Diffuse-Flow Conceptualization and 

Simulation of the Edwards Aquifer, 

San Antonio Region, Texas

By R.J. Lindgren

U.S. Department of the Interior

U.S. Geological Survey

In cooperation with the San Antonio Water System

Scientific Investigations Report 2006–5319
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2006

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Box 25286, Denver Federal Center

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Lindgren, R.J., 2006, Diffuse-flow conceptualization and simulation of the Edwards aquifer, San Antonio region, Texas: 

U.S. Geological Survey Scientific Investigations Report 2006–5319, 48 p.
 iii

Contents

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

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

Purpose and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Conceptualization of the Edwards Aquifer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Hydraulic Conductivity and Transmissivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Hydraulic Conductivity Distribution Developed for Conduit-Flow Edwards Aquifer Model . . . . . . . . 6

Hydraulic Conductivity Distribution Developed for Diffuse-Flow Edwards Aquifer Model . . . . . . . . . 7

Ground-Water Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Simulation of Ground-Water Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Numerical Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Numerical Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Steady-State Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Transient Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

Water Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Steady-State Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Transient Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Comparison of Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Model Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Plate

[Plate in pocket]

1. Map showing locations of Edwards aquifer wells with water levels (hydraulic heads) used 

to calibrate diffuse-flow Edwards aquifer model (steady-state and transient calibration 

target wells), San Antonio region, Texas 

Figures

1–2. Maps showing: 

1. Location of ground-water-flow model area, Edwards aquifer segments, and 

physiographic regions, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. Hydrogeologic zones and catchment area (upper parts of stream basins 

that contribute recharge) of the Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . 4

3. Graphs showing simulated relative to measured hydraulic heads, steady-state simulation, 

conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . 13

4. Map showing simulated distribution of hydraulic conductivity for calibrated diffuse-flow 

Edwards aquifer model, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

5. Graphs showing simulated relative to measured hydraulic heads for (A) August 1956 

(stress period 117) and (B) February 1975 (stress period 339), transient simulation, conduitflow and diffuse-flow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . 16
iv 

6–12. Hydrographs showing: 

6. Measured and simulated water levels (hydraulic heads) for Edwards aquifer wells

in (A) Uvalde County and (B) Medina County, diffuse-flow Edwards aquifer model, 

San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

7. Measured and simulated water levels (hydraulic heads) for Edwards aquifer wells

in Bexar County, diffuse-flow Edwards aquifer model, San Antonio region, Texas . . . . . . . . . . . 22

8. Measured and simulated water levels (hydraulic heads) for Edwards aquifer wells

in (A) Comal County and (B) Hays County, diffuse-flow Edwards aquifer model, San 

Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

9. Measured and simulated springflows for (A) Comal Springs and (B) San Marcos 

Springs, 1947–2000, diffuse-flow Edwards aquifer model, San Antonio region, Texas . . . . . . . . 26

10. Measured and simulated springflows for (A) Leona Springs, (B) San Antonio Springs, 

and (C) San Pedro Springs, 1947–2000, diffuse-flow Edwards aquifer model, San 

Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

11. Measured and simulated water levels (hydraulic heads) for (A) Bexar County index 

well (J–17, 6837203) and (B) Uvalde County index well (J–27, 6950302), 1947–2000, 

conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . 28

12. Measured and simulated springflows for (A) Comal Springs and (B) San Marcos 

Springs, 1947–2000, conduit-flow and diffuse-flow Edwards aquifer models, San 

Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Tables

1. Steady-state simulation target wells and residuals, conduit-flow and diffuse-flow Edwards 

aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2. Comparison of the residuals for hydraulic heads, by synoptic water-level time period 

(steady-state, below-normal rainfall [drought], and above-normal rainfall), conduit-flow 

and diffuse-flow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3. Measured and simulated springflows for steady-state simulation, conduit-flow and diffuseflow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4. Transient simulation target wells and residuals for drought conditions, conduit-flow and 

diffuse-flow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5. Transient simulation target wells and residuals for above-normal rainfall conditions, conduitflow and diffuse-flow Edwards aquifer models, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . 43

6. Comparison of the residuals for hydraulic heads and springflows for selected observation

wells and springs, conduit-flow and diffuse-flow Edwards aquifer models, San Antonio 

region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

7. Simulated annual water budget for the steady-state simulation and for 1956 for the transient 

simulation, conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, 

Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Datums

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

(NGVD 29); horizontal coordinate information is referenced to the North American Datum of 1983 

(NAD 83).
Diffuse-Flow Conceptualization and 

Simulation of the Edwards Aquifer, 

San Antonio Region, Texas

By R.J. Lindgren

Abstract

A numerical ground-water-flow model (hereinafter, the 

conduit-flow Edwards aquifer model) of the karstic Edwards 

aquifer in south-central Texas was developed for a previous 

study on the basis of a conceptualization emphasizing conduit 

development and conduit flow, and included simulating 

conduits as one-cell-wide, continuously connected features. 

Uncertainties regarding the degree to which conduits pervade 

the Edwards aquifer and influence ground-water flow, as well 

as other uncertainties inherent in simulating conduits, raised 

the question of whether a model based on the conduit-flow 

conceptualization was the optimum model for the Edwards 

aquifer. Accordingly, a model with an alternative hydraulic 

conductivity distribution without conduits was developed in a 

study conducted during 2004–05 by the U.S. Geological Survey, in cooperation with the San Antonio Water System. The 

hydraulic conductivity distribution for the modified Edwards 

aquifer model (hereinafter, the diffuse-flow Edwards aquifer 

model), based primarily on a conceptualization in which flow in 

the aquifer predominantly is through a network of numerous 

small fractures and openings, includes 38 zones, with hydraulic 

conductivities ranging from 3 to 50,000 feet per day. Revision 

of model input data for the diffuse-flow Edwards aquifer model 

was limited to changes in the simulated hydraulic conductivity 

distribution. The root-mean-square error for 144 target wells 

for the calibrated steady-state simulation for the diffuse-flow 

Edwards aquifer model is 20.9 feet. This error represents about 

3 percent of the total head difference across the model area. 

