

gaps to be filled, and 168 stations started after January 1, 1990, 

and were hindcasted (table 1). The approach for hindcasting 

and estimating record is the same for this study. A timeline of 

the 237 EDEN stations for this study that shows each station 

and a color-coded timeline of the data type—measured, 

hindcasted, or estimated—is shown in figure 7. One can 

quickly see the predominance of measured data after 2000 and 

the large number of hindcasted sites in the early 1990s.

The challenge for hindcasting stations back to 1990 

is that EDEN stations that are well correlated with another 

EDEN station may not have been operating in 1990. For 

example, station EDEN_11 in WCA2A (map label 144, fig. 1) 

is estimated in Petkewich and Conrads (2013) by using station 

WC2AS1 (map station label 160), WCA2F1 (map station label 

163), or WCA2F4 (map station label 164). These three stations 

are the highest correlated stations in the current (2014) EDEN 

network. To extend the water-level record for EDEN_11 to 

1990, the available measured data are limited to two marsh 

sites located to the southeast of EDEN_11, stations 2A300 

and SITE_17 (map station labels 143 and 157, respectively, on 

figs. 1 and 3).

Because of the large number of stations to hindcast for 

this study, most of the hindcasts were estimated using linear 

regression models. For sites that had unsatisfactory linear 

regression estimates, ANN models were used. The general 

process to compute hindcasts to 1990 was to complete the 

following steps:

• create a database of available data for each Water 

Conservation Area (WCA), BCNP, ENP, and Pennsuco 

Wetlands from 1990 to the 2012; 

• convert all data to the North American Vertical Datum 

of 1988 (NAVD 88);

• fill data gaps of 3 days or less with linear interpolation;

• for Water Conservation Areas (WCA) with a large 

number of stations, perform time-series cluster analysis 

(Risley and others, 2003; Roehl and others, 2006) to 

group gages with similar hydrologic behaviors; 

• develop linear regression or ANN models to extend 

water-level records; 

• hindcast water-level records and (or) fill periods of 

missing record; 

• apply shifts to the hindcast records, if necessary; and 

• evaluate record extensions with model performance 

statistics and comparison of water-surface maps for 

similar hydrologic conditions from the hindcasted 

period (1990–99) and measured period (2000–12).

A more detailed description of the dynamic cluster 

analysis, linear regression models, ANN models, and the 

application of shifts is presented in the “Estimating Water 

Levels” section of the report.

The preference for input data for a model was to use 

measured data rather than hindcasted or estimated data. The 

models used to hindcast and fill missing data have inherent 

errors and using the results of these models as input for 

another model propagates the error into another dataset. There 

were stations where, because of their location and (or) period 

of missing record, the only reasonable input dataset to develop 

a satisfactory model was a hindcasted or estimated dataset.

Limitation of the Datasets 

As with any modeling effort, the reliability of the model 

is dependent on the completeness of the datasets and on the 

quality of the data and range of measured conditions used for 

developing models. The quality of the hindcast models rely 

on the available period of record and historical range of water 

level in addition to the spatial distribution of long-term input 

stations. There are the usual data limitations of measurement 

accuracy, the physical location of the monitoring station, 

instrumentation error, and human error. The agencies that 

collected the EDEN data all have quality-assurance and 

quality-control plans to minimize the error in their measured 

water-level data. For this study, there are two limitations of 

datasets used for hindcasting the EDEN. The first limitation 

is the poor spatial distribution of the monitoring sites and the 

availability of measured data in particular areas of the Everglades for estimating accurate water levels back to 1990. For 

example, the spatial limitation of available data makes it more 

difficult to estimate water levels in BCNP as compared to ENP 

(fig. 3). The second limitation is the range of the water levels 

measured at a particular site that is used for estimating water 

levels at another site. If the range of data inputs to a model is 

small, the estimation model may have to extrapolate more to 

estimate the full range of water level at the output station and 

there will be less certainty in the extrapolated values.

Estimating Water Levels 

The dynamic variability of the water level at a particular 

location in the Everglades is caused by a combination of 

meteorological factors; for example, rainfall, evapotranspiration, and releases through water-control structures to move 

water through the various conservation areas to ENP. The 

water-level inputs at one location that are used for inputs for 

another location incorporate the localized meteorological 

effects and control structure releases. The water releases 

through control structures are regulated through water delivery 

schedules that are designed to minimize the detrimental 

ecological effects of water releases. There have been three 

Water Delivery Schedule Plans in operation during the study 
12 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Figure 7. Timeline from 1990 to 2010 showing data types for the 237 stations used in the study. (Due to the small size of the rows, station labels are not shown. Stations are in the same order as they are listed in table 1).

EDEN data base flags for 1990–2010

1990

BCNP

ENP

WCA1

WCA2AWCA3BWCA3AWCA3B

Pennsuco

wetlands

1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

MeasuredHindcasted or estimated prior to 2000Estimated after 2000MissingMissing (structure)Big Cypress National PreserveEverglades National ParkWater conservation area and name

BCNP

ENP

WCA1

EXPLANATION
Estimating Water Levels 13

period: the Experimental Program of Water Deliveries to 

ENP (1984–99), The Interim Structural and Operational Plan 

(1999–2002), and the Interim Operational Plan (2002–12) 

(South Florida Natural Resource Center, 2005; U.S. Army 

Corps of Engineers, 2011). Although these Water Delivery 

Schedules have the overall effect of altering the volume and 

timing of flows to ENP, for the purposes of this study it is 

assumed that the changes in the operation schedules do not 

have a substantial effect on the localized water-level relations (correlation) between the nearby input stations used to 

estimate water levels.

Estimation models generally are in one of two categories: deterministic (or mechanistic) or empirical. Deterministic models are created from first-principles equations, 

whereas empirical models are created directly from data 

and adapt generalized mathematical functions to fit a line or 

surface through data from one or more variables. Because 

of the large number of sites to hindcast or fill, sites were 

first estimated with ordinary least squares (OLS) regression 

models. If the estimates were not satisfactory, ANN models 

were developed to improve the accuracy of the models. 

For areas with a large number of stations to fill or hindcast, 

time-series cluster analysis was used to group stations by 

similar hydrologic behavior. These groupings facilitated the 

selection of input (predictor) sites. Below are descriptions 

of the time-series clustering technique, the empirical models 

used in the study, statistical measures of model accuracy, and 

the shifting of estimated water-level data.

