U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5183

In cooperation with the Texas Commission on Environmental Quality

Description and Evaluation of Numerical Groundwater Flow 

Models for the Edwards Aquifer, South-Central Texas

EDWARDS KERR

REAL

KINNEY

BANDERA

KENDALL

LLANO

GILLESPIE BLANCO

BURNET

WILLIAMSON

TRAVIS

HAYS

BASTROP

CALDWELL

COMAL

GUADALUPE

GONZALES

WILSON

BEXAR

FRIO ATASCOSA

LA SALLE

DIMMIT

ZAVALA

MAVERICK

UVALDE

MEDINA

0 15 30 45 60 MILES

 LAKE TRAVIS

CANYON 

 LAKE

MEDINA

 LAKE

Medina Riv er

Sabinal

River

San Antonio River

Cibolo Creek

Guadalupe

River

Blanco River

Colorado River

Colorado River

Nueces River Frio River

Dry Frio River

West Nueces

River

Verde Creek

Blanco

Creek

Seco Creek

HondoCreek

Dry Comal Creek

Purgatory Cr

River

San Marcos

Las Moras Springs

Leona Springs

San Pedro Springs

San Antonio Springs

Comal Springs

Hueco Springs

San Marcos

 Springs

Barton

 Springs

1

370

Row

20 40

60 80 100

10

30

50

120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660 680

350

330

310

290

270

250

230

210

190

170

150

130

110

70

90

Column

700

100°

99° 

98°

29°

30°

31°
Cover: Finite-difference grid for MODFLOW model of San Antonio and Barton Springs segments of 

Edwards aquifer (modified from Lindgren and others, 2004, fig. 18). 
Description and Evaluation of Numerical 

Groundwater Flow Models for the Edwards 

Aquifer, South-Central Texas

By Richard J. Lindgren, Charles J. Taylor, and Natalie A. Houston

In cooperation with the Texas Commission on Environmental Quality

Scientific Investigations Report 2009–5183

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Lindgren, R.J., Taylor, C.J., and Houston, N.A., 2009, Description and evaluation of numerical groundwater flow 

models for the Edwards aquifer, south-central Texas: U.S. Geological Survey Scientific Investigations Report 

2009–5183, 25 p.
iii

Contents

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

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

Description of Numerical Groundwater Flow Models ............................................................................2

San Antonio Segment .........................................................................................................................4

Barton Springs Segment ....................................................................................................................7

Evaluation of Numerical Groundwater Flow Models ..............................................................................8

Accessibility and Ease of Use ...........................................................................................................8

Range of Hydrologic Conditions Simulated .....................................................................................8

Accuracy of Simulations ....................................................................................................................9

San Antonio Segment ................................................................................................................9

Barton Springs Segment .........................................................................................................11

Agreement with Dye-Tracer Tests ..................................................................................................13

Groundwater Flow Directions .................................................................................................13

Tracer-Inferred Groundwater Flow Velocities .....................................................................17

Limitations of Models ........................................................................................................................17

Summary and Conclusions ........................................................................................................................21

References ...................................................................................................................................................23

Figures

1–3. Maps showing: 

1. Edwards aquifer, south-central Texas, subdivided into San Antonio and 

Barton Springs segments and hydrogeologic zones ....................................................3

2. Comparison of inferred dye-tracer flow paths in the Barton Springs segment 

of the Edwards aquifer, south-central Texas, with simulated potentiometricsurface contours for September 1998 derived from the MODFLOW conduitflow Edwards aquifer model ...........................................................................................14

3. Comparison of inferred dye-tracer flow paths and simulated particle tracks 

derived from output of MODFLOW conduit-flow model of steady-state 

conditions (1939–46 time period) in the San Antonio segment of the Edwards 

aquifer, northern Bexar County, south-central Texas .................................................15

Tables

1. Comparison of model software and extent, simulation time periods, and model 

structure and hydraulic properties for the numerical groundwater flow models for 

the Edwards aquifer, south-central Texas ...............................................................................5

2. Residual statistics for models of the San Antonio segment of the Edwards aquifer, 

south-central Texas ...................................................................................................................10

3. Residual statistics for models of the Barton Springs segment of the Edwards 

aquifer, south-central Texas ....................................................................................................12

4. Limitations of models for the Edwards aquifer, south-central Texas ................................18
iv

Datums

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

(NGVD 29) and the North American Vertical Datum of 1988 (NAVD 88).

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

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

A substantial number of public water system wells in 

south-central Texas withdraw groundwater from the karstic, 

highly productive Edwards aquifer. However, the use of 

numerical groundwater flow models to aid in the delineation of contributing areas for public water system wells in the 

Edwards aquifer is problematic because of the complex hydrogeologic framework and the presence of conduit-dominated 

flow paths in the aquifer. The U.S. Geological Survey, in cooperation with the Texas Commission on Environmental Quality, 

evaluated six published numerical groundwater flow models 

(all deterministic) that have been developed for the Edwards 

aquifer San Antonio segment or Barton Springs segment, or 

both. This report describes the models developed and evaluates each with respect to accessibility and ease of use, range 

of conditions simulated, accuracy of simulations, agreement 

with dye-tracer tests, and limitations of the models. These 

models are (1) GWSIM model of the San Antonio segment, a 

FORTRAN computer-model code that pre-dates the development of MODFLOW; (2) MODFLOW conduit-flow model of 

San Antonio and Barton Springs segments; (3) MODFLOW 

diffuse-flow model of San Antonio and Barton Springs segments; (4) MODFLOW Groundwater Availability Modeling 

[GAM] model of the Barton Springs segment; (5) MODFLOW 

recalibrated GAM model of the Barton Springs segment; and 

(6) MODFLOW–DCM (dual conductivity model) conduit 

model of the Barton Springs segment. The GWSIM model 

code is not commercially available, is limited in its application 

to the San Antonio segment of the Edwards aquifer, and 

lacks the ability of MODFLOW to easily incorporate newly 

developed processes and packages to better simulate hydrologic processes. MODFLOW is a widely used and tested 

code for numerical modeling of groundwater flow, is well 

documented, and is in the public domain. These attributes 

make MODFLOW a preferred code with regard to accessibility and ease of use. The MODFLOW conduit-flow model 

incorporates improvements over previous models by using 

(1) a user-friendly interface, (2) updated computer codes 

(MODFLOW–96 and MODFLOW–2000), (3) a finer grid 

resolution, (4) less-restrictive boundary conditions, (5) an 

improved discretization of hydraulic conductivity, (6) more 

accurate estimates of pumping stresses, (7) a long transient 

simulation period (54 years, 1947–2000), and (8) a refined 

representation of high-permeability zones or conduits. All 

of the models except the MODFLOW–DCM conduit model 

have limitations resulting from the use of Darcy’s law to 

simulate groundwater flow in a karst aquifer system where 

non-Darcian, turbulent flow might actually dominate. The 

MODFLOW–DCM conduit model is an improvement in the 

ability to simulate karst-like flow conditions in conjunction 

with porous-media-type matrix flow. However, the MODFLOW–DCM conduit model has had limited application and 

testing and currently (2008) lacks commercially available 

pre- and post-processors. The MODFLOW conduit-flow 

and diffuse-flow Edwards aquifer models are limited by the 

lack of calibration for the northern part of the Barton Springs 

segment (Travis County) and their reliance on the use of the 

calibrated hydraulic conductivity and storativity values from 

the calibrated Barton Springs segment GAM model. The 

major limitation of the Barton Springs segment GAM and 

recalibrated GAM models is that they were calibrated 

to match measured water levels and springflows for a restrictive range of hydrologic conditions, with each model having different hydraulic conductivity and storativity values 

appropriate to the hydrologic conditions that were simulated. 

The need for two different sets of hydraulic conductivity and 

storativity values increases the uncertainty associated with the 

accuracy of either set of values, illustrates the non-uniqueness 

of the model solution, and probably most importantly demonstrates the limitations of using a one-layer model to represent 

the heterogeneous hydrostratigraphic units composing the 

Edwards aquifer. In general, the best matches or agreement 

between groundwater flow directions inferred by numerical 

model simulation, and by dye-tracer tests, are observed where 

model outputs accurately reproduce the configuration of the 

potentiometric surface with regard to the positions of major 

and minor groundwater troughs and divides. None of the 

models, with the possible exception of the MODFLOW–DCM 

conduit model, has a documented capability to accurately 

simulate travel times for conduit-dominated velocities in 

the Edwards aquifer. Public water system assessments of 

wells in the Barton Springs segment of the Edwards aquifer, 

and elsewhere where conduit-flow conditions are thought 

to dominate aquifer hydraulic behavior, might be enhanced 

Description and Evaluation of Numerical Groundwater 

Flow Models for the Edwards Aquifer, South-Central Texas

By Richard J. Lindgren, Charles J. Taylor, and Natalie A. Houston
2 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

by use of either the MODFLOW–DCM model or the newly 

developed U.S. Geological Survey MODFLOW ConduitFlow Process module for MODFLOW–2005, because each 

incorporates a type of dual or triple hydraulic conductivity 

approach and has the capability to explicitly simulate turbulent 

flow and conduit hydraulic characteristics. 

Introduction

The Texas Commission on Environmental Quality 

(TCEQ) has the principal responsibility to assess the sustainability and susceptibility to contamination of source water 

provided by public water system (PWS) wells (Texas Commission on Environmental Quality, 1999). To carry out this 

responsibility, the TCEQ uses the most up-to-date hydrogeologic, climatologic, and water-use data available, and output 

obtained from numerical groundwater flow models and from 

SWAP–DSS, a customized computer software package developed by the U.S. Geological Survey (USGS), in cooperation 

with the TCEQ, for source-water assessments (R.L. Ulery, 

U.S. Geological Survey, written commun., 2003). For PWS 

wells, the TCEQ requires that the contributing area of each 

well be delineated as accurately as possible and that potential 

sources of groundwater contamination be identified within an 

estimated 100-year time-of-travel area. The delineation of the 

contributing area for each PWS well is a critical element in 

the TCEQ assessment process because all other assessment 

components are dependent upon the accuracy of the delineated 

contributing area. 

A substantial number of PWS wells in south-central 

Texas withdraw groundwater from the karstic, highly productive Edwards aquifer (fig. 1). For these PWS wells, the 

boundaries for contributing areas are currently (2008) delineated using a combination of tools that includes numerical 

groundwater flow models and the SWAP–DSS software. 

However, the use of numerical groundwater flow models to aid 

in the delineation of contributing areas for PWS wells in the 

Edwards aquifer is problematic because of the complex hydrogeologic framework and the presence of conduit-dominated 

flow paths in the aquifer. 

These complications arise in part from technical limitations involved in applying numerical models designed primarily for simulation of aquifers characterized by laminar or 

non-turbulent groundwater flow conditions. In addition, the 

hydrogeologic data needed to create proper conceptual, mathematical, and digital models of karst aquifers are considerable 

and difficult to obtain without use of quantitative methods that 

take into account the triple porosity and permeability characteristics of karst (Taylor and Greene, 2008). In much of the 

Edwards aquifer, as in many well-developed karst aquifers, 

hydrogeologic data are lacking or insufficient to adequately 

represent karst flow characteristics (Worthington, 2003). It is 

generally accepted by the water-resources community that, 

without access to adequate hydrogeologic input data and use 

of numerical models capable of incorporating, in some way, 

non-laminar karst flow characteristics, poor to limited success 

will be achieved in simulating groundwater flow directions, 

velocities, and contaminant transport characteristics in welldeveloped karst aquifers (Scanlon and others, 2003; Palmer, 

2006). 

To assess the sustainability and susceptibility to contamination of source water provided by PWS wells, the TCEQ 

wishes to apply numerical models that provide the most accurate and scientifically defensible delineation of contributing 

areas that is possible given the existing technological limitations. To this end, the USGS, in cooperation with the TCEQ, 

evaluated six published numerical groundwater flow models 

(all deterministic) that have been developed for the Edwards 

aquifer. 