The simulated springflows for Comal and San Marcos Springs 

for the calibrated steady-state simulation were within 2.4 

and 15 percent of the median springflows for the two springs, 

respectively. The transient calibration period for the diffuseflow Edwards aquifer model was 1947–2000, with 648 monthly 

stress periods, the same as for the conduit-flow Edwards aquifer 

model. The root-mean-square error for a period of drought 

(May–November 1956) for the calibrated transient simulation 

for 171 target wells is 33.4 feet, which represents about 5 percent of the total head difference across the model area. The 

root-mean-square error for a period of above-normal rainfall 

(November 1974–July 1975) for the calibrated transient simulation for 169 target wells is 25.8 feet, which represents about 

4 percent of the total head difference across the model area. The 

root-mean-square error ranged from 6.3 to 30.4 feet in 12 target 

wells with long-term water-level measurements for varying 

periods during 1947–2000 for the calibrated transient simulation for the diffuse-flow Edwards aquifer model, and these 

errors represent 5.0 to 31.3 percent of the range in water-level 

fluctuations of each of those wells. The root-mean-square errors 

for the five major springs in the San Antonio segment of the 

aquifer for the calibrated transient simulation, as a percentage of 

the range of discharge fluctuations measured at the springs, varied from 7.2 percent for San Marcos Springs and 8.1 percent for 

Comal Springs to 28.8 percent for Leona Springs. The rootmean-square errors for hydraulic heads for the conduit-flow 

Edwards aquifer model are 27, 76, and 30 percent greater than 

those for the diffuse-flow Edwards aquifer model for the 

steady-state, drought, and above-normal rainfall synoptic time 

periods, respectively. The goodness-of-fit between measured 

and simulated springflows is similar for Comal, San Marcos, 

and Leona Springs for the diffuse-flow Edwards aquifer model 

and the conduit-flow Edwards aquifer model. The root-meansquare errors for Comal and Leona Springs were 15.6 and 21.3 

percent less, respectively, whereas the root-mean-square error 

for San Marcos Springs was 3.3 percent greater for the diffuseflow Edwards aquifer model compared to the conduit-flow 

Edwards aquifer model. The root-mean-square errors for San 

Antonio and San Pedro Springs were appreciably greater, 80.2 

and 51.0 percent, respectively, for the diffuse-flow Edwards 

aquifer model. The simulated water budgets for the diffuse-flow 

Edwards aquifer model are similar to those for the conduit-flow 

Edwards aquifer model. Differences in percentage of total 

sources or discharges for a budget component are 2.0 percent or 
2 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

less for all budget components for the steady-state and transient 

simulations. The largest difference in terms of the magnitude of 

water budget components for the transient simulation for 1956 

was a decrease of about 10,730 acre-feet per year (about 2 percent) in springflow for the diffuse-flow Edwards aquifer model 

compared to the conduit-flow Edwards aquifer model. This 

decrease in springflow (a water budget discharge) was largely 

offset by the decreased net loss of water from storage (a water 

budget source) of about 10,500 acre-feet per year. 

Introduction

The Edwards aquifer in the Balcones fault zone of southcentral Texas (fig. 1) is one of the most permeable and productive aquifers in the world. The aquifer consists of regionally 

extensive carbonate rocks that crop out within the Edwards 

Plateau and the Balcones fault zone and underlie the Gulf 

Coastal Plain. The northern aquifer boundary is defined by the 

updip limit of contiguous, outcropping rocks of the Edwards 

Group, Georgetown Formation, and their westward stratigraphic equivalents (Edwards rocks). The southern aquifer 

boundary usually is defined by what commonly is referred to as 

the freshwater/saline-water interface and defined on maps as 

the 1,000-milligrams per liter (mg/L) dissolved solids concentration line (fig. 2). This interface marks the northern boundary 

of the freshwater/saline-water transition zone, the zone of the 

aquifer between the 1,000- and 10,000-mg/L dissolved solids 

concentration lines (fig. 2). The San Antonio segment of the 

aquifer primarily includes parts of Kinney, Uvalde, Medina, 

Bexar, Comal, and Hays Counties that lie within and adjacent to 

the Balcones fault zone (fig. 1). This segment is bounded on the 

west and east by ground-water divides near Brackettville and 

Kyle, respectively, and contains the most productive and transmissive parts of the aquifer. The Barton Springs segment of the 

aquifer includes parts of Hays and Travis Counties and is 

bounded on the southwest by the ground-water divide near Kyle 

and on the northeast by the Colorado River. The San Antonio 

segment of the aquifer discharges primarily to Comal and 

San Marcos Springs, whereas the Barton Springs segment 

discharges primarily to Barton Springs (fig. 1).

A numerical ground-water-flow model (hereinafter, the 

original or conduit-flow Edwards aquifer model) of the karstic 

Edwards aquifer in south-central Texas was completed as part 

of a study conducted during 2000–2003 by the U.S. Geological 

Survey (USGS) and The University of Texas at Austin, Bureau 

of Economic Geology (BEG), in cooperation with the U.S. 

Department of Defense and the Edwards Aquifer Authority 

(Lindgren and others, 2004). Karst aquifers can be conceptualized as including a discrete conduit network with frequently turbulent flow conditions, with conduits representing the major 

flow paths in the aquifer. The conceptualization that served as 

the basis for the original Edwards aquifer model emphasizes 

conduit development and conduit flow. As conduit flow might 

be frequently turbulent and restricted to discrete pathways, 

MODFLOW (Harbaugh and others, 2000) is not designed for 

the simulation of conduit flow. Use of a distributed, porousmedia model such as MODFLOW to simulate flow in a karst 

system is a simplification of the flow system. As a way to represent conduits, other than by use of a coupled-continuum pipe 

flow or dual-porosity or triple-porosity model (Birk and others, 

2003; Liedl and others, 2003), conduits were simulated in the 

original Edwards aquifer model by narrow (one-cell, 0.25-mile 

[mi] wide), initially continuously connected zones with large 

hydraulic conductivities (Lindgren and others, 2004).

Although there is evidence to support the conduit-flow 

conceptualization, the degree to which conduits pervade the 

Edwards aquifer and influence ground-water flow remains 

uncertain. An alternative conceptualization, which can be called 

the diffuse-flow conceptualization, reflects the hypothesis that, 

although conduits likely are present, flow in the aquifer predominantly 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. Which is the 

more realistic conceptualization—in other words, whether conduit flow or diffuse flow predominates at the regional scale—is 

an open question. Development of the original Edwards aquifer 

model incorporating the conduit-flow conceptualization thus 

can be considered a test of one reasonable conceptualization. 