Time-Series Cluster Analysis

For areas with a large number of sites, such as the ENP 

and BCNP south of the Tamiami Canal and WCA3A (fig. 1), 

a time-series clustering algorithm was applied to divide sites 

into classes (groups) having similar behaviors (Roehl and 

others, 2006; Stewart and others, 2006; Risley and others, 

2003). Next, the central tendency (low-frequency variability) 

was removed individually for each site by computing the 

difference from a “standard” time series (average of all the 

time-series data for sites in that class), leaving the residuals 

that accentuate differences between signals. Finally, a crosscorrelation matrix (Pearson R) of the residuals was constructed as a measure of the dynamic similarity among sites. 

In the matrix, each cell represented the behavioral similarity 

between the site listed for that row header and that column 

header. The k-means clustering algorithm was applied to 

the cells in the matrix (Weiss and Indurkhya, 1998). For 

k-number of groups, the k-means algorithm optimizes which 

members of the overall group should be in groups 1 through 

k. The optimal number of groups was determined by using 

the root mean square error (RMSE) as a measure of the 

difference in distance between each member and the mean of 

the group. In some cases, the optimal number of groups can 

be selected at the inflection point between a sharp vertical 

decline in RMSE and a horizontal plateau. In other cases, a 

more gradual reduction in RMSE with an increasing number 

of groups happens. 

An example of the time-series clustering is shown 

for 27 sites in WCA3A (fig. 8). The sites were clustered 

into three classes of behaviors (Groups 1–3). The 7-day 

average water level for each group is shown on figure 9. The 

breakout of the three groups generally follows the ground 

elevation gradient with higher water levels to the north and 

lower water levels to the south. Group 1 sites are located in 

the upper region of WCA3A (fig. 8) and have the highest 

average water levels as compared to the other two groups 

(fig. 9). The Group 2 sites are located in the lower region 

near the Tamiami Canal. The Group 3 sites generally are 

located between the Group 1 and 2 sites. The water levels 

for the Group 2 and 3 sites indicate there are often ponding 

conditions at the Group 2 sites that cause the water levels 

to be higher than the Group 3 sites during high-water 

conditions, for example January to March of 2007 and 

2008 (fig. 9). During the dry season, Group 2 and 3 water 

levels are similar, whereas during the height of some wet 

seasons (for example, in October 2006, November 2008, and 

September 2009), the water level for the Group 3 sites is 

higher than the Group 2 sites (fig. 9).

The time-series clustering analysis is valuable for 

selecting candidate input sites for the prediction models. 

The area between two groups indicates that there is a change 

in water-level dynamics and which stations belong to each 

group. For example, 3AS3W1 and EDEN_8 (fig. 8, map 

label 188 and 195, respectively) would make better inputs 

for predicting SITE_65 (fig. 8, map label 219) than W5 

(fig. 8, map label 222) because of their dynamic similarity of 

the sites in Group 3 even though W5, in Group 2, is closer to 

SITE_65. 
14 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Figure 8. Map showing the time-series cluster analysis results for Water Conservation Area 3A.

Florida City

Canal

South New River Canal

Snapper

Creek Canal

Tamiami

Canal

L-2 Canal

Watson River

BROWARD

MIAMI-DADE

MONROE

PALM

BEACH

HENDRY

COLLIER

81°30' 81° 80°30'

26°30'

25°30'

25°

L-40 Canal

Base from Esri® data and maps, 2010 0 5 10 15 20 MILES

U.S. Geological Survey Everglades Depth Estimation Network, 2011

Universal Transverse Mercator projection, zone 17 0 5 10 15 20 KILOMETERS

GULF OF MEXICO

Lake Okeechobee

Florida Bay

WCA1

EXPLANATION

Group and index number

Group 1

Group 2

Group 3

National Park, National Preserve, and Water

 Conservation Areas (WCA) and name

Everglades Depth Estimation Network

 (EDEN) model domain (table 1)

WCA1

BIG CYPRESS

NATIONAL

PRESERVE

EVERGLADES

NATIONAL

PARK

WCA2A

WCA2B

WCA3A

WCA3B Pennsuco

Wetlands

26°

233

Hillsboro

Bolles Canal

Canal

205 206

204

221

203

214

213 222

195

219

188

212

215

187

179

192

180

193

191 225

218

211

224

223

194

198

226 189

L-67 Canal

Area shown

GULF

OF

MEXICO

FLORIDA

ALABAMA GEORGIA

192

189

222

0.14

0.13

0.12

0.11

0.10

0.09

0.08

0.07

0.06

0.05

0.04

1 2 3

Number of groups

Root mean square error

4 5 6
Estimating Water Levels 15

Empirical Estimation Models

The most common empirical modeling approach is 

OLS, which relates variables using straight lines, planes, or 

hyper-planes, whether the actual relations are linear or not. 

Artificial neural network models also are empirical models, 

are developed directly from data, and are a flexible mathematical structure capable of describing complex nonlinear relations 

between input and output datasets. Calibration of either type 

of model attempts to optimally synthesize a line or surface 

through the measured data. The principal advantages of 

empirical models, such as ANN models, over mechanistic 

models are that they can be developed faster and are more 

accurate, provided the modeled systems are well characterized 

by data. Empirical models, however, are prone to problems

when poorly applied. Overfitting and multicollinearity caused 

by correlated input variables can lead to invalid mappings, 

or relations, between input and output variables (Roehl and 

others, 2003). Of the 214 water-level estimation models, 189 

are linear regression models and 25 are ANN models (table 3).

Figure 9. Plot showing the 7-day average water levels for the Group 1, Group 2, and Group 3 gages in Water 

Conservation Area 3A South for the period January 1, 2006 to December 31, 2009.

Linear Regression Models

Linear regression models often are used to estimate 

values of one variable based on another variable that has 

more data (Helsel and Hirsch, 1995). Linear regression 

models for water-level estimation equations are in the form 

of y=mx+b, where y is the estimated value, m is the slope, 

x is the value from the input (“predictor”) station, and b is 

the y-intercept. All the linear regression models in the study 

used only one input station. For some sites, there are periods 

when the input station is missing data and no estimates are 

made using that model. For these cases, a second model was 

developed to estimate the data when the first input is missing. There is one site, CV5NR (fig. 1, map label 41), where 

a third model needed to be developed because of periods 

of missing data from the first two input sites. The input 

variables for the models are listed in table 3. A description 

of the variables is provided in table 1-1 of the appendix.

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

Water level, in feet N

AVD 88

Group 1 average

Group 2 average

Group 3 average

EXPLANATION

Jan. Mar. May Sept. Nov.

2006

July Jan. Mar. May Sept. Nov.

2007

July Jan. Mar. May Sept. Nov.

2008

July Jan. Mar. May Sept. Nov.

