U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5244

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

Analysis and Simulation of Water-Level, 

Specific Conductance, and Total Phosphorus 

Dynamics of the Loxahatchee National Wildlife Refuge, 

Florida, 1995–2006
Cover photographs. Loxahatchee National Wildlife Refuge, Florida.

Banner: Heather S. Henkel, USGS St. Petersburg Coastal and Marine Science Center.

Background: Tracy Enright, USGS St. Petersburg Coastal and Marine Science Center.

Cover illustrations. Located in this report.

Top right: See figure 3.

Top left: See figure 30.

Bottom left: See figure 31.
Analysis and Simulation of Water-Level, 

Specific Conductance, and Total Phosphorus 

Dynamics of the Loxahatchee National Wildlife Refuge, 

Florida, 1995–2006

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

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

Scientific Investigations Report 2010–5244

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Conrads, P.A., and Roehl, E.A., Jr., 2010, Analysis and simulation of water-level, specific conductance, and total 

phosphorus dynamics of the Loxahatchee National Wildlife Refuge, Florida, 1995–2006: U.S. Geological Survey 

Scientific Investigations Report 2010–5244, 64 p.
iii

Contents

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

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................2

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

Previous Studies ...................................................................................................................................7

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

Data-Collection Networks............................................................................................................................8

Data Preparation.................................................................................................................................10

Limitations of the Historical Datasets .............................................................................................10

Characterization of Marsh and Canal Water Levels .............................................................................12

Simulating Water Levels, Specific Conductance, and Total Phosphorus .........................................16

Artificial Neural Networks ................................................................................................................16

Development of Water-Level, Specific Conductance, and Total Phosphorus Models ...........18

Statistical Measures of Prediction Accuracy................................................................................18

Water-Level Models ...........................................................................................................................19

Specific Conductance and Total Phosphorus Models .................................................................25

Modeling Specific Conductance Residual Error (εSC) .........................................................27

Modeling Total Phosphorus Residual Error (εTP) ..................................................................27

Analysis of Specific Conductance and Total Phosphorus Trends Using the 

Spatially Interpolating Artificial Neural Network Models..............................................30

Development of the Decision Support System .......................................................................................33

Architecture.........................................................................................................................................34

Model Simulation Control, Streaming Graphics, and Three-Dimensional 

Visualization Program ..........................................................................................................34

Application of the LOXANN Decision Support System ........................................................................37

Percentage of Historical Flow ..........................................................................................................37

User-Defined Hydrograph .................................................................................................................38

Summary........................................................................................................................................................40

Acknowledgments.......................................................................................................................................40

References Cited..........................................................................................................................................41

Appendix 1. List of Variables Used in the Study ....................................................................................43

Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network 

Decision Support System (LOXANN DSS) .................................................................................49
iv

Figures

1–4. Maps showing—

1. Vegetation map of southern Florida circa 1943 ..............................................................3

2. The Arthur R. Marshall (ARM) Loxahatchee National Wildlife Refuge 

and the Water Conservation Areas of the Everglades, Florida....................................4

3. Water conservation areas, stormwater treatment areas, and boundary canals 

near the Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida............5

4. The four major plant communities of the Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida ......................................................................................6

5. Graph showing water regulation schedule for Water Conservation Area 1, 

Arthur R. Marshall Loxaxatchee National Wildlife Refuge....................................................7

6–8. Maps showing—

6. Location of weather and continuous water-level stations and flow-control 

structures, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida........9

7. Location of District transect water-quality monitoring network (XYZ) and 

the Everglades Protection Area (EVPA) network, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida............................................................11

8. Flow-control structures and aggregation of structures used in the analysis 

and model development, Arthur R. Marshall Loxahatchee National Wildlife 

Refuge, Florida ...................................................................................................................12

9–11. Graphs showing—

9. Daily water levels for six continuous streamgaging stations, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida, January 1995 to December 2004 ....13

10. Average daily rainfall and the 1-day change in water level at site 1-7, 

and daily water level at site 1-7, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida, January 1995 to December 2004 .........................14

11. Two-hundred-twenty-day moving window average of rainfall and daily 

water level at site 1-7, Arthur R. Marshall Loxahatchee National Wildlife 

Refuge, Florida, January 1995 to December 2004 ........................................................15

12–13. Diagrams showing—

12. Multilayer perceptron artificial neural network architecture....................................17

13. Water-level, specific conductance, and total phosphorus model architecture.....18

14. Screen capture of user interface of the super tau tool .......................................................19

15–20. Graphs showing—

15. Measured and linearly predicted daily water levels and SUMQ at site 1-7, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, 

January 1995 to January 2007 .........................................................................................20

16. Linear regression water-level model errors for six continuous streamgaging 

stations, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, 

April 2000 to December 2006............................................................................................21

17. Average daily rainfall and five frequency components for the rainfall 

time series, Arthur R. Marshall Loxahatchee National Wildlife Refuge, 

Florida, January 2002 to December 2003 .......................................................................22

18. Measured and predicted water-level model error for six continuous streamgaging 

stations, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida..........23

19. Measured and predicted water level for six continuous streamgaging 

stations, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida..........23

20. Water levels at sites 1-8T and 1-8C, and a 0.16-foot adjustment to 

water level at site 1-8C, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida, March 2001 to December 2006 ............................................24
v

21–28. Graphs showing—

21. Measured and predicted specific conductance from the static 

SIANN model for XYZ and EVPA networks, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida............................................................26

22. Measured and predicted total phosphorus concentration from the 

static SIANN models for the EVPA network, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida............................................................26

23. Measured and predicted specific conductance model error for 

XYZ and EVPA networks, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida.....................................................................................................28

24. Measured and predicted specific conductance for XYZ and EVPA networks, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida..........................28

25. Measured and predicted total phosphorus model error for the EVPA network, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida..........................29

26. Measured and predicted total phosphorus for the EVPA network, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida..........................29

27. Measured and predicted specific conductance to evaluate trends at

XYZ and EVPA networks, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida.....................................................................................................31

28. Measured and predicted total phosphorus to evaluate trends at EVPA 

networks, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida .......31

29. Color gradient maps of specific conductance and total phosphorus as predicted 

by SIANNs for the Arthur R. Marshall Loxahatchee National Wildlife Refuge, 

Florida, for January 11, 1995; December 28, 1999; and December 14, 2004 ......................32

30. Diagram showing architecture of the LOXahatchee Artificial Neural Network 

(LOXANN) decision support system ...........................................................................................34

31–33. Screen captures showing—

31. Model simulator controls used to set parameters and run a simulation 

in the LOXANN decision support system.......................................................................35

32. Streaming graphics displayed during simulation in the LOXANN 

decision support system...................................................................................................35

33. Three-dimensional surfaces of water levels, specific conductance, and total 

phosphorus, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida ......36

34–38. Graphs showing—

34. Simulated actual conditions and a 40-percent increase to the historical flows 

for aggregated flows of Q4, Arthur R. Marshall Loxahatchee National Wildlife 

Refuge, Florida, May 2000 through April 2006...............................................................37

35. Cumulative frequency of slopes from the canal to marsh for simulated 

actual conditions and a 40-percent increase to the historical flows for 

the aggregated Q4 control-structure flow, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida ....................................................................................38

36. Historical inflow and outflow hydrographs and a user-defined hydrograph 

for the aggregated Q4 flow, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida, January 2001 through December 2004 ...............................38

37. Simulated actual conditions and conditions from a user-defined hydrograph 

for aggregated flows of Q4, Arthur R. Marshall Loxahatchee National Wildlife 

Refuge, Florida, January 2001 to April 2006...................................................................39

38. Cumulative frequency of slopes from the canal to marsh for simulated 

actual conditions and a user-defined hydrograph for the aggregated 

Q4 control-structure flows, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida ....................................................................................................39
vi

Tables

1. Flow, water level, precipitation, and evapotranspiration stations used in the 

model development......................................................................................................................9

2. Water-quality sampling sites used in the model development...........................................11

3. Count, minimum, maximum, mean, standard deviations, and coefficient of 

determination of six water-level gages in the Refuge between 1995 and 2008 ...............13

4. Coefficient of determination of daily water level and average rainfall, 

1-day change in water level, and 2-day change in water level ..........................................14

5. Flow structure, aggregated flow group assignment, moving window average, 

and coefficient of determination between daily rainfall and flow......................................15

6. Coefficient of determination, time delay, and moving window average between 

the 1-day change in water level and rainfall and aggregated flows .................................15

7. Moving window averages for rainfall (RAIN1 and RAIN2), evapotranspiration 

(ET), and total flow (TOTQ-in 1 and TOTQ-in 2) inputs for six linear water-level 

models along with the slope, y-intercept, and coefficient of determination....................21

8. Water-level error correction model performance statistics...............................................24

9. Statistics for final water-level simulations.............................................................................24

10. Model performance statistics for the static and dynamic specific conductance 

and total phosphorus models ...................................................................................................25

11. Model performance statistics for the specific conductance and total 

phosphorus models used for trend analysis ..........................................................................30

Conversion Factors and Datums

Multiply By To obtain

Length

inch 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2

)

acre 0.4047 hectare (ha)

square mile (mi2

) 259.0 hectare (ha)

square mile (mi2

) 2.590 square kilometer (km2) 

Flow rate

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F =(1.8 ×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F – 32)/ 1.8

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29). 

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.
vii

Acronyms and Abbreviations Used in this Report

AI artificial intelligence

ANN artificial neural network

BEP back error propagation

CERP Comprehensive Everglades Restoration Plan

CRADA Cooperative Research and Development Agreement 

DSS decision support system

EVPA Everglades Protection Area

GH gage height

GUI graphical user interface

LOX water-quality sampling sites in the EVPA monitoring network

LOXANN DSS Loxahatchee Artificial Neural Network Decision Support System

ME mean error

MS Microsoft

MSE mean square error

NWIS National Water Information System 

OLS ordinary least squares

PME percent model error

Q flow

Refuge Arthur R. Marshall Loxahatchee Wildlife Refuge 

RMSE root mean square error

R2 coefficient of determination

SC specific conductance

SFWMD South Florida Water Management District

SIANN Spatially Interpolating Artificial Neural Network

SSE sum of square error

STA Stormwater Treatment Area

TP total phosphorus

USACE U.S. Army Corps of Engineers

USFWS U.S. Fish and Wildlife Service

USGS U.S. Geological Survey

UTM Universal Transverse Mercator

WL water level

XYZ District transect water quality monitoring network

3DVis three-dimensional visualization

Analysis and Simulation of Water-Level, 

Specific Conductance, and Total Phosphorus 

Dynamics of the Loxahatchee National Wildlife Refuge, 

Florida, 1995–2006

By Paul A. Conrads1 and Edwin A. Roehl, Jr.2

Abstract 

The Arthur R. Marshall Loxahatchee Wildlife Refuge 

(Refuge) was established in 1951 through a license agreement 

between the South Florida Water Management District and 

the U.S. Fish and Wildlife Service (USFWS) as part of the 

Migratory Bird Conservation Act. Under the license agreement, the State of Florida owns the land of the Refuge and 

the USFWS manages the land. Fifty-seven miles of levees 

and borrow canals surround the Refuge. Water in the canals 

surrounding the marsh is controlled by inflows and outflows 

through control structures. The transport of canal water with 

higher specific conductance and nutrient concentrations to 

the interior marsh has the potential to alter critical ecosystem 

functions of the marsh. 

Data-mining techniques were applied to 12 years 

(1995–2006) of historical data to systematically synthesize 

and analyze the dataset to enhance the understanding of the 

hydrology and water quality of the Refuge. From the analysis, 

empirical models, including artificial neural network (ANN) 

models, were developed to answer critical questions related 

to the relative effects of controlled releases, precipitation, and 

meteorological forcing on water levels, specific conductance, 

and phosphorous concentrations of the interior marsh. Data 

mining is a powerful tool for converting large databases 

into information to solve complex problems resulting from 

large numbers of explanatory variables or poorly understood 

process physics. For the application of the linear regression 

and ANN models to the Refuge, data-mining methods were 

applied to maximize the information content in the raw data. 

Signal processing techniques used in the data analysis and 

model development included signal decomposition, digital 

filtering, time derivatives, time delays, and running averages. 

Inputs to the empirical models included time series, or signals, 

of inflows and outflows from the control structures, precipitation, and evapotranspiration. For a complex hydrologic system 

like the Refuge, the statistical accuracy of the models and 

predictive capability were good. The water-level models have 

coefficient of determination (R2

) values ranging from 0.90 to 

0.98. The R2 for the specific conductance model is 0.82, and 

the R2 for the total phosphorus model is 0.51. The accuracy of 

the models was attributable to the quantity and quality of the 

available data. 

To make the models directly available to all stakeholders, 

an easy-to-use decision support system (DSS) called the 

Loxahatchee Artificial Neural Network Model (LOXANN) 

DSS was developed as a spreadsheet application that 

integrates the historical database, linear regression and ANN 

models, model controls, streaming graphics, and model output. 

The LOXANN DSS allows Refuge managers and other 

users to easily execute the water level, specific conductance, 

and phosphorous models to evaluate various water-resource 

management scenarios. The user is able to choose from three 

options in setting the control-structure flows: as a percentage 

of historical flow, as a constant flow, or as a user-defined 

hydrograph. Output from the LOXANN DSS includes tabular 

time series of predictions of the measured data and predictions 

of the user-specified conditions. A three-dimensional visualization routine also was developed that displays longitudinal 

specific conductance conditions. 

Two scenarios were simulated with the LOXANN DSS. 

One scenario increased the historical flows at four control 

structures by 40 percent. The second scenario used a userdefined hydrograph to set the outflow from the Refuge to the 

weekly average inflow to the Refuge delayed by 2 days. Both 

scenarios decreased the potential of canal water intruding into 

the marsh by decreasing the slope of the water level between 

the canals and the marsh.

1

 U.S. Geological Survey, South Carolina Water Science Center, 

Columbia, SC.

2

 Advanced Data Mining, LLC, Greenville, SC.
2 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Introduction

The Arthur R. Marshall Loxahatchee National Wildlife 

Refuge (Refuge) is the last of the soft-water ecological 

systems in the Everglades. “Soft-water” systems have low 

calcium or magnesium ions as compared to “hard water” 

systems with higher concentrations of calcium or magnesium. 

Historically, the ecosystem was driven by precipitation inputs 

that were low in specific conductance and nutrients (fig. 1). 

Fifty-seven miles of levees and borrow canals surround the 

Refuge and the water in the canals have higher concentrations 

of calcium and magnesium ion compared to the Refuge 

water. The banks of the canal by the interior marsh are not 

continuous, with openings of various sizes where marsh water 

exchanges with water from the canals. With controlled flow 

releases into and out of the canals that surround the Refuge, 

the transport of water from the canals with higher specific 

conductance (an indirect measurement of ionic concentration 

such as calcium and magnesium) and nutrient concentration 

has the potential to alter critical ecosystem functions of 

the interior marsh (fig. 2). With potential alteration of flow 

patterns to accommodate the restoration of the Everglades, the 

Refuge could be affected not only by changes in the timing 

and frequency of flows releases into the canals but by the 

quality of the water that inundates the Refuge. 

 Hydrologic and water-quality data have been collected in 

the Refuge for many years. Data characterizing the hydrology 

of the system—inflows, outflows, precipitation, and water 

levels—have been collected since the 1950s. Data characterizing the water quality of the system, including specific 

conductance and total phosphorus, have been collected since 

the late 1970s. New technologies in environmental monitoring 

have made it cost effective to acquire tremendous amounts of 

hydrologic and water-quality data. The monitoring networks 

supported by the Comprehensive Everglades Restoration 

Plan (CERP) record tremendous amounts of data each day, 

and the database incorporates millions of measurements that 

describe the environmental response of the system to changing 

conditions. Often these active and historical databases are 

underinterpreted and underutilized. Although these data are a 

valuable resource for understanding environmental systems, 

a thorough synthesis and analysis of the data may be lacking. 

New methodologies are available to systematically synthesize 

and analyze the dataset to answer critical questions related 

to the relative effects of controlled releases, precipitation, 

groundwater interaction, and meteorological forcing on water 

level, specific conductance, and phosphorous concentration to 

enhance the understanding of the hydrology and water quality 

of the interior marsh of the Refuge. 

The U.S. Geological Survey (USGS) entered into a Cooperative Research and Development Agreement (CRADA) with 

Advanced Data Mining International in 2002 to collaborate 

on applying data mining and artificial neural network (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 

information for use in solving problems that are otherwise 

imponderable because of the large numbers of explanatory 

variables or poorly understood process physics. Data-mining 

methods come from different technical fields—such as signal 

processing, statistics, artificial intelligence, and advanced 

visualization—and include methods for maximizing the 

information content of data, determining which variables 

have the strongest correlations to the problems of interest, 

and developing models that predict future outcomes. This 

knowledge encompasses both understanding of cause and 

effect relations and predicting the consequences of alternative 

actions. 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 presents the results of an investigation that 

analyzed water level (gage height), specific conductance, and 

total phosphorus dynamics in the Refuge caused by changing 

inflows, outflows, precipitation, and evapotranspiration conditions. In this report, the terms water level and gage height are 

used interchangeably. This report documents the development 

of the Loxahatchee Artificial Neural Network Decision 

Support System (LOXANN DSS), including examples of 

applying the LOXANN DSS to the Refuge to evaluate the 

intrusion of canal water into the marsh.

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, and estuaries by using standardized 

methods and maintains the data from these stations in a national 

database. Often these databases are underutilized and underinterpreted for addressing contemporary hydrologic issues. The 

techniques presented in this report demonstrate how valuable 

information can be extracted from existing disparate databases 

to assist local, State, and Federal agencies understand and 

manage complex hydrologic systems. The application of 

data-mining techniques, including ANN models, to the Refuge 

demonstrates how empirical models of complex hydrologic 

systems can be developed, disparate databases and models can 

be integrated, and study results can easily be disseminated to 

meet the needs of a broad range of end users.
Introduction 3

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

Originally printed 1943, 1:400,000

0 10 20 30 40 MILES

0 10 20 30 40 KILOMETERS

FLORIDA GEOLOGICAL SURVEY BULLETIN TWENTY-FIVE—FIGURE 71

EXPLANATION

General vegetation

Water Conservation Area 1 (Arthur R. Marshall Loxahatchee Wildlife Refuge)

Scrub forest

Hammock

forest

Bay tree forest

Inland swamp

Cypress forest

Cypress heads

or domes

Pine flatwood

forest

High pine forest

Miami Rockland

pine forest

Miami open

pine forest

Mangrove

swamp

Mangrove

swamp and

saltwater marsh

Saltwater

marsh

Salt Prairie

(Cape Sable area)

Freshwater marsh

(outside of E.)

Wet prairies

Saw palmetto

or Dry Prairies

Southern coast

marsh prairie

Coastal beach 

and dune 

vegetation

Saw-grass marsh 

(medium dense 

to sparse)

Saw-grass marsh 

(with wax-myrtle 

thickets)

Saw-grass marsh 

(dense)

Willow and 

elderberry zone 

(mostly cultivated)

Custard-apple zone

(mostly cultivated)

Saw-grass marsh 

(with abundant ferns and cattails)

Tree island, bay tree forest

Tree island, hammock forest

Marsh prairie, southern E.

Slough, pond, and lake

(with aquatic plants)

Main Everglades (E.) vegetation

Figure 1. Vegetation map of southern Florida circa 1943 (modified from Davis, 1943). The Arthur R. Marshall Loxahatchee Wildlife 

Refuge is outlined in magenta and the vegetation type is characterized as slough, pond, and lake (with aquatic plants).