Previous numerical, distributed, porous-media, ground-waterflow models of the Edwards aquifer (Klemt and others, 1979; 

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

Scanlon and others, 2002) and other karstic carbonate aquifers 

(for example, the Floridan aquifer system in Florida and in parts 

of Georgia, South Carolina, and Alabama) (Knowles and 

others, 2002; Sepulveda, 2002; Payne and others, 2005) have 

reasonably simulated measured fluctuations in water levels in 

wells and springflow. 

The hydraulic conductivity distribution for the conduitflow Edwards aquifer model includes two components: (1) a 

base hydraulic conductivity distribution based on nonparametric geostatistics, stochastic simulation, and numerical flow simulation and (2) a network of conduits, simulated as continuously connected (other than a break in eastern Uvalde and 

southwestern Medina Counties), one-cell-wide (1,320 feet [ft]) 

zones with very large hydraulic conductivities (as much as 

300,000 feet per day [ft/d]) (Lindgren and others, 2004). The 

simulated flow directions generally are toward the nearest conduit and subsequently along the conduits from the recharge 

zone into the confined zone and toward the major springs. However, the locations of the conduits were inferred from a qualitative study (Worthington, 2004) 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 conduits in the conduit-flow 

Edwards aquifer model are constrained by the model cell 

dimensions, with most conduits being much smaller than the 

0.25-mi dimensions of the model cells.
Figure 1. Location of ground-water-flow model area, Edwards aquifer segments, and physiographic regions, San Antonio region, Texas. 

EDWARDS PLATEAU

GULF COASTAL PLAIN

BALCONES FAULT ZONE

SAN MARCOS PLATFORM

DEVILS RIVER TREND

MAVERICK BASIN

Ground-water divide

Ground-water divide

Hill Country

EXPLANATION

Active ground-water-model areaSan Antonio segmentBarton Springs segmentInactive ground-water-model areaDepositional province (modified from Maclay, 1995, fig. 2)Boundary of Balcones fault zoneBalcones escarpment (modified from Abbott and Woodruff, 1986, fig. 1)SpringBexar County index well J–17 and identification number 6837203

TE

0 15 30 45 60 MILES

100 ̊

99 ̊

98 ̊

29 ̊

30 ̊

31 ̊

EDWARDS KERR

REAL

KINNEY

BANDERA

KENDALL

LLANO

GILLESPIE BLANCO

BURNET

WILLIAMSON

TRAVIS

HAYS

BAS

CALDWELL

COMAL

GUADALUPE

G

WILSON

BEXAR

FRIO ATASCOSA

LA SALLE

DIMMIT

ZAVALA

MAVERICK

UVALDE

MEDINA

LOC

 Rocksprings

Leakey

Kerrville

Bandera

Boerne

Fredericksburg

Llano

Johnson  City

Burnet

Georgetown

Round Rock

Austin

Buda Dripping Springs

Wimberley

San  Marcos

Kyle

Lockhart

Luling

New Braunfels

Seguin Gon

Floresville

San Antonio

Poteet

Jourdanton Pleasanton

Pearsall

Dilley

Cotulla

Carrizo Springs

Pryor

Eagle Pass Crystal City

Brackettville

Uvalde

Hondo

 LAKE TRAVIS

CANYON  LAKE

MEDINA  LAKE

Medina Riv er

Sabinal

River

San Antonio

River

Cibolo

Creek

Guadalupe

River

Blanco River

Colorado River

Nueces River

Frio River

Dry Frio River

West

Nueces

River

Verde Creek

Blanco

Creek Seco

Creek

Dry Co

mal

Creek

Purgatory Cr

River

San Marco C s reek Cibolo

Creek

Salado

Hondo

Creek

South Llano River

River Pedernales

River

Leona

Las Moras Springs

Leona Springs

San Pedro Springs

San Antonio Springs

Comal Springs

Hueco Springs

San Marcos Springs

Barton Springs

Base modified from U.S. Geological Survey digital data Scales 1:250,000 (county boundaries) and 1:2,000,000 (hydrography)Universal Transverse Mercator projection, Datum NAD 83Zone 14

6837203
Figure 2. Hydrogeologic zones and catchment area (upper parts of stream basins that contribute recharge) of the Edwards aquifer, San Antonio reg

NUECES RIVER BASIN

SAN ANTONIO RIVER BASIN

GUADALUPE RIVER BASIN

1,000 mg/L

10,000 mg/L

1,000 mg/L

10,000 mg/L

1 2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

Nueces-West Nueces River Ba

Frio-Dry Frio River Basin

Sabinal River Basin 

Area between Sabinal and Med

Hondo and Seco Creeks)

Medina River Basin

Area between Medina River BaComal Creek Basins (includes 

Cibolo and Dry Comal Creek B

Guadalupe River Basin (includVerde Creek)

Blanco River Basin (includes B

Creek)Barton Springs segment contrBarton, Williamson, Slaughter, 

KNIPPA

GAP

Stream basin or contributing 

EXPLANATION

Active ground-water-model areaHydrogeologic zonesRecharge zone (outcrop) (modifiedfrom Puente, 1978)Confined zone Freshwater zone Feshwater/saline-water transition zoneInactive ground-water-model areaCatchment area updip of recharge zone;saline zone downdip of transition zone

Major river basin boundaryStream basin or contributing area boundaryLine of 1,000 milligrams per liter dissolvedsolids concentration (A.L. Schultz, consultant,written commun., 2000)Line of 10,000 milligrams per liter dissolvedsolids concentration (A.L. Schultz, consultant, written commun., 2000)Spring

