Prepared in cooperation with the U.S. Geological Survey Greater Everglades Priority

Ecosystem Science

Hydrologic Record Extension of Water-Level Data in the

Everglades Depth Estimation Network (EDEN) Using

Artificial Neural Network Models, 2000–2006

Open-File Report 2007–1350
Cover. Gaging station W11 in Water Conservation Area 3A of the Florida Everglades (photograph taken by Christa Zweig, Graduate 

 Research Assistant, Florida Cooperative Fish and Wildlife Research Unit, University of Florida).
Hydrologic Record Extension of WaterLevel Data in the Everglades Depth 

Estimation Network (EDEN) Using Artificial 

Neural Network Models, 2000–2006

By Paul A. Conrads and Edwin A. Roehl, Jr.

Prepared in cooperation with the U.S. Geological Survey Greater Everglades 

Priority Ecosystems Science

Open-File Report 2007–1350

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2007

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Suggested citation:

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. (only online at http://pubs.water.usgs.gov/ofr2007-1350)
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................4

Description of Study Area ...................................................................................................................5

Previous Studies ...................................................................................................................................5

Approach................................................................................................................................................6

Data-Collection Network..............................................................................................................................6

Limitation of the Datasets....................................................................................................................7

Estimating Water Levels ...............................................................................................................................9

Artificial Neural Networks ..................................................................................................................9

Decorrelation of Variables ................................................................................................................10

Statistical Measures of Prediction Accuracy................................................................................11

Example of Estimating Water Level Using Three-Step Modeling Approach............................11

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN)............20

Water Conservation Area 1...............................................................................................................20

Water Conservation Area 2...............................................................................................................22

Water Conservation Area 3A............................................................................................................25

Water Conservation Area 3B............................................................................................................31

Big Cypress National Preserve ........................................................................................................34

Everglades National Park..................................................................................................................36

Summary and Discussion...........................................................................................................................38

Acknowledgments.......................................................................................................................................38

References Cited..........................................................................................................................................38

Appendix 1. Summary of artificial neural network models used in the study .................................42

Appendix 2. Summary statistics for the models used in the study....................................................50

Appendix 3. Variables used in the artificial neural network models.................................................56

Figures

1–4. Maps showing:

1. Locations of Everglades Depth Estimation Network (EDEN) gaging 

stations in southern Florida................................................................................................2

2. The Everglades Depth Estimation Network (EDEN) digital elevation 

model for Water Conservation Areas (1, 2A, 2B, 3AN, 3AS, 3B), 

Big Cypress National Preserve, and Everglades National Park ..................................3

3. The Everglades Depth Estimation Network (EDEN) water surface 

model for September 10, 2006............................................................................................4

4. Greater Everglades, Florida ...............................................................................................5

5–7. Schematics showing:

5. Multiperceptron artificial neural network architecture................................................9

6. Decorrelation models........................................................................................................10

7. Three-step modeling approach to make final water-level estimates 

at a station ..........................................................................................................................14
iv

8. Example of a stacked dataset used to train the static and dynamic models ..........15

9–14. Graphs showing:

9. Measured and simulated water levels from the static model for Water 

Conservation Area 3A.......................................................................................................15

10. Measured and simulated residual water levels from the dynamic model 

for Water Conservation Area 3A.....................................................................................16

11. Initial water-level estimates for site W2........................................................................16

12. Measured water levels, initial water-level estimates, and residual 

time series for site W2 .....................................................................................................17

13. Residual time series between the measured and initial estimates 

of water levels for site W2 ...............................................................................................17

14. Measured and record extension (predicted) water levels at site W2 

and water levels for Site 64..............................................................................................18

15. Map showing index and hindcast stations for Water Conservation Area 1.....................20

16. Graphs showing water-level record extensions for sites North_CA1 

and South_CA1 in Water Conservation Area 1 for the period October 1, 1999, 

to September 30, 2006 ................................................................................................................21

17. Map showing index and hindcast stations for Water Conservation Area 2.....................22

18–19. Graphs showing:

18. Water-level record extensions for site EDEN11 in Water Conservation Area 2 

for the period October 1, 1999, to September 30, 2006 ................................................23

19. Difference in (A) water levels between Site 99 and site EDEN13 and 

(B) water-level record extensions for site EDEN13 in Water Conservation 

Area 2 for the period October 1, 1999, to September 30, 2006....................................24

20. Map showing index and hindcast stations for Water Conservation Area 3A..................25

21–25. Graphs showing:

21. Water-level record extensions for sites 3A-5, EDEN4, and EDEN8 in 

Water Conservation Area 3A for the period October 1, 1999, 

to September 30, 2006 .......................................................................................................26

22. Water-level record extensions for sites EDEN9, EDEN12, and W2 in Water 

Conservation Area 3A for the period October 1, 1999, to September 30, 2006 ........27

23. Water-level record extensions for sites W5, W11, and W14 in Water 

Conservation Area 3A for the period October 1, 1999, to September 30, 2006 ........28

24. Water-level record extensions for sites W15 and W18 in Water 

Conservation Area 3A for the period October 1, 1999, to September 30, 2006 ........29

25. Water-level record extensions for sites EDEN5 and EDEN14 in Water 

Conservation Area 3A for the period October 1, 1999, to September 30, 2006 ........30

26. Map showing index and hindcast stations for Water Conservation Area 3B..................31

27–28. Graphs showing:

27. Water-level record extensions for sites TI-8 and TI-9 in Water Conservation 

Area 3B for the period October 1, 1999, to September 30, 2006.................................32

28. Water-level record extensions for sites EDEN7 and EDEN10 in Water 

Conservation Area 3B for the period October 1, 1999, to September 30, 2006 ........33

29. Map showing index and hindcast stations for Big Cypress National Preserve...............34

30. Graphs showing water-level record extensions for sites EDEN1 and EDEN6 in Big 

Cypress National Preserve for the period October 1, 1999, to September 30, 2006 ........35

31. Map showing index and hindcast stations for Everglades National Park ........................36

32. Graphs showing water-level record extensions for sites EDEN3 and Met1 in the 

Everglades National Park for the period October 1, 1999, to September 30, 2006...........37
v

Tables

1. Everglades Depth Estimation Network (EDEN) stations, types, periods of record, 

and percent complete record for hindcast and index stations used in this study ............7

2. Model type, model name, input variables, model prediction variables, 

and variables used to estimate water levels at site W2 ......................................................12

3. Summary statistics for the models used to estimate water levels for site W2 ................13

4. Summary statistics for water-level estimates for new Everglades Depth 

Estimation Network (EDEN) stations .......................................................................................19

Conversion Factors and Datums

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Hydraulic gradient

inch per mile (in/mi) 1.5783 centimeter 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)

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.
vi

Acronyms and abbreviations used in the report

ADM Advanced Data Mining

ANN artificial neural network

BCNP Big Cypress National Preserve

BEP back error propagation

CERP Comprehensive Everglades Restoration Plan

CRADA Cooperative Research and Development Agreement 

EDEN Everglades Depth Estimation Network

ENP Everglades National Park

GIS geographic information system

HLN hidden layer neuron

ME mean error

MLP multilayer perceptron

MSE mean square error

OLS ordinary least squares 

PME percent model error

RBF radial basis function

RMSE root mean square error

R2 coefficient of determination

SFWMD South Florida Water Management District

SOFIA South Florida Information Access

USGS U.S. Geological Survey

WCA water conservation area

WL water level
Abstract

The Everglades Depth Estimation Network (EDEN) is 

an integrated network of real-time water-level gaging stations, 

ground-elevation models, and water-surface models designed 

to provide scientists, engineers, and water-resource managers 

with current (2000–present) water-depth information for the 

entire freshwater portion of the greater Everglades. The U.S. 

Geological Survey Greater Everglades Priority Ecosystem 

Science provides support for EDEN and the goal of providing 

quality assured monitoring data for the U.S. Army Corps of 

Engineers Comprehensive Everglades Restoration Plan. To 

increase the accuracy of the water-surface models, 25 realtime water-level gaging stations were added to the network 

of 253 established water-level gaging stations. To incorporate 

the data from the newly 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 simulated 

back in time (hindcasted) to be concurrent with data from 

the established gaging stations in the database. A three-step 

modeling approach using artificial neural network models 

was used to estimate the water levels at the new stations. The 

artificial neural network 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. 

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 

(25 of 25) were greater than 0.82. The model estimates showed 

good agreement with the measured data. For some new EDEN 

stations with limited measured data, the record extension 

(hindcasts) included periods beyond the range of the data used 

to train the artificial neural network 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 the majority of stations (20 of 

25), the percent model error was less than 1 percent.

Introduction

The Everglades Depth Estimation Network (EDEN) is 

an integrated network of real-time water-level gaging stations, 

ground-elevation models, and water-surface models designed 

to provide scientists, engineers, and water-resource managers 

with current (2000–present) water-depth information for the 

entire freshwater portion of the greater Everglades (Telis, 

2005, 2006). EDEN is presented on a 400-square-meter (m2) 

grid, and EDEN offers a consistent and documented dataset 

that can be used by scientists and managers to (1) guide 

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

ecological responses, and (3) support biological and ecological 

assessments that measure ecosystem responses to the Comprehensive Everglades Restoration Plan (CERP; U.S. Army Corps 

of Engineers, 1999). The target users of EDEN are biologists 

and ecologists who can use the information to examine trophic 

level responses to hydrodynamic changes in the Everglades. 

The EDEN database establishes a 7-year dataset of baseline 

conditions prior to the implementation of the CERP that offers 

investigators a single repository for historic hourly water-level 

data.

To estimate water depths in the greater Everglades, 

geographic information system (GIS) models have been 

developed to determine the ground elevation and water-surface 

elevation for the freshwater portion of the Everglades. The 

water-depth estimates are the differences between the two 

surfaces. Data to support the ground-elevation model include 

elevation measurements at over 50,000 sites (Desmond, 2003). 

Data to support the water-surface model include continuous 

Hydrologic Record Extension of Water-Level Data in 

the Everglades Depth Estimation Network (EDEN) Using 

Artificial Neural Network Models, 2000–2006

By Paul A. Conrads and Edwin A. Roehl, Jr.1

1

Advanced Data Mining, LLC, Greenville, South Carolina.
Figure 1. Locations of Everglades Depth Estimation Network (EDEN) gaging stations in southern 

Florida (modified from Pearlstine and others, 2007).

water levels at 253 stations, including 25 stations that were 

added to the EDEN database in 2006 (fig. 1). 

For the development of the ground-elevation model 

(Jones and Price, 2007), the EDEN domain was divided into a 

large number of equal-sized squares (“cells”) that in total are 

referred to as the “grid.” The grid includes information on the 

characteristics of each cell, such as centroid location, the area 

of the Everglades it represents, elevation, and percent vegetation type (slough, prairie, sawgrass, upland, exotic, and other). 

The large number of highly accurate elevation data allows for 

refinement of the ground-elevation model. The geostatistical 

technique of kriging was selected for the EDEN ground2 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

EDEN water-level stations

New EDEN water-level stations

Canals and rivers

EDEN boundary

EXPLANATION

0 7 14 21 28 MILES

0 10 20 30 40 KILOMETERS

N

Figure 1.

BCNP

WCA3AS

WCA3AN

ENP

WCA3B

WCA2B

WCA2A

WCA1
elevation model following extensive testing of multiple interpolation techniques. Kriging produced the lowest average error 

for validating elevation points and provides useful diagnostic 

surfaces. To account for variations within subregions of the 

EDEN area, individual geostatistical models were created for 

each water conservation area (WCA), the Everglades National 

Park (ENP), and portions of Big Cypress National Preserve 

(BCNP). These individual models were combined to create a 

single, 400-m2 resolution elevation model for the entire EDEN 

domain (fig. 2).

Figure 2. The Everglades Depth Estimation Network (EDEN) digital elevation model for Water 

Conservation Areas (1, 2A, 2B, 3AN, 3AS, 3B), Big Cypress National Preserve, and Everglades 

National Park (from Pearlstine and others, 2007).

Introduction 3

4.61 - 5.12

4.47 - 4.60

4.36 - 4.46

4.25 - 4.35

4.13 - 4.24

4.00 - 4.12

3.82 - 3.99

3.59 - 3.81

3.41 - 3.58

3.23 - 3.40

3.05 - 3.22

2.87 - 3.04

2.68 - 2.86

2.52 - 2.67

2.37 - 2.51

2.18 - 2.36

2.00 - 2.17

1.82 - 1.99

1.64 - 1.81

1.46 - 1.63

1.30 - 1.45

1.14 - 1.29

0.94 - 1.13

0.76 - 0.93

0.58 - 0.75

0.39 - 0.57

0.24 - 0.38

0.08 - 0.23

-0.08 - 0.07

-0.22 - -0.09

-0.35 - -0.23

-0.66 - -0.36

Elevation, in

 meters

EXPLANATION

98

441

1

27

1

1

41

41

75

75

595

95

Lake

Ochechobee

1

2A

2B

3AN

3AS

3B

AL

Miami

0 10 20 MILES

0 20 40 KILOMETERS

N

Figure 2.
A water-surface model was developed in GIS using the 

EDEN grid described above. The EDEN water-surface model 

interpolates measured water levels from the EDEN continuous 

monitoring network to ungaged locations using radial basis 

functions (RBF) with multiquadric regression (Pearlstine and 

others, 2007). The model produces a continuous water surface 

for any day within the period of record in the EDEN database. 

An example of the water surface for a sample day is shown in 

figure 3. 

Twenty-five stations were added to EDEN in 2006 to 

address water-level data gaps identified by scientists and 

hydrologists in the original EDEN configuration and to 

improve the continuous water-surface model. To incorporate 

the additional data into the EDEN database, the water-level 

records for the new stations needed to be extended back in 

time (hindcasted) to be concurrent with the records in the 

EDEN database. The U.S. Geological Survey (USGS) South 

Carolina Water Science Center, as part of the EDEN project 

team, developed artificial neural network (ANN) models to 

hindcast data from the new EDEN stations. An ANN model 

is a flexible mathematical structure capable of describing 

complex nonlinear relations between input and output datasets. 

The architecture of ANN models is loosely based on the 

biological nervous system (Hinton, 1992). 

Accurately hindcasting the hydrologic responses at the 

new locations can be challenging due to the limited number 

of reference gaging stations and a limited understanding of 

complex interactions between hydrology and topography. 

Techniques that often are used to hindcast hydrologic 

responses at ungaged locations include combinations of linear 

regression and interpolation; however, the dynamics between 

hydrology, topography, and vegetation often are nonlinear. 