2009

July
16 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Artificial Neural Network Models 

In most cases, water-level data at the input and output 

stations are well correlated and linear regression models 

produced satisfactory results. For stations where the linear 

regression estimates were not adequate, usually evaluated 

by visual inspection of measured and estimated data, an 

ANN model was developed. ANN models are a flexible 

mathematical structure capable of describing complex 

nonlinear relations between input and output datasets. The 

structure of ANN models is loosely based on the biological 

nervous system with interconnections of neurons and 

synapses (Hinton, 1992). Although numerous types of ANN 

models exist, the most commonly used type of ANN model 

is the multilayer perceptron (Rosenblatt, 1958), which is 

used in this study and described in detail by Jensen (1994). 

Multilayer perceptron ANNs can synthesize functions to 

fit multidimensional, nonlinear data. Multilayer perceptron 

ANNs are constructed from layers of interconnected 

processing elements called neurons that execute a simple 

“transfer function” (fig. 10). All input layer neurons are 

connected to all hidden layer neurons, and all hidden layer 

neurons are connected to all output layer neurons. Multiple 

hidden layers are possible, but a single layer is sufficient for 

most problems.

Typically, as well as for this study, linear transfer 

functions are used to scale input values from the input layer 

to the hidden layer, yielding values that generally are within 

the range that corresponds to the most linear part of the 

s-shaped sigmoid nonlinear transfer functions used from the 

hidden layer to the output layer (fig. 10). Each connection 

has a weight (wi) associated with it, which scales the output 

received by a neuron from a neuron in an antecedent layer. 

The output of a neuron is a simple combination of the values 

it receives through its input connections and the associated 

weights, as well as the neuron’s transfer function. 

An ANN is “trained” by iteratively adjusting its 

weights to minimize the error by which it maps inputs 

to outputs for a dataset composed of input/output vector 

pairs. Prediction accuracy during and after training can be 

measured by a number of metrics, including R2 and RMSE. 

An algorithm that commonly is used to train multilayer 

perceptron ANNs is the back error propagation (BEP) training algorithm (Rumelhart and others, 1986). The algorithm 

optimally minimizes the error in the objective function by 

adjusting the weights into and out of the hidden layer of the 

model (fig. 10). 

Experimentation with various ANN model architectural 

and training parameters is a typical part of the modeling 

process. For correlation analysis or predictive modeling 

applications, a number of potential ANN models are trained 

and evaluated for their statistical accuracy and their representation of dynamics of the system. Interactions between 

combinations of variables are considered, in addition to the 

selection of the training dataset from the overall dataset. 

In developing ANN models, it is customary to set aside a 

subset of the data to provide an independent evaluation of 

model performance. Typically, datasets are divided into 

“training” and “testing” datasets. There are many strategies 

for partitioning data into training and testing datasets, but 

the most common is random selection of a specified percentage of the total population of measurements. 

The models were calibrated by using the training 

dataset and evaluated with the testing dataset. For models 

with a large dataset with good representation over the range 

of historical behaviors, a small percentage of the dataset 

(10–25 percent) may be selected for the training dataset. 

For models with limited data, a larger percentage (75–100 

percent) may be used in the training dataset. To mitigate the 

extrapolation and sparseness issues, the ANN models were 

conservatively trained using a method referred to as “stop 

training” to both fit the data and extrapolate in a minimally 

nonlinear and, therefore, predictable fashion. Stop training 

simply means stopping the training process before the ANN 

has fit the data to the maximum extent possible. Architectural and training parameters allow the modeler to control 

the geometric complexity of the surface that the ANN fits 

to the data. The ANN models in this report were developed 

using the iQuest data-mining software11 (Version 2.03C DM 

Rev31). The software writes R2 and RMSE to the graphical 

user interface (GUI) during training, and an inflection in 

the rate of change in these parameters indicates a transition 

from a generally linear, multivariate surface fit to a progressively nonlinear fit. This inflection point was used to trigger 

stop training. 

1

 The iQuest software is exclusively distributed by Advanced Data Mining, 

LLC, http://advdmi.com/Services.aspx
Estimating Water Levels 17

Decorrelation of Input Variables 

Many of the ANN models are multivariate models 

using more than one input variable. Usually, input variables 

share information about the behavior of an output variable. 

It is difficult, if not impossible, to understand the individual 

effects of these input variables (sometimes known as 

confounded or correlated variables), on an output variable. 

Empirical models have no notion of process physics or the 

nature of interrelations between input variables. To clearly 

analyze the effects of confounded variables, the unique informational content of each variable must be determined by 

“de-correlating” the confounded variables. For example, the 

three long-term stations, SITE_64, SITE_65, and SITE_69W 

(fig. 1, map labels 218, 219, and 220, respectively), are 

highly correlated. If the time-series data from these stations 

are used as input to a model they would need to be decorrelated from each other. Decorrelation can be done by using 

a number of cascading models where the output from one 

model is used as input to a subsequent model. For example, 

SITE_65 and SITE_69W can be decorrelated from SITE_64 

in two steps (fig. 11). The first step is to generate a Single 

Input Single Output (SISO) ANN model using SITE_69W 

as input and SITE_64 as output. The residual error (the 

difference between predicted and measured values) is the 

“unshared” information between the two signals and the 

decorrelated signal for SITE_69W. The second step is to 

build an ANN model using SITE_65 and the decorrelated 

signal for SITE_69W to predict SITE_64. The residual of 

this model is the decorrelated signal for SITE_65.

Figure 10. Multilayer perceptron artificial neural network architecture.

Output

layer

Input

layer

(Input examples)

(Output examples)

x1

x3

x2

x4

x5

x1

x3

x2

x4

x5

x1

x3

x2

x4

x5

y1

y1

y1

t

t+1

t+2

t

t+1

t+2

wi

wi+n

“Weights”

control

connections

Neurons with 

linear 

transfer

functions

Neurons with nonlinear

transfer functions

Hidden

layer
18 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Figure 11. Schematic showing the decorrelation of water levels (WL) for SITE_64, SITE_65, and SITE_69W.

Statistical Measures of Water-level Estimation 

Model Prediction Accuracy

Statistical measures of prediction accuracy were 

computed for the water-level estimation models. Each 

statistic measures a different aspect of the accuracy of the 

prediction equations. Estimation accuracy commonly is 

reported in terms of R2 and is interpreted as the goodness-offit of an equation or model. An interpretation of the statistic 

may determine how much information one variable, or a 

group of variables, provides about the behavior of another 

variable. In this context, an R2=0.6 might be unsatisfactory. 

Another interpretation is that R2 is merely an accounting of 

how much information is shared by the variables being used. 