FLORIDA

Map

area

Figure 1. Vegetation map of southern Florida circa 1943 (modified from Davis, 1943). The Arthur R. Marshall 

Loxahatchee Wildlife Refuge vegetation type is characterized as slough, pond, and lake (with aquatic plants).
4 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR Florida Water Management

South

boundary

District

Everglades Protection Area

Rotenberger and Holey Land

 Wildlife Management Areas

Stormwater Treatment Areas

Indian Reservation

EXPLANATION

Bounday of Water Conservation 

 Area (WCA)

Lake

Kissimmee

Lake

Okeechobee

Kissimmee River

Caloosahatchee

Florida Bay

River

Florida Panther

National Wildlife

Refuge

Seminole

Miccosukee

Everglades

National

Park

WCA 3

WCA 2

WCA 1

ARM

Loxahatchee

National

Wildlife

Refuge

Big

Cypress

National

Preserve

Figure 2. The Arthur R. Marshall (ARM) Loxahatchee National Wildlife Refuge and the Water Conservation 

Areas of the Everglades, Florida (modified from U.S. Fish and Wildlife Service, 2000).

Boynton

Beach

Everglades

agricultural

area

0 10 20 30

N

40 MILES

0 10 20 30 40 KILOMETERS

Figure 2. The Arthur R. Marshall (ARM) Loxahatchee National Wildlife Refuge and the Water Conservation 

Areas of the Everglades, Florida (modified from U.S. Fish and Wildlife Service, 2000).
Introduction 5

Description of the Study Area

Historically, the area of the present day Refuge was 

part of an uninterrupted wetland that extended from Lake 

Okeechobee and flowed to the southwestern tip of Florida 

(Richardson and others, 1990; fig. 1). Beginning in the mid 

1800s, drainage activities began to convert the wetlands 

for agriculture and urban development. In the 1940s, the 

U.S. Army Corps of Engineers (USACE) constructed Water 

Conservation Areas 1, 2, and 3 to regulate water for the 

increasing population and agricultural needs of South Florida 

through a series of levees and canals (fig. 2). In general, the 

Water Conservation Areas store water during the wet season 

and supply water during the dry season.

The 143,238-acre Loxahatchee National Wildlife Refuge 

(Water Conservation Area 1) was established in 1951 through 

a license agreement between the South Florida Water Manage

ment District (SFWMD) and the U.S. Fish and Wildlife 

Service (USFWS) as part of the Migratory Bird Conservation 

Act (U.S. Fish and Wildlife Service, 2000). Under the license 

agreement, the State of Florida owns the land of the Refuge 

and the USFWS manages the land. Water in the Refuge is 

controlled by inflows and outflows through control structures 

to the 57 miles of canals that surround the Refuge (fig. 3). 

The eastern boundary of the refuge is the L-40 canal, and the 

western boundary of the Refuge is formed by the L-7 canal to 

the northwest and the L-39 canal (also known as the Hillsboro 

Canal) to the southwest. Land use surrounding the Refuge 

varies with the Everglades Agricultural Area to the northwest, 

urban areas to the east, and the Water Conservation Areas of the 

Everglades to the south and southwest. In 1986, the name of the 

Refuge was changed to A.R.M. Loxahatchee National Wildlife 

Refuge to honor the local conservationist Arthur R. Marshall. 

Although the Refuge is regulated hydrologically, it 

is considered a “unique remnant which still functions as a 

northern refuge for species of the Everglades ecosystem” 

(Richardson and others, 1990). The limestone bottom of the 

freshwater marsh of the Refuge is overlain with peat as much 

as 12 feet thick, and the approximate land-elevation gradient 

is 5 feet from north to south (U.S. Fish and Wildlife Service, 

2007a). Richardson and others (1990) describes the interior of 

the Refuge as a “complex mosaic of wetland communities that 

grade from wetter areas such as sloughs and wet prairies, to 

sawgrass, brush, and finally tree islands occurring at the drier 

end of the scale (fig. 4).” The plant community of the Refuge 

developed under nutrient-poor conditions and was maintained 

with a continuation of low nutrient concentrations (Walker, 

1995). A change in the nutrient-poor conditions of the marsh 

may adversely affect the plant community structure.

Figure 3. Water conservation areas, stormwater treatment 

areas, and boundary canals near the Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida.

80°25'

26°40'

26°35'

26°30'

26°25'

26°20'

80°20' 80°15'

L-12 Canal

L-13 Canal C-51 Canal

L-40 Canal

L-7 Canal

L-6 Canal

L-39 Hillsboro Canal

L-39 Hillsboro Canal

ENR

Collection

Canal

ENR Supply Canal (L-7)

Arthur R. Marshall 

Loxahatchee 

National Wildlife 

Refuge

G-94C

culvert

G-94D (ACME 2)

ACME 1 pump station

S-362

G-94B

culvert

G-94A

culvert

S-39 spillway

S-10C spillway

S-10D spillway

S-10E culvert

S-6 pump station

G-251 pump station

1W

1E

G-310

pump

station

G-301 spillway G-300 spillway

S-5A pump station

S-5AS spillway

G-338

S-10A

spillway

0 2 4 6 MILES

0

Base modified from U.S. Geological Survey 

 digital data 1:24,000

Albers Equal-Area Projection 

North American Datum of 1983 2 4 6 KILOMETERS

EXPLANATION

Stormwater-treatment area and identifier

Figure 3. Water conservation areas, stormwater treatment areas,

and boundary canals near the Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida.

L-6 Canal

G-301 spillway

1W

Water Conservaton Area

1

2

Canal and identifier

Control structure and identifier
6 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Figure 4. The four major plant communities of the Arthur R. Marshall Loxahatchee National Wildlife Refuge, 

Florida (modified from Richardson and others, 1990).

EXPLANATION

Major plant community

Marsh

Shrub

Tree island

Cattail

N

0 2 4 6 MILES

0 2 4 6 KILOMETERS

Figure 4. The four major plant communities of the Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida 

(modified from Richardson and others, 1990).
Introduction 7

Historically, the major sources of water to the area of the 

Refuge were precipitation and sheetflow from the wetlands 

with a low nutrient load to the system. With the development 

of agricultural, suburban, and urban areas, and the channel

ization of flow to and around the Refuge, the nutrient load, 

especially phosphorus, increased substantially (greater than 

100 parts per billion [ppb]; Walker, 1995). In 1994, the Florida 

legislature passed the Everglades Forever Act with one of 

its goals being the reduction of phosphorus concentrations 

in the Everglades to less than 50 ppb with the ultimate goal 

of reducing concentrations to less than 10 ppb. The Act 

provided funding for the construction of stormwater treatment 

areas (STAs) to reduce the phosphorus load to the Water 

Conservation Areas and Everglades National Park (fig. 2). 

Stormwater treatment areas 1E and 1W were constructed to 

reduce excess nutrient loads to the Refuge (fig. 3). The STAs 

are large (greater than 6,000 acres) constructed wetlands with 

a series of cells with varying hydraulic characteristics, aquatic 

plants, and periphyton mats that uptake phosphorus from 

inflow from the Everglades Agricultural Area before releasing 

the water to the Refuge. 

Currently, the major sources of water to the Refuge are 

rainfall (56 percent), the S-5A pump station (40 percent), and 

the ACME-1 and ACME-2 pump stations (4 percent) (U.S. Fish 

and Wildlife Service, 2007a). Of all the water pumped into the 

Refuge, approximately 91 percent is drained from the Everglades Agricultural Area, and 9 percent is from agricultural and 

urban developed lands located east of the Refuge (U.S. Fish 

and Wildlife Service, 2007a). The water level in the canals is 

managed through a cooperative agreement among the USACE, 

SFWMD, and USFWS, referred to as a Water Regulation 

Schedule (U.S. Fish and Wildlife Service, 2007a; fig. 5), to 

meet the needs of the Refuge and its downstream uses. The 

current schedule was implemented in 1995 and designed to 

(1) maintain the health of the Refuge vegetation types by 

flooding all wetlands during the summer and fall; (2) enhance 

feeding opportunities for waterfowl and wading birds by lowering water levels in the spring so that water is concentrated in 

sloughs and shallow ponds during nesting season; (3) maintain 

water storage capacity in the Refuge during the hurricane 

season; (4) store water for irrigating nearby cropland during 

the fall, winter, and early spring; and (5) prevent saltwater 

intrusion into the Biscayne aquifer by storing water for release 

into coastal canal systems during the fall, winter, and spring 

(U.S. Fish and Wildlife Service, 2000). 

Previous Studies

Numerous ecological and hydrologic studies have been 

conducted to support the management of the Refuge and 

the resulting changes of the water-level and water-quality 

dynamics of the canals and marshes of the Refuge. Many of 

the plant ecology studies have focused on the characterization 

of the plant communities and how these communities respond 

to changing soil pore-water quantity and quality. Many of 

the hydrodynamic and water-quality modeling studies have 

focused on developing simulation models to estimate water 

level and water quality in the canals and marshes. These 

models have been used to evaluate various hydrologic 

scenarios and their effect on plant community dynamics, 

water-regulation schedules, and alternative water management. 

A thorough summary of hydrodynamic and water-quality 

models applied to the Everglades in general and the Refuge 

in particular can be found in Arceneaux and others (2007). 

Additional information on model development funded by the 

Refuge can be found in the annual reports of their Enhanced 

Monitoring and Modeling Program (U.S. Fish and Wildlife 

Service, 2007a, 2007b, and 2009).

Figure 5. Water regulation schedule for Water Conservation Area 1, Arthur R. Marshall Loxaxatchee 

National Wildlife Refuge (modified from U.S. Fish and Wildlife Service, 2000; see figure 2 for location). 

The schedule was established in May 1995 and is administered by the U.S. Army Corps of Engineers. 

Surface-water elevation, in feet above

National Geodetic Vertical Datum of 1929

18

17

16

15

14

13

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Zone A1

Active water releases

due to flood conditions

Zone A2

Water releases linked

to amount of rainfall and

elevation of Lake Okeechobee

Zone B

Water releases as needed,

depending on elevation 

of Lake Okeechobee

Zone C

No net water releases

due to drought conditions

Figure 5. Water regulation schedule for Water Conservation Area 1, Arthur R. Marshall Loxaxatchee 

National Wildlife Refuge (modified from U.S. Fish and Wildlife Service, 2000; see figure 2 for location).

The schedule was established in May 1995 and is administered by the U.S. Army Corps of Engineers.
8 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Approach

The emerging field of data mining addresses the issue 

of extracting information from large databases. Data mining 

is composed of several technologies that include signal 

processing, advanced statistics, multidimensional visuali

zation, chaos theory, and machine learning. Machine learning 

is a field of artificial intelligence in which computer programs 

are developed that automatically learn cause-and-effect 

relations from example cases and data. For numerical data, 

commonly used learning methods include ANNs, genetic 

algorithms, multivariate adaptive regression splines, and 

partial and ordinary least squares. 

A number of previous studies by the authors and others 

have used data mining to predict hydrodynamic and waterquality behaviors in the Beaufort, Cooper, Savannah, and 

Waccamaw River estuaries of South Carolina and Georgia 

(Roehl and others, 2000; Conrads and others, 2003; Conrads 

and others, 2006; and Conrads and Roehl, 2007) and stream 

temperatures in western Oregon (Risley and others, 2003). 

Results from the previously developed ANN-based models 

demonstrate that ANN models, combined with data-mining 

techniques, are an effective approach for simulating complex 

hydrologic systems. 

The ultimate goal of this investigation was to produce an 

effective model to simulate water level, specific conductance, 

and total phosphorous for a given set of hydrologic conditions. 

The variability of water levels and water quality in the Refuge 

is a result of many factors, including inflows and outflows to 

the canals, precipitation, evapotranspiration, and groundwater 

losses. The approach taken uses all available flow, water-level, 

specific conductance, and total phosphorous measurements 

from the individual gages and sampling sites since the waterquality sampling networks were begun in 1995. The modeling 

approach uses correlation functions that were synthesized 

directly from data to predict how water level, specific conductance, and total phosphorus at the measurement locations 

respond to changing precipitation, evapotranspiration, inflow, 

and outflow conditions. In order to simulate the dynamic 

response of water levels and water quality, empirical models 

were developed to predict water level, specific conductance, 

and phosphorus for selected gages throughout the Refuge. 

Extensive continuous hydrologic datasets as well as data from 

extensive periodic sampling networks were available for the 

Refuge. Empirical water-level, specific conductance, and total 

phosphorus models were developed directly from these data 

by using data-mining techniques and ANN models. 

The application of data-mining techniques to build 

empirical models to simulate the water levels, specific 

conductance, and total phosphorus was undertaken in three 

phases: (1) obtaining and evaluating the suitability of the 

hydrologic and water-quality data for developing empirical 

models; (2) developing models to simulate the water level at 

six streamgaging stations, specific conductance at 25 sampling 

locations, and total phosphorus at 14 sampling locations; and 

(3) developing a DSS that integrates historical databases, 

model controls, and model output into a spreadsheet application with a graphical user interface that allows the user to 

simulate scenarios of interest. 

Data-Collection Networks

Many resource entities have collected data in the Refuge, 

including the USFWS, USGS, SFWMD, and local colleges 

and universities. Continuous hydrologic and meteorological 

data of water level, flow, precipitation, and evapotranspiration 

were collected in addition to water-quality sampling data 

of specific conductance and total phosphorus from various 

databases to build, train, and test the linear regression and 

ANN models for the LOXANN DSS. Descriptions and 

quality-assurance information of the available data-collection 

networks for the Refuge for the period 1995–2004 can be 

found in Meselhe and others (2005). Summaries and analyses 

of data collected by the Refuge can be found in the annual 

reports for its Enhanced Monitoring and Modeling Program 

(U.S. Fish and Wildlife Service 2007a, 2007b, and 2009). 

The ideal dataset for developing empirical models 

for the Refuge would cover a large range of historical and 

contemporary climatic and operational conditions and have 

the temporal and spatial coverage to be able to characterize the 

hydrologic and water-quality dynamics throughout the Refuge. 

Typically, continuous data, such as water level or flow, are 

temporally dense (15-minute to 60-minute recording intervals) 

but can be spatially sparse. Conversely, water-quality sampling 

data (typically weekly or monthly sampling intervals) are 

usually more temporally sparse but often have a denser spatial 

coverage than continuous data. Extensive water-quality 

sampling began in 1995, and the period of record from 1995 

to 2006 provides the most concurrent continuous hydrologic 

data, including data from the water-quality sampling networks. 

A description of the datasets used in the development of 

LOXANN DSS follows.

Continuous daily hydrologic data included inflows, 

outflows, water levels, precipitation, and evapotranspiration 

(fig. 6; table 1). The flow data represent the 19 hydrologic 

control structures around the perimeter canal and were characterized by their direction of flow—into or out of the Refuge or 

bidirectionally. Water-level data were collected from six USGS 

streamgaging stations; one of the gaging stations was proximal 

to the canal (site 1-8C) and the other five stations were located 

in the interior marsh. Streamgaging stations north and south 

were installed in 2001 and did not cover the period of record. 

Precipitation and weather data were recorded at 16 stations: 

1 was in the marsh, 6 were along the canal, and 9 were outside 

of the Refuge. Evapotranspiration data were available at three 

of the weather stations. Pan evaporation data were available 

at station S5A, located on the canal at the northern tip of the 

Refuge. Evapotranspiration data were available at station 

STA1W to the northwest, and potential evapotranspiration data 

were available at station LOXWS located midway along the 

L-40 canal on the eastern side of the Refuge.
Data-Collection Networks 9

80°25'

26°40'

26°35'

26°30'

26°25'

26°20'

80°20' 80°15'

L-12 Canal

L-13 Canal C-51 Canal

L-40 Canal

L-7 Canal

L-6 Canal

L-39 Hillsboro Canal

L-39 Hillsboro Canal

ENR

Collection

Canal

ENR Supply Canal (L-7)

G-94C

culvert

G-94D (ACME 2)

ACME 1 pump station

S-362

G-94B

culvert

G-94A

culvert

S-39 spillway

S-10C spillway

S-10D spillway

S-10E culvert

S-6 pump station

G-251 pump station

1E

G-310

pump

station

G-301 spillway G-300 spillway

S-5A pump station

S-5AS spillway

G-338

S-10A

spillway

0 2 4 6 MILES

0 2 4 6 KILOMETERS

Figure 6. Location of weather and continuous water-level 

stations and flow-control structures, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida.

Evapotranspiration

Precipitation

Continuous streamgaging station

Canal and identifier

Control structure and identifier

L-6 Canal

G-301 spillway

Arthur R. Marshall 

Loxahatchee 

National Wildlife Refuge

EXPLANATION

Continuous monitor site and identifier

2

3

A A

A

A

A

1-7

1-9

South

North

1-8T

1-8C

LOXWS

WCA1ME

STA1W

3STA1W

2

LOXWS 2

A1-9

A

Base modified from U.S. Geological Survey 

 digital data 1:24,000

Albers Equal-Area Projection 

North American Datum of 1983

Figure 6. Location of weather and continuous water-level 

stations and flow-control structures, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida.

Table 1. Flow, water level, precipitation, and evapotranspiration stations used in the model development.

[UTM, Universal Transverse Mercator; x, easting; y, northing; NAD83, 

North American Datum 1983; STA, stormwater treatment area]

Structure Location UTM x 

(NAD83)

UTM y 

(NAD83)

Flow data

S-5A L-7 Canal 562923.80 2951648.41

S-5AS L-40 Canal 562923.80 2951648.41

G-300 L-40 Canal 563360.30 2950824.02

G-301 L-7 Canal 561649.23 2950621.87

G-310 L-7 Canal 555156.76 2942060.02

G-251 L-7 Canal 555557.05 2942007.13

S-6 L-7 Canal 555237.83 2928059.96

S-10E L-39 Canal 555664.38 2927348.19

G-338 L-39 Canal 555293.06 2927854.37

S-10D L-39 Canal 561683.30 2918858.31

S-10C L-39 Canal 564597.91 2917008.87

S-10A L-39 Canal 568592.55 2915744.44

S-39 L-39 Canal 570050.07 2915284.57

S-362 L-40 Canal 568081.26 2944903.95

ACME #1 L-40 Canal 570829.38 2943161.99

ACME #2 L-40 Canal 572508.66 2941521.83

G-94C L-40 Canal 576431.10 2935866.25

G-94B L-40 Canal 577582.06 2929275.93

G-94A L-40 Canal 576780.29 2924092.71

Water level

Site 1-7 Central marsh 565061.88 2933415.39

Site 1-8T Central marsh 577474.80 2931309.20

Site 1-8C Marsh site 

near canal

575029.51 2932854.66

Site 1-9 Central marsh 570077.53 2927288.80

North Northern marsh 564356.19 2941626.14

South Southern marsh 565752.41 2922897.27

Precipitation

S-5A L-7 Canal 562923.80 2951648.41

S-6 L-7 Canal 555237.83 2928059.96

S-39 L-39 Canal 570050.07 2915284.57

LOXWS L-40 Canal 577503.46 2931177.16

Gage 6 Near L-40 Canal 57365.10 2908757.60

Gage 8 Near L-40 Canal 570877.40 2943262.60

WCA1ME Central marsh 568748.3 2932450.2

Evapotranspiration data

STA1W STA-1W 556983.50 2946136.81
10 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Specific conductance and total phosphorus data were 

obtained from three sampling networks maintained by 

SFWMD—the Everglades Protection Area (EVPA) waterquality monitoring sites, the District Transects monitoring 

network, or “XYZ” data network (fig. 7; table 2), and from 

the hydraulic structures. Fourteen sampling sites in the EVPA 

network (also referred to as the “LOX” sites) were used to 

monitor the physical, chemical, and biological properties. The 

sampling interval generally was monthly but was variable 

depending on hydrologic conditions and site classification. 