This report presents the application of cascading ANN models 

to predict water levels at 23 new EDEN stations that were 

instrumented in 2006 and 2 EDEN stations in WCA1 with 

periods of record beginning in 2001. The ANN models were 

used to extend the 25 stations to be concurrent with the EDEN 

database beginning in January 2000.

To meet the objectives of this study and previous 

studies, the USGS entered into a Cooperative Research and 

Development Agreement (CRADA) with Advanced Data 

Mining (ADM) in 2002 to collaborate on applying data 

mining and ANN models to water-resources investigations. 

The emerging field of data mining addresses the issue of 

extracting information from large databases (Weiss 

and Indurkhya, 1998). Data mining is a powerful tool 

for converting large databases into knowledge for 

solving problems that are otherwise imponderable 

because of the large numbers of explanatory variables 

or poorly understood process physics. This knowledge 

encompasses understanding cause and effect relations 

and predicting the consequences of alternative actions. 

Data-mining methods come from different technical 

fields, such as signal processing, statistics, artificial 

intelligence, and advanced visualization. Data mining 

is used extensively in financial services, banking, 

advertising, manufacturing, and e-commerce to 

classify the behaviors of organizations and individuals 

and to predict future outcomes. 

Purpose and Scope 

This report documents the water-level record 

extensions (hindcasts) of 25 stations in the freshwater 

portion of the Everglades. The geographical extent 

of the hindcasts includes gaging stations in WCA1, 

WCA2, WCA3A, WCA3B, BCNP, and the ENP. 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. The techniques presented in 

this report demonstrate how valuable information can 

be extracted from existing databases to assist local, 

Figure 3. The Everglades Depth Estimation Network (EDEN) water 

surface model for September 10, 2006 (modified from Pearlstine and others, 

2007).

4 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

0 7 14 21 28 MILES

0 10 20 30 40 KILOMETERS

N

Figure 3.

Water stage, in centimeters, North

 American Vertical Datum 1988

High: 480

Low: 10

EXPLANATION
state, and Federal agencies. 

The application of data-mining 

techniques, including ANN 

models, demonstrates how 

empirical models can be developed to hindcast time series of 

complex hydrologic systems and 

how disparate databases can be 

integrated.

Description of Study Area 

The study area is within the 

greater Everglades area, which 

extends from south of Lake 

Okeechobee to the southern part 

of the ENP (fig. 4) 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 slopes with this 

shallow “river” are generally less 

than about 0.2 foot per mile (ft/

mi; German, 2000).

The Everglades contains 

several types of environments, 

including freshwater marshes, 

tree islands, pinelands, mangrove 

swamps, and shallow coastal 

marine waters. This study 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 feet 

(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).

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 ft during the wet 

season. Minimum seasonal water levels generally occur in 

May before onset of the wet season. In particularly dry 

years, large portions of the Everglades may become dry and 

subject to wildfires. Heavy rainfall associated with tropical 

depressions, storms, and hurricanes can have a large effect on 

water levels. A single such event can increase water levels by 

a foot or more over large parts of the Everglades and because 

of the slow runoff rates, this can effect water levels for months 

(German, 2000).

Previous Studies 

Estimating hydrologic and water-quality conditions at 

ungaged sites by using data-mining techniques and ANN 

models has been used in the Everglades, western Oregon, 

and Wisconsin. Conrads and others (2006) used data-mining 

techniques in a snail kite study in WCA3A to hindcast 

Figure 4. Greater Everglades, Florida (modified from German, 2000).

Introduction 5

Location of

study area in

Florida Lake

Okeechobee

WCA1

WCA2

WCA3

Everglades

National Park

Atlantic

Ocean

Gulf

of

Mexico

0 10 20 30 MILES

0 10 20 30 KILOMETERS

27

26

25

82 81 80

Big Cypress National Preserve

Everglades System

Loxahatchee National Wildlife

 Refuge

Canal

Everglades National Park boundary

Water conservation area boundary

WCA-3 Identifier for water conservation area

EXPLANATION

Figure 4.
short-term (less than 5 years) daily water-depth datasets using 

long-term (greater than 15 years) daily water-level data. The 

principal objective of the snail kite study was to separate 

plant community response resulting from typical seasonal and 

inter-annual variances in hydrologic regimes. The vegetative 

community structure of these sites is an expression of present 

and historic hydrologic conditions. A critical element of 

the study was to determine how the vegetative communities 

respond to temporal and spatial changes in hydrology. 

Artificial neural network models were developed to hindcast 

hydrologic histories at 17 transects dating back to 1991 to 

help ecologists in analyzing the water depth and hydroperiods 

over a large range of hydrologic conditions and to integrate 

long-term ecological data. 

Artificial neural network models have been applied in 

western Oregon to estimate stream temperature at ungaged 

sites (Risley and others, 2003). In that study, a dynamic 

clustering technique (Roehl and others, 2006) was used to 

subset 142 temperature stations from first-, second-, and 

third-order streams into three groups of similar dynamic 

behaviors. Using categorical (static) variables and time-series 

variables, water-temperature models were developed for 

ungaged sites. Critical input variables included riparian shade, 

station elevation, and percentage of forested area of the basin. 

Coefficients of determination (R2) and root mean square errors 

(RMSE) for the models ranged from 0.88 to 0.99 and 0.05 to 

0.59 degrees Celsius (°C), respectively.

Stewart and others (2006) describe a modeling application in Wisconsin that, like the Oregon modeling, predicts 

stream temperatures from climate signals, such as ambient 

temperature and rainfall, and categorical station attributes, 

such as land cover and drainage area. The application’s ANNs 

were trained on data, including summer-month daily average 

stream temperature time series, from 254 stations. This work 

was conceptually different from the Oregon application, 

which used concurrently measured signals. The Wisconsin 

stream temperatures were measured during different summers 

over 13 years. This required that an alternative time series 

clustering algorithm be developed that would still segment 

the signals according to their dynamic behaviors. The R2

and RMSE for the predictions at 31 test stations not used in 

ANN training ranged from 0.62 to 0.75 and 1.7 °C to 2.4 °C, 

respectively. The ANN predictions accurately tracked the 

day-to-day variability at the different stations, but the primary 

source of error was offset station-to-station baseline (mean 

summer) temperatures. The predicted baselines depend largely 

on the ANN’s categorical input variables, suggesting that the 

42 variables used can only provide a partial explanation of the 

causes of station-to-station variability or, more likely, that the 

measurements provided for them are quite noisy.

An approach similar to that used in Oregon was tested to 

predict water depths at ungaged locations in a subdomain of 

EDEN (Conrads and Roehl, 2006b). Using a combination of 

static and dynamic variables, predictions were generated in 

two modeling steps. The dynamic variables were 30-month 

time series of daily water depths at 16 stations and water 

levels at 3 other stations. Static variables were obtained from 

the EDEN 400-m2 grid. Values included coordinates of cell 

centroids and percentage vegetation types (slough, prairie, 

sawgrass, or upland) for approximately 2,300 cells, covering 

370 square kilometers. The first ANN model simulated water 

depths using static (categorical) input variables to predict a 

constant baseline water depth (mean for the period of record). 

The second ANN model predicted day-to-day variability about 

the water-depth baseline by using a combination of static 

and dynamic variable inputs. A complete estimation of water 

depth at a given cell was computed by summing the outputs of 

the two models. Five of the water-depth gaging stations were 

withheld from model development to validate model accuracy. 

Using this methodology, prediction accuracy was improved, 

resulting in an average RMSE prediction error at validation 

gaging stations of only 0.1 ft (3 centimeters), or 4 percent of 

the dynamic range.

Approach

The majority of the hindcasts estimated for this study 

used a modification of the two-step modeling approach using 

static and dynamic data described in Conrads and Roehl 

(2006b). The modification was the addition of a third step 

error-correction model. The general approach for estimating 

water levels at a new station was to

1. Identify the EDEN stations that have similar hydrologic responses in a particular area, 

2. Build databases for the static and dynamic variables, 

3. Decorrelate time-series inputs, 

4. Train the static and dynamic ANN models, 

5. Compute initial water-level estimates and residual 

error from the measured data, 

6. Train error-correction ANN models, and 

7. Make final water-level estimates. 

The process was then repeated for subsequent stations and 

areas in the Everglades. For a few stations (3 of the 25) with 

limited data and(or) limited data at nearby stations, a simpler 

single model approach was used. 

Data-Collection Network 

The water-level record extensions (hindcasts) use static 

and dynamic data from the EDEN monitoring network. 

The EDEN monitoring network includes ground-elevation 

measurements and continuous water-level data. Highly 

accurate ground-surface elevation data, collected by the USGS 

(Desmond, 2003), cover nearly the entire greater Everglades 

area. The elevation data were collected at over 50,000 points 

6 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
with an approximate spacing of 400 meters (m) to the North 

American Vertical Datum of 1988 (NAVD 88). The static 

variables were derived from the GIS cell attribute data of the 

400-m EDEN grid. Attributes include location of the centroid 

of the cell and percent vegetation type (slough, prairie, 

sawgrass, upland, exotic, and other). 

The EDEN database is composed of hourly water-level 

data from 253 gaging stations and includes freshwater 

marsh stations, boundary stations on canals, and coastal 

stations operated by the BCNP, ENP, the South Florida 

Water Management District (SFWMD), and the USGS. In 

this report, the names of the EDEN stations may follow the 

naming convention of the agency that maintains the stations. 

Stations with “site” in the name, such as Site 64 or Site 99, 

will be referenced with an uppercase S. All other references to 

a specific station will use a lowercase, such as site W2 or site 

North_CA1. 

The dynamic variables (time series) were obtained from 

the marsh gaging stations of EDEN. The period of record for 

the EDEN water-level network is from October 1, 1999, to 

September 30, 2006. The periods of record for the new EDEN 

gaging station vary from approximately 4 months to 5 years. 

To extend the water-level record at the new EDEN station, a 

subset of 35 of the EDEN stations was used as inputs to the 

model for estimating water levels (referred to as “index” stations in this report). The locations and periods of record of the 

new EDEN stations and the index stations are listed in table 1. 

The stations in WCA3A were separated into two groups.

Limitation of the Datasets 

As with any modeling effort, empirical or deterministic, 

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 training and calibrating the 

model. Estimated data were not used in model development; thus, the majority of the time series used were less 

than 100 percent complete. The available period of record, 

especially the hindcasted stations, can limit the range of water 

level that the ANN model can accurately simulate. For the 

new EDEN stations, the period of record for the measured data 

often is a year or less (table 1). Many of the time series of the 

new EDEN stations provided a range of water-level behaviors 

corresponding to low and high water of the dry and wet 

seasons but did not provide a history of inter-annual variability. Some stations with limited periods of record and(or) 

missing data, only described a limited portion of the expected 

water-level range.

Table 1. Everglades Depth Estimation Network (EDEN) stations, types, periods of record, and percent complete record

 for hindcast and index stations used in this study. — Continued

[USGS, U.S. Geological Survey; SFWMD, South Florida Water Management District; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Period of record

Station Operating

 agency Station type Begin date End date Number of datapoints

Percent 

complete 

record

Water Conservation Area 1 (fig. 15)

South_CA1 USGS Hindcast 6/20/2001 9/30/2006 46,571 75.9

North_CA1 USGS Hindcast 5/11/2001 9/30/2006 45,026 73.4

Site 7 USGS Index 10/1/1999 9/30/2006 59,531 97.0

Site 8T USGS Index 10/1/1999 9/30/2006 60,632 98.8

Site 9 USGS Index 10/1/1999 9/30/2006 61,055 99.5

WCA1ME SFWMD Index 10/1/1999 9/30/2006 60,315 98.3

Water Conservation Area 2 (fig. 17)

EDEN11 USGS Hindcast 6/9/2006 9/30/2006 2,723 4.4

EDEN13 USGS Hindcast 6/8/2006 9/30/2006 2,747 4.5

WCA2F1 SFWMD Index 10/1/1999 9/30/2006 51,177 83.4

WCA2E1 SFWMD Index 10/1/1999 9/30/2006 54,573 88.9

Site 99 USGS Index 10/1/1999 9/30/2006 60,645 98.8

S142H SFWMD Index 10/1/1999 9/30/2006 57,037 92.9

Water Conservation Area 3A (fig. 20)

Group 1

3A-5 USGS Hindcast 6/6/2006 9/30/2006 2,797 4.6

EDEN4 USGS Hindcast 6/9/2006 9/30/2006 2,728 4.4

EDEN8 USGS Hindcast 6/7/2006 9/30/2006 2,771 4.5

EDEN9 USGS Hindcast 6/9/2006 9/30/2006 925 1.5

EDEN12 USGS Hindcast 10/1/2005 9/30/2006 8,760 14.3

W2 USGS Hindcast 10/1/2005 9/30/2006 8,760 14.3

Data-Collection Network 7
Table 1. Everglades Depth Estimation Network (EDEN) stations, types, periods of record, and percent complete record

 for hindcast and index stations used in this study. — Continued

[USGS, U.S. Geological Survey; SFWMD, South Florida Water Management District; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Period of record

Station Operating

 agency Station type Begin date End date Number of datapoints

Percent 

complete 

record

Water Conservation Area 3A (fig. 20) Group 1 — Continued

W5 USGS Hindcast 10/1/2005 9/30/2006 8,760 14.3

W11 USGS Hindcast 10/1/2005 9/30/2006 8,760 14.3

W14 USGS Hindcast 10/1/2005 9/30/2006 8,760 14.3

W15 USGS Hindcast 1/25/2006 9/30/2006 4,991 8.1

W18 USGS Hindcast 10/1/2005 9/30/2006 8,760 14.3

Site 64 USGS Index 10/1/1999 9/30/2006 60,636 98.8

Site 63 USGS Index 10/1/1999 9/30/2006 60,402 98.4

3AS3W1 SFWMD Index 10/1/1999 9/30/2006 52,186 85.0

Site 65 USGS Index 10/1/1999 9/30/2006 61,368 100.0

3ASWa SFWMD Index 10/1/1999 9/30/2006 60,407 98.4

Group 2

EDEN 5 USGS Hindcast 6/5/2006 9/30/2006 1,657 2.7

EDEN 14 USGS Hindcast 7/26/2006 9/30/2006 1,534 2.5

Site 62 USGS Index 10/1/1999 9/30/2006 59,847 97.5

3A9 SFWMD Index 10/1/1999 9/30/2006 58,027 94.5

3A12 SFWMD Index 10/1/1999 9/30/2006 53,915 87.8

Water Conservation Area 3B (fig. 26)