CATCHMENT AREA Rocksprings Leakey

Kerrville

Bandera

Boerne

Fredericksburg

Llano

Johnson  City

Burnet

Georgetown

Round Rock

Austin

Buda Dripping Springs

Wimberley

Bastro

San  Marcos

Kyle

Lockhart

Luling

New Braunfels

Seguin Gonzales

Floresville

San Antonio

Poteet

Jourdanton Pleasanton

Pearsall

Dilley

Cotulla

Carrizo Springs

Pryor

Eagle Pass Crystal City

Brackettville

Uvalde

Hondo

Knippa

0 30 60 MILES 15 45

 LAKE TRAVIS

MEDINA  LAKE

Medina Riv er

Sabinal

River

San Antonio River

Cibolo Creek

Guadalupe

River

Blanco River

Colorado 

Colorado River

Nueces River Frio River Dry Frio River

West Nueces

River

Verde Creek

Blanco

Creek

Seco Creek

Purgatory Cr

River

San Marco

C

s

reek Cibolo

Creek Salado

Hondo

Creek

South Llano

River

River Pedernales

CANYON  LAKE

Dry Comal Creek

EDWARDS KERR

REAL

KINNEY

BANDERA

KENDALL

LLANO

GILLESPIE BLANCO

BURNET

WILLIAMSON

TRAVIS

HAYS

BASTROP

CALDWELL

COMAL

GUADALUPE

GONZAL

WILSON

BEXAR

FRIO ATASCOSA

LA SALLE

DIMMIT

ZAVALA

MAVERICK

UVALDE

MEDINA

100 ̊

99 ̊

98 ̊

29 ̊

30 ̊

31 ̊

Base modified from U.S. Geological Survey digital data Scales 1:250,000 (county boundaries) and 1:2,000,000 (hydrography)Universal Transverse Mercator projection, Datum NAD 83Zone 14

Las Moras Springs

Leona Springs

San Pedro Springs

San Antonio Springs

Comal Springs

Hueco Springs

San Marcos Springs

Barton Springs
Introduction 5

Calibration of the conduit-flow Edwards aquifer model 

indicated that zones of comparatively high hydraulic conductivity are needed to convey water toward the major springs and 

simulate the large measured springflows at Comal and San Marcos Springs (fig. 2). However, steady-state simulations for the 

conduit-flow Edwards aquifer model indicated that wider zones 

with relatively high hydraulic conductivity, but appreciably 

lower than the hydraulic conductivity used for the conduits, also 

could be used. 

The uncertainties inherent in simulating conduits as onecell-wide, continuously connected features raised the question 

of whether a model based on this mode of conduit simulation 

was the optimum model for the Edwards aquifer. Accordingly, 

a model with a hydraulic conductivity distribution without conduits explicitly simulated was considered. To develop an alternative, nonconduit-flow or diffuse-flow hydraulic conductivity 

distribution for the Edwards aquifer model, the USGS in cooperation with the San Antonio Water System, conducted a study 

during 2004–05. The objectives of this study were to (1) modify 

the hydraulic conductivity distribution of the conduit-flow 

Edwards aquifer model to replace conduits with broad zones 

of upscaled (adjusted from field-measurement scale to modelcell scale) hydraulic conductivity and (2) compare the hydrographs and residuals (differences between model-computed and 

measured values) for hydraulic heads and springflows for the 

conduit-flow Edwards aquifer model with those for the model 

containing the nonconduit, diffuse-flow hydraulic conductivity 

distribution (hereinafter, the diffuse-flow Edwards aquifer 

model). The hydraulic conductivity distribution that incorporates the nonconduit, diffuse-flow conceptualization of the 

aquifer emphasizes small-conduit and fracture flow rather than 

large, interconnected-conduit flow. 

Purpose and Scope

This report describes the diffuse-flow conceptualization 

and simulation of the Edwards aquifer. Specifically, (1) the 

diffuse-flow hydraulic conductivity distribution with broad 

zones of upscaled hydraulic conductivity, (2) the calibration of 

the diffuse-flow Edwards aquifer model, and (3) the results of 

comparisons of the hydrographs and residuals for hydraulic 

heads and springflows for the conduit-flow Edwards aquifer 

model (with simulated one-cell-wide conduits) and the diffuseflow Edwards aquifer model (with simulated broad zones of 

upscaled hydraulic conductivity). In addition, the simulated 

water budgets for the diffuse-flow Edwards aquifer model are 

presented, discussed, and compared with the water budgets for 

the conduit-flow Edwards aquifer model. 

The Edwards aquifer area includes both the San Antonio 

and Barton Springs segments of the aquifer and all or parts 

of 11 counties in south-central Texas (fig. 1). The area of 

active model cells for the diffuse-flow Edwards aquifer model 

is the same as for the conduit-flow Edwards aquifer model, 

defined on the north by the northern limit of contiguous outcropping Edwards rocks (updip boundary of the recharge zone) 

and on the south by the 10,000-mg/L dissolved solids concentration line (downdip boundary of the freshwater/salinewater transition zone [the zone of brackish water between the 

1,000- and 10,000-mg/L lines of dissolved solids concentration]) (fig. 2) (A.L. Schultz, consultant, written commun., 

2000). Thus, the active model area includes the transition 

zone between freshwater and saline water (fig. 2). The diffuseflow Edwards aquifer model was calibrated for steady-state 

(1939–46) and transient (1947–2000) conditions, with monthly 

stress periods, as was the conduit-flow Edwards aquifer model. 

As for the conduit-flow Edwards aquifer model, although 

the Barton Springs segment of the aquifer is included in the 

model, calibration was not done for the diffuse-flow Edwards 

aquifer model for the northern part of the segment (Travis 

County). A numerical finite-difference ground-water-flow 

model recently was completed for the Barton Springs segment 

(Scanlon and others, 2002), and a duplication of that work was 

not considered necessary. However, calibration was done in the 

southern part of the Barton Springs segment (northern Hays 

County) because the simulated hydraulic heads and flows in 

that area influenced the location of the simulated ground-water 

divide near Kyle and the simulated hydraulic heads and flows in 

the adjoining part of the San Antonio segment of the aquifer.

Revision of model properties for the diffuse-flow Edwards 

aquifer model was limited to changes in the simulated hydraulic 

conductivity distribution. The other model properties, including 

the aquifer structure (top and bottom altitudes), fault locations 

and conductivity, recharge, pumpage, and drain properties representing the major springs, are the same as for the conduit-flow 

Edwards aquifer model. 

There is uncertainty with regard to the capability of any 

numerical ground-water-flow model to simulate conditions in 

the real ground-water-flow system. To assess the importance of 

uncertainty associated with the conduit-flow Edwards aquifer 

model, a series of sensitivity tests was made to ascertain how 

the model results were affected by variations greater than and 

less than the calibrated values of input data (Lindgren and 

others, 2004). The sensitivity of the model results to variations 

in recharge, withdrawals, hydraulic conductivity, spring-orifice 

conductance for Comal and San Marcos Springs, and northern 

boundary inflow was tested with steady-state and transient simulations. Separate sensitivity tests were not made for the diffuse-flow Edwards aquifer model because (1) the only model 

input data that differs from the conduit-flow Edwards aquifer 

model is hydraulic conductivity, and (2) sensitivity tests were 

beyond the scope and time constraints of this study. 