This report describes the six published groundwater flow 

models for the Edwards aquifer and evaluates each of the models primarily with respect to the following criteria:

•	 Accessibility and ease of use of model code and model 

input and output files 

•	 Range of simulated hydrologic conditions for each 

calibrated model—that is, are both wet and dry periods 

simulated

•	 Accuracy of model simulations—comparison of residuals for hydraulic heads and springflows

•	 Agreement, to the extent possible, with results obtained 

from previously conducted dye-tracer tests 

•	 Limitations of the models

Description of Numerical Groundwater 

Flow Models

Six numerical groundwater flow models for the San 

Antonio segment of the Edwards aquifer or Barton Springs 

segment of the Edwards aquifer, or both (fig. 1), that are published and generally accepted by the water-resources community are described and evaluated in this report. These models 

are

1. Finite-difference model of San Antonio segment of 

Edwards aquifer (GWSIM) (Klemt and others, 1979; 

Thorkildsen and McElhaney, 1992)

2. MODFLOW model of San Antonio and Barton Springs 

segments of Edwards aquifer with hydraulic conductivity distribution based on conduit-flow conceptualization 

(Lindgren and others, 2004)

3. MODFLOW model of San Antonio and Barton Springs 

segments of Edwards aquifer with hydraulic conductivity distribution based on diffuse-flow conceptualization 

(Lindgren, 2006)
Cotulla

CarrizoSprings

Dilley

Crystal City

Pearsall

Jourdanton Pleasanton

Poteet

Hondo

Gonzales

Devine

Floresville Natalia

Uvalde

Brackettville

Castroville

Luling Leakey Bandera

SanAntonio

NewBraunfels

Boerne

Lockhart

SanMarcos

Rocksprings

Kyle Kerrville

Buda

Blanco

Bastrop Dripping

Springs

JohnsonCity

Fredericksburg

Manor

Austin

Round Rock

Georgetown Llano

Burnet

Eagle Pass

Seguine

Colordo River

Pedernales

River

Colordo River

South Llano River

Nueces River

West

Nueces

River

Frio River

Blanco Creek

Sabinal River

Hondo

Creek

Medina

River San Antonio River

Cibolo Creek

Salado Creek

Guadalupe River

San Marcos River

B al nco River

Nueces

River

LAKETRAVIS

CANYONLAKE

MEDINALAKE

EDWARDS

KERR

REAL

BANDERA

MEDINA UVALDE KINNEY

FRIO ZAVALA

MAVERICK

LA SALLE

DIMMIT

TRAVIS

BLANCO GILLESPIE

HAYS

KENDALL

COMAL

GUADALUPE BEXAR

WILSON

ATASCOSA

BASTROP

CALDWELL

GONZALES

BURNET

LLANO

WILLIAMSON

1 0, 00 mg L/

10 0, 00 mg L/

B

ALC

O

NES FA

ULT

Z

O

NE

Knippa Gap area

San MarcosSprings

ComalSprings

BartonSprings

Hueco

Springs

San Antonio

Springs

Leona

Springs

San Pedro

Springs Las Moras

Springs

98°

99°

100°

31°

30°

29°

TEXAS

LOCATION MAP

0 35 70 MILES

EXPLANATION

Edwards aquifer, San Antonio segmentEdwards aquifer, Barton Springs segment

Hydrogeologic zones

Line of 1,000 milligrams per liter dissolved solids concentration (A.L. Schultz, consultant, written commun., 2000)Line of 10,000 milligrams per liter dissolved solids concentration (A.L. Schultz, consultant, written commun., 2000)Approximate boundary of Balcones fault zoneSpring

UnconfinedConfined

Recharge zone (outcrop) (modified from Puente, 1978)Freshwater zoneFreshwater/saline-water transition zone

Base from:U.S. Geological Survey digital data—rivers, lakes,and reservoirsTexas Natural Resources Information System—citiesNational Atlas of the United States—roadsTexas Water Development Board—Edwards aquiferBalcones fault zoneProjection: AlbersLinear unit: FootDatum: NAD 83

Description of Numerical Groundwater Flow Models 3Figure 1. Edwards aquifer, south-central Texas, subdivided into San Antonio and Barton Springs segments and hydrogeologic zones.
4 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

4. MODFLOW model of Barton Springs segment of 

Edwards aquifer (Groundwater Availability Modeling 

[GAM] model) (Scanlon and others, 2002) 

5. MODFLOW model of Barton Springs segment of 

Edwards aquifer for drought conditions (recalibrated 

GAM model) (Smith and Hunt, 2004)

6. MODFLOW–DCM (dual conductivity model) conduit 

model of Barton Springs segment of Edwards aquifer 

incorporating dual conductivity approach and explicit 

simulation of conduits (Painter and others, 2007).

The model software and extent, simulated time periods, and 

model structure and simulated hydraulic properties for each 

model are shown in table 1. A summary of the characteristics 

and history of development of each model, organized by aquifer segment encompassed by the model, follows. 

San Antonio Segment

A number of numerical groundwater flow models have 

been constructed for the San Antonio segment of the Edwards 

aquifer. Klemt and others (1979) developed a numerical 

groundwater flow model (hereinafter, the GWSIM model 

[model no. 1 of 6, p. 2 of this report]) for the San Antonio 

segment of the Edwards aquifer that was used to simulate 

several groundwater withdrawal and climatic scenarios from 

1972 through 2049. The GWSIM model uses a FORTRAN 

computer-model code that pre-dates the development of 

MODFLOW to simulate groundwater flow in the San Antonio 

segment of the Edwards aquifer. The computer program for 

the GWSIM model, including the program documentation 

and user’s manual, was prepared in 1974 by the Texas Water 

Development Board (Texas Water Development Board, 1974). 

The basic simulation program was written by T.A. Prickett 

and C.G. Lonnquist, Illinois State Water Survey (PrickettLonnquist Aquifer Simulation Model) (Prickett and Lonnquist, 

1971). Modifications subsequently were made to the basic program to allow better simulation of an aquifer containing both 

confined and unconfined zones (such as the Edwards aquifer). 

Thorkildsen and McElhaney (1992) reevaluated the 

GWSIM model and refined the simulation of water levels and 

springflows in the San Antonio region. The GWSIM model 

has been used extensively for simulating water-level conditions at the Bexar County index well (observation well, commonly referred to as “J–17,” in which water-level changes are 

assumed to reflect Edwards aquifer water-level changes on a 

regional scale) and springflows at Comal Springs. 

LBG-Guyton Associates (1996) did a study to determine 

whether the GWSIM model accurately predicts water levels 

throughout the model area. They concluded that the model 

can be used to accurately simulate hydrologic conditions 

in the freshwater zone of the Edwards aquifer from eastern 

Uvalde County to western Hays County (fig. 1). However, 

a poor correlation, or no correlation, between measured and 

simulated water levels for 1978–89 was obtained for wells in 

eastern Hays County, the Knippa Gap area and the area west 

of the Frio River in Uvalde County, and in the recharge zone. 

In particular, the model was poorly calibrated for San Marcos 

Springs, one of two major discharge points for the Edwards 

aquifer (the other is Comal Springs).

To evaluate the hydrologic response to various alternative proposals for managing the Edwards aquifer, the Edwards 

Aquifer Authority (EAA, formerly the Edwards Underground 

Water District), with other San Antonio water-resource managers and planners, expressed the need for an improved numerical groundwater flow model. Rather than attempt to update, 

modify, or recalibrate existing models, it was decided that a 

new, comprehensive groundwater flow model, using current 

(2003) user-friendly pre- and post-processing software that 

incorporated important components of the latest conceptualization of the aquifer, was needed. 

To develop a new, comprehensive model, a study was 

done during 2000–03 by the USGS and The University of 

Texas at Austin, Bureau of Economic Geology, in cooperation with the U.S. Department of Defense and the EAA. The 

objective of this study was to improve understanding of the 

complex hydrogeologic processes that control water availability of the Edwards aquifer in the San Antonio area through 

the development, calibration, and testing of a numerical 

groundwater flow model to optimize resource management. To 

accomplish this, all available and pertinent hydrogeologic data 

were compiled and organized into a comprehensive, digitalbased system of data storage and retrieval. The new Edwards 

aquifer numerical groundwater flow model developed in this 

study (hereinafter, the MODFLOW conduit-flow Edwards 

aquifer model [model no. 2 of 6, p. 2]) (Lindgren and others, 2004) incorporates improvements over previous models 

by using (1) a user-friendly interface, (2) updated computer 

codes (MODFLOW–96 [Harbaugh and McDonald, 1996] and 

MODFLOW–2000 [Harbaugh and others, 2000]), (3) a finer 

grid resolution, (4) less-restrictive boundary conditions, (5) an 

improved discretization of hydraulic conductivity, (6) more 

accurate estimates of pumping stresses, (7) a long transient 

simulation period (54 years, 1947–2000), and (8) a refined 

representation of high-permeability zones or conduits. 

The most problematic issue regarding the use of numerical groundwater flow models for delineating contributing areas 

for PWS wells involves determining the extent and hydraulic 

influence of karst development in the Edwards aquifer. The 

aquifer can be conceptualized as having triple porosity and 

permeability because of the presence of intergranular pores, 

fractures, and various solutional openings ranging in size 

from vugs to conduits several meters in diameter (Worthington, 2003). The presence and hydrologic influence of wellintegrated, large-diameter conduits is reflected by the presence 

of large karst springs that discharge from the aquifer and 

by dye-tracer test results. Local dye-tracer tests and hydrogeologic mapping studies (for example, Worthington, 2003; 

Hunt and others, 2005; Hunt and others, 2006) have shown 

that well-integrated conduit networks are important hydraulic 

components of the aquifer system near the regional discharge 
Description of Numerical Groundwater Flow Models

5

Table 1. Comparison of model software and extent, simulation time periods, and model structure and hydraulic properties for the numerical groundwater flow models for the Edwards aquifer, south-central Texas.[GAM, Groundwater Availability Modeling; DCM, dual conductivity model; --, not applicable or data not available; mi, miles; ft, feet; mg/L, milligrams per liter; Kx, horizontal hydraulic conductivity; ft/d, feet per day; Ky, vertical hydraulic conductivity]

Model feature/attribute GWSIM model

MODFLOW conduitflow Edwards aquifer 

model

MODFLOW diffuse-flow 

Edwards aquifer

Barton Springs 

segment GAM model 

(MODFLOW)

Barton Springs segment 

recalibrated GAM 

model (MODFLOW)

MODFLOW–DCM 

conduit model

Model software and extent

Model code FORTRAN MODFLOW MODFLOW MODFLOW–96 MODFLOW–96 MODFLOW–DCM

Pre- and post-processor -- Groundwater Vistas Groundwater Vistas PMWIN PMWIN --

Model extent San Antonio segment San Antonio and Barton 

Springs segments

San Antonio and Barton 

Springs segments

Barton Springs segment Barton Springs segment Barton Springs segment

Simulation time periods

Steady-state Average recharge and 

pumpage 1944–46

Average conditions; 

1939–46

Average conditions; 

1939–46

Average recharge for 

1979–98; monthly pumpage at 1989 rates

-- Average recharge for 

1979–98; monthly pumpage at 1989 rates

Transient Calibration; 1947–59; 

monthly stress periods

Verification; 1978–89; 

monthly stress periods

Monthly stress periods; 

1947–2000

Monthly stress periods; 

1947–2000

Monthly stress periods; 

1989–98

Monthly stress periods; 

1950–59

Monthly stress periods; 

1989–98

Model structure and hydraulic properties

Grid rows and columns 31 rows; 80 columns 370 rows; 700 columns 370 rows; 700 columns 120 rows; 120 columns 120 rows; 120 columns 120 rows; 120 columns

Grid cell dimensions Variable: 0.90 to 5.0 mi 1,320 by 1,320 ft 1,320 by 1,320 ft 1,000 ft long by 500 ft 

wide

1,000 ft long by 500 ft 

wide

1,000 ft long by 500 ft wide

Grid rotation 26.75 degrees from 

horizontal

35 degrees from horizontal 35 degrees from hori- zontal 45 degrees from hori- zontal 45 degrees from hori- zontal 45 degrees from horizontal

Number of layers 1 1 1 1 1 2 (diffuse and conduit)

Southern model 

boundary

1,000-mg/L dissolved 

solids concentration line

10,000-mg/L dissolved 

solids concentration line

10,000-mg/L dissolved 

solids concentration line

1,000-mg/L dissolved 

solids concentration line

1,000-mg/L dissolved 

solids concentration line

1,000-mg/L dissolved solids concentration line

Hydraulic conductivity 

(K) distribution

Varies by cell; Kx range 

0.13 to 23,727 ft/d, Ky range 0.13 to 10,027 ft/d

Diffuse: varies by cell, 

range 1 to 7,347 ft/dConduit cells: range 1,000 to 300,000 ft/d

38 zones; range 3 to 

50,000 ft/d

10 zones; range 1 to 

1,236 ft/d

12 zones; range 0.3 to 

740 ft/d

For 14 conduits: range 

1,000 to 160,000 ft/d

Storativity -- -- -- -- -- --

Specific yield 2 zones; 0.05 and 0.06 5 zones; range 0.005 to 

0.15

5 zones; range 0.005 to 

0.15

0.005 0.0021 10-3 in conduits; 3.0x10-3 in 

diffuse system

Specific storage Varies by cell; range 

5.0x10-7 to 9.25x10-7

ft-1

5 zones; range 5.0x10-7

to 5.0x10-6 ft-1

5 zones; range 5.0x10-7

to 5.0x10-6 ft-1

5.0x10-6 ft-1 5.0x10-7 ft-1 10-5 ft-1 in conduits; 

3.0x10-5 ft-1 in diffuse 

system
6 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

areas such as Comal Springs for the San Antonio segment 

and Barton Springs for the Barton Springs segment. Conduits 

also are important features controlling the subsurface diversion (or piracy) of surface streams along the recharge area of 

the Edwards aquifer. Most well-developed conduits seem to 

be aligned not with major faults of the Balcones fault zone 

(fig. 1) but rather with northwest-southeast trending fractures 

and cross faults (Faith and others, 2005). A regionally extensive system of high-permeability zones—likely influenced by 

the presence of conduits—is defined by broad troughs in the 

potentiometric surface of the freshwater zone of the Edwards 

aquifer (Lindgren and others, 2004). 