TI-8 USGS Hindcast 1/23/2006 9/30/2006 6,013 9.8

TI-9 USGS Hindcast 1/23/2006 9/30/2006 6,014 9.8

EDEN7 USGS Hindcast 6/8/2006 9/30/2006 2,748 4.5

EDEN10 USGS Hindcast 6/8/2006 9/30/2006 2,748 4.5

Site 69 USGS Index 10/1/1999 9/30/2006 61,277 99.8

Site 71 USGS Index 10/1/1999 9/30/2006 60,457 98.5

Site 76 USGS Index 10/1/1999 9/30/2006 61,059 99.4

SRS1b USGS Index 10/1/1999 9/30/2006 60,989 99.3

Big Cypress National Preserve (fig. 29)

EDEN1 BCNP Hindcast 1/13/2006 9/30/2006 4,389 7.1

EDEN6 BCNP Hindcast 7/10/2006 9/30/2006 1,974 3.2

BCA9 BCNP Index 10/1/1999 9/30/2006 60,236 98.1

LOOP1T SFWMD Index 10/1/1999 9/30/2006 56,688 92.3

LOOP2T SFWMD Index 10/1/1999 9/30/2006 56,093 91.4

BCA10 BCNP Index 10/1/1999 9/30/2006 60,084 97.8

BCA5 BCNP Index 10/1/1999 9/30/2006 57,800 94.1

3ASW SFWMD Index 10/1/1999 9/30/2006 60,407 98.4

L28GAP SFWMD Index 10/1/1999 9/30/2006 53,515 87.1

Everglades National Park (fig. 31)

EDEN3 USGS Hindcast 12/12/2005 9/30/2006 6,981 11.4

Met1 USGS Hindcast 8/7/2006 9/30/2006 1,312 2.1

P34 ENP Index 10/1/1999 9/30/2006 58,307 95.0

OT ENP Index 10/1/1999 9/30/2006 57,106 93.0

TMC ENP Index 10/1/1999 9/30/2006 59,178 96.4

P35 ENP Index 10/1/1999 9/30/2006 58,954 96.0

P36 ENP Index 10/1/1999 9/30/2006 59,223 96.4

NE1 USGS Index 10/1/1999 9/30/2006 61,316 99.9

SRS1 USGS Index 10/1/1999 9/30/2006 60,989 99.4

NP201 ENP Index 10/1/1999 9/30/2006 59,252 96.6

NE2 USGS Index 10/1/1999 9/30/2006 58,024 94.5

NESRS3 SFWMD Index 10/1/1999 9/30/2006 52,855 86.1

a

 Station also used for hindcasts in Big Cypress National Preserve.

b

 Station also used for hindcasts in Everglades National Park.

8 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Estimating Water Levels 

The following section describes how the water levels 

were estimated for the new EDEN stations using ANN 

models. Hydrologic systems, such as the Everglades, exhibit 

random, chaotic, and multiple periodic behaviors that are 

driven by gravity flow, weather, and manmade disturbances, 

such as controlled flow releases. Modeling these behaviors 

on a large scale is challenging because of discontinuities in 

behaviors both spatially and temporally. Modeling requires 

calibration and validation data that represent the diversity 

of causes and effects. Subdividing a complex modeling 

problem into subproblems and addressing each subproblem 

is an effective means of achieving the best possible results. 

The creation of the various water conservation areas (WCA) 

in the Everglades transformed the system from a continuous 

“shallow” river from Lake Okeechobee to the Gulf of Mexico 

into a series of discontinuous compartments. The WCAs are 

logical boundaries to subdivide the EDEN into a subnetwork 

of water-level gaging stations to model the new EDEN 

water-level stations separately for WCA1, WCA2, WCA3A, 

WCA3B, BCNP, and ENP. 

Within the compartments, water levels respond to 

large-scale, hydraulic gradients of the “shallow” river and 

small-scale changes in topography and vegetation. As water 

levels change, the restrictions (impedances) to flow change 

as more vegetation is inundated during rising and high water 

levels or as more water is channelized during falling and low 

water levels. The three-step modeling approach presented in 

this report uses information about vegetation and topography 

in addition to time-series 

data to generate accurate 

estimates of water levels. This 

section describes ANN models, 

statistical measures of prediction 

accuracy, the decorrelation of 

input variables, and an example 

that describes how to estimate 

water levels at a new EDEN 

station.

Artificial Neural 

Networks 

Models generally fall 

into one of two categories—

deterministic (mechanistic) or 

empirical. Deterministic models 

are created from first-principle 

equations, and empirical models 

adapt generalized mathematical 

functions to fit a line or surface 

through data from two or more 

variables. The most common 

empirical approach is ordinary 

least squares (OLS), which relates variables using straight 

lines, planes, or hyper-planes, whether the actual relations 

are linear or not. Techniques such as OLS and physics-based 

finite-difference models prescribe the functional form of the 

model’s fit of the calibration data. Machine-learning techniques, like ANNs, synthesize a best fit of the calibration data.

The calibration of deterministic and empirical models 

attempts to optimally synthesize a line or surface through the 

measured data. Calibrating models is difficult when data have 

substantial measurement error or are incomplete, and the variables for which data are available may only be able to provide 

a partial explanation of the causes of variability. The principal 

advantages that empirical models have over deterministic 

models are they can be developed much faster and are more 

accurate when 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 

between input and output variables (Roehl and others, 2003). 

Although there are numerous types of ANNs, the most 

commonly used type of ANN is the multilayer perceptron 

(MLP; Rosenblatt, 1958). As shown in figure 5, MLP ANNs 

are constructed from layers of interconnected processing 

elements called neurons, each executing a simple “transfer 

function.” All input layer neurons are connected to every 

hidden layer neuron (HLN), and every HLN is connected to 

every output neuron. There can be multiple hidden layers, but 

a single hidden layer is sufficient for most problems.

Typically, linear transfer functions are used to scale input 

values to fall within the range that corresponds to the most 

Figure 5. Multiperceptron artificial neural network architecture.

Estimating Water Levels 9

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

Figure 5. 
linear part of the s-shaped sigmoid transfer functions used in 

the hidden layers. 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 their weights, and 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 

is commonly used to train MLP ANNs is the back error propagation (BEP) training algorithm (Rumelhart and others, 1986). 

Jensen (1994) describes the details of the MLP ANN, the type 

of ANN used in this study. Multilayer perceptron ANNs can 

synthesize functions to fit high-dimension, nonlinear multivariate data. Devine and Roehl (2003) and Conrads and Roehl 

(2005) describe their use of ANNs in multiple applications to 

model and control combined manmade and natural systems, 

including disinfection by-product formation, industrial air 

emissions monitoring, and surface-water systems, affected by 

point and nonpoint-source pollution. 

Experimentation with a number of ANN architectural and 

training parameters is a normal part of the modeling process. 

For correlation analysis or predictive modeling applications, 

a number of candidate ANNs are trained and evaluated for 

their statistical accuracy and their representation of process 

physics. Interactions between combinations of variables also 

are considered. Input variables to the models are selected to 

minimize correlation between variables (typically Pearson 

coefficient R of less than 0.5). Finally, a satisfactory model 

can be configured for end-user deployment. In general, a 

high-quality, predictive model can be obtained when

•	 The data are well distributed throughout the behavioral 

range of interest,

•	 The input variables selected by the modeler share 

“mutual information” about the output variables, and

•	 The functional form “prescribed” or “synthesized” for 

the model used to “map” (correlate) input variables 

to output variables is a good one. Techniques, such 

as OLS and physics-based finite-difference models, 

prescribe the functional form of the model’s fit of the 

calibration data. Machine-learning techniques like 

ANNs synthesize a best fit to the data.

Decorrelation of Variables 

Often, explanatory variables share information about the 

behavior of a response variable. It is difficult, if not impossible, to understand the individual effects of these variables 

(sometime known as confounded or correlated variables), on a 

response variable. Using correlated inputs to the models also 

can spuriously increase the model accuracy statistics, such 

as R2. Empirical models have no notion of process physics, 

nor 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 

“decorrelation.” Decorrelation is accomplished by ordering 

confounded variables according to a criterion. For example, 

the relative independence of the correlated variables is 

determined and then empirical functions (ANN models) of 

the less independent variables are developed using the more 

independent variables as inputs. The empirical function’s 

residual error is computed by subtracting its predicted values 

from the actual measurements. The residual error manifests 

the “unshared” information between the model’s more 

independent input variables and its less independent output 

variable. The residual error is the decorrelated version of the 

output variable (decorrelated variable) and can be used in 

water-level models. For example, in WCA3A, there are five 

existing EDEN stations that could be used to predict the water 

levels at the new stations—Site 63, Site 64, Site 65, 3AS3W1, 

and 3ASW. Four of the stations, Site 63, Site 65, 3AS3W1, 

and 3ASW, are systematically decorrelated from Site 64, 

using cascading models (fig. 6). Note that the residual error 

(decorrelated variable) from each anteceding model becomes 

an input to a subsequent model. The input variables and 

statistical summaries for the decorrelation models are listed in 

Appendixes 1 and 2 at the back of the report.

In this study, the decorrelation order was determined by 

minimizing the incomplete record of the decorrelated variable. 

A model cannot compute an output value when an input has 

Figure 6. Decorrelation models.

10 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

WL Site 64pred1 = F1[ WL Site 3ASW1 ]

WL Site 64 measured

WL Site 64 residual

WL Site 64pred2 = F2[WL Site 65 and WL Site 3ASW1 decorrelated]

First Decorrelation Model

Second Decorrelation Model

WL Site 64 residual

WL Site 64 measured
a missing value. For example, if three time series needing to 

be decorrelated and the time series are 90, 75, and 50 percent 

complete records, respectively, and the decorrelation order was 

the third, second, and first datasets, all the decorrelated variables would be 50 percent complete or less (missing data may 

not be concurrent between datasets). Using the third dataset in 

the first decorrelation model (the 50 and 75 percent complete 

datasets) would result in a decorrelated variable only 37.5 

percent complete. Subsequent decorrelation models would 

produce a decorrelated variable that is 34 percent complete (90 

percent x 37.5 percent = 34 percent). The better decorrelation 

order would be the 90-percent, 75-percent, and 50-percent 

datasets. The decorrelation model (the 90- and 75- percent 

datasets) would result in a decorrelated variable 68 percent 

complete. The subsequent decorrelation model would, like the 

first decorrelation order, result in a decorrelated variable that is 

34 percent complete (68 percent x 50 percent = 34 percent). 

Statistical Measures of Prediction Accuracy 

Statistical measures of prediction accuracy were 

computed for the final water-level estimates and for the decorrelation, static, dynamic, and error-correction models. The 

statistics for the final water-level estimates capture the ability 

of the three-step modeling approach to accurately estimate 

the water levels at the station. The statistics for the decorrelation models and individual step models (static, dynamic, 

and error-correction models) document these intermediate 

models. Because several models are used, the statistics for the 

individual models may not be an indication of the quality of 

the final water-level estimates. For example, the static models 

generally have very low R2, especially in the test dataset, as 

would be expected when static variables are used to predict a 

dynamic time series. Ultimately, the hindcasts should be evaluated by the statistics for the final estimates. The decorrelation 

models typically have high R2 values, but the results from the 

model used in the dynamic models are the residuals which 

have a low R2.

The R2, mean error (ME), RMSE, and percent model 

error (PME) were computed for the training and testing 

datasets for each model and are listed in Appendix 2. 

Model accuracy commonly is reported in terms of R2 and is 

interpreted as the “goodness of the fit” of a model. A second 

interpretation may answer the question, “How much information does one variable or a group of variables provide about 

the behavior of another variable?” In the first context, 

an R2 = 0.6 might be disappointing, whereas in the latter, it is 

merely an accounting of how much information is shared by 

the variables being used. 

The ME and RMSE statistics provide a measure of the 

prediction accuracy of the ANN models. The ME is a measure 

of the bias of model predictions—whether the model over 

or under predicts the measured data. The ME is presented as 

the adjustment of the simulated values to equal the measured 

values; therefore, positive and negative MEs indicate an over 

or under prediction bias by the model, respectively. Mean 

errors near zero may be misleading because negative and 

positive discrepancies in the simulations can cancel each other. 

Root mean square errors 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.

 The minimum and maximum values of the measured 

output are listed in Appendix 2. 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 PME is computed by dividing the RMSE by the range of 

the measured data.

Example of Estimating Water Level Using ThreeStep Modeling Approach

Generally, the same modeling approach for estimating 

water levels at a new EDEN site was used in all six areas. 

The three-step modeling approach is described in this section 

along with a detailed example of estimating the water level 

at W2 in WCA3A. Variable inputs for the models used in the 

W2 example are listed in table 2, and summary statistics for 

the models are listed in table 3. The input variables, summary 

statistics, and variable descriptions for all the models are 

listed in Appendixes 1, 2, and 3, respectively, at the back of 

the report (tables 2 and 3 are excerpts of Appendixes 1 and 

2, respectively). (The summary statistics for 25 hindcasts are 

listed in table 4, p. 19.) The ANN models and plots discussed 

in this report were developed using the iQuestTM data-mining 

software1 (Version 2.03C DM Rev31). 

The three-step modeling approach was developed to 

estimate water levels at the new EDEN stations. The approach 

uses output from the first model as input to the second and 

output from the second model as input to the third model. 

A schematic of the three-step modeling approach is shown 

in figure 7. The first model (F1) predicts the water level 

(WL-Sitepred1) using inputs for only the static variables of 

cell location (cell_x and cell_y) of the gaging station and the 

percent vegetation types (pctslough, pctprairie, pctsawgrass, 

pctupland, pctexotic, and pctother). Although, this model (also 

called the “static” model) is not able to predict the dynamic 

variability of the water level, it is able to discriminate general 

station-to-station differences based on location and percent 

vegetation. 

1

 The iQuestTM software is exclusively distributed by Advanced Data Mining, LLC, 3620 Pelham Road, PMB 351, Greenville, SC 29615-5044 Phone: 

(864) 201-8679, email: info@advdatamining.com, http://www.advdatamining.

com.

Estimating Water Levels 11
Table 2. Model type, model name, input variables, model prediction variables, and variables used to estimate water levels at site 

W2. 