From 1995 to 2008, at least 65 samples were collected from 

each site. The XYZ network was made up of 11 sampling sites 

along the southwestern portion of the Refuge and was established to measure the nutrient gradient from the L-39 canal 

into the marsh. Sampling of the XYZ sites was irregular. From 

1995 to 2006, at least 68 samples were collected from each 

site. Water-quality sampling data were available for 15 of the 

hydraulic control structures in the Refuge. Similar to the 

other water-quality networks, the structures were sampled 

irregularly. From 1995 to 2006, the number of samples varied 

from 3 to 597, and more than 100 samples were collected at 

many of the structures.

Data Preparation

Because of the large number of hydrologic inputs to the 

Refuge, much of the flow and precipitation time-series data 

were aggregated to facilitate the analysis and modeling of 

the data. The flow data from the 19 control structures were 

aggregated into six flow groups (fig. 8). Aggregating data 

has the advantages of reducing the number of variables and 

diminishing spurious correlations between large and small 

flows from nearby hydraulic structures. Rainfall data were 

highly temporally and spatially variable and none of the 

precipitation time-series records were complete. A composite 

daily rainfall time-series record was computed by averaging 

the data from the six rain gages closest to the Refuge. If data 

from one or more of the gages were missing, the average was 

computed for the remaining gages. In addition, the rainfall 

values were converted to flow units for the Refuge. Assuming 

a Refuge area of 221 square miles, daily rainfall in inches was 

converted to cubic feet per second. 

Limitations of the Historical Datasets

As with any modeling effort, empirical or deterministic, 

the accuracy of the model is dependent on the quality and 

quantity of the data and range of measured conditions used 

for training or calibrating the model. The available period of 

record for the hydrologic and water-quality data-collection 

networks can limit the range of water-level and water-quality 

conditions that the model can accurately simulate. Although 

data were available from the networks in the Refuge from the 

mid-1990s, the data were not always of a sufficient quality 

to use for developing empirical models. Environmental 

monitoring technology has changed substantially over the last 

15 years. Periods of missing continuous data, especially flow 

and water-level data, limit the periods when the net flow into 

and out of the Refuge is known and when accurate models can 

be developed. Water-quality monitoring networks typically 

are established to meet regulatory compliance requirements 

and often provide sufficient long-term data to evaluate the 

status and trends of water-quality constituents of concern. 

Unfortunately, irregularly sampled water-quality data usually 

do not adequately capture the dynamic variability of complex 

systems, which is needed to develop accurate dynamic models. 

Specific limitations with the data collected for the Refuge to 

develop the LOXANN DSS are as follows.

• The flow data for control structures G-94A, G-94B, 

and G-94C (aggregated into Q5) were missing from 

January 1, 1996, until April 15, 2000. The data that 

were available indicate that at times these flow-control 

structures substantially affect the net flow; therefore, 

the data used to develop models were limited to the 

period after April 15, 2000.

• The south and north water-level stations were 

established in 2001. The shorter period of record, as 

compared to the other water-level sites, limited the 

data available for developing water-level models for 

all the sites.

• The temporal record for the flows, gage height, specific 

conductance, and total phosphorus was incomplete, 

and the specific conductance and total phosphorus 

measurements were particularly sparse. The waterquality sampling occurred on a small percentage of the 

days for which there were corresponding hydrologic 

data from 1995 to 2006. Of the 39 water-quality 

sampling sites, 32 sites had water-quality samples for 

5 percent or less of the days. The site with the greatest 

number of water-quality samples, control structure 

S6, only had concurrent samples with hydrologic data 

for 21 percent of the days. In addition, many of the 

samples were not measured on the same day. This type 

of low frequency, nonconcurrent sampling generally 

is insufficient to represent the dynamics of a complex 

system. Data from the control structures typically 

would be used to provide boundary conditions for the 

water-quality variability at interior sampling sites.
Data-Collection Networks 11

Figure 7. Location of District transect water-quality 

monitoring network (XYZ) and the Everglades Protection 

Area (EVPA) network, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida.

80°25'

26°40'

26°35'

26°30'

26°25'

26°20'

80°20' 80°15'

L-12 Canal

L-13 Canal C-51 Canal

L-40 Canal

L-7 Canal

L-6 Canal

L-39 Hillsboro Canal

L-39 Hillsboro Canal

ENR

Collection

Canal

ENR Supply Canal (L-7)

0 2 4 6 MILES

0 2 4 6 KILOMETERS

Canal and identifier

Water-quality sampling site and identifier

Figure 7. Location of District transect water-quality monitoring

network (XYZ) and the Everglades Protection Area (EVPA) network,

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida.

EVPA

XYZ Z4

LOX12

L-6 Canal

Arthur R. Marshall 

Loxahatchee 

National Wildlife Refuge

EXPLANATION

Base modified from U.S. Geological Survey 

 digital data 1:24,000

Albers Equal-Area Projection 

North American Datum of 1983

LOX9 LOX8

LOX10

X2

X4

Y4

Z4

Z3

Z2 Z1 X3

X0

X1

LOX5

LOX4 LOX3

LOX7

LOX6

LOX11

LOX13

LOX14

LOX16

LOX15

LOX12

Table 2. Water-quality sampling sites used in the model 

development.

[UTM, Universal Transverse Mercator; x, easting; y, northing; NAD83, 

North American Datum 1983]

Site UTM x 

(NAD83)

UTM y 

(NAD83)

 Everglades Protection Area

LOX10 557696.533 2934097.335

LOX11 570618.481 2927057.254

LOX12 561819.067 2923516.529

LOX13 569763.753 2922876.125

LOX14 575259.851 2920565.147

LOX15 564635.159 2918366.964

LOX16 569209.115 2917240.300

LOX3 564139.639 2941524.321

LOX4 570207.126 2942378.775

LOX5 563950.427 2937560.441

LOX6 576727.276 2931944.920

LOX7 572077.711 2933267.939

LOX8 565964.015 2933883.533

LOX9 561072.830 2934147.524

South Florida Water Management District transect (XYZ)

X0 555310.239 2929595.537

X1 555598.128 2929630.011

X2 556387.674 2930041.048

X3 557377.266 2929612.387

X4 559509.952 2930085.087

Y4 559573.425 2927366.295

Z1 555808.002 2927668.322

Z2 557023.968 2927256.124

Z3 558953.035 2926574.838

Z4 560964.178 2925240.763

Control structures

S-5A 562923.797 2951648.413

G-300 563360.301 2950824.018

G-301 561649.234 2950621.874

G-310 555156.761 2942060.022

S-6 555237.829 2928059.963

S-10E 555664.380 2927348.193

S-10D 561683.299 2918858.313

S-10C 564597.907 2917008.867

S-10A 568592.553 2915744.442

S-39 570050.073 2915284.569

ACME #1 570829.375 2943161.990

ACME #2 572508.664 2941521.829

G-94C 576431.096 2935866.250

G-94B 577582.057 2929275.929
12 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Characterization of Marsh and Canal 

Water Levels 

The primary sources for water levels in the Refuge marsh 

are precipitation and inflow and outflows from the control 

structures (U.S. Fish and Wildlife Service, 2000). The water 

levels at the six marsh sites are highly correlated and show 

similar dynamic responses to each other (fig. 9; table 3). Note 

that the length of record for stations north and south was much 

shorter than for the other four stations. Site 1-8C, the gage 

closest to a canal, shows the greatest dynamic variability. 

Three marsh gages, site 1-8T, site 1-9, and south, were highly 

correlated with coefficients of determinations, R2s, from 

0.94 to 0.97 (table 3). The high correlation is due to their 

proximity to canals. The relatively lower correlated stations, 

sites 1-8C and 1-7 (R2 of 0.77), reflect the dampening effect of 

the water-level variability from the canal to the interior marsh. 

The lowest correlated stations, north and south (R2 of 0.73), 

reflect the gradient of the drier northern section and wetter 

southern section of the Refuge. 

Correlation analyses between the inputs (rainfall and 

control-structure flows) and response variable (water level) was 

performed to understand how the sources of water dynamically

affect water levels. The timing effects that rainfall and flow 

inputs have on the water levels was analyzed by computing 

time delays, moving window averages, and time derivatives 

of rainfall, control-structure flows, and water levels. Although 

rainfall is a major source of water for the Refuge, the 

correlation, measured by R2, between daily rainfall and daily 

water level is very low—less than 0.01 at the six water-level 

stations (table 4). The water level in the Refuge is a result 

of inputs from many sources over many temporal scales. To 

compare rainfall and water levels on a similar temporal scale, 

the change in daily water level and the daily rainfall, the 

correlations increased the R2 for the five interior water-level

stations to more than 0.20 and the canal station to 0.14 

(table 4; fig. 10). Using a 2-day average rainfall instead of a 

daily rainfall further increased the correlation with the 1-day 

change in water level to between 0.34 and 0.59.

Rainfall not only has a short-term effect on water level 

as seen in the correlation with 1-day and 2-day changes in 

water levels, but also has an effect on long-term water levels. 

The cycles of the dry and wet seasons in South Florida are 

characterized by reduced rainfall between March and July 

and increased rainfall between August and February. This 

cycle also is seen in the seasonal water-level hydrograph with 

minimum water levels occurring in the late spring/summer 

(May or June) and maximum water levels occurring in the 

fall (October or November). The long-term dynamic between 

rainfall and water level can be seen by correlating moving 

window averages of rainfall with daily water levels. As the 

averaging window increases for rainfall, the correlation 

to water level increases until a maximum is reached. The 

80°25'

26°40'

26°35'

26°30'

26°25'

26°20'

80°20' 80°15'

L-12 Canal

L-13 Canal C-51 Canal

L-40 Canal

L-7 Canal

L-6 Canal

L-39 Hillsboro Canal

L-39 Hillsboro Canal

ENR

Collection

Canal

ENR Supply Canal (L-7)

G-94C

culvert

G-94D (ACME 2)

ACME 1 pump station

S-362

G-94B

culvert

G-94A

culvert

S-39 spillway

S-10C spillway

S-10D spillway

S-10E culvert

S-6 pump station

G-251 

pump 

station

G-310

pump

station

G-301 spillway G-300 spillway

S-5A pump station

S-5AS spillway

G-338

S-10A

spillway

0 2 4 6 MILES

0 2 4 6 KILOMETERS

Canal and identifier

Control structure and identifier

Figure 8. Flow-control structures and aggregation of structures

(magenta) used in the analysis and model development, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida.

L-6 Canal

G-301 spillway

Q1

Q2

Q3

Q4

Q5

Q6

Arthur R. Marshall 

Loxahatchee 

National Wildlife Refuge

EXPLANATION

Base modified from U.S. Geological Survey 

 digital data 1:24,000

Albers Equal-Area Projection 

North American Datum of 1983

Figure 8. Flow-control structures and aggregation of 

structures (magenta) used in the analysis and model 

development, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida.
Characterization of Marsh and Canal Water Levels 13

12 

13 

14 

15 

16

17 

18

19 

1995 

Daily water level, in feet above National Geodetic Vertical Datum of 1929

1996 1997 1998 1999 2000 2001 2002 2003 2004 

1-7 

Continuous streamgaging station

EXPLANATION

1-8T 

1-8C 1-9 

North South 

Figure 9. Daily water levels for six continuous streamgaging stations, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida, January 1995 to December 2004. See figure 6 for site locations.

Figure 9. Daily water levels for six continuous streamgaging stations, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida, January 1995 to December 2004. See figure 6 for site locations.

Table 3. Count, minimum, maximum, mean, standard deviations, and coefficient of determination of six water-level gages in the 

Refuge between 1995 and 2008.

Streamgaging 

station

Count

Minimum Maximum Mean Standard 

deviation Coefficient of determination

Feet Site 1-7 Site 1-8T Site 1-8C Site 1-9 North South

Site 1-7 3,653 14.88 18.12 16.55 0.47 1.00 0.85 0.77 0.91 0.91 0.87

Site 1-8T 3,646 13.94 18.03 16.26 0.70 0.85 1.00 0.95 0.94 0.78 0.97

Site 1-8C 3,565 12.06 18.19 16.31 0.87 0.77 0.95 1.00 0.85 0.79 0.92

Site 1-9 3,653 14.78 17.90 16.35 0.51 0.91 0.94 0.85 1.00 0.81 0.95

North 1,261 15.67 18.00 16.73 0.38 0.91 0.78 0.79 0.81 1.00 0.73

South 1,304 14.23 17.27 16.10 0.72 0.87 0.97 0.92 0.95 0.73 1.00 
14 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

220-day moving window average rainfall is plotted with the 

daily water level for the period 1995–2004 in figure 11. The 

R2 between the two time series is 0.66. The transformation of 

the rainfall time series captures the majority of the interannual 

water-level variability between the dry and wet seasons.

A similar analysis can be performed for the control 

structures to evaluate correlation between flow releases (both 

inflows and outflows) and rainfall and the correlation of flow 

releases and water levels. The correlation between the optimal 

moving window average (highest R2) of flow at control 

structures and rainfall is presented in table 5. Only control 

structures with R2 greater than 0.10 are listed. The R2s and 

moving window sizes in table 5 provide some insight to the 

operations of the control structures. The control structures with 

the higher R2s have a higher response to recent rainfall inputs, 

and their operations are more connected with rainfall than the 

structures with lower R2s that are operated with less regard for 

recent rainfall conditions. The structures with moving window 

average sizes less than 8 days are inflow control structures. 

The structures with higher moving window average sizes 

greater than 15 days are outflow structures. The difference in 

these moving window sizes indicates that water from rainfall 

events moves into the Refuge faster than water that is released 

from control structures in the Refuge.

The correlation among the control-structure flows, 

rainfall, and water levels can be analyzed to show a relative 

proportioning of the influence of flows and rainfall on water 

levels. The aggregated flows (fig. 8) and rainfall R2s, time 

delays, and moving window sizes are presented in table 6. 

The use of time derivatives is a common analytical method 

for analyzing the dynamics of a system. Often time delays 

exist between when an event is measured and the time that 

the response is observed in a system. Modeling a system is 

more complicated when two events of interest, a cause and an 

effect, do not occur simultaneously. The time between cause 

and effect is called the “time delay” or “delay.” Each input 

variable of a model has its own delay. Determining the correct 

13

14

15

16 

17 

18

19

–4

Rainfall and 1-day change in water level, in inches

–2

0 

2 

4 

6 

8 

Site 1-7 1-day change 

 in water level 

Site 1-7 water level

EXPLANATION

Average rainfall

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 

Daily water level, in feet above National Geodetic Vertical Datum of 1929

Figure 10. Average daily rainfall and the 1-day change in water level at site 1-7, and daily water level 

at site 1-7, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, January 1995 to 

December 2004. See figure 6 for site location.

Table 4. Coefficient of determination of daily water level and 

average rainfall, 1-day change in water level, and 2-day change 

in water level.

[R2, coefficient of determination]

Streamgaging 

station

R2

 of daily 

water level

 and daily 

rainfall

R2

 of 1-day 

change in 

water level 

and daily

 rainfall

R2

 of 1-day 

change in 

water level 

and 2-day 

average rainfall

Site 1-7 0.00 0.27 0.59

Site 1-8T 0.00 0.21 0.46

Site 1-8C 0.00 0.14 0.34

Site 1-9 0.00 0.25 0.54

North 0.00 0.26 0.46

South 0.00 0.22 0.49
Characterization of Marsh and Canal Water Levels 15

time delays for pulses and the system response is critical to 

accurately simulate a dynamic system. For example, a control 

structure may release a pulse of water and the water levels at 

a station in a canal may respond immediately (a time delay 

of zero) or there may be a 1- or 2-day delay in the response 

to water levels at an interior marsh station (time delays of 

one and two, respectively). The time delays are computed by 

incrementally lagging the input time series and determining 

the peak correlation with the response variable. Because of the 

shorter period of record for stations north and south, they are 

not included in this correlation analysis.

The 1-day change in water level at the two interior marsh 

sites, sites 1-7 and 1-9, are more correlated with rainfall than 

the site 1-8T and site 1-8C stations (fig. 6). The four waterlevel stations are most responsive to the aggregated Q1 and 

Q3 flows with a 1-day time delay (fig. 8). The stations have 

a 2-day time delay for the Q2 flows. All of the stations have 

negative time delays for the Q4 flows, which are flows out of 

the system. Site 1-8C is fastest to respond to releases with a 

time delay of 1 day. Site 1-7 is the slowest station to respond 

to releases from the canal with a 7-day delay.

Table 5. Flow structure, aggregated flow group assignment, 

moving window average, and coefficient of determination 

between daily rainfall and flow.

[MWA, moving window average; R2, coefficient of determination]

Structure Aggregated 

flow group MWA R2

G-300 Q1 4 0.15

G-301 Q1 5 0.12

S-6 Q3 6 0.43

S-5A Q1 6 0.36

ACME #2 Q6 8 0.37

ACME #1 Q6 8 0.35

G-310 Q2 8 0.28

S-362 Q6 11 0.48

S-10A Q4 15 0.30

S-10D Q4 23 0.42

S-10C Q4 23 0.39

14.5 

15.0 

15.5 

16.0 

16.5 

17.0 

17.5 

18.0 

18.5 

0

Rainfall, in inches

0.04

0.08

0.12

0.16

0.20

0.24

0.28

0.32

Rainfall 

Site 1-7 

Figure 11. Two-hundred-twenty-day moving window average of rainfall and daily water level at site 1-7, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, January 1995 to December 2004. 

See figure 6 for site location.

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 

Daily water level, in feet above

National Geodetic Vertical Datum of 1929

Figure 11. Two-hundred-twenty-day moving window average of rainfall and daily water level at site 1-7, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, January 1995 to December 2004. See 

figure 6 for site location.

Table 6. Coefficient of determination, time delay, and moving window average between the 1-day change in water level and rainfall 

and aggregated flows.

[R2, coefficient of determination; τ, time delay; MWA, moving window average; Q#, aggregated flow assignment]

Streamgaging 

station

Rainfall Q1 Q2 Q3 Q4 Q5 Q6

R2 τ MWA R2 τ MWA R2 τ MWA R2 τ MWA R2 τ MWA R2 τ MWA R2 τ MWA

Site 1-7 0.59 0 2 0.23 1 1 0.05 2 1 0.24 1 1 0.02 –7 8 0.03 1 1 0.12 1 1

Site 1-8C 0.34 0 2 0.14 1 2 0.04 2 2 0.17 1 2 0.03 –1 2 0.05 0 1 0.10 0 1

Site 1-8T 0.46 0 2 0.16 1 1 0.04 2 1 0.19 1 1 0.03 –3 1 0.04 1 1 0.09 1 1

Site 1-9 0.55 0 2 0.19 1 1 0.05 2 1 0.22 1 2 0.02 –3 2 0.04 1 1 0.12 1 2
16 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Simulating Water Levels, Specific 

Conductance, and Total Phosphorus 

Simulating water level, specific conductance, and total 

phosphorus typically is done using dynamic deterministic 

models that incorporate the mathematical descriptions of the 

physics of the hydrodynamics and water chemistry of surfacewater systems. These one-, two-, or three-dimensional models 

often require extensive data collection and are time consuming 

to apply to hydrologic systems. Although mechanistic models 

have been the state of the practice for regulatory evaluations 

of anthropogenic effects on hydrologic systems, developments 

in the field of advanced statistics, machine learning, and data 

mining offer opportunities to develop empirical ANN models 

that are often more accurate. Conrads and Roehl (1999) 

compared the application of a deterministic model and an 

ANN model to simulate dissolved-oxygen concentrations 

for the tidally affected Cooper River in South Carolina. 