Acknowledgments

Information for this report was synthesized from the 

published reports and data of several agencies, companies, 

and institutions. Chief contributors of the information for this 

report are the USGS, the BEG, and the Texas Water Development Board (TWDB). The author is indebted to Robert Mace 

(TWDB), Larry Land (HDR, Engineering), and Alvin Schultz 
6 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

(consultant) for their suggestions regarding the diffuse-flow 

hydraulic conductivity distribution. 

Conceptualization of the Edwards Aquifer

The conceptualization of the Edwards aquifer includes a 

description of the geologic and hydrogeologic setting within 

which the aquifer occurs. The geologic and hydrogeologic 

setting for the Edwards aquifer is discussed in detail in Lindgren 

and others (2004). The conceptualization presented in that 

report, which is the basis for the conduit-flow Edwards aquifer 

model, emphasizes conduit development and conduit flow. 

The hydraulic conductivity distribution simulated in the 

Edwards aquifer model of this report is based on the diffuseflow conceptualization. For this report, the discussion of the 

conceptualization of the Edwards aquifer will be restricted to 

the hydraulic conductivity and transmissivity of the aquifer and 

ground-water flow.

Hydraulic Conductivity and Transmissivity

Hydraulic conductivity and transmissivity of the Edwards 

aquifer reflect matrix, fracture, and conduit permeability and 

each varies over several orders of magnitude. Hovorka and 

others (1998) reported that hydraulic conductivity ranges from 

10-3 to 105

 ft/d and transmissivity from 10-1 to 107 feet squared 

per day (ft2

/d) on the basis of specific-capacity and other aquifer 

tests. Garza (1968, p. 31) estimated the transmissivity in the 

confined zone of the aquifer in the San Antonio region to be 

1 to 2 million ft2

/d. On the basis of numerical modeling, Maclay 

and Land (1988) estimated transmissivities of more than 4.3 

million ft2

/d in Comal County near Comal Springs in the confined freshwater zone of the aquifer; their smallest estimated 

transmissivity was 130 ft2/d in the freshwater/saline-water 

transition zone. The transmissivities for most of the confined 

freshwater zone range from 430,000 to 2.2 million ft2/d, but in 

the recharge (unconfined) zone transmissivities generally are 

less than 430,000 ft2

/d (Maclay and Land, 1988). 

Hydraulic Conductivity Distribution Developed for 

Conduit-Flow Edwards Aquifer Model

Painter and others (2002) estimated hydraulic conductivity 

for the Edwards aquifer in the San Antonio region to provide 

initial values for the conduit-flow Edwards aquifer model. The 

broad objective was to provide representations of the areal distribution of vertically averaged hydraulic conductivities across 

the San Antonio region of the Edwards aquifer using the best 

available quantitative techniques. 

Hydraulic conductivity in heterogeneous aquifers depends 

on the spatial scale of the measurement. Existing hydraulic conductivity measurements in the Edwards aquifer are derived 

mostly from single-well aquifer tests. These measurements 

must be modified or “upscaled” before being applied to the 

0.25- by 0.25-mi cells of the Edwards aquifer model. Painter 

and others (2002) first derived a hydraulic conductivity distribution from a dataset (hereinafter, the Mace dataset) with a few 

data from multiple-well aquifer tests but with most of the data 

from single-well tests (Hovorka and others, 1998; Mace, 2000; 

Mace and Hovorka, 2000). An approach based on nonparametric geostatistics, stochastic simulation, and numerical flow 

simulation then was used to upscale and interpolate to the 

Edwards aquifer model grid. This constituted revision 1 of the 

hydraulic conductivity distribution. Revision 2 of the hydraulic 

conductivity distribution incorporated the use of measured 

hydraulic heads and an approach based on Bayesian statistics to 

infer hydraulic conductivity. However, revision 2 was a preliminary application of the Bayesian technique and was not used 

because of subsequent updates to the recharge and measured 

hydraulic-head datasets for the original Edwards aquifer model. 

Revision 2 is not discussed in this report. Revision 3 of the 

hydraulic conductivity distribution represents a further refinement of the approach and was the distribution used in the conduit-flow Edwards aquifer model.

Initially, the only manipulation of the Mace dataset by 

Painter and others (2002) was to geometrically average values 

when multiple values (representing different tests) existed for 

the same well. After this averaging, the dataset contained 653 

values of hydraulic conductivity in the confined zone and 108 

values in the recharge (unconfined) zone. Univariate statistical 

distributions of hydraulic conductivity data for the confined and 

unconfined zones of the Edwards aquifer are reasonably well 

approximated as lognormal, although the distribution for the 

confined zone does have a lower tail that is enhanced relative to 

the lognormal distribution (Painter and others, 2002, fig. 2-2). 

The mean and variance for the confined and unconfined zones 

of the aquifer are substantially different, with geometric means 

of 18.8 and 1.3 ft/d for the confined and unconfined zones, 

respectively. The logarithmic variance in hydraulic conductivity is 6.4 and 9.7 ft/d for the confined and unconfined zones, 

respectively. Data limitations cited by Painter and others (2002) 

for the single-well tests include data uncertainty, drawdown that 

is below the limit of measurement and recorded as zero (15 percent of the tests), and imprecise well locations. 

Revision 1 of the hydraulic conductivity distribution was 

derived using a simulation approach that addresses data interpolation and the issue of scale consistency in hydraulic conductivity (Painter and others, 2002). Data interpolation was necessary 

because (1) the number of grid cells used in the Edwards aquifer 

model is much greater than the number of data points, and 

(2) the centers of grid cells do not necessarily correspond with 

well locations where measurements of hydraulic conductivity 

are available. Scale consistency is an issue because hydraulic 

conductivity in heterogeneous formations depends on the scale 

over which it is defined. A systematic bias toward lower 

hydraulic conductivity would be introduced by the unaltered 

application of local-scale hydraulic conductivity derived from 

aquifer tests to the 0.25-mi grid cells of the Edwards aquifer 

model. To address the scale dependencies and thereby avoid 
Conceptualization of the Edwards Aquifer 7

this systematic bias, a geostatistical approach was combined 

with numerical simulations in developing the hydraulic conductivity distribution. See Painter and others (2002) for a more 

detailed discussion of this method.