Model type Model name Input variablesa

Model 

prediction 

variable

Variable used 

from model Comment

static cluster1static CELL_Y WLSITE RES_WLSITE Static model for Group 1 stations in 

WCA3a—Water-level prediction 

(WLSITE) used for initial water-level estimate and residual (RES_WLSITE) used 

for model for dynamic model.

PCTEXOTICS

PCTSLOUGH

PCTPRAIRIE

PCTOTHER

dynamic cluster1dynamic SITE_63DEC RES_WLSITE RES_WLSITE Dynamic model for Group 1 stations in 

WCA3a—RES_WLSITE prediction from 

dynamic model and WLSITE prediction 

from static model used for initial waterlevel estimate. 

SITE_64

3AS3W1DEC

CELL_Y

PCTSLOUGH

PCTEXOTICS

PCTOTHER

decorrelation 3as3w1dec 3AS3W1 SITE_64 3as3w1dec Model to decorrelate 3AS3W1 from 

SITE_64.

decorrelation 65dec SITE_65 SITE_64 65dec Model to decorrelate Site_65 from SITE_64 

3AS3W1DEC and 3AS3W. 

decorrelation 63decr1 3AS3W1DEC SITE_64 63decr Model to decorrelate Site_63 from SITE_64, 

SITE_65DEC 3AS3W1, and Site_65.

SITE63

decorrelation 3aswdec 3AS3W1DEC SITE_64 3aswdec Model to decorrelate 3ASW from SITE_64, 

SITE_65DEC 3AS3W1, Site_65, and Site_63.

SITE_63DEC

3ASW

error correction w2res SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial waterlevel estimate and measured data 

for site W2.

SITE_64

3AS3W1DEC 

a

 Descriptions of variables are provided in Appendix 3.

12 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Table 3. Summary statistics for the models used to estimate water levels for site W2.

[HLN, hidden layer neurons; min, minimum; max, maximum; WL, water level; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model type Model name Number of HLN

Training

Range of 

output variable

n R2 ME, WL SSE, WL MSE, WL RMSE, WL PME Min, 

WL

Max, 

WL

static cluster1static 2 8.26 10.28 5 1.000 -0.0002 0.0001 0.000 0.004 0.2decorrelation 3as3w1dec 1 8.51 11.74 11 0.991 0.005 0.11 0.010 0.109 3.4decorrelation 65dec 1 8.30 11.95 90 0.995 -0.005 0.41 0.005 0.068 1.9decorrelation 63decr1 1 8.29 11.95 358 0.941 -0.014 14.50 0.041 0.202 5.5decorrelation 3aswdec 1 8.73 11.95 962 0.951 -0.047 28.67 0.030 0.173 5.4dynamic cluster1dynamic 3 -2.39 2.11 1,622 0.969 0.012 37.84 0.023 0.153 3.4error correction w2res 2 0.76 2.06 128 0.976 -0.002 0.40 0.003 0.056 4.3

Model type Model name Number of HLN

Testing

Range of 

output variable

n R2 ME, WL SSE, WL MSE, WL RMSE, WL PME Min, 

WL

Max, 

WL

static cluster1static 2 6.55 13.39 97,891 0.446 -0.0002 74,110.44 0.757 0.870 12.7decorrelation 3as3w1dec 1 8.28 11.95 51,742 0.970 -0.021 1,047.08 0.020 0.142 3.9decorrelation 65dec 1 8.28 11.95 51,742 0.993 -0.029 260.47 0.005 0.071 1.9decorrelation 63decr1 1 8.28 11.95 50,776 0.939 0.044 2,098.85 0.041 0.203 5.5decorrelation 3aswdec 1 8.69 11.95 49,815 0.959 -0.015 1,337.04 0.027 0.164 5.0dynamic cluster1dynamic 3 -10.26 2.17 83,968 0.960 0.012 2,312.33 0.028 0.166 1.3error correction w2res 2 0.73 2.11 7,648 0.974 0.008 22.42 0.003 0.054 3.9

Estimating Water Levels 13
Figure 7. Three-step modeling approach to make final water-level estimates at a station.

To train and test the static model, a “stacked” dataset 

(Roehl and others, 2006) was generated that included the 

time series and static variables from the index EDEN gaging 

stations (fig. 8). For example, in WCA3A, five index EDEN 

stations were used as inputs (explanatory variables) to develop 

the models to hindcast water-level data at the new stations. 

The static model used in WCA3A uses 5 index stations for 

predicting water levels at 11 of the new EDEN stations. 

The index stations are Site 63, Site 64, Site 65, 3AS3W, 

and 3ASW. The static model uses five static variables: 

cell_y, pctexotics, pctslough, pctprairie, and 

pctother (table 2). The static model uses two hidden layer 

neurons (HLN). The R2 of the training and testing datasets 

are 1.0 and 0.44, respectively (cluster1static, table 3). The 

water-level predictions from the static model for five stations 

in WCA3A are shown in figure 9. The apparent baseline shifts 

(“steps”) in the simulated time series represent a different station used in the static model. The model is able to discriminate 

relative differences in water levels between the stations using 

only the static variables of location and percent vegetation.

Using the water-level predictions and the measured data 

at the five index stations, the residual error (the difference 

between the predicted and measured water level), 

WL-Siteresidual, is computed for each station. The residual 

error manifests the dynamic variability at the station that 

was not simulated by the static model and is simulated by 

a second model (F2, fig. 7). The second model (also called 

the “dynamic” model) uses time series of water level in 

addition to static variables to predict WL-Siteresidual. For the 

WCA3A example, the dynamic model uses three dynamic 

input variables (Site_64, Site_63dec, 3AS3W1dec; table 2) 

and four static input variables (cell_y, pctslough, 

pctexotics, and PCTOTHER; table 2). The input variables 

and summary statistics for the decorrelation models are listed 

in tables 2 and 3, respectively. The dynamic model uses three 

HLNs, and the R2 of the training and testing datasets are 

0.969 and 0.960, respectively (cluster1dynamic, table 3). The 

measured and predicted residual water levels are shown in 

figure 10. The dynamic model uses the same “stacked” dataset 

as the static model. 

To compute the initial estimate of water level at a new 

EDEN station, the static variables are used in the static (F1) 

and dynamic (F2) models. The initial prediction is the sum 

of the water-level predictions from the static model and the 

14 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

Figure 7.

Static Model WL-Sitemeasured

Initial estimate at a new EDEN site

Final estimate at new site

Dynamic Model

WL-Sitepred1 = F1[Static variable] WL-Siteresidual

WL-Newpred1 = WL-Sitepred1 + WL-Siteresidual-pred2

WL-Newpred2 = WL-Newpred1 + WL-Newresidual-pred3

WL-Newresidual

WL-Siteresidual-pred2 = F2[Static and Dynamic Variables]

Models developed from

“old” EDEN sites and 

static data from EDEN grids

WL-Newmeasured

Error Correction Model

WL-Newresidual-pred3 = F3 [Dynamic Variables]
Figure 8. Example of a stacked dataset used to train the static and dynamic models. Each block represents a limited number of rows 

for each index site in the dataset. Note the dynamic variables are in columns 3–8 (WLSITE to 3ASWDEC) and static variables begin in 

column 9 (CELL_X). Not all variables in the dataset are shown.

Figure 9. Measured (blue trace) and simulated (red trace) water levels from the static model for Water Conservation 

Area 3A. The “steps” in the simulated water level indicate a different site.

Estimating Water Levels 15

Site 63

Site 64

Site 65

3AS3W

3ASW

Figure 8

14

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 15,000 30,000 45,000

HOURLY OBSERVATIONS

60,000 75,000 90,000

Measured

Simulated

Figure 9.
Figure 10. Measured (blue trace) and simulated (red trace) residual water levels from the dynamic model for Water 

Conservation Area 3A. The residual water levels were computed from the water-level prediction from the static model. 

The training dataset is shown. There are approximately 325 observations from each of the five index sites.

residual from the dynamic model. For example, to compute 

the initial water-level prediction for site W2 in WCA3A 

(WL-Newpred1, fig. 7), the static variables for the new station 

are used in the static and dynamic models (cell-y, 

pctexotics, pctslough, pctprairie, and

pctother) to compute WL-Sitepred1 and WL-Siteresidual-pred2

(fig. 7). The results from the static and dynamic models, and 

the initial water-level predictions and measured data for site 

W2 are shown in figure 11. Although the initial water-level 

estimates capture the dynamic variability of the measured data, 

the absolute predictions are in error by approximately 1 to 2 ft. 

To improve the accuracy of the water-level predictions, 

a third-step model (F3, error correction model, fig. 7) is used 

to estimate the residual error between the initial water-level 

estimate and the measured data at the new EDEN station. The 

residual error is computed by subtracting the initial water-level 

Figure 11. Initial water-level estimates for site W2. Results from the static and dynamic models are shown with the measured data. 

Breaks in the water-level estimates are caused by incomplete time series for one or more of the model inputs.

16 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

3

2

1

0

-1

-2

-3

RESIDUAL WATER LEVEL, IN FEET

0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600

HOURLY OBSERVATIONS

Measured

Simulated

Figure 10.

11

9

7

5

3

1

-1

-3

-5

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Measured data Static model results

Figure 11.

Dynamic model

results

Initial water-level estimates for W2
estimates from the measured data (fig. 12). The errorcorrection model uses a set of dynamic variables to predict the 

residual error from the initial water-level estimate. The time 

series of computed and predicted error is shown in figure 13. 

The error-correction model for site W2 (W2res) uses three 

dynamic variables: Site_63DEC, Site_64, and 3AS3W1DEC 

(table 2) and two HLNs. The R2 for the training and testing 

datasets for the error-correction model is 0.976 and 0.974, 

respectively (table 3). 

The final water-level estimate at a new EDEN station is 

the sum of the initial water-level estimate and the predicted 

residual from the error-correction model (WL-Newresidual-pred3, 

fig. 7). The results of the error-correction model and final 

water-level estimates for site W2 are shown in figure 14. The 

Figure 12. Measured water levels, initial water-level estimates, and residual time series (difference between 

the measured and initial water-level estimates) for site W2. Breaks in the water-level estimates are caused by 

incomplete time series for one or more of the model inputs.

Figure 13. Residual time series between the measured and initial estimates of water levels for site W2. Breaks in the 

water-level estimates are caused by incomplete time series for one or more of the model inputs.

Estimating Water Levels 17

10

9

8

7

6

5

4

3

2

1

0

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Measured

Residual

Figure 12.

W2 initial estimate

Difference between measured and

estimated values

2.7

2.2

1.7

1.2

0.7

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Residual

Figure 13.

Error model

prediction
R2

 and PME for the final water-level estimate are 0.995 and 

0.1 percent, respectively (table 4). Water levels for Site 64 also 

are plotted to show the general hydrologic response concurrent 

with the record extension for W2.

Empirical and mechanistic models perform best when 

interpolating within the range of data used for training or 

calibration. Although the statistics of the final water-level 

estimate are good, the hindcasts should be evaluated for periods when the model extrapolates to estimate the hydrologic 

response. The range of interpolation of water-level estimation 

model for site W2 (fig. 14) shows that the model estimates 

were extrapolated only for a brief period of low-water conditions. The breaks in the water-level estimates are caused by 

incomplete time series for one or more of the model inputs.

Figure 14. Measured and record extension (predicted) water levels at site W2 and water levels for Site 64. The range of 

measured water levels at W2 is shown with two dashed lines and used as an indication of when the W2 model is interpolating 

within conditions the model was trained. Breaks in the water-level estimates are caused by incomplete time series for one or 

more of the model inputs.

18 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

W2

measured

Site 64

measured

Figure 14.

W2 record

extension

Range of model

interpolation
Table 4. Summary statistics for water-level estimates for new Everglades Depth Estimation Network (EDEN) stations.

[n, number of data values; R, Pearson coefficient; R2, coefficient of determination; Min, minimum; ft, feet; Max, maximum; ME, mean error; RMSE, 

root mean square error; PME, percent model error]

Site n R R2

Data range

Min, ME RMSE PME

in ft

Max, 

in ft

Water Conservation Area 1 (fig. 15)

North_CA1 41,721 0.943 0.889 13.82 16.38 -0.046 0.134 5.2

South_CA1 43,409 0.991 0.983 12.85 15.90 0.008 0.088 2.9

Water Conservation Area 2 (fig. 17)

EDEN11 2,637 0.950 0.902 10.97 13.19 -0.054 0.044 2.0

EDEN13 1,968 0.955 0.912 7.07 7.69 -0.018 0.006 1.0

Water Conservation Area 3A (fig. 20)

3A-5 5,684 0.998 0.995 8.15 10.10 0.002 0.001 0.1

EDEN4 2,399 0.999 0.998 6.96 10.30 0.001 0.002 0.1

EDEN5 1,653 0.999 0.999 8.01 10.20 0.004 0.001 0.1

EDEN8 2,442 0.999 0.999 6.79 9.19 0.001 0.001 0.0

EDEN9 925 0.999 0.998 7.69 10.55 -0.006 0.004 0.1

EDEN12 7,648 0.999 0.998 6.84 9.59 -0.002 0.001 0.0

EDEN14 969 0.906 0.821 8.66 9.59 0.011 0.010 1.1

W2 7,648 0.998 0.995 6.86 9.42 0.008 0.003 0.1

W5 7,648 0.999 0.998 6.84 9.59 -0.001 0.001 0.0

W11 7,628 0.999 0.998 7.08 10.08 -0.012 0.002 0.1

W14 7,628 0.998 0.997 7.00 10.00 -0.013 0.003 0.1

W15 3,859 0.999 0.998 7.47 9.67 -0.001 0.001 0.0

W18 7,628 0.998 0.996 7.92 10.21 -0.000 0.002 0.1

Water Conservation Area 3B (fig. 26)

TI-8 5,684 0.996 0.993 4.59 6.16 0.002 0.001 0.1

TI-9 5,684 0.996 0.992 5.29 6.42 0.009 0.001 0.1

EDEN7 2,419 0.998 0.996 5.24 6.96 0.008 0.001 0.1

EDEN10 2,419 0.995 0.990 5.06 6.32 0.007 0.002 0.1

Big Cypress National Preserve (fig. 29)

EDEN1 3,864 0.960 0.921 7.13 7.82 0.018 0.003 0.4

EDEN6 1,591 0.984 0.968 8.76 10.73 0.030 0.007 0.4

Everglades National Park (fig. 31)

EDEN3 5,294 0.989 0.978 0.07 1.75 -0.042 0.006 0.4

Met1 1,238 0.994 0.989 5.23 5.76 0.000 0.000 0.0

Estimating Water Levels 19
Extension of Water-Level Records 

for the Everglades Depth Estimation 

Network (EDEN)

The water-level record extensions for six areas of the 

Everglades are summarized in the following sections of the 

report. The hindcast and index stations for each area are shown 

in a figure followed by the measured and estimated time 

series. Water levels for one of the index stations in each area 

are also plotted to show the general hydrologic response of the 

area for the 7 years concurrent with the record extension. The 

datasets with the record extensions are available on the EDEN 

Web page on the South Florida Information Access (SOFIA) 

Web site (http://sofia.usgs.gov/eden/index.php).