They found that the ANN models offer some important 

advantages, including faster development time, utilization 

of larger amounts of data, the incorporation of optimization 

routines, and model dissemination in spreadsheet applications. 

With the real-time streamgaging network and water-quality 

sampling network for the Refuge and the availability of large 

databases of hydrologic and water-quality data, the USGS 

and the USFWS realized an opportunity existed to develop 

an empirical model using data-mining techniques, including 

ANNs, to simulate water level, specific conductance, and total 

phosphorus in the Refuge.

Artificial Neural Networks

Models generally fall into one of two categories: deterministic (or mechanistic) or empirical. Deterministic models 

are created from first-principles equations, whereas empirical 

modeling adapts generalized mathematical functions to fit a 

line or surface through data from one 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. 

Calibrating either type of model attempts to optimally synthesize a line or surface through the observed data. Calibrating 

models is difficult when data have substantial measurement 

error or are incomplete, or when the variables for which 

data are available provide only a partial explanation of the 

causes of variability. The principal advantages that empirical 

models, such as ANN models, have over deterministic models 

are that 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). 

An ANN model is a flexible mathematical structure 

capable of describing complex nonlinear relations between 

input and output datasets. The structure of ANN models is 

loosely based on the biological nervous system with interconnections of neurons and synapses (Hinton, 1992). Although 

numerous types of ANN models exist, the most commonly 

used type of ANN is the multilayer perceptron (Rosenblatt, 

1958). As shown in figure 12, multilayer perceptron 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, and every hidden layer neuron is connected to every 

output neuron. Multiple hidden layers are possible, but a 

single layer is sufficient for most problems.

Typically, linear transfer functions are used to scale input 

values from the input layer to the hidden layer and generally 

fall within the range that corresponds to the most linear part 

of the s-shaped sigmoid transfer functions used from the 

hidden layer to the output layer (fig. 12). 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 coefficient of determination 

(R2) and root mean square error (RMSE). An algorithm that 

commonly is used to train multilayer perceptron ANNs is 

the back error propagation training algorithm (Rumelhart 

and others, 1986). Jensen (1994) describes the details of the 

multilayer perceptron ANN, the type of ANN used in this 

study. Multilayer perceptron ANNs can synthesize functions 

to fit high-dimension, nonlinear multivariate data. Devine and 

others (2003) and Conrads and Roehl (2005) describe their 

use of multilayer perceptron ANNs in multiple applications to 

model and control combined manmade and natural systems, 

including disinfection byproduct formation, industrial air 

emissions monitoring, and surface-water systems affected by 

point and nonpoint-source pollution. 

Experimentation with a number of ANN model 

architectural and training parameters typically is part of the 

modeling process. For correlation analysis or predictive 

modeling applications, a number of candidate ANN models 

are trained and evaluated for their statistical accuracy and 

their representation of process physics. Interactions between 

combinations of variables also are considered along with the 

selection of the training dataset from the overall dataset. For 

models where there is a large dataset with good representation 

of the range of historical behaviors, a small percentage of 

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

dataset. For problems with limited data, a larger percentage 

of the dataset (75–100 percent) may be used in the training 
Simulating Water Levels, Specific Conductance, and Total Phosphorus 17

dataset. Finally, a satisfactory model can be exported for enduser deployment. In general, a high-quality predictive model 

can be obtained when

• The data ranges are well distributed throughout the 

stated space of interest,

• The input variables selected by the modeler share 

“mutual information” about the output variables,

• The 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 ANN models 

synthesize a best fit to the data.

Subdividing a complex modeling problem into subproblems and then addressing each is an effective means of 

achieving the best possible results. A collection of submodels 

whose calculations are coordinated by a computer program 

constitutes a “super-model.” For the Refuge investigation, 

daily linear regression and ANN models (submodels) were 

developed for water level, specific conductance, and total 

phosphorous at either continuous gages or at sampling sites. 

These submodels were then incorporated into a super-model 

application that integrates the model controls, model database, 

and model outputs. The super-model for the project is 

LOXANN DSS. The ANN models described in this report 

were developed using the iQuestTM data-mining software3

(Version 2.03C DM Rev31). The ANN models were deployed 

in the DSS using the Visual Basic run-time library of the 

iQuest R/TTM software. 

3

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

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

Figure 12. Multilayer perceptron artificial neural network architecture (from Conrads and Roehl, 2007).

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 12. Multilayer perceptron artificial neural network architecture (from Conrads and Roehl, 2007).
18 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Development of Water-Level, Specific 

Conductance, and Total Phosphorus Models

The data described above were used to develop empirical 

process models of the Refuge and are included in LOXANN 

DSS so that the user can run long-term simulations to evaluate 

permutations of the actual historical record. The LOXANN 

DSS models predict how rainfall, evapotranspiration, and 

flows into and out of the Refuge affect water levels at 6 sites, 

specific conductance at 25 sites, and total phosphorus at 

14 sites. The water-level models are hybrid models that 

employ a linear least-squares regression and a nonlinear 

spatially interpolating ANN (SIANN) model. The specific 

conductance and total phosphorus models cascade from the 

predictions of the water-level model, but use only SIANN 

models. The overall architecture of the water-level, specific 

conductance, and total phosphorus models are shown in 

figure 13. 

Statistical Measures of Prediction Accuracy

Statistical measures of prediction accuracy were computed 

for the water-level, specific conductance, and total phosphorus 

values, and for the linear regression and SIANN models. The 

statistics for the water-level, specific conductance, and total 

phosphorus simulations capture the ability of the multistep 

modeling approaches to accurately estimate water levels at 

the streamgaging stations or specific conductance and total 

phosphorus at the XYZ and LOX sampling sites. The statistics 

for the linear regression and SIANN 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 estimates. Ultimately, the water-level, specific 

conductance, and total phosphorus simulations should be 

evaluated by the statistics for the final simulation. 

Model accuracy typically is reported in terms of R2

and commonly is interpreted as the “goodness of the fit” of 

a model. An alternative interpretation is one of answering 

the question, “How much information does one variable or 

a group of variables provide about the behavior of another 

variable?” For example, in the first context, 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 mean error and RMSE statistics provide a measure 

of the prediction accuracy of the ANN models. The mean error 

is a measure of the bias of model predictions—whether the 

Figure 13. Water-level, specific conductance (SC), and total phosphorus (TP) model architecture. Blue 

items denote input parameters that are calculated from measured data, user-inputs, and sub-model output 

data. Green, yellow, and pink items are sub-models used to predict water level, specific conductance, and 

total phosphorus, respectively.

SCstatic

SIANN

εSC SIANN

εGH SIANN

TPstatic

SIANN

εTP SIANN

Figure 13. Water-level, specific conductance (SC), and total phosphorus (TP) model architecture. Blue 

items denote input parameters that are calculated from measured data, user-inputs, and submodel output 

data. Green, yellow, and pink items are submodels used to predict water level, specific conductance, and 

total phosphorus, respectively.
Simulating Water Levels, Specific Conductance, and Total Phosphorus 19

model overpredicts or underpredicts the measured data. The 

mean error is presented as the adjustment to the simulated 

values to equal the measured values; therefore, a negative 

mean error indicates an oversimulation by the model, and a 

positive mean error indicates an underprediction by the ANN 

model. Mean errors near zero may be misleading because 

negative and positive discrepancies in the simulations can 

cancel each other. Root mean square error addresses the 

limitations of mean error by computing the magnitude, rather 

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

mean error and RMSE statistics are the same as the simulated 

variable of the model.

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

be evaluated with respect to the measured range of the output 

variable. The percent model error is the ratio of the RMSE to 

the range of the output measured data. 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 small range of conditions 

and the model error may be a relatively large percentage of 

the model response. For example, if the RMSE for a model 

is 0.5 foot (ft) and the measured range is 0–2 ft, the percent 

model error would be 25 percent. 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. For example, if the RMSE for a model is 

2 ft and the measured range is 0–20 ft, the percent model error 

would be 10 percent. 

Water-Level Models

The water-level model is composed of seven submodels. 

Six of the submodels use linear regression to predict water 

levels at sites 1-7, 1-8T, 1-8C, 1-9, north, and south. The 

seventh submodel is an ANN model that corrects a portion 

of the prediction error for each of the linear regression 

submodels. The notation for water level or gage height (used 

interchangeably) variables used in the models is “GH.” The 

following steps describe the development and functions of the 

water-level submodels.

The first step is to convert model inputs into similar units. 

The daily averages of the aggregated flows Q1–Q6 in cubic feet 

per second are summed to a total flow (TOTQ, fig. 13). Total flow 

is converted into an estimated, spatially averaged daily change in 

water level in inches (TOTQ-inch) for all of the Refuge.

TOTQ-inch=TOTQ cubic feet per second 

×86,400 seconds per day×1/(221 square miles) 

×(1/(5,280×5,280 square feet per square mile)) 

×12 inches per foot

The second step is to create linear regression models 

for each water-level gage. A spreadsheet tool called the 

super tau tool was used to create linear statistical submodels 

(y=mx+b) that correlate rainfall (RAIN), evapotranspiration 

(ET), and total flow (TOTQ-inches) to each water-level time 

series (fig. 14). The user-controlled super tau tool computes 

Figure 14. Screen capture of user interface of the Super Tau Tool. The middle and upper left are user controls for selecting 

water-level site, input parameters, time delays, and moving window size. The lower left are summary statistics for the 

curve fit. Plot shows the measured data (blue) and the linear fit (yellow).

Figure 14. Screen capture of user interface of the super tau tool. The middle and upper left are user controls for selecting 

water-level site, input parameters, time delays, and moving window size. The lower left are summary statistics for the 

curve fit. Plot shows the measured data (blue) and the linear fit (yellow).
20 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

moving window averages for rainfall, evapotranspiration, 

and flows. The different moving window averages are used 

to represent different spectral components of the forces that 

modulate water-level behavioral dynamics. This process 

transforms the raw input signal into a waveform that is more 

correlated with a water-level signal and more representative 

of the input-output behavior of the physical process. An 

example of the linear fit for site 1-7 is shown in figure 15. 

Because all of the transformed parameters (rainfall and flow) 

are in units of inches, their sum (SUMQ) can be compared 

directly to a water-level signal. The super tau tool fits SUMQ 

linearly (water level=m×SUMQ+b) and nonlinearly 

(water level =a×ln(SUMQ)).

Experimentation with different versions of the super tau 

tool indicated that it provides too many degrees of freedom, 

such that comparable curve-fit statistics can be obtained with 

significantly different input configurations, and that some 

water-level signals are better fit nonlinearly. Too many inputs 

to a model may overfit the data and result in poor predictive 

capabilities of the model. The number of inputs to the models 

was limited to decrease the degrees of freedoms and improve 

the predictive soundness of the final models. The three inputs 

to the model are evapotranspiration, rainfall, and inflows. The 

largely sinusoidal evapotranspiration time series characterizes 

seasonal and annual patterns and therefore was limited to one 

moving window average. Rainfall has a short- and long-range 

water-level response as seen in the correlations to daily 

changes in water level (fig. 10) and large moving window 

averages of rainfall and daily water levels (fig. 11). There, the 

rainfall inputs were limited to two inputs. Similar to the rainfall 

inputs, it was decided to limit the Q1–Q6 inputs to two moving 

window averages to capture the shorter and longer range waterlevel responses to inflows. This effectively limited the number 

of inputs time series to five. The final water-level submodels 

were limited to only linear regressions derived from the mass 

balance of flow and rainfall (SUMQ). The residual error of 

these linear regression water-level models (εGH) was simulated 

with a nonlinear ANN. The residual error of the water-level 

models, εGH, is calculated by subtracting a predicted value from 

a measured value. Summing the outputs of the linear and ANN 

models yields statistically higher prediction accuracy.

The process by which moving window averages were 

set is described as follows. Evapotranspiration (ET) and flows 

(Q1–Q6) were set to zero and the two rainfall (RAIN) moving 

window averages were set to maximize the R2 of the model. 

The two Q1–Q6 moving window averages were set to maximize R2

. Then, the one ET moving window average was set 

to further maximize R2. After the initial setting of the moving 

window average sizes for the five input variables, some small 

adjustments to the moving window average sizes were made 

to arrive at a maximum R2. Table 7 presents the window sizes 

and statistics of the linear water-level submodels for each 

site. It should be noted that rainfall gives the spikiest signal, 

followed by control-structure flows (TOTQ), with evapotranspiration (ET) being largely seasonally sinusoidal. Applying a 

moving window average changes a spiky signal more than it 

does a relatively smooth signal. Figure 16 shows the residual 

error, εGH , for linear regression water-level submodels.

Daily water level, in inches above

National Geodetic Vertical Datum of 1929

Sum of inflows (SUMQ), in inches

Figure 15. Measured and linearly predicted daily water levels and SUMQ at site 1-7, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida, January 1995 to January 2007. A 5-inch increment is used 

for both left and right axes. See figure 6 for location.

220

215

210

205

200

195

190

185

180

175

45

40

35

30

25

20

15

10

5

0

1/95 1/2/96 1/2/97 1/3/98 1/4/99 1/5/00 1/5/01 1/6/02 1/7/03 1/8/04 1/8/05 1/9/06

Measured

Linear fit

Water level

EXPLANATION

SUMQ

Figure 15. Measured and linearly predicted daily water levels and SUMQ at site 1-7, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida, January 1995 to January 2007. A 5-inch increment is used 

for both left and right axes. See figure 6 for location.
Simulating Water Levels, Specific Conductance, and Total Phosphorus 21

–35 

Linear regression water-level model error, in inches

–30 

–25 

–20 

–15 

–10 

–5 

0 

5 

10 

15 

4/15/00 

6/15/00 

8/15/00 

10/15/00 

12/15/00 

2/15/01 

4/15/01 

6/15/01 

8/15/01 

10/15/01 

12/15/01 

2/15/02 

4/15/02 

6/15/02 

8/15/02 

10/15/02 

12/15/02 

2/15/03 

4/15/03 

6/15/03 

8/15/03 

10/15/03 

12/15/03 

2/15/04 

4/15/04 

6/15/04 

8/15/04 

10/15/04 

12/15/04 

2/15/05 

4/15/05 

6/15/05 

8/15/05 

10/15/05 

12/15/05 

2/15/06 

4/15/06 

6/15/06 

8/15/06 

10/15/06 

12/15/06 

Figure 16. Linear regression water-level model errors for six continuous streamgaging stations, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida, April 2000 to December 2006. See figure 6 for site locations.

1-7 

Continuous streamgaging station

EXPLANATION

1-8T 

1-8C 1-9 

North South 

Figure 16. Linear regression water-level model errors for six continuous streamgaging stations, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida, April 2000 to December 2006. See figure 6 for 

site locations.

Table 7. Moving window averages for rainfall (RAIN1 and RAIN2), evapotranspiration (ET), and total flow (TOTQ-in 1 and TOTQ-in 2) 

inputs for six linear water-level models along with the slope, y-intercept, and coefficient of determination.

[MWA, moving window average; R2, coefficient of determination]

Streamgaging 

station

Count RAIN1, 

MWA

RAIN2, 

MWA

ET, 

MWA

TOTQ-in 1, 

MWA

TOTQ-in 2, 

MWA Slope Y-intercept R2

Site 1-7 2,307 262 42 11 146 1 0.663 181.64 0.839

Site 1-8T 1,705 286 82 55 206 45 0.87 172.39 0.913

Site 1-8C 2,159 286 80 42 206 8 1.182 165.78 0.815

Site 1-9 2,312 265 45 39 141 1 0.731 181.15 0.867

North 1,985 289 51 5 140 1 0.619 182.88 0.753

South 1,436 264 58 14 233 19 0.993 165.23 0.933
22 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

The final step in simulating water levels is to create an 

error prediction model to increase the accuracy of the linear 

regression water-level models. A SIANN as described by 

Roehl and others (2006a) was developed to predict the residual 

errors (εGH ) of the linear fit submodels (fig. 16). Here, a single 

SIANN is used to model the εGH signals for all the water-level 

sites. This approach uses a “stacked” dataset that includes 

time series and static variables (spatial coordinates) for the six 

water-level stations. The representation of the dynamic input 

signals is as follows. Moving window averages of 3, 10, 30, 

90, 210, and 330 days were calculated for rainfall (RAIN), 

evapotranspiration (ET), and total inflow and outflow (TOTQ) 

and were named sequentially for the increasing moving 

window size. For example, RAIN_A0 represented the 3-day 

moving window average for rainfall, RAIN_A1 represented 

the 10-day average, RAIN_A2 represented the 30-day average, 

and so on. The moving window sizes were selected to capture 

daily, weekly, monthly, seasonal, intra-annual, and annual 

variability of the parameter. For each parameter, differences 

between each moving window average and the next larger 

window-sized moving window average were calculated, 

for example, RAIN_D0=RAIN_A0–RAIN_A1 and 

RAIN_D1=RAIN_A1–RAIN_A2 and so on. No differences 

were calculated for the 330-day moving window averages 

(fig. 17). This approach is analogous to band-pass spectral 

filtering in that it decomposes a raw signal into different 

spectral components. It is left to the SIANN to learn which 

parameters and spectral ranges are the best predictors of 

behaviors that are manifest in εGH and which were not captured 

by the linear fit water-level models. 

ANN models are developed iteratively by starting with 

a candidate pool of input parameters, training the ANN with 

them, and then using prediction accuracy statistics, such as R2

and input-output sensitivities, to cull the least important inputs. 

Because of the spatial variability in water level among the sites, 

only ET_D3 was culled. The flow of data and linear model 

predictions into and out of the SIANN are shown in figure 13. 

The 20 inputs used in the final SIANN are listed below.

• GH-LFITS=the prediction made by the linear 

submodels at each site

• X, Y=coordinates of the water-level sites 

that have been normalized by subtracting 

the lowest UTM (Universal Transverse Mercator)

coordinates of the Refuge’s boundary

• RAIN_D0, RAIN_D1, RAIN_D2, RAIN_D3, 

RAIN_D4, RAIN_A5

• ET_D1, ET_D2, ET_D3, ET_D4, ET_A5

• TOTQ_D0, TOTQ_D1, TOTQ_D2, TOTQ_D3, 

TOTQ_D4, TOTQ_A5

Variable names and descriptions for all the input variables 

used in the LOXANN DSS are listed in appendix 1.

–1 

0 

1 

Rainfall, in inches 2 

3 

4 

5 

Daily rainfall

EXPLANATION

Rainfall time series

Rain_D0 

Rain_D1 

Rain_D2 

Rain_D3 

Rain_D4 

Figure 17. Average daily rainfall and five frequency components for the rainfall time series, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida, January 2002 to December 2003.

Jan. Feb. Mar. Apr. May June

2002 2003

July Aug. Sept. Oct. Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec.

Figure 17. Average daily rainfall and five frequency components for the rainfall time series, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida, January 2002 to December 2003.
Simulating Water Levels, Specific Conductance, and Total Phosphorus 23

The SIANN was trained using approximately 50 percent 

of the available data, which were randomly selected, with 

the balance being set aside to test the submodel’s prediction 

accuracy. Figure 18 shows the gage height error prediction 

(εGH) of the SIANN model. The stacked dataset used to train 

the SIANN model concatenates the data. The predictions for 

each gaging station are shown beside one another. Note in 

table 8 that the R2 and RMSE of the training and test data are 

similar. The final water-level prediction is the combination of 

the linear water-level models prediction and the SIANN model 

error prediction for the site. The measured and simulated 

water levels for the Refuge are shown in figure 19, and the 

water-level model performance statistics are listed in table 9.