The conceptualization that served as the basis for the 

MODFLOW conduit-flow Edwards aquifer model emphasizes 

the presence of discrete conduit-dominated flow paths through 

the aquifer. Because the use of a distributed, porous-media 

model such as MODFLOW (Harbaugh and others, 2000) is 

not well suited for the simulation of rapid, turbulent conduit 

flow, the application of this model to simulate hydraulic heads 

and groundwater flow requires considerable simplification 

of the karst aquifer system. Rather than applying a coupledcontinuum pipe flow or dual-porosity or triple-porosity model 

conceptualization (Birk and others, 2003; Liedl and others, 

2003), the MODFLOW conduit-flow Edwards aquifer model 

represents inferred conduit-dominated flow paths as narrow 

(one-cell, 0.25-mile wide), continuously connected zones of 

large hydraulic conductivity (Lindgren and others, 2004). 

Even this simplified conceptualization is subject to considerable uncertainty because the extent to which large conduits 

permeate the aquifer, their distribution and integration into 

subsurface drainage networks, and their influence over the 

hydraulics of the aquifer at local-to-regional scales remain 

relatively unknown and poorly characterized in much of the 

aquifer. 

The locations of conduit-dominated high-permeability 

zones applied in the MODFLOW conduit-flow Edwards 

aquifer model were inferred from data and interpretations 

described by Worthington (2003) and are subject to some 

uncertainty. The effect of the uncertainty regarding the locations of conduits becomes more important as the size of the 

area of interest decreases or, in other words, as the scale of 

the simulation decreases. Uncertainty also exists regarding the 

physical dimensions, connectivity, and hydraulic properties of 

conduits. The physical dimensions of the high-permeability 

zones in the MODFLOW conduit-flow Edwards aquifer model 

are constrained by the model cell dimensions, with most 

conduits much smaller than the 0.25-mile dimensions of the 

model cells.

An alternative conceptualization, which can be called the 

diffuse-flow conceptualization, reflects the hypothesis that, 

although conduits likely are present, flow in the aquifer predominately is through a network of small fractures and openings sufficiently numerous that the aquifer can be considered 

a porous-media continuum at the regional scale. Previous 

studies of the distribution of permeability provide support 

for the application of this conceptual model. For example, a 

statistical analysis done by Halihan and others (2000) 

indicated that conduits do not seem to contribute appreciably 

to the average permeability measured in most Edwards 

aquifer wells, and results of a study by Worthington (2003) 

estimate the likelihood that wells intersect large conduits 

at 2 percent or less. Therefore, the diffuse-flow conceptualization might serve as an acceptable means of using a 

numerical model to delineate contributing areas for most PWS 

wells. 

Previous porous-media groundwater flow models created 

for the Edwards aquifer have applied a similar conceptualization of hydraulic characteristics (Klemt and others, 1979; 

Maclay and Land, 1988; Thorkildsen and McElhaney, 1992; 

Scanlon and others, 2002), as have models created for other 

karst aquifers that have been used to simulate measured 

fluctuations in water levels in wells and springflows (for 

example, the aquifers of the Floridan aquifer system [Bush and 

Johnston, 1988; Knowles and others, 2002; Sepulveda, 2002; 

Payne and others, 2005]).

The uncertainties inherent in simulating conduits as onecell-wide, continuously connected features resulted in incorporating an alternative hydraulic conductivity distribution in the 

Edwards aquifer model. To develop an alternative hydraulic 

conductivity distribution for the Edwards aquifer model, a 

study was done during 2004–05 by the USGS, in cooperation 

with the San Antonio Water System. The objectives of this 

study were to (1) modify the hydraulic conductivity distribution of the MODFLOW conduit-flow Edwards aquifer model, 

including broad zones of upscaled hydraulic conductivity, 

and (2) compare the hydrographs and residuals (differences 

between model-computed and measured values) for hydraulic heads and springflows for the MODFLOW conduit-flow 

Edwards aquifer model with simulated one-cell-wide conduits 

and the alternative Edwards aquifer model with the broad 

zones of upscaled hydraulic conductivity (hereinafter, the 

MODFLOW diffuse-flow Edwards aquifer model [model no. 

3 of 6, p. 2]) (Lindgren, 2006). The alternative hydraulic conductivity distribution incorporates the diffuse-flow conceptualization of the aquifer system, with more emphasis on small 

conduit and fracture flow and less emphasis on large, interconnected conduit flow.

Although the Barton Springs segment of the aquifer is 

included in the MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer models, calibration was not done for the 

northern part of the segment (Travis County). A numerical 

finite-difference groundwater flow model had recently been 

completed for the Barton Springs segment (Scanlon and others, 2002), and a duplication of that work was not considered 

necessary. Calibration was done in the southern part of the 

Barton Springs segment (northern Hays County), however, 

because the simulated hydraulic heads and flows in that area 

influenced the location of the groundwater divide near Kyle 

(the feature that separates the San Antonio segment from the 

Barton Springs segment) and the simulated hydraulic heads 

and flows in the adjoining part of the San Antonio segment of 

the aquifer.
Description of Numerical Groundwater Flow Models 7

Barton Springs Segment

A MODFLOW groundwater flow model of the Barton 

Springs segment of the Edwards aquifer (hereinafter, the 

Barton Springs segment GAM model [model no. 4 of 6, p. 4]) 

(Scanlon and others, 2002) was developed as a part of the 

Texas Groundwater Availability Modeling (GAM) program. 

The purpose of the Barton Springs segment GAM model 

was to provide (1) a management tool to the Barton Springs/

Edwards Aquifer Conservation District (BSEACD) and to the 

Regional Water Planning Group1 and (2) a tool for evaluating 

groundwater availability under drought-of-record conditions. 

The Barton Springs segment GAM model was calibrated 

(1) for steady-state conditions using average recharge for a 

20-year period (1979–98) and pumpage at 1989 rates and 

(2) for transient conditions for the 10-year period 1989–98, 

with monthly stress periods. Predictive simulations of water 

levels and springflows for the next 50 years (through 2050) 

also were done on the basis of projected demands from the 

Regional Water Planning Group and the BSEACD. The 

Barton Springs segment GAM model uses streamflow and 

streamflow-loss data to estimate groundwater recharge for the 

transient period 1989–98. Predictive simulations were based 

on 1950s drought (drought-of-record) conditions for which 

no recharge data are available. For the predictive simulations, 

recharge was assumed equal to springflow. Because of this 

assumption, recharge might be slightly overestimated during 

periods of low recharge because some of the water discharged 

might be from aquifer storage rather than directly from 

recharge (Scanlon and others, 2002).

The Barton Springs segment GAM model was constructed to match water levels and springflows from a period 

wetter than that of the 1950s drought. Because the model was 

calibrated to a relatively wet period, it overestimates springflows and underestimates water-level altitudes compared with 

measurements collected during the 1950s drought-of-record. 

The model was recalibrated so that simulated and measured 

springflow and water-level data from the 1950s drought 

matched better. The recalibrated model (hereinafter, the Barton 

Springs segment recalibrated GAM model [model no. 5 of 6, 

p. 4]) (Smith and Hunt, 2004) was then used to predict springflow and water-level declines under 1950s drought conditions 

and various future pumping scenarios. 

Incremental changes, through trial and error, were made 

for the Barton Springs segment recalibrated GAM model to 

specific yield, specific storage, and hydraulic conductivity 

values to recalibrate the transient part of the Barton Springs 

segment GAM model to 1950s drought conditions, resulting 

in the MODFLOW model of the Barton Springs segment 

of Edwards aquifer for drought conditions. Adjustments 

were made to model input data until simulated springflows 

and water levels closely matched measured springflows 

1

 Entity responsible for preparing and adopting a regional water plan for 

the local area per Senate Bill 1 of the 75th Texas Legislature (Texas Water 

Development Board, 2009). 

and water levels from the 1950s drought. By the end of the 

recalibration, specific yield was decreased from 0.005 to 

0.0021, and hydraulic conductivity ranged from 0.3 to 740 feet 

per day, compared with a range of 1 to 1,236 feet per day for 

the Barton Springs segment GAM model. Simulated hydraulic 

conductivity and storativity values under 1950s drought conditions were lower (compared to those of the Barton Springs 

segment GAM model) because of lower simulated hydraulic 

heads in the aquifer. Dissolution of the limestone and consequent conduit development are greater in the shallow part of 

the aquifer than at greater depths (Ogden and others, 1986; 

Maclay, 1995; Small and others, 1996). Therefore, lower 

hydraulic conductivity and storage values are associated with 

the deeper part of the aquifer, as compared to the shallower 

part. Additionally, specific-capacity tests have been done 

in one well in the Barton Springs segment during high- and 

low-flow conditions. Results indicated that hydraulic property values were lower under low-flow conditions (Smith and 

Hunt, 2004). As for the Barton Springs segment GAM model, 

recharge for the Barton Springs segment recalibrated GAM 

model transient calibration (1950s drought conditions) was 

assumed to be equal to springflow. 

Neither the Barton Springs segment GAM model nor 

the Barton Springs segment recalibrated GAM model are 

capable of adequately simulating a wide range of hydrologic 

conditions (that is, from drought conditions to abnormally 

wet conditions). A likely explanation for this limitation is 

the inherent assumption of using Darcy’s law within singlecontinuum models to simulate a dynamic karst system (Painter 

and others, 2007) where groundwater flow might be laminar or 

turbulent. A revised model of the Barton Springs segment was 

constructed using MODFLOW–DCM version 2.0 software to 

match water-level and springflow hydrographs for drought and 

abnormally wet conditions (hereinafter, MODFLOW–DCM 

conduit model [model no. 6 of 6, p. 4]) (Painter and others, 

2007). MODFLOW–DCM version 2.0 incorporates a solver 

capable of solving the highly nonlinear systems associated 

with the conduit/matrix flow regime under confined/unconfined conditions. Because of data requirements associated with 

this solver, the dual conductivity model (DCM) could not be 

implemented in MODFLOW as a self-contained package, and 

the new variant, MODFLOW–DCM version 2.0, was created (Painter and others, 2007). The Barton Springs segment 

GAM model was converted to a MODFLOW–DCM model by 

(1) adding a conduit layer, (2) reducing hydraulic conductivity in the zones of high hydraulic conductivity to values more 

typical for a diffuse-flow system, and (3) increasing storativity in the diffuse-flow system to values more typical for a 

diffuse-flow system (Painter and others, 2007). Steps 2 and 

3 were necessary because most of the flow and all of the fast 

flow is accounted for in the simulated conduit system, which 

is composed of 14 conduit segments. The locations of major 

groundwater flow paths inferred from the dye-tracer studies of 

Hauwert and others (2002) and Hunt and others (2006) were 

used to constrain conduit placement in the model, and inferred 

conduits also were located so as to intercept focused recharge 
8 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

contributed to the aquifer by sinking surface streams. Because 

most of the flow and all of the fast flow is in the conduit system, rapid springflow response can be achieved by assigning 

relatively small values to the conduit storage properties. The 

storage properties for the diffuse system can then be adjusted 

so that hydraulic heads match the relatively subdued waterlevel hydrographs. The MODFLOW–DCM conduit model was 

calibrated for steady-state conditions using the steady-state 

recharge and pumping data from the Barton Springs segment 

GAM model. The MODFLOW–DCM conduit model was calibrated for transient conditions for the 10-year period 1989–98, 

with monthly stress periods, as was the Barton Springs segment GAM model. 

Evaluation of Numerical Groundwater 

Flow Models

The evaluation of the six groundwater flow models of 

the San Antonio or Barton Springs segments of the Edwards 

aquifer, or both, includes a comparison of (1) accessibility 

and ease of use of the model code and model input and output 

files, (2) range of hydrologic conditions simulated by the 

model, (3) accuracy of the simulations, (4) agreement with 

dye-tracing studies, and (5) limitations of the models.