Water Conservation Area 1 (WCA1)

For WCA1, water-level records were extended for two 

stations—North_CA1 and South_CA1—with four stations 

being used as index stations—Site 7, Site 8T, Site 9, and 

WCA1ME (fig. 15; table 1). The static and dynamic models 

used three static-input variables (CELL_Y, PCTPRAIRIE, and 

PCTEXOTICS). The dynamic models also used four waterlevel input variables (SITE_7, SITE8DEC2, WCA1MEDEC, 

and SITE9DEC). The measured and estimated water levels for 

the two stations are shown in figure 16. Site 7 also is plotted 

to show the general water-level behavior through the record 

extension. The water-level estimates for the South_CA1 

gaging station are more accurate than those for the North_CA1 

gaging station with R2 values of 0.98 and 0.89, respectively, 

and PME values of 2.9 and 5.2, respectively (table 4). Both 

sets of water-level estimates capture the full range of the 

measured data.

Figure 15. Index 

and hindcast 

stations for Water 

Conservation Area 1.

20 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

!

!

#

#

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

2640’

26

35’

26

30’

26

25’

26

20’

80

30’ 8025’ 8020’ 8015’

EXPLANATION

Hindcast station and number

Index station and number

NORTH_CA1

Site 7

NORTH_CA1

Site 7

WCA1ME

Site 8T

Site 9

SOUTH_CA1

Water Conservation Area 1

Water Conservation Area boundary

Base from U.S. Geological Survey digital data,

6-meter DOQ mosaic of south Florida, 2000,

Florida East, Zone 0901

Transverse Mercator projection

NAD 83 datum
Figure 16. Water-level record extensions for sites North_CA1 and South_CA1 in Water Conservation Area 1 for the period 

October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one or more 

of the model inputs.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 21

North_CA1

17

16

15

14

13

WATER LEVEL, IN FEET

17

16

15

14

13

12

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 16.

North_CA1

South_CA1

North_CA1 

measured

Site 7 measured

North_CA1

extension

South_CA1

measured Site 7

measured

South_CA1

extension
Water Conservation Area 2 (WCA2)

For WCA2, water-level records were extended for two 

stations—EDEN11 and EDEN13. The two new EDEN stations 

had very limited periods of record of approximately 4 months 

(table 1). For EDEN11, the water-level estimates were made 

using the three-step model described previously. The static and 

dynamic models used four static-input variables (CELL_X, 

PCTPRAIRIE, PCTEXOTICS, and PCTUPLAND). Two 

index stations were used in the models—WCA2E1 and 

WCA2F1 (fig. 17; table 1). The measured and estimated 

water levels for the EDEN11 station are shown in figure 18. 

WCA2E1 is also plotted with the hindcast to show the general 

water-level behavior through the record extension. The R2

Figure 17. Index and hindcast stations for Water Conservation Area 2.

for the estimates is 0.90 with a PME of 2.0 percent (table 4). 

The measured data cover a large range of water levels, and 

there are only a few periods where the models extrapolated to 

estimate low and high water-level periods.

For EDEN13, the water-level estimates using the threestep modeling approach produced an unsatisfactory result, 

probably due to the limited number and spatial extent of index 

stations. An approach used in the snail kite study (Conrads 

and others, 2006) was used to extend the water levels for this 

station. Highly correlated data, by definition, are dynamically 

similar. The modeling challenge is not how the time series are 

similar but how they are dynamically different. The difference 

between EDEN13 and Site 99 (the index station closest to 

the station, fig. 17) was computed (fig.19A) to emphasize the 

22 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

Base from U.S. Geological Survey digital data,

6-meter DOQ mosaic of south Florida, 2000,

Florida East, Zone 0901

Transverse Mercator projection

NAD 83 datum

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

2630’

26

25’

26

20’

26

15’

26

10’

80

30’ 8025’ 8020’ 8015’

Water Conservation Area 2

EXPLANATION

Hindcast station and number

Index station and number

Figure 17.

EDEN6

WCA2F1

EDEN11

WCA2F1

WCA2E1

EDEN13

Site 99

S142H

Water Conservation Area boundary
Figure 18. Water-level record extensions for site EDEN11 in Water Conservation Area 2 for the period October 1, 1999, to 

September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one or more of the model 

inputs.

dynamic difference between the two stations. The difference 

between Site 99 and EDEN13 was modeled using Site 99 

and S142H as inputs. The final prediction is the sum of the 

EDEN13 difference and the Site 99 water level, which is 

shown in figure 19B with the Site 99 measured data. The R2

for the estimates is 0.91, and the PME is 1.0 percent (table 4). 

Although these statistics indicate a good model, it should be 

noted that because of missing data at index station S142H, 

the range of EDEN13 water-level estimates was limited to 

approximately half of the hindcasted range. Water levels 

beyond this range require an extrapolation of the model. 

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 23

15

14

13

12

11

10

9

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 18.

EDEN11

measured

WCA2E1

measured

EDEN11 extension
Figure 19. Difference in (A) water levels between Site 99 and site EDEN13 and (B) water-level record extensions for 

site EDEN13 in Water Conservation Area 2 for the period October 1, 1999, to September 30, 2006. Breaks in the waterlevel estimates are caused by incomplete time series for one or more of the model inputs.

24 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

11

10

9

8

7

6

12

11

10

9

8

7

6

5

WATER LEVEL, IN FEET

2.4

1.4

0.4

-0.6

DIFFERENCE IN WATER LEVEL, IN FEET

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

0 58,000 59,000 60,000 61,000

HOURLY OBSERVATIONS

Figure 19.

Site 99

measured

EDEN 13 

measured

Difference between EDEN3 and Site 99

Site 99

measured

EDEN13

extension

EDEN13

measured

1.9

0.9

-0.1

A.

B.
Water Conservation Area 3A (WCA3A)

For WCA3A, water-level records were extended for 

13 stations. The large number of index stations was separated 

into groups of similar hydrologic behaviors. Previous cluster 

analysis of the EDEN stations in the area indicated two groups 

of stations that had similar water-level behaviors (Conrads 

and Roehl, 2006a). Water-level data for EDEN, including 

WCA3A, manifests short-term variability and long-term 

hydrologic behavior. A dynamic clustering technique (Roehl 

and others, 2006) was used to cluster stations with similar 

long-term behavior. The hourly data were converted to daily 

values of 7-day moving-window averages, and a crosscorrelation matrix of the Pearson 

coefficient of selected water-level 

time series was generated. The 

Pearson coefficient provides a 

numerical value of the amount 

of information that is shared 

between two time series, or 

signals. The cluster analysis 

of the cross-correlation matrix 

grouped together time series 

of similar behaviors. The rows 

were clustered using a k-means 

algorithm. The number of classes 

was determined by the sensitivity 

of the mean square error to k. 

The analysis showed two classes 

(groups) of stations of similar 

behavior in WCA3A (fig. 20). 

Of the two groups of index 

and hindcast stations in WCA3A, 

11 of the new EDEN stations are 

in group 1, and 2 are in group 2 

(table 1; fig. 20). For all of the 

new EDEN stations in WCA3A, 

the three-step modeling 

approach was used for making 

the water-level estimates. For 

the WCA3A group 1 stations, 

five stations were used as 

index stations: Site 63, Site 64, 

Site 65, 3ASW, and 3AS3W1. 

The static and dynamic models 

used five static-input variables 

(CELL_X, PCTEXOTICS, 

PCTSLOUTH, PCTPRAIRIE, 

and PCTOTHER). The R2 for the 

water-level estimates for the 11 

new EDEN stations in group 1 

were all above 0.99, and the 

PME were all 0.1 percent or less 

(table 4). The measured 

and estimated water levels for the 

11 stations in group 1 are shown in figures 21–24. Site 64 also 

is plotted with the hindcasts for group 1 to show the general 

water-level behavior through the record extension. For the 

majority of the stations, the water-level estimation models 

cover a large range of the data and do not have to extrapolate 

over large portions of the range of the hindcasted data. The 

exception is EDEN9 (fig. 22) for which there was less than 

40 days of measured data (tables 1 and 4).

For group 2 in WCA3A, there are two hindcast stations 

(EDEN5 and EDEN14) and three index stations (Site 62, 3A9, 

and 3A12) (fig. 20). The static model used three static-input 

variables (CELL_X, CELL_Y, and PCTPRAIRIE) and the 

dynamic model used two static-input variables (CELL_Y and 

Figure 20. Index and hindcast stations for Water Conservation Area 3A.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 25

!

!

#

#

#

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

Base from U.S. Geological Survey digital data,

6-meter DOQ mosaic of south Florida, 2000,

1-meter DOQQ of "North of Fortymile Bend" quad, 1999

Florida East, Zone 0901

Transverse Mercator projection

NAD 83 datum

2620’

26

10’

26

2550’

80

50’ 8040’ 8030’

Water Conservation Area 3A

Water Conservation Area boundary

EXPLANATION

Hindcast station and number, group1

Index station and number, group 1

Hindcast station and number, group 2

Index station and number, group 2

Figure 20.

EDEN9

Site 64

3A12

EDEN9

Site 63

Site 62

3A12

EDEN5 3A9

EDEN14

EDEN4

3A-5

W15 EDEN12

W18

W11 W14

Site 64

3ASW

3AS3W1 EDEN8

Site 65

W5

W2

EDEN14
Figure 21. Water-level record extensions for sites 3A-5, EDEN4, and EDEN8 in Water Conservation Area 3A for the 

period October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time 

series for one or more of the model inputs.

26 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

13

12

11

10

9

8

7

WATER LEVEL, IN FEET

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 21.

EDEN4

EDEN8

3A-5 extension

3A-5

Site 64 

measured

3A-5

measured

EDEN4 extension

Site 64 measured

EDEN4 measured

EDEN8 extension

Site 64 measured

EDEN8

measured
Figure 22. Water-level record extensions for sites EDEN9, EDEN12, and W2 in Water Conservation Area 3A for the 

period October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series 

for one or more of the model inputs.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 27

13

12

11

10

9

8

7

WATER LEVEL, IN FEET

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 22.

EDEN12

W2

EDEN9 extension

EDEN9

Site 64 measured

EDEN9 measured

EDEN12 extension

Site 64 measured

EDEN12 measured

W2 extension

Site 64 measured

W2 measured
Figure 23. Water-level record extensions for sites W5, W11, and W14 in Water Conservation Area 3A for the period 

October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for 

one or more of the model inputs.

28 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

13

12

11

10

9

8

7

WATER LEVEL, IN FEET

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

13

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 23.

W11

W14

W5 extension

W5

Site 64 measured

W5 measured

W11 extension

Site 64 measured

W11 

measured

W14 extension

Site 64 measured

W14 measured
Figure 24. Water-level record extensions for sites W15 and W18 in Water Conservation Area 3A for the period October 1, 1999, to 

September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one or more of the model inputs.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 29

13

12

11

10

9

8

7

WATER LEVEL, IN FEET

W15 extension

W15

Site 64 measured

W15 measured

W18 extension

W18

Site 64 measured

W18 measured

13

12

11

10

9

8

7

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 24.
PCTPRAIRIE) in addition to the dynamic input variables from 

the three index stations. The measured and estimated water 

levels for the group 2 hindcasts are shown in figure 25. Similar 

to EDEN9 in the group 1 stations, EDEN5 and EDEN14 

have short periods of record. EDEN5 has less than 4 months 

of data, and EDEN14 has 2 months of data. The measured 

data for EDEN5 is at the extremes of the measured range of 

data with a large data gap in the mid-range of the data. The 

water-level estimates capture the overall trend of the high and 

low water levels as evident in the R2 of 0.99 (table 4). Because 

the measured water levels are during periods of the low and 

high water levels, the model only has to extrapolate for a few 

high and low water periods. The measured data for EDEN14 

are limited to the mid and lower water levels. The R2 for the 

water-level estimate for EDEN14 is 0.82, the lowest of all the 

water-level estimates. The model has to extrapolate to estimate 

all of the high-water conditions.

Figure 25. Water-level record extensions for sites EDEN5 and EDEN14 in Water Conservation Area 3A for the period 

October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one 

or more of the model inputs.

30 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 25.

EDEN5

EDEN14

EDEN5 extension

Site 62 measured

EDEN5 measured

EDEN14 extension

Site 62 measured EDEN14 

measured
Water Conservation Area 3B (WCA3B)

For WCA3B, water-level records were extended for four 

stations—TI-8, TI-9, EDEN7, and EDEN10 (fig. 26; table 1). 

The static and dynamic models used three static-input variables (pctprairie, pctsawgrass, and pctupland). The dynamic 

models used dynamic-input variables from four index stations. 

The measured and estimated water levels for the WCA3B 

hindcasts are shown in figures 27 and 28 in addition to water 

levels for index station Site 69. All of the final estimates were 

able to accurately simulate the measured data (R2 above 0.99), 

but only one station, EDEN7 (fig. 28), had measured data with 

a range similar to the range of the hindcasts. The other three 

stations did not have data in the higher water-level range, and 

the model had to extrapolate to estimate high-water conditions 

at these stations. 

Figure 26. Index and hindcast stations for Water Conservation Area 3B.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 31

0 1 2345 Miles

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

Base from U.S. Geological Survey digital data,

6-meter DOQ mosaic of south Florida, 2000,

Florida East, Zone 0901

Transverse Mercator projection

NAD 83 datum

2605’

25

55’

25

50’

25

45’

26

8040’ 8035’ 8030’ 8025’

Water Conservation Area 3B

EXPLANATION

Hindcast station and number

Index station and number

EDEN7

Site 76

EDEN7

Site 76

Site 69

Site 71

TI-9

TI-8

EDEN10

SRS1

Water Conservation Area boundary

Figure 26.
Figure 27. Water-level record extensions for sites TI-8 and TI-9 in Water Conservation Area 3B for the period October 1, 

1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one or more of the 

model inputs.