The standard error is the measure of the scatter of the actual 

observations about the regression line and is the standard 

deviation of the error of the predicted values in the regression. The standard error can be used to compute confidence 

intervals for the predictions. The mean error (ME) and RMSE 

statistics provide a measure of the prediction accuracy of 

the estimation equations. The ME is a measure of the bias of 

model predictions—whether the model over- or under-predicts 

the measured data. The ME is the overall adjustment of the 

estimated values required to equal the measured values; 

therefore, positive and negative MEs indicate an over- or 

under-prediction bias by the model, respectively. MEs near 

zero may be misleading because negative and positive 

discrepancies in the simulations can cancel each other. RMSEs 

address the limitations of ME by computing the magnitude, 

rather than the direction (sign) of the discrepancies. The units 

of the ME and RMSE statistics are the same as the variable 

simulated by the model. ME and percent model bias (ME 

divided by the mean observed value) were mostly zero for all 

equations and, therefore, are not included in the goodness-offit statistics. ME and percent model bias equal zero because 

simple linear regression equations, such as those described 

in this report, inherently minimize the sum of the residuals 

(error) between the estimates and the measured data. The sum 

of the residuals, and therefore, ME, are zero for all stations. 

The accuracy of the models, as given by RMSE, should be 

evaluated with respect to the range of the output variable. A 

model may have a low RMSE, but if the range of the output 

variable is small, the model may only be accurate for a limited 

range of conditions and the model error may be a relatively 

large percentage of the model response. Likewise, a model 

may have a large RMSE, but if the range of the output variable 

is large, the model error may be a relatively small percentage 

of the total model response. The percent model error (PME) is 

computed by dividing the RMSE by the range of the measured 

data.

The performance statistics for the water-level estimation 

models are listed in table 1-2 of the appendix. The period 

used to compute the model statistics is January 1, 1991, to 

December 31, 2010. The statistics for the individual ANN 

model development (table 4) are not necessarily indicative of 

the quality of the final water-level estimates, which are based 

on multiple models. The number of data points used to train 

and test the ANN models, including the decorrelation models, 

are listed in table 4 along with the number of hidden layer 

neurons (HLNs). Many of the ANN models are multivariate 

models that use more than one explanatory variable. The 

statistics for the ANN models in table 1-2 in the appendix 

are based on all the water-level estimates, and not computed 

separately by the training and (or) testing datasets. Overall, 

the water-level estimation model performance statistics are 

satisfactory. Ninety percent of the water-level estimation 

models have PMEs of 10 percent or less (fig. 12) with the 

median value as 5 percent (table 5). The median R2 for the 

models is 0.91 and the median standard error is 0.19 ft.

WL SITE_64pred1 = F1[WL SITE_69W]

First decorrelation model

Second decorrelation model

WL SITE_64pred = F2[WL SITE_65 and WL SITE_69Wdecorrelated]

WL SITE_64measured

WL SITE_69Wdecorrelated

WL SITE_65decorrelated

WL SITE_64measured
Estimating Water Levels 19

Table 4. Summary of the performance statistics for the training and testing ANN models.[EDEN, Everglades Depth Estimation Network;HLN, hidden layer neruons; Min, minimum; ft, feet; Max, maximum; N, number of data points; SSE, sum of squared error; RMSE, root mean square error; MSE, mean square error; R2, coefficient of determination; PME, percent model error;_f, filled; _dec, decorrelated]

Model 

name

EDEN 

station

 name

Map label 

number HLN Min, ft Max, ft Ntrain SSEtrain, ft R2train RMSEtrain, ft MSEtrain, ft PMEtrain, percent Ntest SSEtest, ft R2test RMSEtest, ft MSEtest, ft PMEtest, percent

Big Cypress National Preserve

bca2.n32 BCA2 4 2 8.66 14.63 357 197.28 0.77 0.74 0.55 12.45 6,913 3,290.5 0.69 0.69 0.48 5.80bca3.n32 BCA3 5 3 8.98 13.52 56 4.29 0.91 0.28 0.08 6.10 6,977 758.2 0.83 0.33 0.11 5.47bca4.n32 BCA4 6 2 5.62 10.61 101 11.17 0.93 0.33 0.11 6.66 7,269 1,665.6 0.79 0.48 0.23 7.31bca5_1.n32 BCA5 7 3 6.29 10.36 362 30.33 0.92 0.29 0.08 7.12 6,952 620.0 0.92 0.30 0.09 4.25bca12_1 BCA12 13 3 10.30 14.63 371 48.52 0.89 0.36 0.13 8.35 6,610 799.7 0.84 0.35 0.12 4.23bca13.n32 BCA13 14 4 7.31 12.39 101 5.75 0.96 0.24 0.06 4.70 7,243 905.6 0.84 0.35 0.13 7.62bca14_1.n32 BCA14 15 2 4.14 9.97 369 152.68 0.83 0.64 0.41 11.02 6,856 1,988.6 0.78 0.54 0.29 5.08bca15_1.n32 BCA15 16 1 0.63 7.89 296 15.03 0.87 0.23 0.05 3.10 3,327 147.0 0.84 0.21 0.04 6.89bca16_1.n32 BCA16 17 2 8.11 12.15 286 46.53 0.85 0.40 0.16 9.97 3,156 347.3 0.85 0.33 0.11 3.38bca18_1.n32 BCA17 18 3 12.05 14.41 300 8.31 0.94 0.17 0.03 7.04 3,311 104.2 0.91 0.18 0.03 2.53bca17_1.n32 BCA18 19 3 8.25 13.63 296 44.41 0.90 0.39 0.15 7.20 3,333 446.3 0.88 0.37 0.13 5.19eden6_1.n32 EDEN_6 22 3 8.55 10.87 53 0.75 0.97 0.12 0.01 5.14 1,169 26.9 0.90 0.15 0.02 2.96s343a_t_3.n32 S343A_T 30 4 6.70 10.26 292 8.34 0.94 0.17 0.03 4.75 5,374 133.9 0.92 0.16 0.02 3.34s343B_T_r1.n32 S343B_T 31 3 6.49 10.11 4,080 195.48 0.82 0.22 0.05 6.05 1,402 67.9 0.81 0.22 0.05 3.67

Water Conservation Area 2A

eden_11_m1.n32 EDEN_11 144 4 10.59 13.57 1081 56.42 0.85 0.23 0.05 7.67 377 22.3 0.79 0.24 0.06 3.20wca2an1.n32 WC2AN1 159 2 8.77 14.13 273 61.11 0.67 0.47 0.22 8.83 99 24.3 0.72 0.50 0.25 5.76wca2as1.n32 WC2AS1 160 2 11.03 12.91 262 7.32 0.88 0.17 0.03 8.89 95 2.8 0.90 0.17 0.03 1.95wca2art_m1.n32 WCA2RT 165 2 9.32 14.23 3951 130.01 0.95 0.18 0.03 3.69 1,313 44.0 0.95 0.18 0.03 5.00