Accessibility and Ease of Use

The GWSIM model code is not commercially available, 

is limited in its application to the San Antonio segment of 

the Edwards aquifer, and lacks the ability of MODFLOW to 

easily incorporate newly developed processes and packages to 

better simulate hydrologic processes. MODFLOW is a widely 

used and tested code for numerical modeling of groundwater 

flow, is well documented, and is in the public domain. These 

attributes make MODFLOW a preferred code with regard to 

accessibility and ease of use. The MODFLOW–DCM code 

currently (2008) has been used and tested only for the Barton 

Springs segment of the Edwards aquifer and the Santa Fe 

River Sink/Rise system in the Floridan aquifer (Painter and 

others, 2007) and therefore lacks the wide use and testing 

associated with the MODFLOW code. 

A variety of pre- and post-processors have been 

developed to facilitate data entry and allow analysis of 

model output. The GWSIM model has not been adapted for 

any commercially available pre- and post-processors. The software Groundwater Vistas version 3.0 (Environmental Simulations, Inc., 2002) was used as a pre- and post-processor to 

facilitate data entry and allow analysis of model output for the 

MODFLOW conduit-flow and diffuse-flow Edwards aquifer 

models. The Barton Springs segment GAM and recalibrated 

GAM models used the software Processing MODFLOW for 

Windows (PMWIN) version 5.0.54 (Chiang and Kinzelbach, 

1998) and version 5.1.7 (Chiang and Kinzelbach, 2001), 

respectively. The addition of a Groundwater Vistas graphical 

user interface (GUI) for MODFLOW–DCM was coordinated 

with Environmental Simulations, Inc., and final implementation of the GUI was completed as part of a separate karst 

modeling project with the University of Florida (Painter and 

others, 2007). However, the Groundwater Vistas GUI for 

MODFLOW–DCM currently (2008) is not commercially 

available. The lack of any commercially available pre- and 

post-processors for the GWSIM model and the MODFLOW–

DCM conduit model is a disadvantage of these models with 

regard to ease of use.

Range of Hydrologic Conditions Simulated

The GWSIM model was initially calibrated for transient 

conditions for a 25-year time period, 1947–71 (Klemt and 

others, 1979). Stress-period lengths, pumpage rates, recharge 

rates and distributions, and model hydraulic properties (transmissivity, storage coefficient, and aquifer anisotropy) were 

subsequently revised by Thorkildsen and McElhaney (1992). 

The revised GWSIM model (Thorkildsen and McElhaney, 

1992) was calibrated for transient conditions for two separate 

time periods, 1947–59 and 1978–89. 

The MODFLOW conduit-flow and diffuse-flow Edwards 

aquifer models were calibrated for transient conditions for a 

relatively long time period of 54 years (1947–2000). This time 

period included the drought-of-record during the 1950s as well 

as annual recharge to the San Antonio segment of the Edwards 

aquifer during 1992 (2,486,000 acre-feet) that was about 

3.5 times the long-term (1934–2002) mean annual recharge 

(698,930 acre-feet) (Hamilton and others, 2003). 

The Barton Springs segment GAM model and the 

MODFLOW–DCM conduit model were calibrated for transient conditions for a relatively short time period of 10 years 

(1989–98). The Barton Springs segment recalibrated GAM 

model was calibrated for transient conditions for a 10-year 

time period (1950–59) during the 1950s drought-of-record. 

The Barton Springs segment GAM model was calibrated for 

a time period most representative of average to abnormally 

wet hydrologic conditions. Conversely, the Barton Springs 

segment recalibrated GAM model was calibrated for a time 

period representative of drought conditions, with a resulting 

different set of calibrated hydraulic conductivity and storativity values. Hypothetical drought conditions were simulated 

using the MODFLOW–DCM conduit model by starting with 

a calibrated steady-state model and then eliminating recharge 

for a 5-year period (Painter and others, 2007). The simulations adequately represent drought conditions comparable to 

the 1950s drought-of-record with regard to estimated recharge 

rates and springflows but do not specifically represent the 

historical drought period. 

 The MODFLOW conduit-flow and diffuse-flow Edwards 

aquifer models and the MODFLOW–DCM conduit model 

adequately simulate the full range of hydrologic conditions 

from period-of-record drought conditions to extreme wet 

conditions (1992) with the same calibrated values for hydraulic properties. In contrast, the transient calibration periods for 
Evaluation of Numerical Groundwater Flow Models 9

the GWSIM model and the Barton Springs segment GAM 

and recalibrated GAM models are relatively short and do not 

include the full range of hydrologic conditions. The transient 

calibration period for the GWSIM model does not include 

extreme wet conditions such as occurred in 1992. The Barton Springs segment GAM model does not include extreme 

drought conditions such as the 1950s drought, whereas the 

Barton Springs segment recalibrated GAM model does not 

include average to extreme wet hydrologic conditions and 

is restricted to the predominately drought conditions of the 

1950s. The relatively short transient calibration periods for 

the Barton Springs segment GAM and recalibrated GAM 

models result in two different sets of calibrated values for 

hydraulic conductivity and storativity that are dependent on 

the specific hydrologic conditions being simulated. The 

value and importance of relatively long transient calibration 

periods that encompass a range of hydrologic conditions is 

discussed further in the next section of this report, “Accuracy 

of Simulations.” 

Accuracy of Simulations

The accuracy of the model simulations was evaluated by 

comparing the residuals (differences between the simulated 

and measured values) for hydraulic heads and springflows 

for the six numerical groundwater flow models. The GWSIM 

model and the MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer models are compared for the San Antonio 

segment of the Edwards aquifer, and the Barton Springs 

segment GAM and recalibrated GAM models and the 

MODFLOW–DCM conduit model are compared for the 

Barton Springs segment.

San Antonio Segment

The goodness of fit between simulated and measured 

hydraulic heads and springflows can be quantified using the 

root mean square (RMS) error. The RMS error is derived from 

the residuals between the measured and simulated hydraulic 

heads (or springflows), as given below:

RMS

n

h h m s

i

n

i

2

= − ( ) 











 =  ∑

1

1

0 5.

where

RMS is the root mean square error [L],

n is the number of calibration points,

hm is the measured hydraulic head (or springflow) at point 

i [L], and

hs is the simulated hydraulic head (or springflow) at point 

i [L].

The RMS error of the residuals and the RMS error as 

a percentage of the range of the measured values ([RMS 

error divided by the range of measured values] x 100) for the 

GWSIM model and the MODFLOW conduit-flow and 

diffuse-flow Edwards aquifer models are shown in table 2. 

These statistics are used as quantitative measures of the goodness of fit between the measured and simulated hydraulic 

heads and springflows. For two synoptic water-level time 

periods (May–November 1956, drought conditions; November 1974–July 1975, above-normal rainfall) (not applicable 

for GWSIM model), the RMS error for hydraulic heads for 

the MODFLOW diffuse-flow Edwards aquifer model are 

appreciably smaller than those for the MODFLOW conduitflow Edwards aquifer model (table 2). The RMS errors for 

the MODFLOW conduit-flow Edwards aquifer model are 

76 and 30 percent greater than for the MODFLOW diffuseflow Edwards aquifer model for the drought conditions and 

above-normal rainfall synoptic time periods, respectively. 

The mean RMS error for the 1947–2000 time period for 12 

target wells for the MODFLOW conduit-flow and diffuseflow Edwards aquifer models are similar (14.7 and 15.5 feet, 

respectively). The mean RMS error for the MODFLOW 

diffuse-flow Edwards aquifer model is smaller than for the 

MODFLOW conduit-flow Edwards aquifer model for six of 

the 12 target wells with long-term water-level measurements. 

Conversely, the mean RMS error for the MODFLOW diffuseflow Edwards aquifer model is larger than for the MODFLOW 

conduit-flow Edwards aquifer model for six of the 12 target 

wells.

The mean RMS error for the five simulated springs 

(Comal, San Marcos, Leona, San Antonio, and San Pedro) 

for the time period 1947–2000 is minimally higher (1.1 cubic 

feet per second) for the MODFLOW diffuse-flow Edwards 

aquifer model than for the MODFLOW conduit-flow Edwards 

aquifer model (table 2). For the same time period, the RMS 

error is lower (7.1 cubic feet per second) for Comal Springs 

and higher (1.0 cubic foot per second) for San Marcos Springs 

for the MODFLOW diffuse-flow Edwards aquifer model than 

for the MODFLOW conduit-flow Edwards aquifer model. 

The mean algebraic differences between the simulated and 

measured springflows indicate that the springflows are lower 

for all springs, except San Antonio Springs, for the MODFLOW diffuse-flow Edwards aquifer model as compared 

to the MODFLOW conduit-flow Edwards aquifer model. 

This, coupled with the observation that greater differences 

between simulated and measured springflows for the diffuseflow model than for the conduit-flow model occur during 

the periods of greatest springflows, might indicate that the 

MODFLOW diffuse-flow Edwards aquifer model is somewhat 

less responsive than the MODFLOW conduit-flow Edwards 

aquifer model (Lindgren, 2006).

Hydraulic heads and springflows simulated by the 

MODFLOW conduit-flow Edwards aquifer model for selected 

observation wells and springs were compared to the corresponding hydraulic heads and springflows simulated by the 

GWSIM model. The time periods used for the comparisons 

were 1947–59 and 1978–89 because published simulated 

hydraulic heads and springflows for the GWSIM model were 
10 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

available for these time periods (Thorkildsen and McElhaney, 

1992). Comparisons of simulated hydraulic heads and springflows were made for the 1947–59 and 1978–89 periods using 

the Bexar County index well (J–17) and Comal and San Marcos Springs. Also, hydraulic heads simulated by the MODFLOW conduit-flow Edwards aquifer model for 25 observation wells, in addition to the Bexar County index well, were 

compared to the corresponding hydraulic heads simulated by 

the GWSIM model for the 1978–89 time period. Hydraulic 

heads simulated by the GWSIM model for this time period 

were provided by LBG-Guyton Associates (Andrew Donnelly, 

LBG-Guyton Associates, written commun., 2003). Head data 

from one well (Frio River well 6935501) provided by LBGGuyton Associates was not used in the comparison between 

the MODFLOW conduit-flow Edwards aquifer model and the 

GWSIM model because an accurate location for the well is not 

available. 

The RMS error of the residuals and the RMS error 

as a percentage of the range of the measured values for 

the MODFLOW conduit-flow Edwards aquifer model are 

Table 2. Residual statistics for models of the San Antonio segment of the Edwards aquifer, south-central Texas.

[RMSE, root mean square error between simulated and measured hydraulic heads and springflows; --, not applicable or data not available]

Type of 

measurement Time period Number of wells

Hydraulic head residuals

(feet)

GWSIM model MODFLOW 

conduit-flow model

MODFLOW 

diffuse-flow model

RMSE (RMSE/ 

range)x100 RMSE (RMSE/ range)x100 RMSE (RMSE/ range)x100

Synoptic May–November 1956 

(drought)

175, 171 -- -- 58.7 8.0 33.4 5.0

Synoptic November 1974–July 1975 

(above normal)

172, 169 -- -- 33.5 5.0 25.8 4.0

Hydrographs 1947–59 1 (Bexar Co. 

index well)

7.4 11.3 5.2 7.9 -- --

Hydrographs 1978–89 1 (Bexar Co. 

index well)

12.7 18.4 9.9 14.5 -- --

Hydrographs 1978–89 26 17.4 35.3 26.3 58.1 -- --

Hydrographs 1947–2000 12 -- -- 14.7 13.3 15.5 14.5

Spring Time period Number 

of springs

Springflow residuals 

(cubic feet per second)

GWSIM model MODFLOW 

conduit-flow model

MODFLOW 

diffuse-flow model

RMSE (RMSE/ 

range)x100 RMSE (RMSE/ range)x100 RMSE (RMSE/ range)x100

All simulated1 1947–2000 5 -- -- 27.1 14.3 28.2 15.0

Comal 1947–59 1 60.2 14.8 30.9 7.6 -- --

Comal 1978–89 1 63.0 15.7 58.8 14.7 -- --

Comal 1947–2000 1 -- -- 45.9 9.5 38.8 8.1

San Marcos 1947–59 1 43.5 20.2 23.1 10.7 -- --

San Marcos 1978–89 1 68.0 22.8 38.3 12.8 -- --

San Marcos 1947–2000 1 -- -- 31.2 7.0 32.2 7.2

1

 Comal, San Marcos, Leona, San Antonio, and San Pedro Springs.
Evaluation of Numerical Groundwater Flow Models 11

appreciably smaller than those for the GWSIM model for both 

time periods (1947–59 and 1978–89) for the Bexar County 

index well (J–17) and for San Marcos Springs, and for the 

1947–59 time period for Comal Springs (table 2). The RMS 

errors for the Bexar County index well for the GWSIM model 

are about 42 and 28 percent greater than those for the Edwards 

aquifer model for the 1947–59 and 1978–89 time periods, 

respectively. For San Marcos Springs, the RMS errors for the 

GWSIM model are about 88 and 78 percent greater for the 

1947–59 and 1978–89 time periods, respectively. Conversely, 

the statistical measures for the MODFLOW conduit-flow 

Edwards aquifer model generally are larger than those for 

the GWSIM model for the observation wells in and near the 

recharge zone (unconfined conditions) (Lindgren and others, 

2004). The statistical measures for the MODFLOW conduitflow Edwards aquifer model and the GWSIM model generally 

are similar for observation wells in the confined zone of the 

aquifer (Lindgren and others, 2004).