32 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

9

8

7

6

5

4

3

WATER LEVEL, IN FEET

9

8

7

6

5

4

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 27.

TI-8

TI-9

TI-8 extension

Site 69 

measured

TI-8 measured

TI-9 extension

Site 69 measured

TI-9

measured
Figure 28. Water-level record extensions for sites EDEN7 and EDEN10 in Water Conservation Area 3B for the period 

October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one 

or more of the model inputs.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 33

9

8

7

6

5

4

9

8

7

6

5

4

WATER LEVEL, IN FEET WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 28.

EDEN7

EDEN10

EDEN7 extension

Site 69

measured

EDEN7

measured

EDEN10 

extension

Site 69 measured

EDEN10

measured
Big Cypress National Preserve (BCNP)

For BCNP, water-level records were extended for two 

stations—EDEN1 and EDEN6 (fig. 29; table 1). The initial 

three-step model produced satisfactory water-level estimates 

for EDEN1 but not for EDEN6. To improve the water-level 

estimates for EDEN6, the same three-step modeling approach 

was used but with a different combination of static- and 

dynamic-input variables. The dynamic model for EDEN6 also 

used water-level data from 3ASW in WCA3A (fig. 20). As 

with the other areas, the measured data from the new EDEN 

station were not used until computing the residual error of 

the initial water-level estimates. The static model for EDEN1 

used five static-input variables, whereas the static model for 

EDEN6 used two static-input variables. The dynamic model 

for EDEN1 used four static-input variables and four dynamicinput variables, whereas the dynamic model for EDEN6 used 

two static variables and three dynamic variables. 

The measured and estimated water levels for the two 

stations are shown in figure 30. The R2 for the water-level 

estimates for EDEN1 and EDEN6 are 0.92 and 0.97, 

respectively (table 4). Water levels for BCA9 also are shown 

with the hindcasts for EDEN1, and water levels for BCA5 are 

shown with the hindcasts for EDEN6 (fig. 30). The measured 

data for the two new EDEN stations in BCNP are limited to 

the mid- and high-water ranges. The measured data range for 

EDEN1 is less than a foot, whereas the range of the hindcasts 

is more than 3 ft. For EDEN6, the range of the measured data 

is about 2 ft, and the range of the hindcasts is about 5 ft.

Figure 29. Index and hindcast stations 

for Big Cypress National Preserve.

34 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

!

#

Big Cypress National Preserve

Big Cypress National Preserve boundary

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

Base from U.S. Geological Survey digital data,

6-meter DOQ mosaic of south Florida, 2000,

Florida East, Zone 0901

Transverse Mercator projection

NAD 83 datum

2605’

25

55’

25

50’

25

45’

26

8105’ 81 8055’ 8050’ 8045’

EXPLANATION

Hindcast station and number

Index station and number

Figure 29.

EDEN6

L28GAP

EDEN6

L28GAP

EDEN1

BCA5

BCA9

LOOP1T

LOOP2T

BCA10
Figure 30. Water-level record extensions for sites EDEN1 and EDEN6 in Big Cypress National Preserve for the period 

October 1, 1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one or 

more of the model inputs.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 35

8

7

6

5

4

3

WATER LEVEL, IN FEET

12

11

10

9

8

7

6

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 30.

EDEN1

EDEN6

EDEN1 

extension

BCA9 measured

EDEN1 measured

BCA5 measured EDEN6 extension

EDEN6

measured
Everglades National Park (ENP)

For the ENP, water-level records were extended for two 

stations—EDEN3 and Met1 (fig. 31; table 1). Similar to the 

two new EDEN stations in BCNP, the stations were modeled 

separately with the three-step modeling approach. Both 

static models used four static-input variables. Three of the 

static-input variables were the same (CELL_Y, pctsawgrass, 

and pctSLOUGH) for both models. The static model for Met1 

included percent upland (PCTUPLAND), and the static model 

for EDEN3 included percent prairie (PCTPRAIRIE). Both 

dynamic models used four static variables but used two different combinations of five dynamic variables. The measured 

and estimated water levels for the two stations are shown in 

figure 32. The R2 for the water-level estimates for EDEN3 and 

Met1 is 0.98 and 0.99, respectively (table 4). Water levels for 

P34 also are shown with the hindcasts for EDEN3, and water 

levels for NE1 are shown with the hindcasts for Met1. The 

range of the measured data for EDEN3 covers the majority 

of the range of the hindcasts (fig. 32). The range of measured 

data for Met1 is less than 0.5 ft, and the model must extrapolate to estimate annual high and low water.

Figure 31. Index and hindcast stations for Everglades National Park.

36 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

!

!

# #

#

#

#

Base from U.S. Geological Survey digital data,

6-meter DOQ mosaic of south Florida, 2000,

Florida East, Zone 0901

Transverse Mercator projection

NAD 83 datum

Figure 31.

0 1 2 3 4 5 MILES

0 1 2 3 4 5 KILOMETERS

2550’

25

40’

25

30’

25

20’

8050’ 8040’ 8030’

EXPLANATION

Hindcast station and number

Index station and number

EDEN3

NP201

Everglades National Park

Met1 NP201

NE1

NE2

NESRS3

EDEN3

TMC

P34

OT

P36

P35

Everglades National Park 

boundary
Figure 32. Water-level record extensions for sites EDEN3 and Met1 in the Everglades National Park for the period October 1, 

1999, to September 30, 2006. Breaks in the water-level estimates are caused by incomplete time series for one or more of the model 

inputs.

Extension of Water-Level Records for the Everglades Depth Estimation Network (EDEN) 37

4

3

2

1

0

-1

-2

WATER LEVEL, IN FEET

9

8

7

6

5

4

WATER LEVEL, IN FEET

0 10,000 20,000 30,000 40,000 50,000 60,000

HOURLY OBSERVATIONS

Figure 32.

EDEN3

Met1

EDEN3

extension

P34 measured

EDEN3

measured

Met1 extension

NE1 measured

Met1 measured
Summary and Discussion

The Everglades Depth Estimation Network (EDEN) is 

an integrated network of real-time water-level gaging stations, 

ground-elevation models, and water-surface models. The 

network provides scientists, engineers, and water-resource 

managers with current (2000–present) water-depth information 

for the entire freshwater portion of the greater Everglades. 

To increase the accuracy of the water-surface models, 25 

real-time gaging stations were added to EDEN. To incorporate 

the newly added stations to the 7-year EDEN database of 253 

water-level gaging stations in the greater Everglades, the shortterm water-level records (generally less than 1 year) needed to 

be simulated back in time (hindcasted) to be concurrent with 

data from the established gaging stations. A three-step modeling approach using artificial neural networks (ANN) models 

was used to estimate the water levels at the new stations. The 

ANN models used static variables of gaging station location 

and percent vegetation in addition to dynamic variables of 

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. 

The three-step modeling approach for estimating water 

levels produced satisfactory results, with coefficients of 

determination for 21 of the 25 for the new EDEN stations 

greater than 0.95 and all of the estimates greater than 0.82. 

For some new EDEN stations having limited data, the record 

extension (hindcasts) included periods beyond the range of 

data used to train the water-level estimate models. A comparison of the hindcasts from these models with long-term water 

levels proximal to the new EDEN station indicated that the 

water-level estimates showed a similar hydrologic response to 

the long-term water levels.

 There are opportunities to improve the completeness 

and accuracy of the hindcasts of the new EDEN stations. The 

completeness of the hindcasts could be improved by filling 

in the missing data for the established EDEN stations using 

similar techniques as presented in this report, which in turn 

would provide more complete input time series to the waterlevel estimation models for the new stations. 

For the majority of the new EDEN stations, there 

was 1 year or less of data to train and test the water-level 

estimation models. Over time, a greater record of hydrologic 

behaviors at the new EDEN stations will be collected, 

including inter-annual variability. Retraining the water-level 

estimation ANN models will improve the ability of the models 

to predict the behaviors at the new EDEN stations. Additional 

cell attribute data for the EDEN grid and enhancements to the 

existing attribute data will also improve the models.

Acknowledgments 

The complexity of this study required interagency 

cooperation in addition to individual contributions. The 

authors thank the members of the EDEN project team: Ikuko 

Fujisaki, Aaron Higer, Monica Palaseanu, Leonard Pearlstine, 

and Darcy Thomas from the University of Florida and Heather 

Henkel, John W. Jones, Eduardo Patino, Carolyn Price, Pamela 

Telis, and Arturo Torres of the USGS and Roy Sonenshein 

of the National Park Service (formerly with the USGS). The 

authors also thank the funding agencies that support the EDEN 

project team—U.S. Army Corps, Jacksonville District, and the 

USGS Greater Everglades Priority Ecosystems Science. 

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40 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006

(Blank)
Appendixes 41

Appendixes

1. Summary of artificial neural network models used in the study.

2. Summary statistics for the models used in the study.

3. Variables used in the artificial neural network models.
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

WCA1 Models

wca1-static static CELL_Y WLSITE WLSITE Static model for WCA1- Water-level prediction (WLSITE) used for initial 

water-level estimate and residual (RES_WLSITE) used for dynamic model. PCTPRAIRIE RES_WLSITE

PCTEXOTICS 

wca1-dynamic dynamic CELL_Y RES_WLSITE RES_WLSITE Dynamic model for WCA1- RES_WLSITE prediction from dynamic model 

and WLSITE prediction from static model are used for initial water-level estimate.

PCTPRAIRIEPCTEXOTICSSITE_7 SITE8TDEC2 WCA1MEDECSITE9DEC 

site8tdecor decorrelation SITE_8T SITE_7 SITE8TDEC2 Model to decorrelate SITE8t from SITE_7.wca1medecor2 decorrelation WCA1ME SITE_7 WCA1MEDEC Model to decorrelate WCA1ME from SITE_8 and SITE_7.

SITE8TDEC2 

northres error correction SITE_7 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site NORTH. SITE8TDEC 

WCA1MEDEC

southres error correction SITE_7 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site SOUTH. SITE8TDEC

WCA1MEDEC 

WCA2 Models

wca2a-static static CELL_X WLSITE WLSITE Static model for EDEN11 in WCA2 - Water-level prediction (WLSITE) used for 

initial water-level estimate and residual (RES_WLSITE) used for dynamic model.

PCTPRAIRIE RES_WLSITEPCTEXOTICSPCTUPLAND

wca2a-dynamic2 dynamic CELL_X RES_WLSITE RES_WLSITE Dynamic model for EDEN11 in WCA2 RES_WLSITE prediction from 

dynamic model and WLSITE prediction from static model used for initial water-level estimate.

PCTPRAIRIEPCTEXOTICSPCTUPLANDWCA2E1WCA2F1DEC 

wca2f1decor decorrelation WCA2F1 WCA2E1 WCA2F1DEC Model to decorrelate WCA2F1 from WCA2E1.eden11res2 error correction WCA2E1 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN11. WCA2F1DEC 

42 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

eden13 error correction SITE_99 EDEN13DIF Model to estimate water-level difference with SITE_99. Sum of difference 

and water-level estimate for SITE_99 are the water-level estimates for site EDEN13.

S142H 

WCA3A Models

Group 1 Models

cluster1static static CELL_Y WLSITE WLSITE Static model for Group 1 stations in WCA3A—Water-level prediction 

(WLSITE) used for initial water-level estimate and residual (RES_WLSITE) used for dynamic model.

PCTEXOTICS RES_WLSITEPCTSLOUGHPCTPRAIRIEPCTOTHER

cluster1dynamic dynamic SITE_63DEC RES_WLSITE RES_WLSITE Dynamic model for Group 1 stations in WCA3A—RES_WLSITE prediction 

from dynamic model and WLSITE prediction from static model used for initial water-level estimate.

SITE_643AS3W1DECCELL_YPCTSLOUGHPCTEXOTICSPCTOTHER

3as3w1dec decorrelation 3AS3W1 SITE_64 3AS3W1DEC Model to decorrelate 3AS3W1 from SITE_64.65dec decorrelation SITE_65 SITE_64 SITE_65DEC Model to decorrelate Site_65 from SITE_64 and 3AS3W1.

3AS3W1DEC 

 63decr1 decorrelation 3AS3W1DEC SITE_64 SITE_63DEC Model to decorrelate Site_63 from SITE_64, 3AS3W1, and Site_65

SITE_65DECSITE63

3aswdec decorrelation 3AS3W1DEC SITE_64 3ASWDEC Model to decorrelate 3ASW from SITE_64, 3AS3W1, Site_65, and Site_63.

SITE_65DECSITE_63DEC3ASW

3a-5res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site 3A-5. SITE_64

3AS3W1DECSITE_65DEC

eden4res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN4. SITE_64

3AS3W1DECSITE_65DEC3ASWDEC

Appendixes 43
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

eden8res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN8. SITE_64

3AS3W1DECSITE_65DEC3ASWDEC

eden9res2 error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN9. SITE_64

3AS3W1DECSITE_65DEC3ASWDEC

eden12res2 error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN12. SITE_64

3AS3W1DECSITE_65DEC

w2res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site W2. SITE_64

3AS3W1DEC 

w5res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site W5. SITE_64

3AS3W1DECSITE_65DEC

w11res2 error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site W11. SITE_64

3AS3W1DECSITE_65DEC3ASWDEC

w14res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site W14. SITE_64

3AS3W1DECSITE_65DEC3ASWDEC

w15res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site W15. SITE_64

3AS3W1DECSITE_65DEC3ASWDEC

44 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

w18res error correction SITE_63DEC WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site W18. SITE_64

3AS3W1DEC3ASWDEC

Group 2 Models

cluster3_static static CELLX WLSITE WLSITE Static model for Group 2 stations in WCA3A—Water-level prediction (WLSITE) used for initial water-level estimate and residual (RES_WLSITE) used 

for dynamic model.

CELLY RES_WLSITEPCTPRAIRIE 

cluster3_dynamic dynamic SITE_62 RES_WLSITE RES_WLSITE Dynamic model for Group 2 stations in WCA3A—RES_WLSITE prediction 

from dynamic model and WLSITE prediction from static model used for initial water-level estimate.

3A9DEC3A12DECCELLYPCTPRAIRIE 

3a9decor decorrelation 3A9 SITE_62 3A9DEC Model to decorrelate 3A9 from SITE_62.3a12decor decorrelation 3A9DEC SITE_62 3A12DEC Model to decorrelate 3A12 from SITE_63 and 3A9.