Hydraulic-head data imply considerable information about 

the underlying hydraulic conductivity distribution. In revision 3 

of the hydraulic conductivity distribution, revision 1 was taken 

as a starting point and then modified to be more consistent with 

measured hydraulic-head data (Painter and others, 2002). Specifically, a recently developed Bayesian updating procedure 

(Woodbury and Ulrych, 1998, 2000) was used to update the 

hydraulic conductivity distribution. In this approach, the nonunique nature of the inverse problem is explicitly acknowledged, and results are given in terms of probability distributions 

for the hydraulic conductivity in each cell. In addition, the 

Bayesian method allows prior information of various types to 

be incorporated into the inversion procedure, which allows the 

previous work on upscaled hydraulic conductivity (revision 1) 

to be retained and used in the inversion. The model properties 

were assumed to be random, and the inversion approached from 

the viewpoint of probability theory, with Bayesian solutions 

being sought for the problem. See Painter and others (2002) for 

a more detailed discussion of this method. The estimated 

hydraulic conductivity for revision 3 ranges from 1 to 7,347 ft/d 

(Lindgren and others, 2004, fig. 8).

Hydraulic Conductivity Distribution Developed for 

Diffuse-Flow Edwards Aquifer Model

A hydraulic conductivity distribution based primarily on 

the diffuse-flow conceptualization was developed for use in the 

Edwards aquifer model. For the Barton Springs segment of the 

aquifer, the hydraulic conductivity distribution of Scanlon and 

others (2002) was used. The initial diffuse-flow hydraulic conductivity distribution that was developed for the San Antonio 

segment of the aquifer comprised 29 zones and was based on 

a synthesis of information from multiple sources, including 

previous reports, available aquifer tests, mapping of fractures/

caverns observed in wells (A.L. Schultz, consultant, written 

commun., 2004), geologic structures, hydraulic gradients, and 

geochemistry. The primary basis for the diffuse-flow hydraulic 

conductivity distribution differed for each of the three hydrogeologic zones (recharge zone, confined freshwater zone, and 

confined freshwater/saline-water transition zone). The initial 

hydraulic conductivity zones and assigned values for the 

recharge zone were derived from Maclay and Land (1988, 

fig. 10), who reported relative transmissivity values by subareas, or zones, for the San Antonio segment of the Edwards aquifer. These estimates of relative transmissivity were made by 

Maclay and Small (1984) and were based on available geologic, 

hydrochemical, and hydrologic information. Eight zones were 

delineated in the recharge zone for the diffuse-flow hydraulic 

conductivity distribution, with assigned hydraulic conductivities ranging from 20 to 70 ft/d. 

The initial hydraulic conductivity zones and assigned values for the confined freshwater zone of the Edwards aquifer 

were derived from revision 1 of the hydraulic conductivity distribution developed by Painter and others (2002) and described 

in the previous section. For the diffuse-flow hydraulic conductivity distribution, the cell-by-cell values for revision 1 of the 

hydraulic conductivity distribution were contoured, and 

hydraulic conductivity zones for the confined freshwater zone 

were delineated on the basis of the contour lines. An average 

hydraulic conductivity between the bounding contour lines for 

a delineated zone was assigned as the hydraulic conductivity for 

the zone. Fifteen zones were delineated in the confined freshwater zone for the diffuse-flow hydraulic conductivity distribution, with assigned hydraulic conductivity values ranging from 

15 to 1,000 ft/d. 

The confined freshwater/saline-water transition zone was 

delineated as a single zone, with an assigned hydraulic conductivity of 10 ft/d. The assignment of a uniform, comparatively 

low hydraulic conductivity for the freshwater/saline-water 

transition zone is consistent with previous models of Maclay 

and Land (1988), Scanlon and others (2002), and Lindgren and 

others (2004).

The preliminary diffuse-flow hydraulic conductivity 

distribution comprised 24 zones—8 for the recharge zone, 15 

for the confined freshwater zone, and 1 for the freshwater/saline-water transition zone. Additionally, calibration of the 

original Edwards aquifer model indicated that zones of comparatively high hydraulic conductivity are needed to convey water 

toward the major springs and simulate the large measured 

springflows at Comal and San Marcos Springs. The revision 1 

hydraulic conductivity distribution developed by Painter and 

others (2002) represents the best available mapping of hydraulic conductivity in the Edwards aquifer, on the basis of aquifer 

tests and upscaling and interpolation to the Edwards aquifer 

model grid. However, model simulation results indicate that 

using the revision 1 hydraulic conductivity distribution yields 

simulated springflows for Comal and San Marcos Springs that 

are much lower than measured flows. Further upscaling of 

hydraulic conductivity is required to simulate the high measured springflows. The required upscaling of the hydraulic conductivity can be accomplished by the insertion of broad, high 

hydraulic conductivity (HHC) zones within the model domain. 

The location, width, and hydraulic conductivities for these 

HHC zones were determined on the basis of the hydrogeology 

of the Edwards aquifer and known zones of high permeability 

in the aquifer. 

The major areas of known high permeability in the aquifer 

include (1) areas in the central part of the aquifer in Medina 

and Bexar Counties (Maclay and Small, 1984; Maclay and 

Land, 1988, fig. 19; Hovorka and others, 1998, fig. 23; Painter 

and others, 2002) and (2) a relatively narrow zone between 

well J–17 (Bexar County index well; fig. 1) and Comal Springs 

(Worthington, 2004). For the diffuse-flow hydraulic conductivity distribution, an HHC zone was delineated in the central 

part of the aquifer in Medina and Bexar Counties, corresponding with the zones of high transmissivity mapped by 
8 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Maclay and Land (1988, fig. 19). The highest hydraulic conductivity in Bexar County might be in a zone less than 1.25-mi 

wide in eastern Bexar County and about 2 to 3 mi from the 

freshwater/saline-water interface, based on water-quality data 

(Worthington, 2004). A relatively broad zone of high transmissivity also was simulated by Maclay and Land (1988) in the 

confined zone of the aquifer in east-central Bexar County; and 

high matrix permeability was mapped by Hovorka and others 

(1998, fig. 12) in an overlapping area of east-central Bexar 

County. 