The RMS error in some cases is not a complete measure 

of the goodness of fit between the measured and simulated 

hydraulic heads. In the case of three wells, the hydrographs 

indicate that the MODFLOW conduit-flow Edwards aquifer 

model more accurately simulates the magnitude and pattern of fluctuations in measured water levels than does the 

GWSIM model, although the residual statistics are smaller 

for the GWSIM model than for the MODFLOW conduit-flow 

Edwards aquifer model (Lindgren and others, 2004).

The goodness of fit between measured and simulated 

hydraulic heads and springflows also is influenced by the 

time period of the comparison. Eight of the 26 wells used 

in the comparison between the MODFLOW conduit-flow 

Edwards aquifer model and the GWSIM model were used 

as calibration targets in the MODFLOW conduit-flow 

Edwards aquifer model for longer time periods (for most 

wells, 1947–2000) than the 1947–59 and 1978–89 periods 

(Lindgren and others, 2004). For four of the eight wells, the 

residual statistics for the MODFLOW conduit-flow Edwards 

aquifer model were smaller (indicating a closer match between 

measured and simulated hydraulic heads) for the longer time 

period than those for the shorter time period. For three of 

the eight wells, the residual statistics for the MODFLOW 

conduit-flow Edwards aquifer model for the longer time 

period were smaller than the residual statistics for the 1978–89 

time period for the GWSIM model. The values of RMS error 

as a percentage of the range of measured values are smaller 

for the longer time periods because the decreases or comparatively small increases in the RMS errors are coupled 

with greater ranges in measured hydraulic heads. The residual 

statistics for the Bexar County index well (J–17) and for 

Comal and San Marcos Springs for the longer time period 

are about equal to the average of those for the 1947–59 and 

1978–89 time periods. The residual statistics indicate that, 

in some cases, the goodness of fit for any given time period 

does not accurately reflect the goodness of fit for a longer 

time period for which measured hydraulic heads might be 

available. 

To summarize: The comparison of the RMS error and the 

RMS error as a percentage of the range of measured values 

for the MODFLOW conduit-flow and diffuse-flow Edwards 

aquifer models and the GWSIM model indicates some of 

the differences and comparative strengths and weaknesses of 

the models. The MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer models were calibrated for transient conditions for the entire period from 1947–2000, whereas the 

GWSIM model was calibrated for two separate, much shorter 

time periods, 1947–59 and 1978–89. As discussed previously, 

the residual statistics indicate that, in some cases, the goodness 

of fit for any given time period does not accurately reflect 

the goodness of fit for a longer time period for which measured hydraulic heads might be available. This illustrates 

the value and importance of relatively long transient calibration periods that encompass a range of hydrologic conditions 

and the potential for erroneous conclusions regarding goodness of fit based on comparatively short periods of comparison between measured and simulated hydraulic heads and 

springflows.

A noteworthy limitation of the GWSIM model is the 

means used to best match the measured flows for San Marcos 

Springs. In the GWSIM model, 43 percent of the total basin 

recharge for the Blanco River Basin was assigned directly 

to the spring cell representing San Marcos Springs to better simulate the local component of flow from the outcrop 

area (Thorkildsen and McElhaney, 1992, p. 7). This means 

of obtaining the best match between measured and simulated 

flows for San Marcos Springs was not necessary for calibration of the MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer models. For San Marcos Springs, the RMS 

errors for the GWSIM model are (as noted previously in this 

section) about 88 and 78 percent greater for the 1947–59 and 

1978–89 time periods, respectively, than for the MODFLOW 

conduit-flow Edwards aquifer model, despite the application 

of recharge water directly to the spring cell representing San 

Marcos Springs. 

Barton Springs Segment

The RMS errors for the Barton Springs segment GAM 

model, recalibrated GAM model, and MODFLOW–DCM 

conduit model are shown in table 3. These statistics are used 

as quantitative measures of the goodness of fit between the 

measured and simulated hydraulic heads and springflows. The 

RMS error and the RMS error as a percentage of the range of 

measured values for hydraulic heads for 10 target wells are 

much smaller for the Barton Springs segment recalibrated 

GAM model (RMS error of 18.5 feet) than that for the Barton 

Springs segment GAM model (RMS error of 86.8 feet) for the 

period including the 1950s drought (1950–59). The RMS error 

and the RMS error as a percentage of the range of measured 

values for springflows are similar for the two models for the 

1950–59 period as a whole. However, the values of these 

statistical measures are lower for the Barton Springs segment 

recalibrated GAM model than for the Barton Springs segment 
12 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

GAM model for the time periods when springflow is less than 

18 cubic feet per second (table 3).

Because the Barton Springs segment GAM model was 

calibrated to a relatively wet period, it tends to overestimate 

springflows and underestimate water-level altitudes compared 

with measurements collected during the 1950s drought-ofrecord. In contrast, the Barton Springs segment recalibrated 

GAM model was calibrated specifically to better match measured springflow and water-level data from the 1950s drought, 

resulting in the lower RMS error and RMS error as a percentage of the range of measured values for the Barton Springs 

segment recalibrated GAM model.

The Barton Springs segment recalibrated GAM model 

provides a good match between simulated and measured water 

levels for the 1950s drought conditions during periods of 

lowest flow, particularly during July and August 1956 (Smith 

and Hunt, 2004). During periods when recharge increases to 

near-average conditions, such as in 1953, simulated waterlevel altitudes in the Barton Springs segment recalibrated 

GAM model tend to be higher than the measured values. 

This might be due to the inability of the model to simulate 

high rates of conduit flow during high water-level conditions. 

However, the Barton Springs segment recalibrated GAM 

model succeeds in adequately simulating periods of low flow, 

Table 3. Residual statistics for models of the Barton Springs segment of the Edwards aquifer, south-central Texas.

[GAM, Groundwater Availability Modeling; RMSE, root mean square error between simulated and measured hydraulic heads and springflows; DCM, dual 

conductivity model; --, not applicable or data not available]

Type of 

simulation

Type of 

measurement Time period Number of wells

Hydraulic head residuals 

(feet)

GAM model

(MODFLOW)

Recalibrated 

GAM model

(MODFLOW)

MODFLOW–DCM 

conduit model

RMSE (RMSE/ 

range)x100 RMSE (RMSE/ range)x100 RMSE (RMSE/ range)x100

Steady-state Synoptic July–August 1999 99, 74 24 7 -- -- 16.8 6

Transient Synoptic March–April 1994 27 29 11 -- -- -- --

Transient Synoptic July–August 1996 23 37 10 -- -- -- --

Transient Synoptic July–August 1998 35 64 22 -- -- -- --

Transient Hydrographs 1989–98 8 3.8–83.7 16–63+ -- -- -- --

Transient Synoptic 1950–59; lowest 

measured values

10 86.8 39.1 18.5 8.3 -- --

Type of 

simulation Spring Time period Numberof springs

Springflow residuals 

(cubic feet per second)

GAM model

(MODFLOW)

Recalibrated 

GAM model

(MODFLOW)

MODFLOW–DCM 

conduit model

RMSE (RMSE/ 

range)x100 RMSE (RMSE/ range)x100 RMSE (RMSE/ range)x100

Steady-state Barton July–August 1999 1 0 -- -- -- -- --

Transient Barton 1989–98 1 12 11 -- -- -- --

Transient Barton 1950–59 1 12.4 21 13.8 23 -- --

Transient Barton 1950–59; flow less 

than 18 cubic 

feet per second

1 9.7 16 6.0 10 -- --
Evaluation of Numerical Groundwater Flow Models 13

such as during 1952 and 1954–56. The lowest monthly mean 

flow from Barton Springs was 11 cubic feet per second from 

four flow measurements in July and August 1956 (Slade 

and others, 1986). Subtracting a pumping rate of 0.66 cubic 

foot per second from 13.7 cubic feet per second (simulated 

springflow by the Barton Springs segment GAM model under 

1950s drought conditions with no pumping) yields a difference 

of about 2 cubic feet per second between the Barton Springs 

segment GAM model results and measured values of springflow. The Barton Springs segment recalibrated GAM model 

was able to simulate a springflow of 11 cubic feet per second, 

matching the lowest monthly mean for measured springflow 

(Smith and Hunt, 2004).

The RMS error and the RMS error as a percentage of the 

range of measured values for hydraulic heads are smaller for 

the MODFLOW–DCM conduit model (74 target wells) than 

for the Barton Springs segment GAM model (99 target wells) 

for a steady-state simulation representing average conditions 

for July–August 1999 (table 3). The MODFLOW–DCM 

conduit model produces substantially lower springflows and 

better matches to the measured springflows during the peak 

discharge events in 1992, 1997, and 1998 than does the Barton 

Springs segment GAM model. The substantially lower peaks 

during the periods of high recharge are caused by the simulation of turbulent flow in the model (Painter and others, 2007). 

In the Edwards aquifer, springflow responds very quickly to 

changes in recharge. In the Barton Springs segment GAM and 

recalibrated GAM models, this rapid spring response time was 

reproduced by decreasing specific yield and specific storage in 

the system. Although this strategy was successful in matching 

springflow hydrographs, it resulted in water-level hydrographs 

that are overly responsive (Painter and others, 2007). The 

Barton Springs segment GAM and recalibrated GAM models 

(Scanlon and others, 2002; Smith and Hunt, 2004) produce 

unrealistic rises in hydraulic head at many wells, with the discrepancy as large as 250 feet at one well during 1992 (Painter 

and others, 2007). The MODFLOW–DCM conduit model 

produces a much more subdued water-level hydrograph that 

better matches the observed water levels. This ability to match 

both the rapid spring response and the more subdued waterlevel hydrographs demonstrates the inherent flexibility in the 

MODFLOW–DCM conduit model to match both low base 

flows and large spring discharges (Painter and others, 2007).

To summarize: The inherent limitation of the Barton 

Springs segment GAM and recalibrated GAM models is that 

they were each calibrated to match measured water levels and 

springflows for a relatively narrow range of hydrologic conditions. The Barton Springs segment GAM model has calibrated 

hydraulic conductivity and storativity values that are appropriate for (and best match water levels and springflows for) average and above-average precipitation and recharge conditions. 

The Barton Springs segment recalibrated GAM model has 

calibrated hydraulic conductivity and storativity values that 

are appropriate for (and best match water levels and springflows for) low precipitation and recharge (drought) conditions. 

Simulated hydraulic conductivity and storativity values for the 

aquifer under 1950s drought conditions were expected to be 

lower (as compared to those of the Barton Springs segment 

GAM model) (Smith and Hunt, 2004) because of differences 

in the simulated hydrologic conditions and the resulting lower 

simulated hydraulic heads for the Barton Springs segment 

recalibrated GAM model. However, the inability of either 

model to adequately match measured water levels and springflows under differing hydrologic conditions is a substantial 

limitation, which increases the uncertainty of the simulated 

results.

The principal advantage of the MODFLOW–DCM 

conduit model is the ability to adequately simulate measured 

water levels and springflows for the full range of hydrologic 

conditions (above-average precipitation and recharge conditions and drought conditions) using the same set of hydraulic 

properties (hydraulic conductivity and storativity). 

Agreement with Dye-Tracer Tests

Many of the capabilities, limitations, and modifications of the various models relative to their handling of karst 

characteristics have already been described in the preceding 

sections. One of the continuing points of debate regarding the 

application of these models to Edwards aquifer well assessments is in regard to the accuracy of model-derived groundwater flow directions and perceived discrepancies between 

simulated and tracer-inferred flow characteristics. At issue is 

the predictive capability, that is, how well do model-derived 

flow paths predict actual groundwater flow directions in parts 

of the aquifer that are conduit dominated? To make this determination objectively, it would be necessary to design a study 

wherein a targeted series of dye-tracer tests were conducted to 

test flow directions predicted by model output (particle tracking) in various parts of the aquifer under specified hydrologic 

conditions. Given the scarcity of existing tracer-inferred flow 

paths, variability in the timing and hydrologic conditions 

under which dye-tracer tests have been conducted, and relative 

lack of one-to-one correlation between the time periods during 

which tracer tests have been conducted and model-simulated 

stress periods, only relatively broad generalizations can be 

made with regard to agreement between model output and 

dye-tracer tests. 