3A12 

eden5res error correction SITE_62 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN5. 3A9DEC

3A12DEC 

eden14res SITE_62 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN14. 3A9DEC

3A12DEC

WCA3B Models

cluster1-static static PCTPRAIRIE WLSITE WLSITE Static model for Group 2 stations in WCA3A—Water-level prediction (WLSITE) used for initial water-level estimate and residual (RES_WLSITE) used 

for dynamic model.

PCTSAWGRASS RES_WLSITEPCTUPLAND 

cluster1-dynamic dynamic PCTPRAIRIE RES_WLSITE RES_WLSITE Dynamic model for WCA1- RES_WLSITE prediction from dynamic model 

and WLSITE prediction from static model used for initial water-level estimate. PCTSAWGRASS PCTUPLAND

SITE_69CSITE71DECSRS1DEC

SITE76DEC 

site71dec decorrelation SITE_71C SITE_69C SITE71DEC Model to decorrelate SITE_71 from SITE_69.

Appendixes 45
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

srs1dec decorrelation SITE71DEC SITE_69C SRS1DEC Model to decorrelate SRS1 from SITE_69 and SITE_71.

SRS1C

site76dec decorrelation SITE71DEC SITE_69C SITE76DEC Model to decorrelate SITE_76 from SITE_69, SITE_71, and SRS1.

SRS1DECSITE_76

TI-8res error correction SITE_69C WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site TI-8. SITE71DEC

SRS1DECSITE76DEC 

TI-9res error correction SITE_69C WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site TI-9. SITE71DEC

SRS1DECSITE76DEC 

eden7res error correction SITE_69C WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN7. SITE71DEC

SRS1DECSITE76DEC

eden10res error correction SITE_69C WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN10. SITE71DEC

SRS1DECSITE76DEC 

BCNP Models

bcnp-static static CELL_X WLSITE WLSITE Static model for EDEN1 in BCNP - Water-level prediction (WLSITE) used for 

initial water-level estimate and residual (RES_WLSITE) used for dynamic model.

CELL_Y RES_WLSITEPCTPRAIRIE PCTSAWGRASSPCTEXOTICS

bcnp-dynamic dynamic CELL_X RES_WLSITE RES_WLSITE Dynamic model for EDEN1 in BCNP- RES_WLSITE prediction from dynamic 

model and WLSITE prediction from static model used for initial water-level estimate.

CELL_YPCTPRAIRIEPCTEXOTICS BCA9

LOOP1TDECLOOP2TDECBCA10DEC 

46 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

loop1tdecor decorrelation LOOP1T BCA9 LOOP1TDEC Model to decorrelate LOOP1T from BCA10.

loop2tdecor decorrelation LOOP1TDEC BCA9 LOOP2TDEC Model to decorrelate LOOP2T from BCA9 and LOOP1T.

LOOP2T

bac10decor decorrelation LOOP1TDEC BCA9 BCA10DEC Model to decorrelate BCA10 from BCA9, LOOP1T, and LOOP2T.

LOOP2TDECBCA10

eden1res BCA9 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN1. LOOP1TDEC

LOOP2TDECBCA10DEC

eden6-static static PCTUPLAND WLSITE WLSITE Static model for station EDEN6 in BCNP—Water-level prediction (WLSITE) 

used for initial water-level estimate and residual (RES_WLSITE) used for model for dynamic model.

CELL_Y RES_WLSITE

eden6-dynamic dynamic PCTUPLAND RES_WLSITE RES_WLSITE Dynamic model for station EDEN6 in BCNP—RES_WLSITE prediction from 

dynamic model and WLSITE prediction from static model used for initial water-level estimate.

CELL_YBCA53ASWDECL28GAPDEC

l28gapdecor2 decorrelation L28GAP BCA5 L28GAPDEC Model to decorrelate L28GAP from BCA5.

3ASWDEC 

eden6res2 error correction BCA5 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN6. 3ASWDEC

L28GAPDEC

ENP Models

eden3stack-static static CELL_Y WLSITE WLSITE Static model for station EDEN3 in ENP - Water-level prediction (WLSITE) 

used for initial water-level estimate and residual (RES_WLSITE) used for 

dynamic model.

PCTSLOUGH RES_WLSITEPCTPRAIRIEPCTSAWGRASS

eden3stackdynamic dynamic CELL_Y PCTSLOUGH

PCTPRAIRIEPCTSAWGRASSP34OTDECTMCDECP36DECP35DEC

RES_WLSITE RES_WLSITE Dynamic model for station EDEN3 in ENP - RES_WLSITE prediction from 

dynamic model and WLSITE prediction from static model used for initial water-level estimate.

Appendixes 47
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

otdecor decorrelation OT P34 OTDEC Model to decorrelate OT from P34.tmcdecor decorrelation TMC P34 Model to decorrelate TMC from P34 and OT.

OTDEC 

p36decor decorrelation OTDEC P34 P36DEC Model to decorrelate P36 from P34, OT, and TMC.

P34TMCDEC

p35decor decorrelation OTDEC P34 P35DEC Model to decorrelate P35 from P34, OT, TMC, and P36.

TMCDECP34P36DEC

eden3res error correction P34 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site EDEN3. OTDEC

TMCDECP36DECP35DEC

met1-static static CELL_Y WLSITE WLSITE Static model for station MET1 in ENP—Water-level prediction (WLSITE) used 

for initial water-level estimate and residual (RES_WLSITE) used for dynamic model.

PCTSLOUGH RES_WLSITEPCTSAWGRASSPCTUPLAND

met1-dynamic dynamic NE1 RES_WLSITE RES_WLSITE Dynamic model for WCA—RES_WLSITE prediction from dynamic model 

and WLSITE prediction from static model used for initial water-level estimate. SRS1DEC NP201DEC

NE2DECNESRS3DECCELL_YPCTSLOUGHPCTSAWGRASSPCTUPLAND

srs1decor decorrelation SRS1 NE1 SRS1DEC Model to decorrelate SRS1 from NE1.np201decor decorrelation SRS1DEC NE1 NP201DEC Model to decorrelate NP201 from NE1 and SRS1.

NP201 

ne2decor decorrelation SRS1DEC NE1 NE2DEC Model to decorrelate NE2 from NE1, SRS1, and NP201.

NP201DECNE2 

48 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 1. Summary of artificial neural network models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park]

Model Model type Input variablesa Model prediction variable Variable used from the model Comment

nesrs3decor decorrelation SRS1DEC NE1 NESRS3 Model to decorrelate NESRS3 from NE1, SRS1, NP201, and NE2.

NP201DECNESRS3NE2DEC

met1res error correction NE1 WLESTERR WLESTERR Model to estimate error between initial water-level estimate and measured data 

for site Met1. SRS1DEC

NP201DECNE2DECNESRS3DEC

a Descriptions of variables are provided in Appendix 3.

Appendixes 49
Appendix 2. Summary statistics for the models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park; HLN, hidden layer neurons; min, minimum; max, maximum; feet, ft; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model name Model type Number of HLN

Training

Range of output variable

n R2

ME, 

Water 

level, ft

SSE,

Water 

level, ft

MSE,

Water 

level, ft

RMSE,

Water 

level, ft

PME Min, 

Water 

level, ft

Max, 

Water 

level, ft

WCA1 Models

wca1-static static 2 14.70 14.94 4 0.948 0.000 0.03 0.007 0.12 52.1%site8tdecor2 decorrelation 1 13.86 16.58 11 0.939 -0.279 0.43 0.039 0.22 8.1%wca1medecor2 decorrelation 1 13.53 16.31 60 0.983 0.007 0.56 0.009 0.10 3.5%wca1-dynamic dynamic 3 -2.27 1.84 2,108 0.984 0.058 16.64 0.008 0.09 2.2%northres error correction 2 -1.12 0.43 252 0.861 -0.026 4.24 0.017 0.13 8.4%southres error correction 2 -2.04 -0.62 234 0.877 0.004 2.82 0.012 0.11 7.8%

WCA2 Models

wca2a-static static 1 9.77 11.37 5 0.987 0.000 0.02 0.005 0.09 5.4%wca2f1decor decorrelation 1 10.17 14.37 11 0.998 0.003 0.03 0.003 0.06 1.4%wca2a-dynamic2 dynamic 3 -1.61 3.35 317 0.961 0.007 17.41 0.055 0.24 4.7%eden11res2 error correction 1 -0.73 1.10 40 0.863 -0.008 1.55 0.039 0.20 11.0%eden13 difference model 1 -0.54 1.51 35 0.987 0.000 0.17 0.005 0.07 3.6%

WCA3A Models

cluster1static static 2 8.26 10.28 5 1.000 -0.000 0.000 0.000 0.004 0.2%3as3w1dec decorrelation 1 8.51 11.74 11 0.991 0.005 0.11 0.010 0.109 3.4%65dec decorrelation 1 8.30 11.95 90 0.995 -0.005 0.41 0.005 0.068 1.9%63decr1 decorrelation 1 8.29 11.95 358 0.941 -0.014 14.50 0.041 0.202 5.5%3aswdec decorrelation 1 8.73 11.95 962 0.951 -0.047 28.67 0.030 0.173 5.4%cluster1dynamic dynamic 3 -2.39 2.11 1,622 0.969 0.012 37.84 0.023 0.153 3.4%3a-5res error correction 2 -0.88 0.26 188 0.978 0.001 0.38 0.002 0.045 3.9%eden12res2 error correction 3 -3.21 -2.43 188 0.953 -0.001 0.39 0.002 0.046 5.9%eden4res error correction 2 -3.30 -2.35 261 0.938 -0.006 1.27 0.005 0.070 7.3%eden8res error correction 3 -2.65 -2.27 266 0.903 -0.001 0.19 0.001 0.027 6.9%eden9res2 error correction 3 1.59 2.43 132 0.991 -0.001 0.10 0.001 0.028 3.4%

50 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 2. Summary statistics for the models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park; HLN, hidden layer neurons; min, minimum; max, maximum; feet, ft; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model name Model type Number of HLN

Training

Range of output variable

n R2

ME, 

Water 

level, ft

SSE,

Water 

level, ft

MSE,

Water 

level, ft

RMSE,

Water 

level, ft

PME Min, 

Water 

level, ft

Max, 

Water 

level, ft

w11res2 error correction 3 -0.23 0.30 383 0.803 -0.011 1.03 0.003 0.052 9.8%w14res error correction 3 -2.16 -1.46 383 0.788 -0.014 1.36 0.004 0.060 8.6%w15res error correction 3 -2.49 -1.80 275 0.967 -0.003 0.32 0.001 0.034 4.9%w18res error correction 3 0.64 1.85 239 0.972 -0.005 0.62 0.003 0.051 4.2%w2res error correction 2 0.76 2.06 128 0.976 -0.002 0.40 0.003 0.056 4.3%w5res error correction 3 -2.85 -2.15 259 0.927 -0.001 0.38 0.001 0.038 5.5%cluster3_static static 1 8.91 9.41 3 1.000 0.000 0.00 0.000 0.000 0.0%cluster3_dynamic dynamic 2 -2.44 2.64 624 0.980 0.093 14.69 0.024 0.154 3.0%3a9decor decorrelation 1 7.27 11.52 11 0.996 0.002 0.07 0.006 0.088 2.1%3a12decor decorrelation 1 6.95 11.77 78 0.983 0.042 2.34 0.030 0.175 3.6%eden14res error correction 2 -1.17 -0.67 71 0.761 -0.000 0.26 0.004 0.061 12.0%eden5res error correction 3 -0.87 0.05 61 0.981 -0.001 0.06 0.001 0.032 3.5%

WCA3B Models

cluster1-static static 1 7.05 7.86 4 0.994 -0.000 0.002 0.000 0.032 3.9%cluster1-dynamic dynamic 3 -2.29 2.16 3,152 0.982 0.014 24.74 0.008 0.089 2.0%site71dec decorrelation 1 5.75 8.63 11 0.995 0.003 0.05 0.004 0.071 2.5%srs1dec decorrelation 1 5.57 8.74 70 0.979 0.018 0.98 0.014 0.120 3.8%site76dec decorrelation 1 5.56 8.74 263 0.972 -0.013 3.22 0.012 0.111 3.5%ti-8res error correction 1 -4.56 -3.23 227 0.983 -0.001 0.44 0.002 0.044 3.4%ti-9res error correction 3 -2.33 -1.59 227 0.961 0.004 0.20 0.001 0.030 4.0%eden7res error correction 2 -3.51 -2.08 137 0.993 -0.001 0.13 0.001 0.032 2.2%eden10res error correction 2 -2.07 -1.09 137 0.968 0.001 0.18 0.001 0.036 3.7%

BCNP Models

bcnp-static static 1 2.52 8.60 5 0.997 -0.005 0.05 0.010 0.131 2.2%bcnp-dynamic dynamic 4 -3.25 1.41 2,125 0.911 0.116 143.35 0.067 0.260 5.6%loop1tdecor decorrelation 1 3.06 7.15 11 0.993 0.019 0.15 0.014 0.130 3.2%

Appendixes 51
Appendix 2. Summary statistics for the models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park; HLN, hidden layer neurons; min, minimum; max, maximum; feet, ft; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model name Model type Number of HLN

Training

Range of output variable

n R2

ME, 

Water 

level, ft

SSE,

Water 

level, ft

MSE,

Water 

level, ft

RMSE,

Water 

level, ft

PME Min, 

Water 

level, ft

Max, 

Water 

level, ft

loop2tdecor decorrelation 1 3.06 6.85 69 0.882 -0.043 5.60 0.081 0.289 7.6%bac10decor decorrelation 1 3.03 6.87 278 0.895 0.152 23.20 0.083 0.290 7.5%eden1res error correction 3 0.55 1.92 181 0.973 0.009 0.36 0.002 0.045 3.3%eden6-static static 1 8.60 10.42 3 0.790 -0.018 0.42 0.139 0.646 35.5%eden6-dynamic dynamic 3 -2.42 2.08 594 0.944 0.007 37.87 0.064 0.253 5.6%l28gapdecor2 decorrelation 1 6.70 10.28 68 0.908 0.019 5.75 0.085 0.295 8.3%eden6res2 error correction 2 -1.36 -0.55 53 0.862 0.003 0.24 0.004 0.068 8.4%