Water Conservation Area 2B

s144t_m1.n32 S144_T 173 2 8.32 10.37 1252 36.30 0.88 0.17 0.03 8.31 1,188 34.2 0.89 0.17 0.03 2.05s145t_m1.n32 S145_T 174 3 8.20 10.36 1252 40.35 0.84 0.18 0.03 8.28 1,188 37.7 0.86 0.18 0.03 2.16s146t_m1.n32 S146_T 175 2 8.37 10.59 1231 54.25 0.82 0.21 0.04 9.46 1,161 56.2 0.80 0.22 0.05 2.34

Water Conservation Area 3A

eden1_2.n32 EDEN_1 190 2 7.14 8.60 44 0.28 0.97 0.08 0.01 5.44 1,090 5.5 0.95 0.07 0.01 1.31s343b_h-1.n32 S343B_H 214 2 7.58 11.66 11 0.05 1.00 0.06 0.00 1.57 5,482 28.1 0.99 0.07 0.01 4.58W2_r2.n32 W2 221 2 6.68 9.58 698 4.49 0.98 0.08 0.01 2.77 724 5.0 0.98 0.08 0.01 3.00W18_r2.n32 W18 226 2 7.92 10.41 559 9.08 0.96 0.13 0.02 5.12 600 8.5 0.96 0.12 0.01 2.33

Decorrelation

 model name

Decorrelated 

variable

Correlated 

variable HLN Min, ft Max, ft Ntrain SSEtrain, ft R2train RMSEtrain, ft MSEtrain, ft PMEtrain, percent Ntest SSEtest, ft R2test RMSEtest, ft MSEtest, ft PMEtest, percent

S7_tdecor.n32 S7_T_dec EDEN11_f 3 7.83 14.47 5,736 3,102 0.69 0.74 0.54 11.08 1,928 938 0.71 0.70 0.49 6.62S7_t_dec-site17.n32 Site17_dec-S7T S7_T 1 7.73 13.65 5,732 1,170 0.75 0.45 0.20 7.63 1,925 372 0.76 0.44 0.19 5.92S190-t_dec.n32 S190-T_dec L28GAP 2 7.84 12.07 3,785 454 0.82 0.35 0.12 8.19 3,679 445 0.82 0.35 0.12 4.31bca14_dec.n32 BCA14_dec BCA2_f 2 9.30 14.20 11 0 0.98 0.21 0.04 4.28 7,853 3,948 0.68 0.71 0.50 16.74loop1_h_dec.n32 LOOP1_H_dec S343A_T 3 6.49 10.45 2,737 67 0.93 0.16 0.02 3.97 2,637 67 0.92 0.16 0.03 4.06
20 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Shifting Water-Level Estimates

Once water levels are estimated, hydrographs of each 

station are evaluated to identify potential errant data and to 

evaluate the fit of the water-level estimates. For some stations, 

estimated data are a good representation of the missing data and 

can be used without any adjustment. Some of the water-level 

estimates follow the trend of the measured data but are offset 

from the measured data. At these sites, the relative water-level 

estimates are good but the absolute estimates are in error. In 

the Everglades, differences in water level of only 2 or 3 in. 

can be important to the ecology. To improve the quality of the 

water-level estimates, shifting techniques are applied to the 

estimates similar to gage-height correction techniques used 

for computing continuous water-level data records (Rantz and 

others, 1982). The applications of shifts are applied for periods 

of missing water-level data and therefore do not affect the 

model performance statistics.

Figure 12. Frequency distribution of percent model error of the water-level estimation models.

Table 5. Minimum, median, and maximum values for the summary statistics for 237 water-level 

estimation models.

[R2, coefficient of determination; RMSE, root mean square error]

Statistic Standard error, 

in feet R2 Mean error, in feet

RMSE,

 in feet

Percent model 

error

Minimum 0.00 0.26 –0.92 0.03 0.50

Maximum 0.85 1.00 0.88 1.11 22.32

Median 0.19 0.91 0.00 0.20 5.04

The most straight-forward type of data correction is one 

where a uniform (constant) correction value is applied to the 

estimates. Prorated corrections are applied over time to improve 

the quality of the water-level estimates. An example of applying 

constant and prorated shifts to water-level estimates for NP46 

(map label 87, fig. 1) are shown in figure 13. The water-level 

estimation model of the site captures the overall trend of 

the data but the estimates are over-predicted by 0.2 – 0.3 ft. 

Shifts were applied to improve the absolute prediction of 

the estimates while maintaining the dynamic variability of 

the model. The shifts were determined by subtracting the 

modeled water level from the measured water level for the 

day before and after the data gap. For the short data gaps from 

September 25 to October 15, 1993, a shift of –0.31 ft was 

started on September 25 and prorated to –0.24 ft on 

October 15. For the large data gap from November 11, 1993, 

to January 20, 1994, a shift of –0.26 ft was applied on 

November 11 and prorated to –0.22 ft on January 20.

100

90

80

70

60

50

40

30

20

10

0

0 2 4 6 8 10 12 14 16 18 20 22 24

Cumulative percent

Percent model error
Evaluation of Hindcasts using Modeled Water-Level Surfaces 21

Evaluation of Hindcasts using Modeled 

Water-Level Surfaces

The statistical evaluation of the water-level estimation 

models quantifies the predictive ability of the model to 

capture the water-level dynamics for the individual station 

on a temporal basis. For generating water-level surfaces 

for the Everglades using the V2 model, the hindcasted 

water-level estimation models must perform spatially as 

a group to create water-surface maps that are credible. 

Individual models may be accurate but model error between 

sites may cause erroneous water-surface gradients between 

stations. To evaluate the performance of the hindcast models 

as a group, contour maps of modeled water-level surfaces 

at 2-centimeter (cm) intervals were generated using the 

hindcasted data. The 2-cm contour maps were examined for 

selected days to verify that modeled water surfaces from 

the V2 model were consistent with the input data. The high 

resolution provided by the 2-cm contour intervals highlights 

areas of the model domain where input data may be incorrect and where water-level gradients may not be consistent 

with current knowledge of sheet flow in the marshes.