High-permeability zones often are associated with proximity to major faults and structural grabens. Comal and San Marcos Springs are associated with faults and structural grabens 

within the very narrow zone of freshwater in the confined zone 

of the aquifer in Comal and Hays Counties. A marked increase 

in hydraulic conductivity occurs in a downgradient direction 

along the major flow path to Comal Springs (Worthington, 

2004). Comparatively narrow HHC zones were delineated 

immediately upgradient from both Comal and San Marcos 

Springs in the confined zone of the aquifer, corresponding with 

narrow zones of high transmissivity simulated by Maclay and 

Land (1988). 

Hunter channel (Maclay and Land, 1988, fig. 23), a narrow 

channel between major faults, lies between Comal and San 

Marcos Springs and contains extremely transmissive rocks. An 

HHC zone also was delineated between Comal and San Marcos 

Springs, reflecting the geologic structure and extremely transmissive rocks. 

The major areas of known high permeability in the 

aquifer include areas along the freshwater/saline-water 

interface (Maclay and Small, 1984; Hovorka and others, 1998; 

Worthington, 2004). Relatively high porosity and permeability 

in the deepest parts of the aquifer near the freshwater/salinewater interface, anomalously high well yields, and sharp 

chemical gradients indicate that flow might be focused in this 

area. Therefore, an HHC zone was delineated along the freshwater/saline-water interface using the 1,000-mg/L dissolved 

solids concentration line as a guide. A highly permeable belt of 

rocks exists along segments of the freshwater/saline-water 

interface in areas where mixing ground water of two different 

chemical types increases the solution capacity of the water 

(Maclay and Small, 1984). Part of the freshwater/saline-water 

interface south of Knippa (fig. 2) might be associated with a 

syncline at the base of the Edwards aquifer, and conduit development resulting in increased permeability in this area might 

have preferentially occurred in this syncline (Worthington, 

2004). The HHC zone delineated ranges from 3 to 13 cells 

wide and is located predominantly adjacent to and north of the 

1,000-mg/L concentration line, except in Bexar County, where 

it includes areas both north and south of the 1,000-mg/L concentration line. The area between the 1,000- and 3,000-mg/L 

dissolved solids concentration lines was initially delineated as a 

single zone with a hydraulic conductivity of 500 ft/d. 

The widths of the five delineated HHC zones (central 

Medina and Bexar Counties, immediately upgradient of Comal 

Springs, immediately upgradient of San Marcos Springs, 

between Comal and San Marcos Springs, and along the freshwater/saline-water interface) vary from as narrow as three 

model cells (0.75 mi) near the freshwater/saline-water interface 

and San Marcos Springs to as wide as about 5 to 10 mi. The confined freshwater zone of the Edwards aquifer is extremely narrow, or perhaps nonexistent, in sections between San Marcos 

and Comal Springs. 

The magnitude of the hydraulic conductivity of the HHC 

zones was initially set at 20,000 ft/d, on the basis of the high end 

of the range of reported transmissivities. Garza (1968, p. 31) 

and Maclay and Land (1988) estimated maximum transmissivities of from 2 million to more than 4.3 million ft2

/d for the 

Edwards aquifer. Corresponding hydraulic conductivities for 

these maximum transmissivities would be on the order of 

10,000 to 20,000 ft/d.

Ground-Water Flow

The ground-water-flow system of the Edwards aquifer in 

the San Antonio region includes the following components:

1. The catchment area (fig. 2) in the Edwards Plateau (fig. 1), 

where the rocks of the Edwards-Trinity and Trinity aquifers are exposed and receive direct recharge to the water 

table. Erosion has removed Edwards Group rocks in the 

Hill Country (fig. 1), as the southern margin of the plateau 

is known locally (hence Trinity aquifer rather than 

Edwards-Trinity aquifer in the Hill Country).

2. The recharge zone (fig. 2) in the northern and 

northeastern parts of the Balcones fault zone (fig. 1), 

where streams lose flow directly into the unconfined 

Edwards aquifer outcrop and where the aquifer receives 

direct recharge to the water table from infiltration of 

precipitation.

3. The confined zone (fig. 2) in the southern and 

southeastern part of the Balcones fault zone, which 

comprises the freshwater zone and the freshwater/salinewater transition zone.

A recent potentiometric-surface map of the Edwards 

aquifer (Roberto Esquilin, Edwards Aquifer Authority, written 

commun., 2004) indicates that water entering the catchment 

area and recharge zone moves from unconfined to confined 

zones of the aquifer through generally southeasterly flow paths. 

In the confined zone, the water moves under low hydraulic gradients through fractured, highly transmissive rocks toward the 

east and northeast, where it is discharged through springs and 

wells.

Ground-water flow in karst typically includes diffuse or 

matrix flow (slow flow system), flow through fractures, and 

flow through large conduits (fast flow system). The multimodal 

permeability distribution of the Edwards aquifer (Hovorka and 

others, 1998) implies that the fastest-moving water can travel 

many times faster than the largest volume of water. Hovorka 

and others (1998) developed empirical relations between porosity (total porosity, including fracture and solution-enhanced 
Conceptualization of the Edwards Aquifer 9

porosity) and permeability, and then used these relations to 

estimate matrix permeability from log (neutron and resistivity)-

based porosity. On the basis of comparisons between mean 

matrix permeability and mean hydraulic conductivities estimated from aquifer tests, it is likely that the contribution of 

matrix permeability to regional-scale hydraulic conductivity is 

minor and that most Edwards aquifer water flows through fractures and conduits (Hovorka and others, 1998). Maclay and 

Land (1988) identified zones of high transmissivity, with values 

as much as 112 feet squared per second (ft2

/s) (9,676,800 ft2/d), 

along flow paths leading to Comal Springs. The zone of highest 

transmissivity corresponds with the Comal Springs graben, 

a narrow graben containing extremely transmissive rocks. 

Hovorka and others (2004) and Worthington (2004) relate 

zones of high transmissivity to conduit development and preferential flow paths in the aquifer. Proximity to large faults and 

high dolomite content indicated by facies distribution and 

mapped by Rose (1972) indicate that conduits are major contributors to flow in the confined zone of the Edwards aquifer in 

Hays and Comal Counties (Hovorka and others, 1998). Maclay 

and Small (1984) assigned this zone the highest transmissivities 

in the aquifer. 