Groundwater Flow Directions

As noted, dye-tracer test data are relatively sparse 

or lacking in many parts of the Edwards aquifer. For this 

evaluation, groundwater flow directions inferred from model 

outputs (simulated potentiometric surfaces) were compared 

with tracer-inferred flow paths obtained from dye-tracer tests 

conducted in the San Antonio and Barton Springs segments of 

the Edwards aquifer during 1996–2002 and 2005 (Worthington, 2003; Schindel and others, 2005; Hunt and others, 2006). 

Additional data obtained from several unpublished dye-tracer 

tests conducted during 2004–05 in the San Marcos Springs 
14 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

area in the San Antonio segment were provided for evaluation 

by the EAA (Steven Johnson, Edwards Aquifer Authority, 

written commun., 2008). Results of approximately 20 dye 

injections conducted in the Barton Springs segment have been 

plotted as curvilinear dye flow paths that conform to gradients of mapped potentiometric-surface contours and illustrate 

conjectured tributary junctions between individual conduitdominated flow paths (fig. 2). 

In other locations, previously reported dye-tracer test 

results have been plotted as straight-line vectors used solely to 

represent the point-to-point connections between dye injection sites and dye recovery or dye detection sites (fig. 3). The 

trajectories, distances, and apparent upstream sources and 

downstream receptors of water represented by these dye-tracer 

flow paths are constrained by the time period and detection 

method used during the individual dye-tracer tests and by the 

numbers and locations of dye injection and dye recovery sites. 

Ideally the comparison between tracer-inferred flow 

paths and model-derived flow paths would be conducted 

under the same hydrologic conditions. Most of the reported 

dye-tracer tests have been conducted under high-flow hydrologic conditions. For the present evaluation, dye-tracer flow 

paths were compared with simulated potentiometric surfaces 

obtained from the MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer models for the September 1998 model stress 

period, assumed to be representative of average hydrologic 

conditions (fig. 2), or with simulated particle tracks derived 

from output of steady-state conditions (1939–46 time period) 

(fig. 3). These two models include the San Antonio and Barton 

Springs segments of the Edwards aquifer and adequately 

Figure 2. Comparison of inferred dye-tracer flow paths in the Barton Springs segment of the Edwards aquifer, south-central Texas, 

with simulated potentiometric-surface contours for September 1998 derived from the MODFLOW conduit-flow Edwards aquifer model. 

River

AVIS

Buda

San Marcos

Onion

Creek

560

600

540

640

800

500

520

580

640

480

660

760

780

760

440

740

720

700

680

660

460

620

580

560

540

520

620

600

Barton Springs segment

Inferred dye-tracer flow path

Flow path that terminates at spring

Flow path that terminates at local well

Simulated potentiometric-surface

contour—Shows altitude at which water

level would have stood in tightly cased

well; interval 20 feet. Datum is 

NGVD 29

EXPLANATION

0 4 8 MILES

97°50'

98°

30°

97°40'

30°10'

Base from:

U.S. Geological Survey digital data—

rivers, lakes, and reservoirs

Texas Natural Resources Information 

System—cities

National Atlas of the United States—roads

Texas Water Development Board—Edwards 

aquifer Balcones fault zone

Projection: Albers

Linear unit: Foot

Datum: NAD 83
Evaluation of Numerical Groundwater Flow Models 15

SAN ANTONIO

Rosillo

Creek

Creek

Walzem

Creek

Beitel

Creek

Salado

Creek

Mud

Creek

Creek

Elm

Elm

Elm

East

West

Creek

Creek

Mud

Creek

Cibolo

Elm

Waterhole

Creek

Springs

Pathner

River

San

Antonio

281

281

410

410

35

35

1604

1604

281

368

EXPLANATION

Edwards aquifer (unconfined)

Edwards aquifer (confined)

Tracer-inferred flow path

Simulated particle track

Base from:

U.S. Geological Survey digital data—rivers, 

lakes, and reservoirs

General Land Office of Texas—cities

National Atlas of the United States—roads

Texas Water Development Board—Edwards

aquifer Balcones fault zone

Texas Centric Mapping System

Projection: Albers Equal Area

Linear unit: Meter

Datum: NAD 83

0 2 4 MILES

98°32' 98°30' 98°28' 98°26' 98°24' 98°22'

29°40'

29°38'

29°36'

29°34'

29°32'

29°30'

Figure 3. Comparison of inferred dye-tracer flow paths and simulated particle tracks derived from output of MODFLOW conduit-flow 

model of steady-state conditions (1939–46 time period) in the San Antonio segment of the Edwards aquifer, northern Bexar County, 

south-central Texas (modified from Steven Johnson, Edwards Aquifer Authority, written commun., 2008). 
16 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

simulate hydraulic heads and springflows for the full range of 

hydrologic conditions, except for the eastern part of the Barton 

Springs segment. For the eastern part of the Barton Springs 

segment of the aquifer, the MODFLOW conduit-flow and 

diffuse-flow Edwards aquifer models incorporate the hydraulic properties from the Barton Springs segment GAM model 

and, therefore, share the limitations of that model for that 

part of the model area. The hydraulic heads, and particularly 

the springflows, are poorly simulated for drought conditions. 

However, the Barton Springs segment GAM model does 

adequately simulate hydraulic heads and springflows for average and high-flow hydrologic conditions, consistent with the 

hydrologic conditions for most of the dye-tracer tests.

As a general observation, wherever the models accurately 

simulate the locations and configurations of major potentiometric-surface troughs and groundwater divides, a good 

general agreement between model-inferred and tracer-inferred 

groundwater flow directions can be observed. In the Barton Springs segment, relatively good agreement is observed 

between output from the MODFLOW conduit-flow and 

diffuse-flow Edwards aquifer models and plotted dye-tracer 

flow paths. Here, groundwater flow directions indicated by 

both model outputs and dye-tracer tests are largely influenced 

by the presence of a major east-northeast-trending potentiometric-surface trough (fig. 2). In karstic carbonate aquifers, 

such groundwater troughs generally are coincident with the 

locations of major conduit drains, zones of enhanced fracture 

or solution permeability, or some combination of these. A relatively high density of dye-tracer injections conducted in the 

Barton Springs segment confirms that flow directions in the 

aquifer follow the slope of hydraulic head gradients that define 

the presence of the trough. The MODFLOW conduit-flow and 

diffuse-flow Edwards aquifer models incorporate known and 

conjectured conduit-dominated flow paths through the Barton 

Springs segment as zones of higher hydraulic conductivity, as 

does the Barton Springs segment GAM model, and effectively 

replicate the configuration of the groundwater trough. The 

models therefore yield potentiometric-surface contours that 

match quite well with tracer-inferred flow paths delineated in 

the Barton Springs segment (fig. 2).

In other locations where groundwater flow directions 

inferred by MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer model output show a general agreement 

with results of dye-tracer tests, it is uncertain to unlikely that 

interpretations of model output alone, or made prior to data 

obtained by dye tracing, are sufficient to predict complex, 

local flow directions in the aquifer. Results of dye-tracer tests 

conducted in 2005 in the Barton Springs segment and groundwater flow model simulations (Lindgren and others, 2004) 

indicated the presence of a groundwater divide separating 

the Barton Springs and San Antonio segments that had been 

inferred from previous dye-tracer tests conducted in 2002 

(Hunt and others, 2005; Hunt and others, 2006). However, the 

2005 dye-tracer test results also provided evidence indicating 

that the position of the groundwater divide might fluctuate in 

response to changes in local hydrologic conditions (Hunt and 

others, 2006). During periods of relatively low flow conditions 

such as those occurring in 2005, the groundwater divide seems 

to disappear as water levels in wells near San Marcos Springs 

decrease to altitudes lower than the altitude of the spring pool, 

implying that, under these conditions, groundwater might flow 

north across the divide and toward Barton Springs. Similarly, 

transient groundwater flow model simulations for 1947–2000 

(Lindgren and others, 2004) indicated that during drought conditions the position of the groundwater divide shifts westward 

to near San Marcos Springs, and recharge from the Blanco 

River moves eastward toward Barton Springs, rather than 

westward toward San Marcos Springs.

Hydraulic heads in the aquifer are influenced by the 

amount of water recharging at major karst features such as 

sinking streams, and local mounding of the potentiometric 

surface in the vicinity of such recharge features in the San 

Antonio segment has been observed under high flow conditions (Hunt and others, 2005). Both the 2002 and 2005 dyetracer tests were conducted during periods of relatively high 

flow conditions in the aquifer. However, the flow conditions 

in 2002 were judged to have been higher than those during 

the 2005 dye injections (Hunt and others, 2006). Substantially 

lower flows in the Blanco River (fig. 1) and Onion Creek 

(fig. 2)—two losing or sinking streams in the study area—during 2005 compared to 2002 are thought to have resulted in 

a reduction of local recharge, decrease of hydraulic heads, 

and decrease in hydraulic gradients across the groundwater 

divide in this part of the aquifer. The complexity of groundwater flow directions and hydraulic response in this part of the 

aquifer could not have been deduced from the regional-scale 

MODFLOW conduit-flow and diffuse-flow Edwards aquifer 

models, even though some arching or mounding of the simulated potentiometric surface is recognizable around the 600- to 

620-foot contours on the map in figure 2. In karst aquifers 

where temporal variations in conduit-dominated flow paths 

are likely to occur, identification and confirmation of flow 

complexities such as the bifurcation of local flow paths are 

best made using results of dye-tracer tests and are not likely to 

be determined on the basis of model-generated potentiometricsurface gradients. 

 In other locations where Edwards aquifer karst characteristics are not as well characterized and thus not adequately 

represented by model input data, agreement between model 

output and tracer-inferred flow paths are not particularly good 

and are sometimes subject to error. This is illustrated in a part 

of the Panther Springs Creek Basin of the San Antonio segment where predictions of flow directions in the aquifer in this 

area are complicated by the presence of faults and uncertainties regarding possible direction and extent of solutional conduit development. There, groundwater flow paths generated 

by output from the MODFLOW conduit-flow Edwards aquifer 

model differ considerably from tracer-inferred flow paths 

(fig. 3) obtained by dye injections conducted during 2004–05 

from various well locations in Bexar County (Johnson and 

others, in press). The tracer-inferred flow paths indicate that 

groundwater flows south, apparently crossing a series of 
Evaluation of Numerical Groundwater Flow Models 17

east-west-trending fault traces (not shown in fig. 3) (Schindel 

and others, 2005). The apparent trends of the tracer-inferred 

flow paths are oriented almost orthogonally to the trends of 

the mapped fault traces and to the simulated groundwater 

flow paths predicted by the MODFLOW output (Johnson and 

others, in press). An additional complication is that natural 

hydraulic gradients in this area have been altered by large 

withdrawals from San Antonio water-supply wells. Although 

the tracer-inferred flow directions in the aquifer were not 

predicted by simulation, model calibration results reported 

by Lindgren (2004) indicate that major groundwater conduits 

with relatively high hydraulic capacity might exist in northern Bexar County. Specifically, large positive head residuals 

resulted from simulations in that area. Therefore, the model 

probably underrepresents the number of conduit-dominated 

flow paths or hydraulic influence of conduit-dominated flow 

paths, or both, in that area. 

Tracer-Inferred Groundwater Flow Velocities

The issue of numerically estimated groundwater flow 

velocities and travel times deserves consideration, for it is this 

issue that highlights the greatest apparent disparity between 

model output and dye-tracer test results. The use of a distributed, porous media model to simulate flow in a karst system 

requires simplification of aquifer hydraulic characteristics, 

and except for the MODFLOW–DCM model, all models 

reviewed here apply Darcian flow equations and are incapable of simulating the rapid, turbulent flow conditions likely 

prevalent along conduit-dominated flow paths. Time-of-travel 

obtained by the existing numerical groundwater flow models 

and the SWAP methodology is almost certainly overestimated 

(is too long) for parts of the aquifer where conduit-dominated 

flow occurs. Dye-tracer tests conducted in the Edwards 

aquifer routinely yield results indicating flow velocities of 

thousands of feet per day, whereas the maximum flow velocities obtained in the numerical simulations typically are two to 

three orders of magnitude lower. PWS well assessments done 

using the SWAP–DSS software apply a standardized 27-foot 

per day average flow velocity, a value based on literaturereported velocities obtained by methods other than tracer tests 

(R.L. Ulery, U.S. Geological Survey, written commun., 2008). 

This average flow velocity is in marked contrast with velocity ranges commonly reported for dye-tracer test results. For 

example, groundwater velocities ranging from 3,000 to 12,000 

feet per day were inferred from results of dye-tracer tests conducted during 2003–04 in the San Antonio segment near the 

recharge zone of the aquifer (Schindel and others, 2005). 

A full discussion of this topic, as well as methods that 

might be applied in addressing it, is beyond the scope of this 

report. However, future development and use of models such 

as MODFLOW–DCM that explicitly incorporate conduit 

hydraulic equations might yield better approximations of 

the range of groundwater flow velocities and time-of-travel 

characteristics obtained by dye-tracer tests conducted in the 

Edwards aquifer. 