After the development of the gage height models, it came 

to the authors’ attention that there is an approximately 0.16 ft 

discrepancy between the water level at site 1-8C and the vertical 

datum (Michael Waldon, U.S. Fish and Wildlife Service, oral 

commun., January 7, 2010; fig. 20). This discrepancy does not 

affect the prediction of water level at site 1-8C but would affect 

analysis of water-level slopes between site 1-8C and the other 

five gaging stations. To account for this discrepancy, a –0.16 ft 

adjustment was made to the site 1-8C gage-height predictions.

Figure 18. Measured and predicted water level model error for six continuous streamgaging stations, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. See figure 6 for locations. 

Water-level model error, in inches

10

0

–10

–20

–30

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

EXPLANATION

Measured

Predicted

Database row number

Figure 18. Measured and predicted water-level model error for six continuous streamgaging stations, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. See figure 6 for locations. 

Water level, in inches above

National Geodetic Vertical Datum of 1929

220

210

200

190

180

170

160

150

140

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

EXPLANATION

Measured

Predicted

Database row number

Figure 19. Measured and predicted water level for six continuous streamgaging stations, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida. See figure 6 for locations. 

Figure 19. Measured and predicted water level for six continuous streamgaging stations, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida. See figure 6 for locations.
24 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

12

13

14

15

16

17

18

3/10/01 

5/10/01 

7/10/01 

9/10/01 

11/10/01 

1/10/02 

3/10/02 

5/10/02 

7/10/02 

9/10/02 

11/10/02 

1/10/03 

3/10/03 

5/10/03 

7/10/03 

9/10/03 

11/10/03 

1/10/04 

3/10/04 

5/10/04 

7/10/04 

9/10/04 

11/10/04 

1/10/05 

3/10/05 

5/10/05 

7/10/05 

9/10/05 

11/10/05 

1/10/06 

3/10/06 

5/10/06 

7/10/06 

9/10/06 

11/10/06 

EXPLANATION

1-8T 

1-8C 

1-8C-adj 

Figure 20. Water levels at sites 1-8T and 1-8C, and a 0.16-foot adjustment to water level at site 1-8C, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, March 2001 to December 2006. 

See figure 6 for site locations.

Water level, in feet above

National Geodetic Vertical Datum of 1929

Continuous streamgaging station

Figure 20. Water levels at sites 1-8T and 1-8C, and a 0.16-foot adjustment to water level at site 1-8C, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, March 2001 to December 2006. See 

figure 6 for site locations.

Table 9. Statistics for final water-level simulations.

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

Streamgaging

station Count R2 RMSE Minimum Maximum Range Model error,

percent Inches

Site 1-7 2,123 0.932 1.36 178.6 210.8 32.2 4.2

Site 1-8T 1,705 0.976 1.35 167.3 209.6 42.3 3.2

Site 1-8C 2,123 0.932 1.36 144.7 211.6 66.9 2.0

Site 1-9 2,312 0.953 1.34 177.4 209.2 31.8 4.2

North 1,985 0.902 1.47 188 216.0 28.0 5.3

South 1,436 0.972 1.38 170.8 207.2 36.4 3.8

Table 8. Water-level error correction model performance statistics.

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

Dataset Count R2 RMSE 

inches

Training 5,847 0.72 1.46

Testing 5,873 0.73 1.52
Simulating Water Levels, Specific Conductance, and Total Phosphorus 25

Specific Conductance and 

Total Phosphorus Models

A two-step modeling approach was used to simulate 

specific conductance and total phosphorus at the XYZ and LOX 

sampling sites. The specific conductance and total phosphorus 

process models use water-level inputs, either historical or from 

the water-level models, and specific conductance and total phosphorus inputs from control structures (fig. 13). The approach 

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

SIANN model. The first submodel (SCstatic SIANN and TPstatic

SIANN, fig. 13) for each of the models uses only static variable 

input of location (X and Y coordinates) of the sampling site to 

predict either specific conductance or total phosphorus. The 

static models predict a baseline specific conductance or total 

phosphorus that varies by location but not time. Although the 

static models are not able to predict the dynamic variability of 

the specific conductance or total phosphorus, the models are 

able to discriminate general site-to-site differences on the basis 

of sampling site location. The baseline is similar to a historical 

average, but the SIANN automatically spatially interpolates to 

predict baseline values at unmonitored locations without using 

a post-processing scheme, such as kriging. The measured 

data with the specific conductance (25 sampling sites of the 

XYZ and LOX network) and total phosphorus (14 sampling 

sites of the LOX network) baseline predictions are shown 

in figures 21 and 22, respectively, and model performance 

statistics are listed in table 10. As with the gage height error 

correction SIANN model, the specific conductance and total 

phosphorus models used stacked datasets, and the model 

results are shown with the sampling sites beside one another.

To predict the dynamic components of the specific conductance and total phosphorus signals, the baseline predictions 

were subtracted from the measured data to compute residual 

errors from the static SIANN models, εSC and εTP (εSC SIANN 

and εTP SIANN, fig. 13). The residual error time series from 

the static SIANN models (εSC and εTP, respectively) are the 

dynamic components of the specific conductance and total 

phosphorus signals. The εSC and εTP time series were then 

modeled with SIANNs, such that the sum of the predicted 

baselines and errors yield predictions of specific conductance 

and total phosphorus. 

Many configurations of inputs for the SIANN models 

were considered. Itemized below are comments and observations made from evaluating many ANN configurations. The 

evaluations were made difficult by the sparseness (table 2) 

and lack of coincidence in measurement of the specific 

conductance and total phosphorus data from the control 

structures and the XYZ and LOX sites. 

• The specific conductance and total phosphorus data 

from the control structures were linearly interpolated 

up to 90 days. The variable name includes “I90” to 

indicate the 90-day interpolation. The interpolation 

was necessary in order to use control structure 

data for input water-quality boundary conditions 

(S39 SCcomponents and S6 TPcomponents, fig. 13); however, 

using a window size that is relatively large compared 

to sampling frequency to interpolate presumably 

spiky signals decreases their signal-to-noise ratio and 

reliability as predictors.

• Missing site 1-8C water-level values were synthesized 

by an ANN using water-level inputs calculated from 

sites having fewer missing values. These filled values 

in the time series increased the number of site 1-8C 

values from 3,838 to 3,926. While the increase is 

small, when missing values are scattered throughout 

the signal, the number of calculable window averages 

decreases with increasing window size. (The filled 

parameter is called F_GH_1-8C, appendix 1.)

Table 10. Model performance statistics for the static and dynamic specific conductance and total phosphorus models.

[R2, coefficient of determination; RMSE, root mean square error; —, not applicable]

Model Training dataset

count

Testing dataset

count

R2

(training/testing)

RMSEa

(training/testing)

Models—Static

Specific conductance 2,185 0 0.72/0 174/0

Total phosphorus 637 706 0.0185/0.0471 0.0061/0.0047

Models—Dynamic

Specific conductance 1,470 682 0.522/0.428 119/136

Total phosphorus 1,032 255 0.464/0.601 0.00318/0.00305

Final predictionb

 (sum of static and dynamic model predictions)

Specific conductance — — 0.822 —

Total phosphorus — — 0.509 —

a Units for RMSE are microsiemens per centimeter for specific conductance and milligrams per liter for total phosphorus.

b Statistic computed using all measured and predicted data.
26 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR Specific conductance, in microsiemens per centimeter

1,600

1,400

1,200

1,000

800

600

400

200

0

EXPLANATION

Measured

Predicted

0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000

Database row number 

Figure 21. Measured and predicted specific conductance from the static SIANN model for XYZ and EVPA networks,

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, 

were used to develop the models. See figure 7 for locations. 

X0 X1 X2 X3 X4 Y4 Z0 Z1 Z2 Z3 Z4 LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Total phosphorus, in milligrams per liter

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0

50,000 60,000 70,000 80,000 90,000 100,000

EXPLANATION

Measured

Predicted

Database row number

Figure 22. Measured and predicted total phosphorus concentration from the static SIANN models for the 

EVPA network, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, 

to December 14, 2004, were used to develop the models. See figure 7 for locations. 

LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Figure 21. Measured and predicted specific conductance from the static SIANN model for XYZ and EVPA 

networks, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, to 

December 14, 2004, were used to develop the models. See figure 7 for locations.

Figure 22. Measured and predicted total phosphorus concentration from the static SIANN models for the 

EVPA network, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, 

to December 14, 2004, were used to develop the models. See figure 7 for locations.
Simulating Water Levels, Specific Conductance, and Total Phosphorus 27

Modeling Specific Conductance 

Residual Error (εSC) 

The approach for modeling the dynamic specific conductance signal is similar to the approach used for modeling 

the error of the linear regression water-level models. The 

rainfall (RAIN) and evapotranspiration (ET) time series were 

summed at each time step, and the combined variable was 

named RAIN-ET-COMB. The water levels were normalized 

by using site 1-8T as a standard, and the daily water levels for 

the other sites (site 1-7, site 1-8C, site 1-9, north, and south) 

were subtracted from the water level for site 1-8T. Normalized 

water-level variable names are designated with the prefix “N_.” 

Moving window averages of 3, 9, 30, 90, and 180 days were 

calculated for RAIN-ET-COMB, water level at site 1-8T, the 

normalized water-level parameters, and the 90-day interpolated 

S-39 control structure specific conductance. For example, 

RAIN-ET-COMB_A3 is the 3-day moving window average 

of the combined rainfall and evapotranspiration parameter, 

RAIN-ET-COMB. Differences between each moving window 

average and the next larger window-sized moving window 

average were calculated for each parameter. For example, 

RAIN-ET-COMB_D3 is the difference between the 3-day 

(RAIN-ET-COMB_A3) and 9-day (RAIN-ET-COMB_A9) 

moving window average for the combined rainfall and 

evapotranspiration parameter. No differences were calculated 

for the 180-day moving window averages. The following 

inputs were used in the εSC SIANN model:

• X, Y coordinates of the XYZ and LOX specific 

conductance monitoring sites

• RAIN-ET-COMB_D30, RAIN-ET-COMB_D90, 

RAIN-ET-COMB_A180

• N_GH_1-7_D10

• GH _1-8T_D3, water level_1-8T_D10, 

GH _1-8T_D30, GH _1-8T_A90

• N_F_ GH _1-8C_D3, N_F_ GH _1-8C_D9, 

N_F_ GH _1-8C_D30

• S39-specific conductance_I90_A30

The SIANN was trained using approximately 70 percent 

of the available data, which were randomly selected, with 

the balance being set aside to test the prediction accuracy 

of the submodel. The SIANN’s predictions of εSC are shown 

in figure 23, and model performance statistics are listed in 

table 10. The final predictions of specific conductance were 

calculated by summing the output values from the static and 

SIANN models (fig. 24). 

Modeling Total Phosphorus Residual Error (εTP) 

Input variables were computed for the εTP SIANN model 

as were done for the εSC SIANN models with the following 

changes based on higher correlation of input variables to total 

phosphorus. The water level at site 1-8C instead of site 1-8T 

was used as the standard to normalize the water levels. The 

90-day interpolated control structure input data were from the 

S6 control structure instead of the S-39 control structure. The 

following inputs were used in the εSC SIANN model:

• X, Y=UTM coordinates of the XYZ and LOX 

specific conductance monitoring sites

• RAIN-ET-COMB_D3, RAIN-ET-COMB_D9, 

RAIN-ET-COMB_D30, RAIN-ET-COMB_A90

• N_ GH _1-7_D3, N_ GH _1-7_D9, 

N_ GH _1-7_D30, N_ GH _1-7_A90

• N_ GH _1-9_D9, N_ GH _1-9_D30, 

N_ GH _1-9_A90

• S6-TP_I90_D90, S6-TP_I90_A180

The εTP SIANN was trained using approximately 

80 percent of the available data, which were randomly 

selected, with the balance being set aside to test the prediction 

accuracy of the submodel. The SIANN’s predictions of εTP

are shown in figure 25. The final predictions of specific 

conductance were calculated by summing the output values 

from the static and εTP-prediction SIANN models (fig. 26), 

and model performance statistics are listed in table 10. 
28 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Figure 23. Measured and predicted specific conductance model error for XYZ and EVPA networks, Arthur 

R. Marshall Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, 

were used to develop the models. See figure 7 for locations. 

Figure 24. Measured and predicted specific conductance for XYZ and EVPA networks, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, were used 

to develop the models. See figure 7 for locations. 

Figure 24. Measured and predicted specific conductance for XYZ and EVPA networks, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, were used to develop the models.

See figure 7 for locations. 

Specific conductance, in microsiemens per centimeter1,500

1,300

1,100

900

700

500

300

100

–100

0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100

EXPLANATION

Measured

Predicted

Database row number

X0 X1 X2 X3 X4 Y4 Z0 Z1 Z2 Z3 Z4 LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Figure 23. Measured and predicted specific conductance model error for XYZ and EVPA networks, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, 

were used to develop the models. See figure 7 for locations. 

Specific conductance model error,

 in microsiemens per centimeter

800

600

400

200

0

–200

–400

–600

0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100

EXPLANATION

Measured

Predicted

Database row number

X0 X1 X2 X3 X4 Y4 Z0 Z1 Z2 Z3 Z4 LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16
Simulating Water Levels, Specific Conductance, and Total Phosphorus 29

Figure 25. Measured and predicted total phosphorus model error for the EVPA network, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, were used to develop the models. 

See figure 7 for locations. 

Total phosphorus model error, in milligrams per liter

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

–0.01

Database row number

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

EXPLANATION

Measured

Predicted

LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Figure 26. Measured and predicted total phosphorus for the EVPA network, Arthur R. Marshall Loxahatchee National 

Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, were used to develop the models. See 

figure 7 for locations. 

Total phosphorus, in milligrams per liter

0.06

0.05

0.04

0.03

0.02

0.01

0.00

Database row number

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

EXPLANATION

Measured

Predicted

LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Figure 25. Measured and predicted total phosphorus model error for the EVPA network, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, were used to 

develop the models. See figure 7 for locations. 

Figure 26. Measured and predicted total phosphorus for the EVPA network, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida. Data from January 11, 1995, to December 14, 2004, were used to develop the 

models. See figure 7 for locations. 
30 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Analysis of Specific Conductance and Total 

Phosphorus Trends Using the Spatially 

Interpolating Artificial Neural Network Models

The long-term specific conductance and total phosphorus 

trends can be evaluated using SIANN models that use only 

inputs of sampling site location (X and Y) and time, the latter 

represented by an integer counter. This result would be similar 

to fitting a time-series record with a least-square linear fit and 

evaluating the trend of the data by the slope of the regression 

line. Training and testing datasets were selected by a zoneaveraging filter that segments the input vector space into 

partitions of equal size and then selects a user-defined number 

of vectors from each partition to be used for model training. 

This ensures that the training data represent the breadth of 

behaviors manifest in the full dataset, while at the same time 

balances the prevalence of more and less common behaviors 

in the training data. The testing data includes the full dataset. 

The specific conductance SIANN model predictions at the 

XYZ and LOX sites are shown in figure 27, and the model 

performance statistics are listed in table 11. Like the other 

datasets used in the development of the SIANN models, data 

from the sites are shown with the sampling sites beside one 

another. The period modeled was from January 11, 1995, to 

December 14, 2004. The long-term trends at the majority of 

sites show increasing specific conductance. 

 The total phosphorus SIANN model for trend analysis 

used the same inputs of location and time as the specific 

conductance SIANN model. The training and testing datasets 

were selected randomly with approximately 80 percent of the 

data used for training. The total phosphorus SIANN model 

predictions at the XYZ and LOX sites are shown in figure 28, 

and the model performance statistics are listed in table 11. 

Data from the sites are shown with the sampling sites beside 

one another. The period modeled was from January 11, 1995, 

to December 14, 2004. Unlike the linear increase seen at the 

majority of the specific conductance sites, the total phosphorus 

predictions show an oscillatory response with a peak concentration approximately halfway through the simulation period 

and an increasing trend at the end of the simulation period. 

Color gradient maps of specific conductance and total 

phosphorus were created using the SIANN model predictions 

for dates corresponding to the beginning, midpoint, and end of 

the modeled period, or January 11, 1995, December 28, 1999, 

and December 14, 2004, respectively. In figure 29, red 

triangles and magenta squares mark the XYZ and LOX 

sampling sites, respectively. The magenta boundaries mark 

the convex hull (or region of model interpolation) of the X 

and Y coordinates of the sites included in each SIANN model. 

Simulations outside the convex hulls are model extrapolations. 

The specific conductance maps for the successive dates show 

an increasing trend throughout the Refuge that also is seen 

in the specific conductance simulations at the majority of the 

sampling sites (fig. 27). The figure indicates that there may 

be mixing of the higher conductance canal water with lower 

conductance marsh water. The maps of total phosphorus 

show variability in both concentrations and prevailing 

gradient directions. The total phosphorus simulations (fig. 28) 

also show the temporal variability and a similarity in the 

nonlinear trends between the sampling sites. The variability 

may be caused by changes in annual loading to the system, 

effectiveness of the stormwater-treatment areas, interannual 

hydrologic variability of the magnitude of wet and dry 

seasons, or storm activity, such as hurricanes.

Table 11. Model performance statistics for the specific conductance and total phosphorus models used for trend analysis.

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

Model Training dataset

count

Testing dataset

count

R2

(training/testing)

RMSEa

(training/testing)

Specific conductance 210 2,212 0.80/0.69 109/187

Total phosphorus 1,054 273 0.078/0.055 0.0035/0.0033

a Units for RMSE are microsiemens per centimeter for specific conductance and milligrams per liter for total phosphorus.
Simulating Water Levels, Specific Conductance, and Total Phosphorus 31

Figure 27. Measured and predicted specific conductance to evaluate trends at XYZ and EVPA networks, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida. Simulations were made by a SIANN using only X, Y, and time as inputs. 

Data from January 11, 1995, to December 14, 2004, were used to develop the models. See figure 7 for locations. 

Specific conductance, in microsiemens per centimeter 2,000

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

Database row number

0 100 200 300 400 500 600 700 800 900 1,000 1,100 1,200 1,300 1,400 1,500 1,600 1,700 1,800 1,900 2,000 2,100 2,200

EXPLANATION

Measured

Predicted

X0 X1 X2 X3 X4 Y4 Z0 Z1 Z2 Z3 Z4 LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Figure 28. Measured and predicted total phosphorus to evaluate trends at EVPA networks, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida. Simulations were made by a SIANN using 

only X, Y, and time as inputs. Data from January 11, 1995, to December 14, 2004, were used to 

develop the models. See figure 7 for locations. 

Total phosphorus, in milligrams per liter

0.032

0.022

0.012

0.002

Database row number

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

EXPLANATION

Measured

Predicted

LOX3 LOX4 LOX5 LOX6 LOX7 LOX8 LOX9 LOX10 LOX11 LOX12 LOX13 LOX14 LOX15 LOX16

Figure 27. Measured and predicted specific conductance to evaluate trends at XYZ and EVPA networks, Arthur R. 

Marshall Loxahatchee National Wildlife Refuge, Florida. Simulations were made by a SIANN using only X, Y, and time as 

inputs. Data from January 11, 1995, to December 14, 2004, were used to develop the models. See figure 7 for locations. 

Figure 28. Measured and predicted total phosphorus to evaluate trends at EVPA networks, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Simulations were made by a 

SIANN using only X, Y, and time as inputs. Data from January 11, 1995, to December 14, 2004, 

were used to develop the models. See figure 7 for locations. 
32 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Figure 29. Color gradient 

maps of specific conductance 

and total phosphorus as 

predicted by SIANNs for the 

Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, 

Florida. (A) January 11, 1995; 

(B) December 28, 1999; 

(C) December 14, 2004.