Rather than evaluate water-surface maps for each of 

the 3,650 days of the hindcasted period, which was time 

prohibitive, the water-level surfaces generated by the hindcasted dataset (1990–99) were compared with water-level 

surfaces generated with the measured dataset (2000–10) for 

a few high- and low-water days. Daily hydrographs were 

generated using measured long-term data from BCNP, ENP, 

and the WCAs for 1990 to 2010. The 21-year hydrographs 

were used to select dates for representative water conditions 

in the measured period (2000–10) and hindcasted period 

(1990–99). Because of the natural interannual climate 

variability in addition to operational differences between the 

WCAs and BCNP and ENP, it is difficult to identify periods 

of similar water-level conditions (within +/– 0.3 ft) for the 

domain of the V2 model. Priority was set on finding similar 

conditions between ENP and WCA3A. For high-water 

conditions, the hindcasted surfaces for September 26 and 

November 19, 1995, were compared with the measured 

water-level surfaces for October 2, 2008. For low-water 

conditions, the hindcasted surfaces of March 3, 1994; 

April 24, 1997; and May 21, 1999 were compared with the 

measured water-level surface for March 2, 2008. 

Figure 13. Example of measured, estimated, and shifted estimated data at NP46 over the period June 1993 

to March 1994.

–1.00

–0.80

–0.60

–0.40

–0.20

0

0.20

0.40

0.60

0.80

1.00

NP46 measured

NP46 estimated

NP46 measured and shifted estimated data

EXPLANATION

Water level, in feet N

AVD 88

June July Aug. Sept.

1993 1994

Oct. Nov. Dec. Jan. Feb. Mar.
22 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Overall, the hindcasted 2-cm contours for the highwater condition were similar to the contours generated 

with the measured data. There were areas on the hindcasted 

surfaces where potential problems with the hindcasted waterlevel data were evident along the Tamiami Canal, along the 

L-67 Canal near SITE_69W, and in central and northern 

areas of WCA2A. The issues with the contours are not only 

issues with the water-level estimations of the hindcasts 

but also are caused by issues with the data. For example, 

the irregularities along the Tamiami Trail were caused by 

the datum correction from the National Geodetic Vertical 

Datum of 1929 to NAVD 88 not being applied to S12B_T 

(map label 109, fig. 1). S12B_T was not a hindcasted site 

but data gaps in the record were filled. For the irregularities 

near SITE_69W, the water-level data were compared with 

SITE_64, SITE_71, and SITE_76 and no apparent data problems were observed. There are two stations at the locations 

along the L67 canal: SITE_69W in the canal and SITE_69E 

(not shown in fig. 1) in the marsh of WCA3B to the east 

of the canal levee. The water-level data for SITE_69E was 

mistakenly used in the model rather than SITE_69W and the 

lower water levels caused the irregularities in the contours. 

Correcting the datum conversion at S12B_T and substituting 

data for SITE_69W for modeling WCA3B produced waterlevel surfaces consistent with adjacent station data. 

The issues in the northern area of WCA2A (fig. 14) 

were a result of a limited number of stations in the areas to 

use for input stations for the water-level estimation models 

(fig. 3). The initial linear regression models for WC2AN1, 

WC2AS1, and EDEN_11 used measured data from the S7_T 

(for the WC2AN1 and EDEN_11 models) and SC11C_T (for 

the WC2AS1 model). Individually, the initial linear regression water-level estimates for WC2AN1, WC2AS1, and 

EDEN_11 seemed satisfactory, but plotted together (fig. 15), 

the water levels did not follow the ground elevation slope. 

The topographic slope in WCA2A generally is to the south 

and southwest (Jones and others, 2007b, 2012). If water 

levels generally were the same depth, the water levels at 

the three hindcasted sites would be similar and water levels 

at a station to the south, such as SITE_17 would be lower. 

The four sites would have a general downward gradient 

from WC2AN1 to WC2AS1 to EDEN_11 to SITE_17. The 

initial water-level estimation models did not follow the 

general gradient with water levels because WC2AN1 was 

similar to SITE_17 farther to the south (fig. 15A). The three 

sites were re-modeled using ANN models and different 

input stations. Rather than only using measured input 

datasets, hindcasted and filled datasets were used for input 

stations. EDEN_11 was modeled with the hindcasted and 

filled dataset for WCA2F1 (map label 163, fig. 1, table 3). 

WC2AS1 was then modeled with a multivariate model using 

the EDEN_11 predictions and S7_T that was decorrelated 

from the EDEN_11 predictions (table 3). WC2AN1 was then 

modeled using the WC2AS1 predictions (table 3). The final 

water-level estimations (fig. 15B) follow the general ground 

elevation gradient. 

In addition to comparing the 2-cm contoured waterlevel maps for the selected high-water and low-water 

days, 240 2-cm contour water-level maps were generated 

for the 1st and 15th of each month for January 1, 1990, to 

December 31, 1999. Irregularities in contours were evaluated 

and issues involving data inputs and (or) water-level estimation models were resolved. The biweekly 2-cm contour 

maps did indicate a higher number of issues in the 1990s. 

In May 1990, the lowest water levels of the 21-year dataset 

used for the hindcasting study happened in the Everglades 

(for example, see long-term measured water levels for 

SITE_64 shown in fig. 5). To estimate these low-water 

levels, the water-level estimation models had to extrapolate 

beyond the range of measured data. As discussed in the 

“Approach” section of this report, the models assume that the 

relation between input and output variable remains constant 

between the measured conditions and the extrapolated 

conditions. For the extreme low-water level during 1990, 

this assumption is not valid. For the low water in May 1990, 

many of the models would have to be extrapolated about 

2 ft lower than the measured data used to develop the 

models. In addition, models that use a hindcasted dataset for 

input would have the errors for two models compounded to 

extrapolate to the extreme low-water levels. Additionally, the 

effort to resolve the water-level estimation model extrapolation is challenging because of the lack of measured data in 

1990 for many areas of the EDEN domain (fig. 3). For these 

reasons, it was decided to limit the hindcasted data to the 

period January 1, 1991, to December 31, 1999. 

An example of the hindcasted and measured watersurface maps is shown in figure 16. The two maps were 

generated for days with similar high-water conditions. The 

map on the left was generated using the hindcasted data for 

September 26, 1995, and the map on the right was generated 

using the measured data for October 2, 2008. The high-water 

conditions for ENP and WCA3A, as represented by NP62 

and SITE_64, respectively (fig. 1, map labels 88 and 218) 

were within 0.13 ft at both gages for the two dates. Overall, 

the hindcasted water-elevation surface for the high-water 

condition is similar to the surface generated with the measured data. Overall, the hindcasted and gap-filled data are 

believed to provide reasonable estimates of station-specific 

water-level data for an extended historical period to inform 

research and natural resource management in the Everglades. 