The USGS has recently released the Conduit Flow 

Process (CFP) module for MODFLOW–2005 (Shoemaker 

and others, 2008). The CFP module provides the capability 

to simulate laminar or turbulent groundwater flow in dualporosity and conduit-dominated aquifers. The CFP module 

has three simulation modes: Mode 1 allows for simulation 

of flow within a discrete network of cylindrical conduits 

(or pipes); Mode 2 allows for simulation of flow within a 

preferential, high-conductivity model layer in which flow 

can transition between laminar and turbulent; and Mode 3 

allows for simultaneous simulation of flow within a conduit 

network and high-conductivity model layer. Conduits might 

represent dissolution or biological burrowing features in carbonate aquifers, voids in fractured rock, or lava tubes in basaltic aquifers. Preferential flow layers might represent a porous 

media in which turbulent flow is suspected to occur under the 

observed hydraulic gradients; a single, secondary-porosity 

subsurface feature such as a well-defined, laterally extensive 

cave; or a horizontal layer consisting of many interconnected 

voids. 

Application of the CFP module likely would enhance 

the ability of USGS MODFLOW-based models to simulate 

conduit flow in karst aquifers, including the Edwards. However, regardless of which type of conduit-modified modeling 

code might be applied in future PWS well assessments—

MODFLOW–DCM or MODFLOW–2005 with the CFP module—effective simulation of a conduit-dominated flow system 

in the Edwards aquifer will require the collection of large 

amounts of field data throughout the extent of the aquifer, 

particularly through the use of quantitative dye-tracer tests and 

carefully designed aquifer tests. 

Limitations of Models

All numerical groundwater flow models are simplifications of the real system and therefore have limitations. Many 

limitations are inherent to all six of the models discussed in 

this report, whereas some limitations are specific to or more 

apparent for one or more, but not all, of the models. Limitations that are inherent to all six models are related to the 

quality and quantity of the input data, the scale at which the 

model can be applied, and the assumptions used to develop 

the conceptual and numerical models (table 4). The input 

datasets for all six models are based on sparse information 

for some properties and in some areas. Regarding hydraulic 

properties, the available data for storativity is sparse, and 

the available data for hydraulic conductivity tends to be 

concentrated in some areas and sparse in other areas. Waterlevel data for constructing potentiometric surfaces and well 

hydrographs might affect the evaluation of the goodness of fit 

of the models because comparisons of simulated and measured 

water levels are limited to areas where water levels have been 

measured. The available hydrogeologic data are relatively 

meager for the recharge zone, for the freshwater/saline-water 

transition zone, and for the Kinney County area of the San 

Antonio segment. 
18 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

Table 4. Limitations of models for the Edwards aquifer, south-central Texas.

[GAM, Groundwater Availability Modeling; DCM, dual conductivity model]

Common to all six models: 

1. Quality and quantity of input data: 

 

(A) Datasets based on sparse or clustered information for some properties and in some areas 

 

● Properties and data based on sparse or clustered information: (1) hydraulic conductivity, (2) storativity distribution, 

and (3) water-level data 

● Areas with sparse information: (1) recharge zone, (2) freshwater/saline-water transition zone (MODFLOW conduitflow and diffuse-flow Edwards aquifer models), and (3) Kinney County (San Antonio segment models) 

 

(B) Data of uncertain accuracy that warrant further analysis 

 

● Spatial and temporal distribution of recharge 

● Spatial and temporal distribution of withdrawals by wells 

2. Scale of application: 

(A) Models are regional scale, and therefore their application to local, site-specific issues is not appropriate 

(B) Local effects and water-level declines and flow directions depend on site-specific hydraulic properties and hydrologic 

conditions and thus need to be addressed with a finer grid discretization and with estimates of local hydraulic properties 

and hydrologic conditions 

3. Assumptions for conceptual and numerical models: 

(A) Discretization of the model grid 

● Vertical—one model layer 

 

● Horizontal—relatively coarse cell size 

 

(B) Temporal discretization for transient simulation—monthly stress periods 

 

(C) Uncertainties regarding flow across northern, southern, and lower model boundaries 

 

Common to all models except the MODFLOW–DCM conduit model: 

 

1. Use of a Darcian, laminar flow model to simulate flow in a karst system results in 

 

(A) Inability to simulate rapid, potentially turbulent flow in conduits 

 

(B) Inability to simulate fast travel times in the aquifer 

(C) Inability to simulate vertical heterogeneity of the aquifer 

 
Evaluation of Numerical Groundwater Flow Models 19

Recharge data for the area of the models generally are 

considered much more accurate than are recharge data available for many other regions. However, the recharge estimates 

are based on streamflow data from gaging stations that in 

some cases are appreciably upstream from or downstream 

from the Edwards aquifer outcrop area; and for the San 

Antonio segment, computation of recharge estimates involves 

estimated runoff in ungaged areas (about 30 percent of the 

recharge area). Estimates of monthly recharge during periods 

of high runoff probably contain the major errors (Puente, 

1978). In addition, assumptions are made regarding the distribution of the recharge applied in the models, with most of 

the simulated recharge being distributed uniformly along the 

streambeds in the outcrop area. However, little information is 

available regarding the spatial focusing of recharge in particular locations, and the spatial distribution of recharge might 

substantially affect the simulated directions of groundwater 

flow. Withdrawals by wells were compiled and distributed 

temporally and spatially for the models. Factors contributing 

to uncertainty in temporal and spatial distribution of simulated withdrawals include (1) incomplete information for well 

location and construction, (2) lack of withdrawal data for 

individual wells, and (3) the need to temporally and spatially 

distribute withdrawals on the basis of properties other than 

individual withdrawal rates.

All six of the models are regional scale, best suited to 

evaluate variations in spring discharge, regional water-level 

changes, and the relative comparison of regional water-management scenarios. Accuracy and applicability of the models 

decrease when changing from regional to local scale. The 

models are not appropriate for local issues, such as water-level 

declines surrounding individual wells, because of the relatively 

coarse grid sizes. Water-level declines and flow directions 

depend on site-specific hydraulic properties and hydrologic 

conditions and thus need to be addressed with a finer grid 

discretization and with estimates of local hydraulic properties 

and hydrologic conditions.

The assumptions used to develop the conceptual and 

numerical models are related to the discretization of the model 

grids, the temporal discretization for transient simulations, 

and uncertainties regarding flow across the model boundaries. All six of the models use a relatively coarse cell size and 

one model layer. Although substantial vertical heterogeneity 

occurs in the Edwards aquifer, the available information is 

insufficient to delineate hydrogeologic units, and corresponding model layers, on a regional scale. All six of the models 

also use monthly stress periods, although appreciable fluctuations occur in hydraulic heads and springflows over much 

shorter time periods. However, well withdrawals and recharge 

rates are not generally available for shorter than monthly 

Table 4. Limitations of models for the Edwards aquifer, south-central Texas—Continued.

Applicable to GWSIM model: 

1. Lack of accessibility and portability of the model code 

 

2. Limited in its application to the San Antonio segment of the Edwards aquifer 

 

3. Lack of pre- and post-processors for the model 

4. Application of a part of the total basin recharge for the Blanco River Basin directly to the spring cell representing 

 San Marcos Springs to better simulate the local component of flow from the outcrop area 

 

Applicable to the MODFLOW conduit-flow and diffuse-flow Edwards aquifer models: 

 

1. Although the Barton Springs segment of the aquifer is included in the models, calibration was not done for the 

 northern part of the segment (Travis County) 

 

Applicable to Barton Springs segment GAM and recalibrated GAM models: 

 

1. Calibrated to match measured water levels and springflows for a restrictive range of hydrologic conditions, with 

 each model having different hydraulic conductivity and storativity values appropriate to the hydrologic conditions 

 that were simulated 

 

Applicable to the MODFLOW–DCM conduit model: 

 

1. Relative newness of the model code (documented in 2007) and its limited application and testing 

 

2. Present lack of commercially available pre- and post-processors for the model 
20 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

time periods, constraining the length of simulated stress periods. The San Antonio segment models simulate a no-flow 

boundary at the western model boundary, based on the location of a mapped groundwater divide. However, the location of 

the groundwater divide is known to change temporally, introducing uncertainty regarding flow at the simulated boundary. 

In addition, uncertainty exists regarding the hydraulic connection between the Edwards and Trinity aquifers at the northern 

boundaries of the models and the potential for and rate of 

movement of water across the northern model boundaries. 

Numerical groundwater flow model codes, such as the 

GWSIM model code and MODFLOW, developed for Darcian 

flow in porous media-type aquifers, cannot accurately simulate 

both the rapid flow of groundwater through conduits and the 

slow flow and storage of groundwater in the matrix of karst 

aquifers. Because all the models except the MODFLOW–

DCM conduit model are Darcian-flow models, substantial 

limitations are associated with their ability to simulate triple 

porosity and permeability and conduit-dominated flow paths 

characteristic of well-developed karst aquifers. Also the limitation associated with simulating only one model layer (inability 

to simulate vertical heterogeneity of the aquifer) is common to 

all the models except the MODFLOW–DCM conduit model. 

And none of the models, with the possible exception of the 

MODFLOW–DCM conduit model, has a documented capability to accurately simulate travel times for conduit-dominated 

velocities in the Edwards aquifer. Time-of-travel obtained 

by the existing numerical groundwater flow models and the 

SWAP methodology is almost certainly overestimated for parts 

of the aquifer where conduit-dominated flow occurs. However, 

tracer-test-based estimates of flow velocities, particularly for 

varying hydrologic conditions, presently are not readily available for most locations. Assuming tracer-inferred velocity data 

are available for use in model calibration, the MODFLOW–

DCM conduit model might potentially provide improved 

simulation of fast travel times, but currently (2008) that model 

does not have a particle-tracking capability.

The GWSIM model, MODFLOW conduit-flow and 

diffuse-flow Edwards aquifer models, and Barton Springs 

segment GAM and recalibrated GAM models all use zones 

of high hydraulic conductivity to approximate conduit flow. 

This works well for simulating potentiometric surfaces, 

springflows, and regional groundwater flow, but it is unsuitable for simulating the rapid, turbulent flow of groundwater 

through conduits and for simulating conduit-like (nonDarcian) travel times (Scanlon and others, 2003). The GWSIM 

model, MODFLOW diffuse-flow Edwards aquifer model, and 

Barton Springs segment GAM and recalibrated GAM models use relatively broad zones of high hydraulic conductivity, 

with hydraulic conductivity values on the order of thousands 

or tens of thousands of feet per day, to approximate conduit 

flow. The MODFLOW conduit-flow Edwards aquifer model 

uses generally continuously connected, one-cell-wide zones 

with hydraulic conductivity values of as much as 300,000 feet 

per day to approximate conduit flow. A substantial limitation of the MODFLOW conduit-flow Edwards aquifer model 

associated with the representation of conduits is the lack of 

knowledge of the appropriate location and characteristics of 

the simulated one-cell-wide high-permeability zones used 

to represent conduit flow. A network of conduits (generally 

continuously connected, one-cell-wide zones) was simulated, 

although the conduit locations were inferred from few data and 

subject to considerable uncertainty. Considerable uncertainty 

also exists regarding the physical dimensions, connectivity, 

and hydraulic properties of conduits. The physical dimensions 

of the conduits in the model are constrained by the model cell 

dimensions. 

Simulations done for the Barton Springs segment of the 

Edwards aquifer using the MODFLOW–DCM conduit model 

have demonstrated its ability to match both the rapid flow 

of groundwater through conduits and the slow flow and storage of groundwater in the matrix of karst aquifers, as reflected 

in the rapid springflow response and the more subdued 

water-level hydrographs observed for the Edwards aquifer 

(Painter and others, 2007). For the five models other than the 

MODFLOW–DCM conduit model, simulated recessions in 

the springflows tend to be slower than observed, and simulated 

springflows during high-flow periods tend to be larger than 

observed. Also, the simulated water-level hydrographs for 

monitoring wells tend to fluctuate more in response to changes 

in recharge than the observed water-level hydrographs. The 

MODFLOW–DCM conduit model produces substantially 

lower discharge and better matches to the measured discharge 

during the peak discharge events in 1992, 1997, and 1998 than 

does the Barton Springs segment GAM model (Painter and 

others, 2007). The substantially lower peaks during the periods 

of high recharge are because of the ability of the MODFLOW–

DCM conduit model to simulate turbulent conduit flow, which 

decreases flow velocities due to the formation of complex 

flow patterns, such as eddies. The overly responsive simulated 

water-level hydrographs for the five models other than the 

MODFLOW–DCM conduit model are the result of inputting 

relatively small storativity values to simulate the observed 

rapid springflow response to changes in recharge. The MODFLOW–DCM conduit model produces a much more subdued 

water-level hydrograph that better matches the observed water 

levels. Because most of the flow and all of the fast flow is in 

the conduit system of the MODFLOW–DCM conduit model, 

rapid springflow response can be achieved by assigning small 

values to the conduit storage parameters. The storage properties for the diffuse system are then free to be adjusted to match 

the relatively subdued water-level hydrographs. 