Kilometers

Kilometers Kilometers Kilometers

Kilometers

Specific conductance

A. January 11, 1995 

B. December 28, 1999

Specific conductance—

 In microsiemens per 

 centimeter

EXPLANATION

1,100

1,000

900

800

700

600

500

400

300

200

100

0

C. December 14, 2004

Total phosphorus

Total phosphorus—In

 milligrams per liter

0.0116

0.0114

0.0112

0.0110

0.0108

0.0106

0.0104

0.0102

0.0100

0.0098

0.0096

0.0094

0.0092

0.0090

0.0088

0.0086

0.0084

0.0082

0.0080

0.0078

35

30

25

20

15

10

5

0

35

30

25

20

15

10

5

0

35

30

25

20

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5

0

35

30

25

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5

0

35

30

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0

35

30

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5

0

0 5 10 15 20 0 5 10 15 20
Development of the Decision Support System 33

Development of the 

Decision Support System

Resource managers and stakeholders face difficult 

challenges when managing interactions between natural 

and manmade systems. Complex mechanistic models based 

on first principles physical equations are often developed 

and operated by scientists at considerable costs to evaluate 

options for using a resource while minimizing harm. However, 

varying technical abilities and financial constraints among 

different stakeholders effectively restrict access to relevant 

scientific knowledge and tools. Decision support system 

technology can help meet the need to provide equal access 

to the knowledge and tools required for informed decision 

making. Even though the collective interests and computer 

skills within the community of managers, scientists, and other 

stakeholders are quite varied, equal access to the scientific 

information is needed in order to make the best possible 

decisions. Dutta and others (1997) define DSSs as “systems 

helping decision-makers to solve various semi-structured and 

unstructured problems involving multiple attributes, objectives, and goals... Historically, the majority of DSSs have 

been either computer implementations of mathematical models 

or extensions of database systems and traditional management 

information systems.” While there appears to be no strict 

criteria that distinguish a DSS from other types of programs, 

Dutta and others (1997) suggest that artificial intelligence (AI) 

is a characteristic of more advanced DSSs: “With the help of 

AI techniques DSSs have incorporated the heuristic models 

of decision makers and provided increasingly richer support 

for decision making. Artificial intelligence systems also have 

benefited from DSS research as they have scaled down their 

goal from replacing to supporting decision makers.” 

The authors of this report have previously developed 

three DSSs in South Carolina and Georgia to evaluate 

(1) wastewater discharges and dissolved-oxygen concentration 

in the Beaufort River estuary (Conrads and others, 2003; 

Roehl and others, 2006b); (2) salinity effects on freshwater 

tidal wetland and a proposed deepening of the Savannah 

Harbor (Conrads and others, 2006); and (3) the effect of 

controlled flow releases from reservoirs on the Pee Dee River 

in North Carolina and on salinity dynamics along the South 

Carolina coast (Conrads and Roehl, 2007). These DSSs are 

spreadsheet applications that provide predictive models with 

real-time databases for ANN model simulation, graphical user 

interfaces, and displays of results. Additional features include 

optimizers, integrations with other models and software tools, 

and color contouring of simulation output data. These features 

make the DSSs easily distributable and immediately usable by 

all resource managers and stakeholders. 

The development of a DSS for the Refuge required 

a number of steps (described previously), including 

(1) merging all the data into a single comprehensive database; 

(2) developing water-level, specific conductance, and total 

phosphorus linear regression and SIANN submodels; and 

(3) developing a Microsoft Office Excel® application that 

integrates the new database, submodels, and visualization 

routines into a single package that is easy to use and disseminate. The user’s manual for the installation and operation of 

the LOXANN DSS is available in appendix 2.
34 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Architecture

The basic architectural elements of the LOXANN DSS 

are shown in figure 30. The DSS reads and writes files for 

the various run-time options that can be selected by the user 

through the system’s graphical user interface. A historical 

database, containing 12 years of hydrologic data, is read into 

the simulator along with the linear regression and SIANN 

submodels at the start of a simulation. By using graphical 

user interface controls, the user can evaluate alternative flow 

scenarios. The outputs generated by the simulator are written 

to files for post processing in Microsoft Office Excel® or other

analysis software packages. The DSS also provides streaming

graphics for each gage during simulations and three-dimensional

visualization of the water-level, specific conductance, and total 

phosphorus response for the Refuge models. 

Model Simulation Control, Streaming Graphics, 

and Three-Dimensional Visualization Program 

The simulator in the LOXANN DSS integrates the 

historical database with the six linear regression models 

and five SIANN models. The date/time controls on the user 

control panel (fig. 31) are used to adjust start and end dates 

and parameters (water level, specific conductance, and (or) 

total phosphorus) for a simulation. The simulator allows the 

user to run “what-if” simulations by varying the controlstructure flows from their historical values. There are two 

types of inputs to a model: (1) controllable variables, such 

as the control-structure flows, and (2) uncontrollable state 

variables, such as rainfall and evapotranspiration. To evaluate 

alternative courses of action, the controllable inputs can be 

manually manipulated by the user while the uncontrollable 

and constantly changing variables representing rainfall and 

evapotranspiration are set to their historical values. The user 

has three simulation input variable options: 

• percentage of historical control-structure flow 

to the system, 

• user-defined control-structure flow to a 

constant value, or 

• user-defined flow hydrograph for one or more 

control structures.

Explanations of how to use each of the options in the LOXANN DSS can be found in the user’s manual in appendix 2.

For each water-level gage or sampling site, a worksheet 

displays streaming graphics while a simulation is running for 

any three simulated variables selected by the user (fig. 32). The 

graphs display the historical measured data, simulated historical 

conditions (to show model accuracy), and the simulated output 

using control-structure flow set by the user using the graphical 

user interface controls or an input file. A table in the worksheet 

shows the input data to the model, including rainfall, evapotranspiration, and aggregated control-structure flows.

The three-dimensional visualization (3DVis) worksheet 

in the LOXANN DSS provides graphical profiles of water 

level, specific conductance, and total phosphorus for the 

region of the Refuge simulated by the models (fig. 33). The 

3DVis worksheet is designed to visualize and animate periods 

of special interest. Data and the controls for operating the 

3DVis worksheet are on the left side of the 3DVis worksheet. 

The data are a subset of those in the “Control” worksheet 

(appendix 2) and are provided for reference while using 

the 3DVis worksheet. Surfaces of gage height, specific 

conductance, and total phosphorus are shown in figure 33. 

The surface on the left shows the profile representing the 

actual historical data (when available), and the surface on 

the right shows the surface predicted by the models using the 

user-specified flow conditions. 

Historical databases:

water level, 

specific conductance, 

total phosphorus

Input-output files

Linear regression

and ANN models

Simulation output

files

Simulator controls

Constrained optimization

routine

Simulator

(iQuest/RTTM, VBA)

Streaming graphics

Three-dimensional

visualization

Graphical User Interface

Users

Other analysis

packages

Figure 30. Architecture of the LOXahatchee Spatially Interpolating Artificial Neural

Network Model (LOXANN) LOXANN decision support system.

Figure 30. Architecture of 

the LOXahatchee Artificial 

Neural Network (LOXANN) 

decision support system.
Development of the Decision Support System 35

Figure 31. Model simulator controls used to set parameters and run a simulation in the LOXANN decision support system.

Figure 32. Streaming graphics displayed during simulation in the LOXANN decision support system.

Figure 31. Model simulator controls used to set parameters and run a simulation in the LOXANN decision support system. 
36 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Figure 33. Three-dimensional surfaces of (A) water levels, (B) specific conductance, and (C) total phosphorus, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Maps on the left show the region of the particular 

model interpolation. Surfaces on the left represents actual conditions and surfaces on the right represents a userdefined scenario. Values in the cells are calculated by linear interpolation (water levels) or spatially interpolating 

artificial neural network models. 

A

B

C

0.040

 0.035

 0.030

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1,400

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36

32

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0.040

0.035

 0.030

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 0.020

 0.015

 0.010

 0.005

 0

TPpm (mg/L) SCpm (μS/cm) GHm-MIN(GHm) (inches)

GHpu-MIN(GHm) (inches)

TPpu (mg/L)

S1 S6 S11 S16 S21

26

21

16

6

1

Y (km)

Y (km)

11

26

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6

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X (km)

S1

S1

S6

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X (km)

1,400

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1,200

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SCpu (μS/cm)

S1 S6 S11 S16 S21

26

21

16

6

1

Y (km)

11

X (km)

S1 S6 S11 S16 X (km) S21

Figure 33. Three-dimensional surfaces of (A) water levels, (B) specific conductance, and (C) total phosphorus, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida. Maps on the left show the region of the particular 

model interpolation. Surfaces on the left represent actual conditions and surfaces on the right represent a userdefined scenario. Values in the cells are calculated by linear interpolation (water levels) or spatially interpolating 

artificial neural network models. 
Application of the LOXANN Decision Support System 37

Application of the LOXANN 

Decision Support System 

The development of the linear regression and SIANN 

models and the DSS application for the Refuge provides 

resource managers with a tool to evaluate water level, specific 

conductance, and total phosphorus dynamics in the areas of the 

Refuge. The LOXANN DSS allows users to simulate various 

control structure flow conditions and analyze the water-level, 

specific conductance, and total phosphorus response as an aid 

to understanding water-quantity and water- quality dynamics 

in the Refuge. The increase in specific conductance and total 

phosphorus in the marsh is a result of canal water intruding into 

the marsh. This increase occurs when water levels are higher in 

the canal than the water level in the marsh and higher nutrient 

concentration of canal water mixes with marsh water near the 

canals. The greater the water-level gradient between the canal 

and the marsh, the further the high nutrient concentration water 

will enter into the marsh. Large increases in the water-level 

gradient could have the negative effect of increasing flows 

leaving the marsh and drying out the wetland.

In the LOXANN DSS, the user is able to set controlstructure flows as a constant flow, a percentage of historical 

flow, or as a user-defined hydrograph. These settings also can 

be set in combinations. For example, some structures can be 

set to a constant flow, while others are set to a percentage 

of historical flow, and others to a user-defined flow. The 

following section describes applications of the LOXANN-DSS 

to two hydrologic scenarios. The results from these scenarios 

are intended to demonstrate the utility of the LOXANN DSS 

and are not intended to be interpreted as potential hydraulic 

operations or a regulatory application of the DSS.

Percentage of Historical Flow

One user-specified option is to set the control-structure 

flows at a percentage of the historical flow. To evaluate 

the change to the slope between the canal (site 1-8C) and 

the marsh (site 1-7), the flow for the aggregated Q4 flows 

(structures S-39, S-10A, S-10C, and S-10D) was set to 

140 percent of the historical flows for the 6-year period of 

May 1, 2000, to April 30, 2006. The Q4 flows are negative, 

or out of the Refuge, so an increase in the flows indicates an 

increase in the flows leaving the Refuge. The slope between 

sites 1-8C and 1-7 was computed for the simulated actual 

flow conditions and the user-specified setting of 40-percent 

increase in the Q4 flows (fig. 34). The increased flow out 

of the canal decreased the water-level elevation in the canal 

and reduced the occurrence of negative slopes and potential 

intrusion conditions for flows into the interior of the marsh as 

seen for extended periods of time such as September 2001 to 

April 2002 and September 2003 to April 2004. 

Another method for evaluating the model results is to plot 

the results as a cumulative frequency distribution rather than a 

time series (fig. 35). The simulated actual conditions show that 

the negative slopes (of all magnitudes) occur about 40 percent 

of the time. Increasing the flows out of the four Q4 control 

structures by 40 percent decreased the percentage of time that 

negative slopes occurred to less than 10 percent of the time. 

Figure 34. Simulated actual conditions and a 40-percent increase to the historical flows for 

aggregated flows of Q4, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, 

May 2000 through April 2006. Gaps in simulations are due to one or more missing inputs to the 

models. See figure 8 for location.

Figure 34. Simulated actual conditions and a 40-percent increase to the historical flows for aggregated 

flows of Q4, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, May 2000 through April 2006. 

Gaps in simulations due to one or more missing inputs to the models. See figure 8 for locations. 

5/1/00 5/1/01 5/1/02 5/1/03 5/1/04 5/1/05 5/1/06

Simulated

actual conditions 

Simulated userdefined flow inputs

–10

Slope, in inches

–5

5

0

10

15

20

25

30

35

40
38 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

User-Defined Hydrograph

Another user-specified option is to create a user-defined 

hydrograph to use for input for one or more of the control 

structures. With this option, daily hydrographs for the control 

structure(s) of interest are created outside of the LOXANN 

DSS. The simulation period is selected and the DSS uses the 

user-defined hydrographs as inputs for the simulation period. 

One scenario was simulated using this option. The sum of 

the inflows and outflows was computed for the 4-year period 

2001–2004, and flows into the Refuge were 50-percent greater 

than flows out of the Refuge (2,080,000 and 812,000 cubic 

feet per second, respectively; fig. 36). A user-defined hydrograph was computed for the flow structure for Q4 where the 

outflow from the Refuge equals the weekly average of the 

inflows to the Refuge delayed by 2 days. Although the userdefined outflow hydrograph does not appear to be substantially 

different from the measured outflow hydrograph, the total 

outflow is increased by more than 50 percent to equal the 

inflow hydrograph. There are periods, such as November 2001 

through February 2002, August 2002 through November 2002, 

and September 2003 through November 2003, where the 

outflows are noticeably increased from the actual outflows. 

Time series and cumulative frequency plots show that 

increasing the outflow from the Refuge had the effect of 

reducing the magnitude of the negative slopes and potential 

for intrusion of canal water into the marsh (figs. 37, 38). 

Increasing the outflow also had the effect of increasing the 

positive slopes above 15 inches by up to 20 inches (fig. 37) 

and decreasing the negative slopes between 0 and 8 inches to 

3 inches or less.

Figure 35. Cumulative frequency of slopes from the canal 

to marsh for simulated actual conditions and a 40-percent 

increase to the historical flows for the aggregated Q4 

control-structure flow, Arthur R. Marshall Loxahatchee 

National Wildlife Refuge, Florida. Data generated from a 

simulation from May 2000 through April 2006. See figure 8

for locations.

–0.8 –0.6 –0.4 –0.2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 

0

Cumulative frequency, in percent

10

20

30

40

50

60

70

80

90

100

Simulated

actual

conditions 

Simulated userdefined flow inputs 

Slope, in feet

Figure 35. Cumulative frequency of slopes from the 

canal to marsh for simulated actual conditions and 

a 40-percent increase to the historical flows for the 

aggregated Q4 control-structure flow, Arthur R. Marshall 

Loxahatchee National Wildlife Refuge, Florida. Data 

generated from a simulation from May 2000 through 

April 2006. See figure 8 for location.

Figure 36. Historical inflow and outflow hydrographs and a user-defined hydrograph for 

the aggregated Q4 flow, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, 

January 2001 through December 2004. See figure 8 for location.

–10,000 

Flow, in cubic feet per second

–8,000 

–6,000 

–4,000 

–2,000 

0 

2,000 

4,000 

6,000 

8,000 

10,000 

1/1/01 

3/1/01 

5/1/01 

7/1/01 

9/1/01 

11/1/01 

1/1/02 

3/1/02 

5/1/02 

7/1/02 

9/1/02 

11/1/02 

1/1/03 

3/1/03 

5/1/03 

7/1/03 

9/1/03 

11/1/03 

1/1/04 

3/1/04 

5/1/04 

7/1/04 

9/1/04 

11/1/04 

Inflow 

Measured total for Refuge

EXPLANATION

Outflow 

User-defined outflow for

 aggregated Q4 flow

Figure 36. Historical inflow and outflow hydrographs and a user-defined hydrograph for 

the aggregated Q4 flow, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, 

January 2001 through December 2004. See figure 8 for locations.
Application of the LOXANN Decision Support System 39

0

Cumulative frequency, in percent

10

Slope, in inches

20

30

40

50

60

70

80

90

100

–10.0 

–9.0 

–8.0 

–7.0 

–6.0 

–5.0 

–4.0 

–3.0 

–2.0 

–1.0 

0

1.0 

2.0 

3.0 

4.0 

5.0 

6.0 

7.0 

8.0 

9.0 

10.0 

Simulated

actual

conditions 

Simulated userdefined flow inputs 

Figure 38. Cumulative frequency of slopes from the canal to

marsh for simulated actual conditions and a user-defined

hydrograph for the aggregated Q4 control-structure flows,

Arthur R. Marshall Loxahatchee National Wildlife Refuge, 

Florida. Data generated from a simulation from January 2001 

through December 2006. See figure 8 for locations.

Figure 38. Cumulative frequency of slopes from the canal 

to marsh for simulated actual conditions and a user-defined 

hydrograph for the aggregated Q4 control-structure flows, 

Arthur R. Marshall Loxahatchee National Wildlife Refuge, 

Florida. Data generated from a simulation from January 2001 

through December 2006. See figure 8 for location.

Figure 37. Simulated actual conditions and conditions from a user-defined hydrograph for aggregated 

flows of Q4, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, January 2001 to April 2006. 

Gaps in simulations due to one or more missing inputs to the models. See figure 8 for location.

–10

Slope, in inches

–5

5

0

10

15

20

25

30

35

40

Simulated

actual conditions 

Simulated userdefined flow inputs 

Figure 37. Simulated actual conditions and conditions from a user-defined hydrograph for aggregated 

flows of Q4, Arthur R. Marshall Loxahatchee National Wildlife Refuge, Florida, January 2001 to April 2006. 

Gaps in simulations due to one or more missing inputs to the models. See figure 8 for locations.

11/6/00 

2/4/01 

5/5/01 

8/3/01 

4/30/02 

7/29/02 

10/27/02 

1/25/03 

4/25/03 

7/24/03 

10/22/03 

1/20/04 

4/19/04 

7/18/04 

10/16/04 

1/14/05

4/14/05

7/13/05

10/11/05

11/1/01 

1/30/02 

1/9/06

4/9/06
40 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Summary

The Arthur R. Marshall Loxahatchee National Wildlife 

Refuge (Refuge) is the last of the soft-water ecological 

systems with low calcium or magnesium ion concentrations 

in the Everglades. Historically, the ecosystem was driven by 

precipitation inputs to the system that were low in specific 

conductance and nutrients. Water levels and water quality 

in the flow-controlled canals surrounding the Refuge have 

the potential to alter the critical ecosystem functions of the 

Refuge marsh because of the transport of water with higher 

specific conductance and nutrient concentrations. 

The U.S. Geological Survey and the U.S. Fish and 

Wildlife Service realized an opportunity existed to develop 

an empirical model using data-mining techniques, including 

artificial neural networks (ANNs), to simulate water level, 

specific conductance, and total phosphorus in the interior 

marsh of the Refuge by using the large databases of hydrologic and water-quality data. Hydrologic and water-quality 

data have been collected in the Refuge for many years. 

Data characterizing the hydrology of the system—inflows, 

outflows, precipitation, and water levels—have been 

collected since the 1950s. Data characterizing the water 

quality of the system, including specific conductance and 

total phosphorus, have been collected since the late 1970s. 

New technologies in environmental monitoring have made it 

cost effective to acquire tremendous amounts of hydrologic 

and water-quality data. 

Empirical linear regression and ANN models to simulate 

water level, specific conductance, and total phosphorus were 

developed using data-mining techniques. Data mining is a 

powerful tool for converting large databases into information 

to solve complex problems resulting from large numbers of 

explanatory variables or poorly understood process physics. 