The datasets with the record extensions are available on the 

EDEN Web site using the Explore and View EDEN (EVE) 

graphical interface (http://sofia.usgs.gov/eden/eve/index.php).
Evaluation of Hindcasts using Modeled Water-Level Surfaces 23

Figure 14. Example of 2-centimeter contour water-surface elevation maps for high-water conditions on 

September 26, 1995 used to evaluate the preliminary hindcasted data.

277

281

279

275

273

271

269

267

265

263

261

259

257

255

Water-elevation contour–Contour interval is

 2 centimeters. Vertical datum is NAVD 88.

281

EXPLANATION
24 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

Figure 15. Measured data for SITE_17 and hindcasted water-level data for EDEN_11, WC2AN1, and

WC2AS1 for A, preliminary water-level estimation models and B, final water-level estimation models.

8

7

9

10

11

12

13

14

A

Jan. Apr. July

1993 1994 1995

Oct. Jan. Apr. July Oct. Jan. Apr. July Oct.

8

7

9

10

11

12

13

14

B

SITE 17

EDEN 11

WC2AN1

WC2AS1

EXPLANATION

Water level, in feet NAVD 88

SITE_17

EDEN_11

WC2AN1

WC2AS1

EXPLANATION
Summary 25

Figure 16. Example of water-surface elevation maps for high water conditions using A, hindcasted data for 

September 26, 1995 and B, measured data for October 2, 2008.

Summary 

The Everglades Depth Estimation Network (EDEN) 

water-surface elevation model uses data from approximately 

240 gages in the Everglades to create daily continuous 

interpolations of the water-surface elevation for the freshwater 

portion of the Everglades from 2000 to the present (2014). To 

provide a longer period for assessing biological and ecological 

impacts, the EDEN team decided to hindcast (extend waterlevel data records back in time) to 1990. Before 2000, many of 

the EDEN gages used to generate water surfaces were not in 

operation. Of the 237 stations used in the EDEN water-surface 

model in 2000, only 106 stations were in operation in 1990. 

Of the 106 stations in operation, only 23 stations had complete 

datasets (no missing data). To create an input dataset for the 

EDEN water-surface model, 168 data records were hindcasted 

and 46 data records had missing data gaps filled. 

The water-level data records were hindcasted using 

empirical water-level estimation models. Of the 214 

water-level estimation models used to hindcast and fill data 

records, 189 are linear regression models and 25 are artificial 

neural network models. Ninety percent of the models have 

percent model error (root mean square error divided by 

the range of the measured data) of 10 percent or less. The 

median coefficient of determination for the models is 0.91 

and the median standard error is 0.19 foot. In addition to 

evaluating performance of each water-level estimation model, 

2-centimeter (cm) vertical resolution water-level maps 

were generated using the hindcasted data and evaluated for 

irregular contours indicating a potential problem with the 

hindcasted data. May 1990 had the lowest water levels in the 

Everglades of the 21-year dataset used for the hindcasting 

study. To estimate these extreme low-water levels, the models 

needed to extrapolate beyond the range of the measured 

data. Model extrapolation assumes that the relation between 

input and output variables remains constant and limited 

model extrapolation is often appropriate. For the extreme low 

water in 1990, however, it was decided that large water-level 

estimation model extrapolations were not appropriate and the 

hindcasted dataset was begun on January 1, 1991, and ended 

on December 31, 1999. The hindcasted and gap-filled data 

provide reasonable estimates of station-specific water-level 

data for an extended historical period to inform research and 

natural resource management in the Everglades.

Water elevation,

in centimeters (NAVD 88)

5

105

205

305

405

A B
26 Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99

References Cited

Conrads, P.A., and Roehl, E.A., Jr., 2007, Hydrologic record 

extension of water-level data in the Everglades Depth 

Estimation Network (EDEN) using artificial neural network 

models, 2000–2006: U.S. Geological Survey Open-File 

Report 2007–1350, 56 p., accessed October 23, 2014, at 

http://pubs.water.usgs.gov/ofr2007–1350.

Conrads, P.A., and Petkewich, M.D., 2009, Estimation of 

missing water-level data for the Everglades Depth Estimation Network (EDEN): U.S. Geological Survey Open-File 

Report 2009–1120, 53 p.

Daamen, R.C., Roehl, E.A., Jr., and Conrads, P.A., 2010, 

Development of inferential sensors for real-time quality 

control of water-level data for the Everglades Depth Estimation Network, in Proceedings of the 2010 South Carolina 

Water Resources Conference, Columbia, S.C., 2010, 4 p.

Davis, J.H., Jr., 1943, Vegetation map of Southern Florida: 

Florida Geological Survey, Bulletin 25, figure 71, 1 sheet, 

1:400,000 scale.

German, E.R., 2000, Regional evaluation of evapotranspiration in the Everglades: U.S. Geological Survey WaterResources Investigations Report 00–4217, 48 p.

Helsel, R.M., and Hirsch, D.R., 1995, Studies in environmental science 49—Statistical methods in water resources: 

Amsterdam, Elsevier Science, 529 p.

Hinton, G.E., 1992, How neural networks learn from experience: Scientific American, v. 267, no. 3, p. 145–151.

Jensen, B.A., 1994, Expert systems—Neural networks, 

chap. 1.7 of Lipták, B.G., ed., Instrument engineers’ 

handbook (3d ed.): Radnor, Pa., CRC Press, p. 48–54.

Jones, J.W., Desmond, G.B., Henkle, Charles, and Glover, 

Robert, 2012, An approach to regional wetland digital 

elevation model development using a differential global 

positioning system and a custom-built helicopter-based 

surveying system: International Journal of Remote Sensing, 

v. 33, p. 450–465.

Jones, J.W., and Price, S.D., 2007a, Conceptual design of the 

Everglades Depth Estimation Network (EDEN) grid: U.S. 

Geological Survey Open-File Report 2007–1200, 20 p.

Jones, J.W., and Price, S.D., 2007b, Initial Everglades 

Depth Estimation Network (EDEN) digital elevation 

model research and development: U.S. Geological Survey 

Open-File Report 2007–1034, 29 p.

Jones, J.W., Desmond, G.B., Henkle, Charles, and Glover, 

Robert, 2012, An approach to regional wetland digital 

elevation model development using a differential global 

positioning system and a custom-built helicopter-based 

surveying system: International Journal of Remote Sensing, 

v. 33, p. 450–465.

Lodge, T.E., 1994, The Everglades handbook, Understanding 

the ecosystem: Delray Beach, Fla., St. Lucie Press, 228 p.