Limitations specific to the GWSIM model include 

(1) the lack of accessibility and portability of the model code, 

(2) applicable only to the San Antonio segment of the Edwards 

aquifer, (3) a lack of pre- and post-processors for the model, 

and (4) the application of a part of the total basin recharge for 

the Blanco River Basin directly to the spring cell representing 

San Marcos Springs to better simulate the local component of 

flow from the outcrop area. 

A limitation specific to the MODFLOW conduit-flow 

and diffuse-flow Edwards aquifer models is that, although 
Summary and Conclusions 21

the Barton Springs segment of the aquifer is included in the 

models, calibration was not done for the northern part of the 

segment (Travis County), and the calibrated hydraulic conductivity and storativity values from the Barton Springs segment 

GAM model were used without revision. Therefore that part of 

the MODFLOW conduit-flow and diffuse-flow Edwards aquifer models is subject to the same limitations that are applicable 

to the Barton Springs segment GAM model. 

The limitation specific to the Barton Springs segment 

GAM and recalibrated GAM models is that they were each 

calibrated to match measured water levels and springflows for 

a restrictive range of hydrologic conditions, with each model 

having different hydraulic conductivity and storativity values 

appropriate to the hydrologic conditions that were simulated. 

The Barton Springs segment GAM model has calibrated 

hydraulic conductivity and storativity values that are appropriate for (and best match water levels and springflows for) average and above-average precipitation and recharge conditions. 

The Barton Springs segment recalibrated GAM model has 

calibrated hydraulic conductivity and storativity values that are 

appropriate for (and that best match water levels and springflows for) low precipitation and recharge (drought) conditions. 

The need for two different sets of hydraulic conductivity and 

storativity values increases the uncertainty associated with the 

accuracy of either set of values, illustrates the non-uniqueness 

of the model solution, and probably most importantly demonstrates the limitation of using a one-layer model to represent 

the heterogeneous hydrostratigraphic units (Maclay, 1995, 

fig. 11) composing the Edwards aquifer. 

Limitations specific to the MODFLOW–DCM conduit 

model include (1) the relative newness of the model code 

(documented in 2007) and its limited application and testing 

and (2) the lack of commercially available pre- and postprocessors for the model. Additional validation and testing of 

MODFLOW–DCM is needed. Although hypothetical drought 

conditions with severity comparable to the drought-of-record 

were simulated for the Barton Springs segment of the Edwards 

aquifer using the MODFLOW–DCM conduit model, they do 

not specifically represent the drought of the 1950s.

Summary and Conclusions

The Texas Commission on Environmental Quality 

(TCEQ) has the principal responsibility to assess the sustainability and susceptibility to contamination of source water 

provided by public water system (PWS) wells. A substantial number of PWS wells in south-central Texas withdraw 

groundwater from the karstic, highly productive Edwards 

aquifer. To assess the sustainability and susceptibility to contamination of source water provided by PWS wells, the TCEQ 

wishes to apply numerical groundwater flow models that 

provide the most accurate and scientifically defensible delineation of contributing areas that is possible given the existing 

technological limitations. However, the use of numerical 

groundwater flow models to aid in the delineation of contributing areas for PWS wells in the Edwards aquifer is problematic 

because of the complex hydrogeologic framework and the 

presence of conduit-dominated flow paths in the aquifer. 

The U.S. Geological Survey (USGS), in cooperation with 

the TCEQ, evaluated six published numerical groundwater 

flow models (all deterministic) that have been developed for 

the Edwards aquifer. This report describes the six published 

groundwater flow models developed for the Edwards aquifer 

(San Antonio segment or Barton Springs segment, or both) 

and evaluates the models with respect to accessibility and ease 

of use, range of conditions simulated, accuracy of simulations, 

agreement with dye-tracer tests, and limitations of the models. 

These models are 

1. Finite-difference model of San Antonio segment of 

Edwards aquifer (GWSIM). The GWSIM model uses 

a FORTRAN computer-model code that pre-dates the 

development of MODFLOW to simulate groundwater 

flow in the San Antonio segment of the Edwards aquifer. 

The computer program for the GWSIM model is based on 

the 1971 Prickett-Lonnquist Aquifer Simulation Model. 

2. MODFLOW conduit-flow model of San Antonio and 

Barton Springs segments of Edwards aquifer. The 

MODFLOW conduit-flow model incorporates improvements over previous models by using (1) a user-friendly 

interface, (2) updated computer codes (MODFLOW–96 

and MODFLOW–2000), (3) a finer grid resolution, 

(4) less-restrictive boundary conditions, (5) an improved 

discretization of hydraulic conductivity, (6) more accurate 

estimates of pumping stresses, (7) a long transient simulation period (54 years, 1947–2000), and (8) a refined representation of high-permeability zones or conduits.

3. MODFLOW diffuse-flow model of San Antonio and 

Barton Springs segments of Edwards aquifer. This model 

incorporates an alternative, diffuse-flow conceptualization, which reflects the hypothesis that, although conduits 

likely are present, flow in the aquifer predominately is 

through a network of small fractures and openings sufficiently numerous that the aquifer can be considered a 

porous-media continuum at the regional scale.

4. MODFLOW model of Barton Springs segment of 

Edwards aquifer (Groundwater Availability Modeling 

[GAM] model). The Barton Springs segment GAM model 

was developed to provide (1) a management tool to the 

Barton Springs/Edwards Aquifer Conservation District 

and to the local Regional Water Planning Group and 

(2) a tool for evaluating groundwater availability under 

drought-of-record conditions. 

5. MODFLOW model of Barton Springs segment of 

Edwards aquifer for drought conditions (recalibrated 

GAM model). The Barton Springs segment GAM model 

was recalibrated so that simulated and measured springflow and water-level data from the 1950s drought matched 

better. 
22 Description and Evaluation of Numerical Groundwater Flow Models for the Edwards Aquifer, South-Central Texas

6. MODFLOW–DCM (dual conductivity model) conduit 

model of Barton Springs segment of Edwards aquifer 

incorporating dual conductivity approach and explicit 

simulation of conduits. The MODFLOW–DCM conduit 

model incorporates a solver capable of solving the highly 

nonlinear systems associated with the conduit/matrix 

flow regime under confined/unconfined conditions. The 

Barton Springs segment GAM model was converted to 

a MODFLOW–DCM model by (1) adding a conduit 

layer, (2) reducing hydraulic conductivity in the zones of 

high hydraulic conductivity to values more typical for a 

diffuse-flow system, and (3) increasing storativity in the 

diffuse-flow system to values more typical for a diffuseflow system.

The GWSIM model code is not commercially available, 

is limited in its application to the San Antonio segment of 

the Edwards aquifer, and lacks the ability of MODFLOW to 

easily incorporate newly developed processes and packages to 

better simulate hydrologic processes. MODFLOW is a widely 

used and tested code for numerical modeling of groundwater 

flow, is well documented, and is in the public domain. These 

attributes make MODFLOW a preferred code with regard to 

accessibility and ease of use. The MODFLOW–DCM code 

currently (2008) lacks the wide use and testing associated with 

the MODFLOW code.

The MODFLOW conduit-flow and diffuse-flow Edwards 

aquifer models were calibrated for transient conditions for the 

entire period from 1947–2000, whereas the GWSIM model 

was calibrated for two separate, much shorter time periods, 

1947–59 and 1978–89. The residual statistics indicate that, 

in some cases, the goodness of fit for any given time period 

does not accurately reflect the goodness of fit for a longer time 

period for which measured hydraulic heads might be available. 

This illustrates the value and importance of relatively long 

transient calibration periods that encompass a range of hydrologic conditions and the potential for erroneous conclusions 

regarding goodness of fit based on comparatively short periods 

of comparison between measured and simulated hydraulic 

heads and springflows.

The inherent limitation of the Barton Springs segment 

GAM and recalibrated GAM models is that they were each 

calibrated to match measured water levels and springflows for 

a relatively narrow range of hydrologic conditions. The Barton 

Springs segment GAM model has calibrated hydraulic conductivity and storativity values that are appropriate for average 

and above-average precipitation and recharge conditions. 

The Barton Springs segment recalibrated GAM model has 

calibrated hydraulic conductivity and storativity values that 

are appropriate for low precipitation and recharge (drought) 

conditions. The inability of either model to adequately match 

measured water levels and springflows under differing hydrologic conditions is a substantial limitation, which increases the 

uncertainty of the simulated results.

The principal advantage of the MODFLOW–DCM 

conduit model is the ability to adequately simulate measured 

water levels and springflows for the full range of hydrologic 

conditions (above-average precipitation and recharge conditions and drought conditions) using the same set of hydraulic 

properties (hydraulic conductivity and storativity). 

All of the models except the MODFLOW–DCM conduit 

model have limitations resulting from the use of Darcy’s law 

to simulate groundwater flow in a karst aquifer system where 

non-Darcian, turbulent flow might actually dominate. The 

MODFLOW–DCM conduit model is an improvement in 

the ability to simulate karst-like flow conditions in conjunction with porous-media-type matrix flow. However, the 

MODFLOW–DCM conduit model has had limited application 

and testing and currently (2008) lacks commercially available 

pre- and post-processors. A variety of practical and technical 

limitations characterize the other numerical models. For example, the GWSIM model is limited by (1) the lack of accessibility, portability, and applicability of the model code, (2) the 

lack of pre- and post-processors, and (3) the method used to 

improve the match with measured springflows for San Marcos 

Springs. The MODFLOW conduit-flow and diffuse-flow 

Edwards aquifer models are limited by the lack of calibration 

for the northern part of the Barton Springs segment (Travis 

County) and their reliance on the use of the calibrated hydraulic conductivity and storativity values from the calibrated Barton Springs segment GAM model. The major limitation of the 

Barton Springs segment GAM and recalibrated GAM models 

is that they were calibrated to match measured water levels 

and springflows for a restrictive range of hydrologic conditions, with each model having different hydraulic conductivity 

and storativity values appropriate to the hydrologic conditions 

that were simulated. The need for two different sets of hydraulic conductivity and storativity values increases the uncertainty 

associated with the accuracy of either set of values, illustrates 

the non-uniqueness of the model solution, and probably most 

importantly demonstrates the limitations of using a one-layer 

model to represent the heterogeneous hydrostratigraphic units 

composing the Edwards aquifer. 

In general, the best matches or agreement between 

groundwater flow directions inferred by numerical model 

simulation, and by dye-tracer tests, are observed where model 

outputs accurately reproduce the configuration of the potentiometric surface with regard to the positions of major and 

minor groundwater troughs and divides. Comparison of model 

outputs with actual dye-tracer test data, if available, can be 

helpful in validating predicted groundwater flow paths and in 

correcting or refining simulated groundwater flow directions, 

velocities, and contaminant-transport characteristics, especially in locations where major conduit-dominated flow paths 

are known or suspected to exist. 

None of the models, with the possible exception of the 

MODFLOW–DCM conduit model, has a documented capability to accurately simulate travel times for conduit-dominated 

velocities in the Edwards aquifer. Time-of-travel obtained 

by the existing numerical groundwater flow models and the 

SWAP methodology is almost certainly overestimated for parts 

of the aquifer where conduit-dominated flow occurs. However, 

tracer-test-based estimates of flow velocities, particularly for 
References 23

varying hydrologic conditions, presently are not readily available for most locations. Assuming tracer-inferred velocity data 

are available for use in model calibration, the MODFLOW–

DCM conduit model might potentially provide improved 

simulation of fast travel times, but currently (2008) does not 

have a particle-tracking capability. 

PWS assessments of wells in the Barton Springs segment 

of the Edwards aquifer, and elsewhere where conduit-flow 

conditions are thought to dominate aquifer hydraulic behavior, 

might be enhanced by use of either the MODFLOW–DCM 

model or the newly developed USGS MODFLOW ConduitFlow Process module for MODFLOW–2005, because each 

incorporates a type of dual or triple hydraulic conductivity 

approach and has the capability to explicitly simulate turbulent flow and conduit hydraulic characteristics. Predictions 

made with these models might continue to be subject to large 

uncertainties as the models will require more field data about 

groundwater flow and hydraulic properties in conduit-dominated parts of the aquifer than are available at present. Data 

limitations are particularly acute at present in the San Antonio 

segment, where there is a paucity of available dye-tracer tests 

and a relative lack of knowledge of the location and trends of 

active groundwater conduits. 

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