For the application of the linear regression and ANN models 

to the Refuge, data-mining methods were applied to maximize 

the information content in the raw data. Inputs to the empirical 

models include time series, or signals, of inflows and outflows 

from the control structures, precipitation, and evapotranspiration. For a complex hydrologic system like the Refuge, the 

statistical accuracy of the models and predictive capability 

are good. The water-level models have coefficient of 

determination (R2

) values ranging from 0.90 to 0.98. Specific 

conductance at 25 sites and total phosphorus at 14 sites were 

modeled using spatially interpolating ANN models. The R2

for the specific conductance model is 0.82, and the R2 for the 

total phosphorus model is 0.51. The accuracy of the models 

is attributable to the quantity and quality of the available 

data. The water-level models were developed using daily 

water-level, flow, rainfall, and evapotranspiration data. The 

available specific conductance and total phosphorus data were 

temporally sparse for developing daily models.

The water-level, specific conductance, and total phosphorus models, historical database, model simulation controls, 

streaming graphics, and model output were integrated into 

a decision support system (DSS) named the Loxahatchee 

Artificial Neural Network Model (LOXANN) DSS. The 

LOXANN DSS allows the user to manipulate the flow inputs 

to the system. Three options are available to the user in setting 

the control-structure flows: percentage of historical flow, 

constant flow, and a user-defined hydrograph. Output from 

the LOXANN DSS includes tabular time series of predictions 

of the measured data and predictions of the user-specified 

conditions. A three-dimensional visualization routine also 

was developed that displays longitudinal specific conductance 

conditions. The visualization routine uses predictions at the 

gaging station or sampling locations and interpolates values 

among stations. The LOXANN DSS is a spreadsheet application that facilitates the dissemination and utility of the DSS.

Two scenarios were simulated with the LOXANN 

DSS. One scenario increased the historical flows at the S-39, 

S-10A, S-10C, and S-10D control structures by 40 percent. 

The second scenario used a user-defined hydrograph to set 

the outflow from the Refuge to the weekly average inflow to 

the Refuge delayed by 2 days. Both scenarios decreased the 

potential of canal water intruding into the marsh by decreasing 

the slope of the water level between the canal (site 1-8C) and 

the marsh (site 1-7). 

Acknowledgments

The complexity of this study required interagency 

cooperation in addition to individual contributions. The 

authors thank Drs. Mike Waldon and Laura Brandt of the 

U.S. Fish and Wildlife Service for their coordination of the 

project and for sharing their technical expertise and knowledge 

of the system, Dr. Ehab Moselle and his graduate students 

at the University of Louisiana Lafayette for sharing their 

compiled historical data, and Dr. Donnato Surratte of the 

U.S. Fish and Wildlife Service for providing data and technical 

feedback of interim project technical presentations.
References Cited 41

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Arthur R. Marshall Loxahatchee National Wildlife Refuge 

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heterogeneous hydrologic systems—Part 1, in Voinov, A., 

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Kaufmann Publishers, Inc., 228 p. 
Appendix 1. List of Variables Used in the Study
44 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Appendix 1. List of variables used in the study.—Continued

Variable Description

ET_A0 3-day moving window average of evapotranspiration (ET)

ET_A1 10-day moving window average of evapotranspiration (ET)

ET_A2 30-day moving window average of evapotranspiration (ET)

ET_A3 90-day moving window average of evapotranspiration (ET)

ET_A4 210-day moving window average of evapotranspiration (ET)

ET_A5 330-day moving window average of evapotranspiration (ET)

ET_D0 Difference between the 3-day and 10-day moving window average of evapotranspiration (ET)

ET_D1 Difference between the 10-day and 30-day moving window average of evapotranspiration (ET)

ET_D2 Difference between the 30-day and 90-day moving window average of evapotranspiration (ET)

ET_D3 Difference between the 90-day and 210-day moving window average of evapotranspiration (ET)

ET_D4 Difference between the 210-day and 330-day moving window average of evapotranspiration (ET)

F_GH_1-8C Filled gage heights for the site 1-8C gaging station

GH_1-8C_D3 Difference between the 3-day and 9-day moving window average of site 1-8C gage heights

GH_1-8C_D30 Difference between the 30-day and 90-day moving window average of site 1-8C gage heights

GH_1-8C_D9 Difference between the 9-day and 30-day moving window average of site 1-8C gage heights

GH_1-8C_D90 Difference between the 90-day and 180-day moving window average of site 1-8C gage heights

GH_1-8T_D3 Difference between the 3-day and 9-day moving window average of site 1-8T gage heights

GH_1-8T_D30 Difference between the 30-day and 90-day moving window average of site 1-8T gage heights

GH_1-8T_D9 Difference between the 9-day and 30-day moving window average of site 1-8T gage heights

GH_1-8T_D90 Difference between the 90-day and 180-day moving window average of site 1-8T gage heights

GH-1-8C_A10 10-day moving window of site 1-8C gage height (GH)

GH-1-8C_A180 180-day moving window of site 1-8C gage height (GH)

GH-1-8C_A30 30-day moving window of site 1-8C gage height (GH)

GH-1-8C_A30 3-day moving window of site 1-8C gage height (GH)

GH-1-8C_A90 90-day moving window of site 1-8C gage height (GH)

GH-1-8T_A10 10-day moving window of site 1-8T gage height (GH)

GH-1-8T_A180 180-day moving window of site 1-8T gage height (GH)

GH-1-8T_A30 30-day moving window of site 1-8T gage height (GH)

GH-1-8T_A30 3-day moving window of site 1-8T gage height (GH)

GH-1-8T_A90 90-day moving window of site 1-8T gage height (GH)

GH-ERR Difference between linear regression water-level model estimates and measured water levels 

GH-LFITS Gage height estimate from linear regression water-level models

N_GH_1-7_D3 Difference between the 3-day and 9-day moving window average of site 1-7 normalized gage heights

N_GH_1-7_D30 Difference between the 30-day and 90-day moving window average of site 1-7 normalized gage heights

N_GH_1-7_D9 Difference between the 9-day and 30-day moving window average of site 1-7 normalized gage heights

N_GH_1-7_D90 Difference between the 90-day and 180-day moving window average of site 1-7 normalized gage heights

N_GH_1-8C_D3 Difference between the 3-day and 9-day moving window average of site 1-8C normalized gage heights

N_GH_1-8C_D30 Difference between the 30-day and 90-day moving window average of site 1-8C normalized gage heights

N_GH_1-8C_D9 Difference between the 9-day and 30-day moving window average of site 1-8C normalized gage heights

N_GH_1-8C_D90 Difference between the 90-day and 180-day moving window average of site 1-8C normalized gage heights
Appendix 1. List of Variables Used in the Study 45

Appendix 1. List of variables used in the study.—Continued

Variable Description

N_GH_1-9_D3 Difference between the 3-day and 9-day moving window average of site 1-9 normalized gage heights

N_GH_1-9_D30 Difference between the 30-day and 90-day moving window average of site 1-9 normalized gage heights

N_GH_1-9_D9 Difference between the 9-day and 30-day moving window average of site 1-9 normalized gage heights

N_GH_1-9_D90 Difference between the 90-day and 180-day moving window average of site 1-9 normalized gage heights

N_GH-1-7_A10 10-day moving window of site 1-7 normalized gage height (GH)

N_GH-1-7_A180 180-day moving window of site 1-7 normalized gage height (GH)

N_GH-1-7_A30 30-day moving window of site 1-7 normalized gage height (GH)

N_GH-1-7_A30 3-day moving window of site 1-7 normalized gage height (GH)

N_GH-1-7_A90 90-day moving window of site 1-7 normalized gage height (GH)

N_GH-1-8C_A10 10-day moving window of site 1-8C normalized gage height (GH)

N_GH-1-8C_A180 180-day moving window of site 1-8C normalized gage height (GH)

N_GH-1-8C_A30 30-day moving window of site 1-8C normalized gage height (GH)

N_GH-1-8C_A30 3-day moving window of site 1-8C normalized gage height (GH)

N_GH-1-8C_A90 90-day moving window of site 1-8C normalized gage height (GH)

N_GH-1-9_A10 10-day moving window of site 1-9 normalized gage height (GH)

N_GH-1-9_A180 180-day moving window of site 1-9 normalized gage height (GH)

N_GH-1-9_A30 30-day moving window of site 1-9 normalized gage height (GH)

N_GH-1-9_A30 3-day moving window of site 1-9 normalized gage height (GH)

N_GH-1-9_A90 90-day moving window of site 1-9 normalized gage height (GH)

Q1_A0 3-day moving window average of Q1 aggregated flows

Q1_A1 10-day moving window average of Q1 aggregated flows

Q1_A2 30-day moving window average of Q1 aggregated flows

Q1_A3 90-day moving window average of Q1 aggregated flows

Q1_A4 210-day moving window average of Q1 aggregated flows

Q1_A5 330-day moving window average of Q1 aggregated flows

Q1_D0 Difference between the 3-day and 10-day moving window average of Q1 aggregated flows

Q1_D1 Difference between the 10-day and 30-day moving window average of Q1 aggregated flows

Q1_D2 Difference between the 30-day and 90-day moving window average of Q1 aggregated flows

Q1_D3 Difference between the 90-day and 210-day moving window average of Q1 aggregated flows

Q1_D4 Difference between the 210-day and 330-day moving window average of Q1 aggregated flows

Q2_A0 3-day moving window average of Q2 aggregated flows

Q2_A1 10-day moving window average of Q2 aggregated flows

Q2_A2 30-day moving window average of Q2 aggregated flows

Q2_A3 90-day moving window average of Q2 aggregated flows

Q2_A4 210-day moving window average of Q2 aggregated flows

Q2_A5 330-day moving window average of Q2 aggregated flows

Q2_D0 Difference between the 3-day and 10-day moving window average of Q2 aggregated flows

Q2_D1 Difference between the 10-day and 30-day moving window average of Q2 aggregated flows

Q2_D2 Difference between the 30-day and 90-day moving window average of Q2 aggregated flows

Q2_D3 Difference between the 90-day and 210-day moving window average of Q2 aggregated flows
46 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Appendix 1. List of variables used in the study.—Continued

Variable Description

Q2_D4 Difference between the 210-day and 330-day moving window average of Q2 aggregated flows

Q3_A0 3-day moving window average of Q3 aggregated flows

Q3_A1 10-day moving window average of Q3 aggregated flows

Q3_A2 30-day moving window average of Q3 aggregated flows

Q3_A3 90-day moving window average of Q3 aggregated flows

Q3_A4 210-day moving window average of Q3 aggregated flows

Q3_A5 330-day moving window average of Q3 aggregated flows

Q3_D0 Difference between the 3-day and 10-day moving window average of Q3 aggregated flows

Q3_D1 Difference between the 10-day and 30-day moving window average of Q3 aggregated flows

Q3_D2 Difference between the 30-day and 90-day moving window average of Q3 aggregated flows

Q3_D3 Difference between the 90-day and 210-day moving window average of Q3 aggregated flows

Q3_D4 Difference between the 210-day and 330-day moving window average of Q3 aggregated flows

Q4_A0 3-day moving window average of Q4 aggregated flows

Q4_A1 10-day moving window average of Q4 aggregated flows

Q4_A2 30-day moving window average of Q4 aggregated flows

Q4_A3 90-day moving window average of Q4 aggregated flows

Q4_A4 210-day moving window average of Q4 aggregated flows

Q4_A5 330-day moving window average of Q4 aggregated flows

Q4_D0 Difference between the 3-day and 10-day moving window average of Q4 aggregated flows

Q4_D1 Difference between the 10-day and 30-day moving window average of Q4 aggregated flows

Q4_D2 Difference between the 30-day and 90-day moving window average of Q4 aggregated flows

Q4_D3 Difference between the 90-day and 210-day moving window average of Q4 aggregated flows

Q4_D4 Difference between the 210-day and 330-day moving window average of Q4 aggregated flows

Q5_A0 3-day moving window average of Q5 aggregated flows

Q5_A1 10-day moving window average of Q5 aggregated flows

Q5_A2 30-day moving window average of Q5 aggregated flows

Q5_A3 90-day moving window average of Q5 aggregated flows

Q5_A4 210-day moving window average of Q5 aggregated flows

Q5_A5 330-day moving window average of Q5 aggregated flows

Q5_D0 Difference between the 3-day and 10-day moving window average of Q5 aggregated flows

Q5_D1 Difference between the 10-day and 30-day moving window average of Q5 aggregated flows

Q5_D2 Difference between the 30-day and 90-day moving window average of Q5 aggregated flows

Q5_D3 Difference between the 90-day and 210-day moving window average of Q5 aggregated flows

Q5_D4 Difference between the 210-day and 330-day moving window average of Q5 aggregated flows

Q6_A0 3-day moving window average of Q6 aggregated flows

Q6_A1 10-day moving window average of Q6 aggregated flows

Q6_A2 30-day moving window average of Q6 aggregated flows

Q6_A3 90-day moving window average of Q6 aggregated flows

Q6_A4 210-day moving window average of Q6 aggregated flows

Q6_A5 330-day moving window average of Q6 aggregated flows
Appendix 1. List of Variables Used in the Study 47

Appendix 1. List of variables used in the study.—Continued

Variable Description

Q6_D0 Difference between the 3-day and 10-day moving window average of Q6 aggregated flows

Q6_D1 Difference between the 10-day and 30-day moving window average of Q6 aggregated flows

Q6_D2 Difference between the 30-day and 90-day moving window average of Q6 aggregated flows

Q6_D3 Difference between the 90-day and 210-day moving window average of Q6 aggregated flows

Q6_D4 Difference between the 210-day and 330-day moving window average of Q6 aggregated flows

R_SC Residual time series computed from static spatially interpolating specific conductance model

R_TP Residual time series computed from static spatially interpolating total phosphorus model

RAIN_A0 3-day moving window average of rainfall

RAIN_A1 10-day moving window average of rainfall

RAIN_A2 30-day moving window average of rainfall

RAIN_A3 90-day moving window average of rainfall

RAIN_A4 210-day moving window average of rainfall

RAIN_A5 330-day moving window average of rainfall

RAIN_D0 Difference between the 3-day and 10-day moving window average of rainfall

RAIN_D1 Difference between the 10-day and 30-day moving window average of rainfall

RAIN_D2 Difference between the 30-day and 90-day moving window average of rainfall

RAIN_D3 Difference between the 90-day and 210-day moving window average of rainfall

RAIN_D4 Difference between the 210-day and 330-day moving window average of rainfall

RAIN-ET-COMB_A180 180-day moving window average of the combined rainfall and evapotranspiration variable

RAIN-ET-COMB_A3 3-day moving window average of the combined rainfall and evapotranspiration variable

RAIN-ET-COMB_A30 30-day moving window average of the combined rainfall and evapotranspiration variable

RAIN-ET-COMB_A9 9-day moving window average of the combined rainfall and evapotranspiration variable

RAIN-ET-COMB_A90 90-day moving window average of the combined rainfall and evapotranspiration variable

RAIN-ET-COMB_D3 Difference between the 3-day and 9-day moving window average of combined rainfall and 

evapotranspiration variable

RAIN-ET-COMB_D30 Difference between the 30-day and 90-day moving window average of combined rainfall and 

evapotranspiration variable

RAIN-ET-COMB_D9 Difference between the 9-day and 30-day moving window average of combined rainfall and 

evapotranspiration variable

RAIN-ET-COMB_D90 Difference between the 90-day and 180-day moving window average of combined rainfall and 

evapotranspiration variable

S39-SC_I90_A10 10-day moving window average of the 90-day interpolated specific conductance concentration 

at the S-39 control structure

S39-SC_I90_A180 180-day moving window average of the 90-day interpolated specific conductance concentration 

at the S-39 control structure

S39-SC_I90_A30 30-day moving window average of the 90-day interpolated specific conductance concentration 

at the S-39 control structure

S39-SC_I90_A30 3-day moving window average of the 90-day interpolated specific conductance concentration 

at the S-39 control structure

S39-SC_I90_A90 90-day moving window average of the 90-day interpolated specific conductance concentration 

at the S-39 control structure

S39-SC_I90_D10 Difference between the 10-day and 30-day moving window average of interpolated specific conductance 

concentration at the S-39 control structure
48 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

Appendix 1. List of variables used in the study.—Continued

Variable Description

S39-SC_I90_D3 Difference between the 3-day and 10-day moving window average of interpolated specific conductance 

concentration at the S-39 control structure

S39-SC_I90_D30 Difference between the 30-day and 90-day moving window average of interpolated specific conductance 

concentration at the S-39 control structure

S39-SC_I90_D90 Difference between the 90-day and 180-day moving window average of interpolated specific conductance 

concentration at the S-39 control structure

S6-TP_I90_A10 10-day moving window average of the 90-day interpolated total phosphorus concentration 

at the S-6 control structure

S6-TP_I90_A180 180-day moving window average of the 90-day interpolated total phosphorus concentration 

at the S-6 control structure

S6-TP_I90_A30 30-day moving window average of the 90-day interpolated total phosphorus concentration 

at the S-6 control structure

S6-TP_I90_A30 3-day moving window average of the 90-day interpolated total phosphorus concentration 

at the S-6 control structure

S6-TP_I90_A90 90-day moving window average of the 90-day interpolated total phosphorus concentration 

at the S-6 control structure

S6-TP_I90_D10 Difference between the 10-day and 30-day moving window average of interpolated total phosphorus 

concentration at the S-6 control structure

S6-TP_I90_D3 Difference between the 3-day and 10-day moving window average of interpolated total phosphorus 

concentration at the S-6 control structure

S6-TP_I90_D30 Difference between the 30-day and 90-day moving window average of interpolated total phosphorus 

concentration at the S-6 control structure

S6-TP_I90_D90 Difference between the 90-day and 180-day moving window average of interpolated total phosphorus 

concentration at the S-6 control structure

SC Total phosphorus at the XYZ sampling sites—stacked variable

TOTQ_A0 3-day moving window average of total flow (TOTQ)

TOTQ_A1 10-day moving window average of total flow (TOTQ)

TOTQ_A2 30-day moving window average of total flow (TOTQ)

TOTQ_A3 90-day moving window average of total flow (TOTQ)

TOTQ_A4 210-day moving window average of total flow (TOTQ)

TOTQ_A5 330-day moving window average of total flow (TOTQ)

TOTQ_D0 Difference between the 3-day and 10-day moving window average of total flow (TOTQ)

TOTQ_D1 Difference between the 10-day and 30-day moving window average of total flow (TOTQ)

TOTQ_D2 Difference between the 30-day and 90-day moving window average of total flow (TOTQ)

TOTQ_D3 Difference between the 90-day and 210-day moving window average of total flow (TOTQ)

TOTQ_D4 Difference between the 210-day and 330-day moving window average of total flow (TOTQ)

TP Specific conductance at the LOX and XYZ sampling sites—stacked variable

X X location of gaging station or water quality sampling site

Y Y location of gaging station or water quality sampling site
Appendix 2. User’s Manual for the LOXahatchee Artificial 

Neural Network Decision Support System (LOXANN DSS)

Figures

2–1 to 2–14. Screen capures showing—

2–1. “Controls” worksheet .......................................................................................................51

2–2. On-line description of parameter dGH(u-m) on the “Run” worksheet .....................52

2–3. “Info” worksheet ...............................................................................................................53

2–4. Simulation controls on “Controls” worksheet..............................................................53

2–5. Pop-up window that appears when a simulation is interrupted 

by using the “Esc” key......................................................................................................54

2–6. GH fields on “Controls” worksheet.................................................................................54

2–7. Q fields on “Controls” worksheet ...................................................................................55

2–8. Upper portion of “Q Setpoints” worksheet ...................................................................55

2–9. Example of measured data from the “Database” worksheet ....................................56

2–10. Example output from the “Output” worksheet showing user-set 

control structure flows .....................................................................................................58

2–11. Example of “UserDefQs” worksheet showing user-defined 

control structure flows .....................................................................................................60

2–12. Example of “GH Graphs” worksheet showing simulation controls 

and streaming graphics....................................................................................................62

2–13. Bar graph on “‘3DVis” worksheet showing GHm and GHpu at each GH site .........62

2–14. Three-dimensional displays of GHm and GHpu ...........................................................63

2–15. Three-dimensional displays of SCpm and SCpu ..........................................................63

2–16. Three-dimensional displays of TPpm and TPpu...........................................................63

Tables 

2–1. Descriptions of “Database” worksheet parameters............................................................57

2–2. Descriptions of “OUTPUT” worksheet parameters..............................................................59
50 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

1. Introduction

This document describes how to install and operate an empirical model (LOXANN DSS) of the Arthur R. Marshall 

Loxahatchee National Wildlife Refuge (Refuge). LOXANN is a decision support system (DSS) built around a suite of empirical 

hydrologic and water-quality models. 