McPherson, B.F., Higer, A.L., Gerould, S., and Kantrowitz, 

I.H., 1995, South Florida Ecosystem Program of the 

U.S. Geological Survey: U.S. Geological Survey 

Fact Sheet FS-134-95, accessed June 19, 2012, at 

http://sofia.usgs.gov/publications/fs/134-95/index.html.

Pearlstine, L., Higer, A., Palaseanu, M., Fujisaki, I., and 

Mazzotti, F., 2007, Spatially continuous interpolation of 

water stage and water depths using the Everglades Depth 

Estimation Network (EDEN): Gainesville, Fla., Institute 

of Food and Agricultural, University of Florida, CIR1521, 

18 p., 2 apps.

Petkewich, M.D., and Conrads, P.A., 2013, Estimation of 

missing water-level data for the Everglades Depth Estimation Network (EDEN), 2013 update: U.S. Geological 

Survey Open-File Report 2013–1251, 45 p.

Rantz, S.E., and others, 1982, Measurement and computation 

of streamflow: U.S. Geological Survey Water-Supply Paper 

2175, 631 p.

Richardson, J.R., Bryant, W.L., Kitchens, W.M., Mattson, 

J.E., and Pope, K.R., 1990, An evaluation of the refuge 

habitats and relationships to water quality, quantity, and 

hydroperiods—A synthesis report: Gainesville, Fla., Florida 

Cooperative Fish and Wildlife Research Unit, University of 

Florida,166 p.

Risley, J.C., Roehl, E.A., Jr., and Conrads, P.A., 2003, Estimating water temperatures in small streams in western 

Oregon using neural network models: U.S. Geological 

Survey Water-Resources Investigations Report 02–4218, 

60 p.

Roehl, Ed, Jr., Conrads, P.A., and Cook, J.B., 2003, Discussion of “Using complex permittivity and artificial neural 

networks for contaminant prediction”: Journal of Environmental Engineering, v. 129, p. 1069–1071.

Roehl, E., Risley, J., Stewart, J., and Mitro, M., 2006, 

Numerically optimized empirical modeling of highly 

dynamic, spatially expansive, and behaviorally heterogeneous hydrologic systems—Part 1, in Proceedings of 

the International Environmental Modelling and Software 

Society 2006 Summit on Environmental Modelling and 

Software, Burlington, Vt., 6 p, accessed July 8, 2014, at 

http://www.iemss.org/iemss2006/.
References Cited 27

Rosenblatt, F., 1958, The perceptron, a probabilistic model for 

information storage and organization in the brain: Psychological Review, v. 65, p. 386–408.

Rumelhart, D.E., Hinton, G.E., and Williams, R.J., 1986, 

Learning internal representations by error propagation, in 

Rumelhart, D.E., McClelland, J.L., and the PDP Research 

Group, Parallel distributed processing—Explorations in the 

microstructure of cognition, volume 1: Cambridge, Mass., 

MIT Press, p. 318–362.

South Florida Natural Resource Center, 2005, An assessment 

of the Interim Operational Plan: Homestead, Fla., South 

Florida Natural Resources Center, Everglades National 

Park, Project Evaluation Report, SFNRC Technical Series 

2005:2, 47 p., accessed DATE, at http://www.nps.gov/ever/

naturescience/upload/SecureIOPReportSmall.pdf. 

Stewart, J., Mitro, M., Roehl, E., and Risley, J., 2006, Optimized empirical modeling of highly dynamic, spatially 

expansive, and behaviorally heterogeneous hydrologic 

systems—Part 2, in Gourbesville, Philippe, Cunge, Jean, 

Guinot, Vincent, and Liong, Shie-Yui, eds., Proceedings 

of the 7th International Conference on Hydroinformatics, 

August 2006, Nice, France, v. 2, p. 831–838.

Telis, P.A., 2005, Project description, South Florida Surface 

Water Monitoring Network for the Support of MAP Projects 

(known as EDEN, Everglades Depth Estimation Network): 

accessed October 2, 2007, at http://sofia.usgs.gov/projects/

eden/.

Telis, P.A., 2006, The Everglades depth estimation network 

(EDEN) for support of ecological and biological assessments: U.S. Geological Survey Fact Sheet 2006–3087, 4 p.

Telis, P.A., and Henkel, Heather, 2009, Everglades Depth 

Estimation Network (EDEN) applications—Tools to view, 

extract, plot, and manipulate EDEN data: U.S. Geological 

Survey Fact Sheet 2009–3052, 4 p.

Telis, P.A., Xie, Zhixiao, Lui, Zhongwei, Li, Yingru, and 

Conrads, P.A., 2014, The Everglades Depth Estimation Network (EDEN) surface-water model Version 2: 

U.S. Geological Survey Scientific Investigations Report 

2014–5209

U.S. Army Corps of Engineers, 1999, Central and Southern 

Florida Project comprehensive review study: Jacksonville, 

Fla., Final Integrated Feasibility Report and Programmatic Environmental Impact Statement, [variously paged], 

4 annexes, 15 apps.

U.S. Army Corps of Engineers, 2011, Everglades Restoration 

Transition Plan final environmental impact statement—

Volume 1: U.S. Army Corps of Engineers, Jacksonville 

District, [variously paged].

U.S. Fish and Wildlife Service, 2000, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge Comprehensive 

Conservation Plan: U.S. Fish and Wildlife Service, 362 p.

U.S. Geological Survey, 2007, Facing tomorrow’s challenges—U.S. Geological Survey science in the decade 

2007–2017: U.S. Geological Survey Circular 1309, x + 

70 p.

Weiss, S.M., and Indurkhya, Nitin, 1998, Predictive data mining—A practical guide: San Francisco, Morgan Kaufmann 

Publishers, Inc., 228 p.

Xie, Zhixiao, Liu, Zhongwei, Jones, J.W., Higer, A.L., and 

Telis, P.A., 2011, Landscape unit based digital elevation 

model development for the freshwater wetlands within the 

Arthur C. Marshall Loxahatchee National Wildlife Refuge, 

Southeastern Florida: Applied Geography, v. 31, no. 2, 

p. 401–412.
For further information about this publication contact:

Director

U.S. Geological Survey

South Atlantic Water Science Center

North Carolina–South Carolina–Georgia

Stephenson Center, Suite 129

Columbia, SC 29210

http://sc.water.usgs.gov/

Prepared by the Raleigh Publishing Service Center
Conrads—Hydrologic Record Extension of Water-Level Data in the Everglades Depth Estimation Network (EDEN), 1991–99—Scientific Investigations Report 2014–5226

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20145226