ENP Models

eden3stack-static static 1 0.29 2.72 5 0.999 -0.002 0.01 0.002 0.050 2.1%eden3stack-dynamic dynamic 3 -3.40 2.19 7,630 0.937 0.072 299.37 0.039 0.198 3.5%otdecor decorrelation 1 -1.06 3.17 11 0.990 0.000 0.17 0.016 0.139 3.3%tmcdecor decorrelation 1 -1.33 3.04 86 0.953 -0.003 5.03 0.058 0.245 5.6%p36decor decorrelation 1 -1.48 3.30 311 0.880 -0.001 40.39 0.130 0.362 7.6%p35decor decorrelation 1 -1.48 3.30 957 0.876 -0.011 94.54 0.099 0.315 6.6%eden3res error correction 1 -0.98 -0.34 521 0.752 -0.047 2.27 0.004 0.066 10.3%met1-static static 1 5.30 7.52 5 0.996 -0.000 0.01 0.002 0.062 2.8%met1-dynamic dynamic 1 -2.68 2.37 5,420 0.961 0.008 110.27 0.020 0.143 2.8%srs1decor decorrelation 1 5.16 8.09 11 0.986 -0.003 0.13 0.012 0.119 4.1%np201decor decorrelation 1 4.78 8.50 80 0.914 0.016 5.01 0.063 0.253 6.8%ne2decor decorrelation 1 5.68 8.54 263 0.980 -0.036 1.95 0.007 0.087 3.0%nesrs3decor decorrelation 1 5.84 8.54 764 0.959 -0.026 8.28 0.011 0.104 3.9%met1res error correction 3 -0.68 -0.32 215 0.950 0.001 0.06 0.000 0.016 4.5%

52 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 2. Summary statistics for the models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park; HLN, hidden layer neurons; min, minimum; max, maximum; feet, ft; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model name Model type Number of HLN

Testing

Range of output variable

n R2

ME, 

Water 

level, ft

SSE,

Water level, 

ft

MSE,

Water level, 

ft

RMSE,

Water 

level, ft

PME Min, 

Water 

level, ft

Max, 

Water 

level, ft

WCA1 Models

wca1-static static 2 12.44 16.68 80,510 0.023 0.000 24997.05 0.000 0.56 13.1%site8tdecor2 decorrelation 1 13.39 16.68 59,142 0.819 -0.301 2327.94 -0.129 0.20 6.0%wca1medecor2 decorrelation 1 13.26 16.54 57,804 0.970 -0.005 458.57 -0.005 0.09 2.7%wca1-dynamic dynamic 3 -2.27 1.87 77,068 0.982 0.061 435.26 0.061 0.08 1.8%northres error correction 2 -1.15 0.45 41,721 0.813 -0.046 659.76 -0.046 0.13 7.9%southres error correction 2 -2.06 -0.60 43,409 0.850 0.016 323.44 0.016 0.09 5.9%

WCA2 Models

wca2a-static static 1 8.41 14.67 89,154 0.340 0.004 56750.07 0.004 0.80 12.7%wca2f1decor decorrelation 1 9.63 14.63 53,469 0.986 0.012 480.12 0.012 0.09 1.9%wca2a-dynamic2 dynamic 3 -1.61 3.40 80,897 0.889 -0.017 5745.87 -0.017 0.27 5.3%eden11res2 error correction 1 -0.87 1.17 2,637 0.828 -0.054 108.68 -0.054 0.20 9.9%eden13 difference model 1 -0.59 1.57 1,968 0.988 0.038 12.51 0.038 0.08 3.7%

WCA3A Models

cluster1static static 2 6.55 13.39 97,891 0.446 -0.000 74110.43 0.757 0.870 12.7%3as3w1dec decorrelation 1 8.28 11.95 51,742 0.970 -0.021 1047.08 0.020 0.142 3.9%65dec decorrelation 1 8.28 11.95 51,742 0.993 -0.029 260.47 0.005 0.071 1.9%63decr1 decorrelation 1 8.28 11.95 50,776 0.939 0.044 2098.85 0.041 0.203 5.5%3aswdec decorrelation 1 8.69 11.95 49,815 0.959 -0.015 1337.04 0.027 0.164 5.0%cluster1dynamic dynamic 3 -10.26 2.17 83,968 0.960 0.012 2312.33 0.028 0.166 1.3%3a-5res error correction 2 -0.89 0.27 2,486 0.979 0.009 4.81 0.002 0.044 3.8%eden12res2 error correction 3 -3.23 -2.42 2,488 0.960 0.003 4.87 0.002 0.044 5.5%eden4res error correction 2 -3.30 -2.33 2,399 0.941 0.008 11.34 0.005 0.069 7.1%eden8res error correction 3 -2.65 -2.26 2,442 0.894 0.001 1.76 0.001 0.027 6.8%eden9res2 error correction 3 1.59 2.43 925 0.989 -0.000 0.83 0.001 0.030 3.5%

Appendixes 53
Appendix 2. Summary statistics for the models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park; HLN, hidden layer neurons; min, minimum; max, maximum; feet, ft; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model name Model type Number of HLN

Testing

Range of output variable

n R2

ME, 

Water 

level, ft

SSE,

Water level, 

ft

MSE,

Water level, 

ft

RMSE,

Water 

level, ft

PME Min, 

Water 

level, ft

Max, 

Water 

level, ft

w11res2 error correction 3 -0.27 0.36 7,628 0.860 -0.012 14.15 0.002 0.043 6.9%w14res error correction 3 -2.16 -1.44 7,628 0.828 -0.013 21.58 0.003 0.053 7.4%w15res error correction 3 -2.51 -1.79 3,859 0.978 -0.001 3.11 0.001 0.028 3.9%w18res error correction 3 0.64 1.87 7,628 0.978 0.000 16.27 0.002 0.046 3.7%w2res error correction 2 0.73 2.11 7,648 0.974 0.008 22.42 0.003 0.054 3.9%w5res error correction 3 -2.87 -2.15 7,648 0.935 -0.001 9.45 0.001 0.035 4.9%cluster3_static static 1 6.74 12.01 58,701 0.072 -0.000 35385.10 0.603 0.776 14.7%cluster3_dynamic dynamic 2 -2.45 2.70 53,841 0.982 0.125 593.08 0.011 0.105 2.0%3a9decor decorrelation 1 6.95 11.84 58,016 0.953 -0.008 1654.52 0.029 0.169 3.5%3a12decor decorrelation 1 6.95 11.84 53,837 0.983 0.075 541.43 0.010 0.100 2.1%eden14res error correction 2 -1.17 -0.66 1,416 0.580 0.007 9.92 0.007 0.084 16.3%eden5res error correction 3 -0.93 0.06 1,654 0.975 0.004 1.82 0.001 0.033 3.3%

WCA3B Models

cluster1-static static 1 5.21 9.80 81,262 0.218 -0.000 25801.41 0.318 0.563 12.3%cluster1-dynamic dynamic 3 -2.33 2.22 79,576 0.983 0.025 437.13 0.005 0.074 1.6%site71dec decorrelation 1 5.56 8.75 60,366 0.958 -0.023 662.95 0.011 0.105 3.3%srs1dec decorrelation 1 -0.36 0.50 59,987 0.944 -0.000 878.27 0.015 0.121 14.0%site76dec decorrelation 1 5.56 8.75 59,678 0.938 0.014 957.11 0.016 0.127 4.0%ti-8res error correction 1 -4.56 -3.20 5,684 0.983 0.003 8.26 0.001 0.038 2.8%ti-9res error correction 3 -2.34 -1.58 5,685 0.962 0.009 4.65 0.001 0.029 3.8%eden7res error correction 2 -3.51 -2.07 2,419 0.991 0.008 2.56 0.001 0.033 2.3%eden10res error correction 2 -2.08 -1.09 2,419 0.969 0.007 3.62 0.001 0.039 3.9%

BCNP Models

bcnp-static static 1 -1.43 10.51 115,719 0.837 -0.032 73866.48 0.638 0.799 6.7%bcnp-dynamic dynamic 4 -3.25 1.58 99,626 0.844 0.091 8532.91 0.086 0.293 6.1%loop1tdecor decorrelation 1 3.01 7.33 55,719 0.993 0.019 0.15 0.000 0.002 0.0%

54 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
Appendix 2. Summary statistics for the models used in the study. — Continued

[WCA1, Water Conservation Area 1; WCA2, Water Conservation Area 2; WCA3A, Water Conservation Area 3A; WCA3B, Water Conservation Area 3B; BCNP, Big Cypress National Preserve; ENP, Everglades National Park; HLN, hidden layer neurons; min, minimum; max, maximum; feet, ft; n, number of vectors; R2, coefficient of determination; ME, mean error; SSE, sum of square error; MSE, mean square error; RMSE, root mean square error; PME, percent model error]

Model name Model type Number of HLN

Testing

Range of output variable

n R2

ME, 

Water 

level, ft

SSE,

Water level, 

ft

MSE,

Water level, 

ft

RMSE,

Water 

level, ft

PME Min, 

Water 

level, ft

Max, 

Water 

level, ft

loop2tdecor decorrelation 1 3.02 6.92 51,354 0.886 0.038 3145.49 0.061 0.247 6.3%bac10decor decorrelation 1 3.02 6.92 50,807 0.928 0.272 1964.69 0.039 0.197 5.0%eden1res error correction 3 0.50 1.92 3,864 0.830 0.018 9.70 0.003 0.050 3.5%eden6-static static 1 6.21 12.17 57,244 0.366 -0.035 49317.07 0.862 0.928 15.6%eden6-dynamic dynamic 3 -2.42 2.11 49,053 0.955 -0.026 1880.37 0.038 0.196 4.3%l28gapdecor2 decorrelation 1 6.48 10.52 49,047 0.831 0.086 5630.72 0.115 0.339 8.4%eden6res2 error correction 2 -1.36 -0.53 1,591 0.706 0.030 9.59 0.006 0.078 9.4%

ENP Models

eden3stack-static static 1 -1.49 3.59 93,051 0.673 -0.005 44887.56 0.482 0.695 13.7%eden3stack-dynamic dynamic 3 -3.41 2.20 93,270 0.941 0.058 2943.13 0.032 0.178 3.2%otdecor decorrelation 1 -1.49 3.32 56,161 0.919 -0.015 2870.91 0.051 0.226 4.7%tmcdecor decorrelation 1 -1.49 3.32 56,087 0.924 0.061 2689.96 0.048 0.219 4.6%p36decor decorrelation 1 -1.49 3.32 56,080 0.892 0.007 3826.45 0.068 0.261 5.4%p35decor decorrelation 1 -1.49 3.32 55,804 0.783 0.154 7665.94 0.137 0.371 7.7%eden3res error correction 1 -1.02 -0.34 5,294 0.784 -0.042 21.80 0.004 0.064 9.5%met1-static static 1 2.90 9.71 94,949 0.566 0.001 42924.03 0.452 0.672 9.9%met1-dynamic dynamic 1 -2.73 2.37 80,735 0.963 0.011 1182.90 0.015 0.121 2.4%srs1decor decorrelation 1 4.74 8.62 60,937 0.903 0.011 1462.12 0.024 0.155 4.0%np201decor decorrelation 1 4.74 8.54 58,821 0.832 0.048 2294.77 0.039 0.198 5.2%ne2decor decorrelation 1 5.60 8.54 55,743 0.952 -0.035 479.66 0.009 0.093 3.2%nesrs3decor decorrelation 1 5.83 8.54 48,255 0.965 -0.020 293.35 0.006 0.078 2.9%met1res error correction 3 -0.68 -0.32 1,238 0.966 0.000 0.24 0.000 0.014 3.8%

Appendixes 55
Variables Description

3A12 water level at site 3A12

3A12DEC decorrelated water level at site 3A12

3A9 water level at site 3A9

3A9DEC decorrelated water level at site 3AS3W1

3AS3W1DEC decorrelated water level at site 3A10

3ASW water level at site 3ASW

3ASWDEC decorrelated water level at site 3ASW

BCA10 water level at site BCA10

BCA10DEC decorrelated water level at site BCA11

BCA5 water level at site BCA5

BCA9 water level at site BCA9

CELL_X UTM Easting of cell center

CELL_Y UTM Northing of cell center

L28GAP water level at site L28GAP

L28GAPDEC decorrelated water level at site L28GAP

LOOP1T water level at site LOOP1T

LOOP1TDEC decorrelated water level at site LOOP1T

LOOP2T water level at site LOOP2T

NE1 water level at site NE1

NE2 water level at site NE2

NE2DEC decorrelated water level at site NE2

NESRS3 water level at site NESRS3

NESRS3DEC decorrelated water level at site NESRS3

NP201 water level at site NP201

NP201DEC decorrelated water level at site NP201

OT water level at site OT

OTDEC decorrelated water level at site OT

P34 water level at site P34

P35 water level at site P35

P35DEC decorrelated water level at site P35

P36 water level at site P36

P36DEC decorrelated water level at site P36

PCTEXOTICS percent exotics

PCTOTHER percent other

PCTPRAIRIE percent prairie

Variables Description

PCTSAWGRASS percent sawgrass

PCTSLOUGH percent slough

PCTUPLAND percent upland

S142H water level at site S142H

SITE_62 water level at Site 62

SITE_63 water level at Site 63

SITE_63DEC decorrelated water level at Site 63

SITE_64 water level at Site 64

SITE_65 water level at Site 65

SITE_65DEC decorrelated water level at Site 65

SITE_69C water level at Site 69 adjusted to NAVD88

SITE_7 water level at Site 7

SITE_71C water level at Site 71 adjusted to NAVD88

SITE_76 water level at Site 76

SITE_8T water level at Site 8T

SITE_9 water level at Site 9

SITE_99 water level at Site 99

SITE71DEC decorrelated water level at Site 71

SITE76DEC decorrelated water level at Site 76

SITE8TDEC decorrelated water level at Site 8T

SITE8TDEC2 decorrelated water level at Site 8T-second 

version

SITE9DEC decorrelated water level at Site 9

SRS1 water level at site SRS1

SRS1C water level at site SRS1adjusted to NAVD88

SRS1DEC decorrelated water level at site SRS1

TMC water level at site TMC

TMCDEC decorrelated water level at site TMC

WCA1ME water level at site WCA1ME

WCA1MEDEC decorrelated water level at site WCA1ME

WCA1MEDEC2 decorrelated water level at site WCA1MEsecond version

WCA2E1 water level at site WCA2E1

WCA2F1 water level at site WCA2F1

WCA2F1DEC decorrelated water level at site WCA2F1

Appendix 3. Variables used in the artificial neural network models.

[NAVD88, North American Vertical Datum of 1988]

56 Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006
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Conrads and Roehl—Hydrologic Record Extension of Water-Level Data in the EDEN Using Artificial Neural Network Models, 2000–2006—Open-File Report 2007–1350