2. LOXMODEL Installation, Removal, and Technical Assistance

NOTE: LOXANN will not run on 64-bit Windows XP® and Vista® operating systems because of incompatibility 

of the NNCALC32.xll Add-in with these operating systems. NNCALC32.xll is used to execute the Artificial Neural Network 

(ANN) models.

2.1. Installation

1. Create a folder called LOXMODEL at the top level of your C: drive.

2. Extract all files from LOXMODEL-yyyymmdd.zip1 from the CD–ROM provided by the USGS into the LOXMODEL 

folder. The zip file contains the following application files:

• LOXMODEL-yyyymmdd.xls—A Microsoft (MS) Excel® spreadsheet application.

• Files with an “enn” extension are the ANN files—there are five ANN files:

1. p_gh_errs-use.enn

2. p_sc-use.enn

3. p_r_sc-use.enn

4. p_tp-use.enn

5. p_r_tp-use.enn

• NNCALC32.xll—An MS Excel Add-in used to execute the ANN model (*.enn) files.

• LOXMODELUserGuide-yyyymmdd.doc—The MS Word® file that you are reading right now.

• LOXMODEL-Install-yyyymmdd.doc—An MS Word file with these installation instructions.

3. Open your copy of MS Excel® for MS Office 2000® (or newer). Ensure that the standard Excel Add-ins listed below are

installed and checked “available.” 

Analysis Toolpak

Analysis Toolpak—VBA

Add-ins are accessed from Excel’s Tools menu. If any are missing, it may be necessary to install them from your MS 

Office CD–ROM.

4. Set the macro security level of Excel to either medium or low using Tools > Macro > Security. LOXANN uses VBA macros 

for a variety of purposes and must be able to execute them to operate correctly.

5. Install the NNCALC32 Add-in that resides in the NNCALC folder described in Step 1. This may be accomplished by 

clicking on Tools > Add-ins > Browse, browse to the LOXMODEL folder you created, click on the NNCALC32 icon, 

then click OK.

6. Open the LOXMODEL-yyyymmdd.xls Excel spreadsheet application. When Excel asks if you want to run macros click 

“Enable Macros,” otherwise LOXMODEL will not operate correctly.

1

 yyyymmdd is the version date of the LOXMODEL image to be installed.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 51

Select the “Controls” worksheet (fig. 2–1). “Controls” is the worksheet that lets the user set up and run simulations. 

At the top-left corner of “Controls” is a text box labeled “Path Where ANN Model Files Are Located.” The model files 

are the *.enn files of the ANNs. Type in the fully qualified path name of the folder setup in (1) above and save the Excel 

application using File > Save for the setup changes to be permanent.

Just below the text box is a field labeled “ANNs Connected.” This field will have a value=“TRUE” if the application 

is properly configured and ready to use. If the field is blank, try exiting Excel and reopening Excel and the 

LOXMODEL application.

A blank field indicates that one or more ANNs cannot execute because either the NNCALC32 Add-in is not installed 

per (5) or NNCALC32 cannot find *.enn files because the folder path name in the “Where model files are located” 

text box is incorrect. 

If you cannot get LOXMODEL to operate, re-check the configuration items in (3)–(6) above. 

2.2. Removal

Simply delete the folder created to hold the LOXANN DSS files and its contents. Consider removing the Add-ins and 

reverting to the default MS Excel security settings.

2.3. Technical Assistance

Please contact Paul Conrads of the USGS at (803) 750-6140, pconrads@usgs.gov, if you have questions or problems 

with LOXANN DSS.

Figure 31. Model simulator controls used to set parameters and run a simulation in the LOXANN decision support system. Figure 2–1. Screenshot of “Controls” worksheet. 
52 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

3. LOXANN DSS Features and Operation

LOXMODEL is opened like any standard Excel workbook. Simply open the LOXMODEL-yyyymmdd.xls file and 

you are ready to go. LOXANN DSS and its graphical user interface (GUI) are made up of a number of worksheets that are 

detailed below.

3.1. Parameter Descriptions, Nomenclature, and “ReleaseNotes” Worksheet

LOXANN refers to many input and output parameters usually in the form of column headers (fig. 2–2). Moving the 

mouse over a header marked with a red caret in the right hand corner of the header will provide a description of the 

header parameter. 

Descriptions of parameters also are provided in the “ReleaseNotes” worksheet. This worksheet describes changes made in 

different releases of LOXANN’s development history and any new features. Some of the prefixes, suffixes, and other modifiers 

that are used in parameter names include

• “d”: used as a prefix to indicate that the parameter is a difference between two other parameter values

• “p”: used to indicate that the parameter is a model prediction

• “m”: used to indicate that the parameter’s value is either

◦ an actual measurement

◦ a model prediction made using an actual measurement as an input value

• “u”: used to indicate that a parameter’s value is set by the user.

Modifiers can be used in combination, for example, dGH(u-m) as shown in figure 2–2.

Figure 2–2. On-line description of parameter dGH(u-m) on the “Run” worksheet.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 53

3.2. “Info” Worksheet 

The “Info” worksheet is automatically displayed when LOXANN is first loaded (fig. 2–3). It contains the program’s 

version date and the contact information of its developers.

3.3. “Controls” Worksheet

The “Controls” worksheet (fig. 2–4) is the GUI component that lets the user setup and run simulations. 

A text box labeled “Path Where ANN Model Files Are Located” (fig. 2–4) is located on the “Controls” worksheet. It is 

used to configure LOXANN when it is first installed on a user’s computer and is described further in section 4. The “Start” 

and “End” dates for simulations can be set using the scroll bars at center left. The end date must be more recent than the start 

date. The “SimDate” field indicates the time stamp for which LOXANN’s models are currently generating output values. The 

“Step#” is an integer counter that indicates how many time steps (days) have been executed since the start of a simulation. The 

“SimDate=Start” button sets the current time stamp to the Simulation “Start” date. The “Step>>” button increases the current 

time stamp by one time step.

Figure 2–3. “Info” worksheet.

Figure 2–4. Simulation controls on “Controls” worksheet.
54 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

The “RUN” button will start and run a simulation between 

the dates indicated by the Simulation “Start” and “End” dates. 

A simulation may be stopped at any time during a run by 

holding down the “Esc” key, after which a pop-up window will 

appear like that shown in figure 2–5. Click on the “End” button 

to stop the simulation, then click the “Reset” button shown at 

center right in figure 2–4. The user will not need to use other 

options (Continue, Debug, or Help) on the pop-up window. The 

“Reset” button activates Excel’s automatic calculation feature 

(autocalc). Because the model programmatically manipulates 

autocalc for performance reasons, interrupting a simulation 

can sometimes leave the model in a state where autocalc is not 

activated. This is remedied by clicking the “Reset” button.

LOXANN provides detailed numerical and streaming 

graphical information that can be observed during simulations or when incrementally stepping through time. This allows the 

user to examine specific periods and behaviors of interest in detail. Because of the added computational load, simulations 

are slowed as more models are activated, and streaming graphics and simulation output are generated. To speed calculations 

and the generation of output, a number of check boxes (lower left in figure 2–4) allow the user to activate/deactivate models, 

LOXANN’s graphics features, and write model input and output data. 

The gage height (GH) linear models are always active because their output is required by the specific conductance (SC) 

and total phosphorus (TP) models. The spatially interpolating artificial neural network model (SIANN) that partially 

corrects for the prediction error εGH of the linear GH models is toggled ON/OFF using the “GH error ANN ON” box. 

The SC and TP models are toggled using the “...Predictions ON” boxes. Trend graphs on the “Input Graphs” and “GH Graphs” 

are toggled using the “GH Graphs ON” box. Trend graphs on the “SC Graphs” and “TP Graphs” are toggled using the 

“SC Graphs ON” and “TP Graphs ON” boxes, respectively. Three-dimensional (3D) color gradient displays of GHs and 

SC and TP concentrations on the “3DVis” worksheet are toggled using the “... 3D ON” boxes.

A minimum of 330 days (time steps) of control structure flow values is required for the GH model to execute because 

the model uses moving window averages up to that size to simulate GH dynamics. The measured data for most structures is 

complete; however, the data for the G-94A, G-94B, and G-94C (summed into Q5) are missing prior to April 15, 2000. Thus, 

GH model runs that use the “use%” Input Option will not execute until 330 time steps after this date, which is March 10, 2001. 

The GH model will execute for earlier dates when using user options “cfs” and “UserDefQ” for G-94A, G-94B, and G-94C on 

the “Q Setpoints” worksheet because the user inputs for these sites are then purely synthetic (see Section 3.4). 

A minimum of 180 time steps of GH predictions is required for the SC and TP models to execute because the models use 

moving window averages up to that size to simulate SC and TP dynamics. Therefore, the total requirement in terms of run time 

before SC and TP predictions are made is 330 time steps for the GH model plus 180 time steps for the SC and TP models. Use 

the displayed “Step#” value (fig. 2–4) on the “Controls” and other worksheets to assist in setting up and monitoring simulations.

LOXANN also will write input and output data to the “Output” worksheet. The “Write Output” check box at the lower

right in figure 2–4 toggles this feature. The “Clear Output” button erases all data in the “Output” worksheet to allow data 

from a new simulation to be recorded.

Figure 2–6 shows the GH information fields on the “Controls” worksheet. By site location, the GHm column shows the 

measured GHs for the current time step. The GHpm column shows the predicted GH values made by the GH model while using 

measured control structure flows for input data. Whether or 

not the GH error correction ANN model (“GH error ANN 

ON,” fig. 2–4) is activated will affect these values. The 

dGH(u-m) column shows the predicted GH using user-defined 

Q inputs minus either the measured GH, when available, or 

the GH predicted using measured Q inputs when the measured 

GH is unavailable. The GHpu column shows dGH(u-m) plus 

either the measured GH, when available, or the GH predicted 

using measured Q inputs.

Figure 2–5. Pop-up window that appears when a simulation 

is interrupted by using the “Esc” key.

Figure 2–6. GH fields on “Controls” worksheet.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 55

Figure 2–7 shows the control structure flow information fields on the “Controls” worksheet. By structure, the Option 

column shows the input flow option selected by the user on the “Q Setpoints” worksheet. The %, cfs, and UserDefQ columns 

show what the user-set flow input values would be for the current time step if Option was set at %, cfs, or UserDefQ, 

respectively. The user-set input flow values also are set on “Q Setpoints.” The Qm column shows the current measured 

flows. The Qu column shows which of the input flow options (%, cfs, or UserDefQ) is being input per the Option setting.

3.4. “Q Setpoints” Worksheet

Figure 2–8 shows the upper portion of the “Q Setpoints” worksheet, which is the component of LOXANN’s GUI 

that allows the user to set flow setpoints for each control structure. Actual setpoint values used for each structure are 

determined by the associated scroll bars. By structure, the scroll bars in the “Input Option” column are used to select the 

type of user-set input to use. The type selected is shown in a field immediately above each scroll bar. The “%” option multiplies 

the measured flow by a percentage set using the % scroll bar shown at the right in figure 2–8. The “cfs” option sets the flow

 to a constant value in units of cubic feet per second using the cfs scroll bar immediately below the % scroll bar. The 

“UserDefQ” option causes LOXANN to read values from a flow time series copied by the user into the “UserDefQs” 

worksheet. To minimize the extrapolation of the models to conditions much different than those used to train the models, 

the “Q Setpoints” worksheet also lists the historical maximum and minimum values for each structure during the study period, 

and upper and lower limits allowed for the user setting. 

Figure 2–8. Upper 

portion of “Q Setpoints” 

worksheet.

Figure 2–7. Q fields on 

“Controls” worksheet.
56 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

3.5. “Database” and “Output” Worksheets

The “Database” worksheet contains the measured data used by LOXANN to run simulations (fig. 2–9). These data 

are described in table 2–1 and are derived from the raw field measurements. The data are augmented by calculated 

parameters, the values of which are calculated “on-the-fly” by LOXANN’s computer code. The user should not alter 

data in the “Database” worksheet.

Figure 2–9. Example of measured data from the “Database” worksheet.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 57

Table 2–1. Descriptions of “Database” worksheet parameters.
58 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

LOXANN writes a record of key parameters for a particular simulation run to the “Output” worksheet (fig. 2–10). 

The “Write Output” check box on the “Controls” worksheet must be checked for output to be written. The parameters 

written to the “Output” worksheet are described in table 2–2. The user can copy output values into another Excel workbook 

for further analysis. The “Clear Output” button located on the “Controls” worksheet erases all data in the “Output” worksheet 

to allow data from a new simulation to be recorded.

Figure 2–10. Example output from the “Output” worksheet showing user-set control structure flows.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 59

Table 2–2. Descriptions of “OUTPUT” worksheet parameters.
60 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

3.6. “UserDefQs” Worksheet

The “UserDefQs” worksheet allows the user to create customized flow time series for each control structure and have 

them run as the user-set inputs during simulations (fig. 2–11). The time series are simply pasted into the “UserDefQs” 

worksheet and individually activated for the control structure flows when their Input Option is set to “UserDefQ.” The time 

series must be time-synchronized with the dates shown in the “DATE” column at the left. Options for each structure are set 

to “UserDefQ” on the “Q Setpoints” worksheet. 

Figure 2–11. Example of “UserDefQs” worksheet showing user-defined control structure flows.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 61

3.7 “Inputs Graphs,” “GH Graphs,” “SC Graphs,” and “TP Graphs” Worksheets

LOXANN provides streaming numerical and graphical trends for input parameters on the “Inputs Graphs” worksheet 

and as output GH, SC, and TP predictions on the “GH Graphs,” “SC Graphs,” and “TP Graphs” worksheets, respectively 

(fig. 2–12). The trend graphs show 90-day moving windows that update automatically as the time step is changed. The 

“Graphs ON” check box on each worksheet must be checked for its graphs to be active. These worksheets also provide a 

subset of the simulation controls that are found on the “Controls” worksheet so that the user can observe the behaviors of 

specific parameters of interest during simulation or manual stepping using the “Step>>” button. A summary of each of these 

worksheets follows.

• “Inputs Graphs”

◦ current values of:

· by control structure—user input option (Option), and measured (Qm) and user-set (Qu) flows

· by GH site—measured GH (GHm), GH predicted with user-set flows (GHu), and their difference dGH(u-m)

◦ 90-day trend graphs of:

· RAIN+ET (rainfall and evapotranspiration) and measured and user-set control structure summed flows 

(TOTQm and TOTQu)

· by control structure—measured and user-set flows differentiated by “m” and “u” suffixes

• “GH Graphs”

◦ current values of:

· under headings of A3, A10, A30, A90, A210, and A330—the 3, 10, 30, 90, 210, and 330-day MWAs of 

summed RAIN+ET and TOTQm and TOTQu

· by GH site—GHm, GHu, and dGH(u-m)

◦ 90-day trend graphs of:

· GHm and GHu on one graph

· by GH site—GHm, predicted GH using input measured control structure flows (GHpm), predicted GH using 

input user-set control structure flows (GHpu), and the predicted εGH calculated by the SIANN using input 

measured control structure flows (GH-ERRpm)

• “SC Graphs”

◦ current values of:

· under headings of A3, A10, A30, A90, A210, and A330—the 3, 10, 30, 90, 210, and 330-day MWAs of 

summed RAIN+ET and TOTQm and TOTQu

· measured SC (SCm), SC predicted with measured flows (SCpm), and SC predicted with user-set flows 

(SCpu)

◦ 90-day trend graphs by site of SCm, SCpm, and SCpu

• “TP Graphs”

◦ current values of:

· under headings of A3, A10, A30, A90, A210, and A330—the 3, 10, 30, 90, 210, and 330-day MWAs of 

summed RAIN+ET and TOTQm and TOTQu

· measured TP (TPm), TP predicted with measured flows (TPpm), and TP predicted with user-set flows (TPpu)

◦ 90-day trend graphs by site of TPm, TPpm, and TPpu
62 Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR

3.8. “3DVis” Worksheet

LOXANN’s “3DVis” worksheet provides 3D graphical displays of the spatial and temporal variability of GH, SC, 

and TP in portions of the Refuge. The appropriate “3D ON” check boxes must be checked for the displays to operate. 

The SC and (or) TP models must be active and have been run under simulation for enough time steps for them to generate 

predictions. “3DVis” provides a subset of the simulation controls that are found on the “Controls” worksheet so that the 

user can observe the behaviors of specific parameters of interest during simulation or manual stepping using the “Step>>” 

button. The 3D displays will update for each time step and appear as animations when the models are run under simulation. 

At the top of the “GH Graphs” worksheet under the headings of A3, A10, A30, A90, A210, and A330, the current values 

of 3, 10, 30, 90, 210, and 330-day MWAs of summed RAIN+ET and TOTQm and TOTQu are shown. The topmost graph 

is a bar chart showing GHm and GHpu at each GH site for the current time step (fig. 2–13). As shown in figures 2–14 to A–16, 

pairs of 3D graphs are shown for GHm and GHpu, SCpm and SCpu, and TPpm and TPpu, respectively. To orient the user as to 

the portion of the Refuge being displayed, maps showing the Refuge and location of the gages or sampling sites are displayed 

to the left of the 3D graphs. 

Figure 2–12. Example of “GH Graphs” worksheet showing simulation controls and streaming graphics.

Figure 2–13. Bar graph on “‘3DVis” worksheet showing GHm and GHpu at each GH site.
Appendix 2. User’s Manual for the LOXahatchee Artificial Neural Network Decision Support System (LOXANN DSS) 63

Figure 2–15. Three-dimensional displays of SCpm (left) and SCpu (right). Values in all cells are calculated by the SC 

SIANN-based model.

Figure 2–16. Three-dimensional displays of TPpm (left) and TPpu (right). Values in all cells are calculated by the TP 

SIANN-based model.

Figure 2–14. Three-dimensional displays of GHm (left) and GHpu (right). Values in cells not having monitoring sites for 

which predictions are made are calculated by linear interpolation. 
Manuscript approved November 29, 2010

For more information about this publication contact:

USGS South Carolina Water Science Center

Stephenson Center, Suite 129

720 Gracern Road

Columbia, SC 29210-7651

telephone: 803-750-6100

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

Edited by Kay E. Hedrick

Illustrations and layout by Caryl J. Wipperfurth
Conrads and Roehl—Analysis and Simulation of Water-Level, Specific Conductance, and Total Phosphorus Dynamics of the Loxahatchee NWR—Scientific Investigations Report 2010–5244