Areas of high transmissivity and preferential flow paths

in the Edwards aquifer might be associated with a number 

of features or processes, including (1) geologic structures, 

(2) geochemical solution processes, and (3) potentiometric 

surface troughs. Favorable structural location can be inferred 

to coincide with high transmissivity and preferential flow paths. 

For example, the known highest-yielding Edwards aquifer 

well (Rettman, 1991) is in a major structural trough. Largescale structural troughs, grabens, and synclines, with high transmissivity and increased flow, occur in the Edwards aquifer. 

Worthington (2004) hypothesized that grabens and synclines 

are particularly favorable sites for development of conduits and 

identified nine major structural troughs in the San Antonio segment of the aquifer (Worthington, 2004, fig. 17). These include 

troughs in central Uvalde, Medina, and Bexar Counties, southwestern Medina County, within the recharge zone in Comal 

County, and near the freshwater/saline-water interface from 

west of Comal Springs to San Marcos Springs. Carbonate dissolution theory also indicates that grabens are a favorable location for conduit development. Maclay and Land (1988, table 6) 

listed 11 geologic gaps, grabens, and channels, many containing 

very transmissive rocks, that convey ground water. The conveying structures cited as exerting the most influence on regional 

ground-water flow are the Knippa gap, Leona Springs gap, 

Uvalde graben, Dry Frio-Frio River gap, and Hunter channel 

(Maclay and Land, 1988, fig. 23). A narrow zone within a graben north of San Marcos Springs is fully saturated and contains 

several wells that yield no measurable drawdown when pumped 

and several wells that yield water undersaturated with respect to 

calcite, which indicate a likely location of a conduit and rapid 

ground-water flow (Hovorka and others, 2004).

Faults can either increase or decrease total transmissivity 

(Hovorka and others, 1998). Some of the abundant, interconnected fractures in intensely fractured zones adjacent to faults 

have been enlarged, and they might focus flow parallel to faults. 

Where calcite cement fills breccia, cross-fault flow might be 

decreased. Stratigraphic offset of permeable zones along faults 

might also decrease the cross-fault flow (Maclay and Small, 

1983, 1984). Holt (1959) observed nearly 100 ft of head difference across faults in northern Medina County, and George 

(1952) reported head differences of 6 to 26 ft across segments 

of major faults in unconfined, less-transmissive parts of the 

aquifer in Comal County. An inferred conduit between Comal 

Springs and eastern Bexar County is aligned parallel to major 

faults near Comal Springs but cuts across faults at a high angle 

to occur deeper in the subsurface in Bexar County (Hovorka and 

others, 2004). Maclay (1995) and Groschen (1996) characterized flow in the Edwards aquifer as being controlled laterally by 

barrier faults that locally compartmentalize the aquifer, especially toward the eastern part of the San Antonio segment. 

Maclay and Land (1988) hypothesized that large-throw faults 

segment the aquifer and divert flow in the recharge zone to the 

west before flow is redirected toward the east.

In southern Bexar County, there is a plume of water with 

electrical conductivity similar to or lower than that at Comal 

Springs, which implies the existence of one or more major 

conduits (Worthington, 2004, fig. 19). As noted in the previous 

section, the highest hydraulic conductivity in Bexar County 

might be in a zone less than 1.25-mi wide and about 2 to 3 mi 

from the freshwater/saline-water interface, on the basis of 

water-quality data (Worthington, 2004). High transmissivity 

and thus the potential for large flow near the interface might 

also be the case in Medina, western Uvalde, and eastern Kinney 

Counties, but a lack of hydraulic-head or chemistry data close 

to the freshwater/saline-water interface makes this assumption 

uncertain. Numerical models of dissolution of carbonate aquifers and tracer tests provide evidence that continuous conduits 

connect sinking streams and springs in carbonate aquifers 

(Worthington, 2004). Maclay and Small (1984) hypothesized 

that solution channels within the Edwards aquifer might be oriented parallel to the courses of streams recharging the Edwards 

aquifer and that vertical solution channels are well developed 

below segments of stream channels in the recharge zone.

A regionally extensive system of high-permeability zones 

is defined by broad troughs in the potentiometric surface (conduit indicators) in the confined zone of the Edwards aquifer. 

Indications of connections of the confined aquifer to the 

recharge zone are less well defined by troughs in the potentiometric surface. Worthington (2004) conceptualized a dendritic 

pattern of conduit connection from the recharge zone to the confined zone. Three approximately synoptic water-level maps 

constructed by Hovorka and others (2004, figs. 7, 8, 9) show 

two main trends: (1) a steep and fairly uniform gradient of more 

than 100 feet per mile (ft/mi) between the Edwards and Trinity 

aquifers (generally north-northwest to south-southeast) and 

(2) a gradual gradient from west to east ranging from 2.8 ft/mi 

in eastern Medina County to 1.2 ft/mi in the eastern part of the 

aquifer. Superimposed on these regional trends are a number of 

troughs and divides. Prominent in all three water-level maps is 

a wide trough that extends westward from central Bexar County 
10 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

to western Medina County. This trough is clearly defined in 

synoptic maps compiled by or for the Edwards Aquifer Authority (Roberto Esquilin, Edwards Aquifer Authority, written commun., 2003; Hovorka and others, 2004, fig. 10) and has been 

recognized as a zone of high transmissivity in previous models 

(Klemt and others, 1979; Maclay and Land, 1988; Painter and 

others, 2002). In all three water-level maps, the trough can be 

traced westward to Uvalde County. Westward into Kinney 

County, the trough becomes broad and poorly defined. Both 

Hovorka and others (2004, fig. 24) and Worthington (2004, 

fig. 21) infer the presence of conduits and major flow paths 

from western Medina County to central Bexar County, with an 

east-west trend that indicates structural influence. Hovorka and 

others (2004) hypothesize a complex of interconnected conduits, with about one-half of the segments parallel to faults and 

one-half of them crossing faults at an appreciable angle. The 

presence of conduits and major flow paths also is indicated in a 

potentiometric-surface trough that loops northward around the 

volcanic center of southeastern Uvalde County.

A steepening of the Edwards aquifer potentiometricsurface gradient occurs in eastern Uvalde County. Maclay and 

Land (1988) called the area of steepening the Knippa gap and 

interpreted it as a narrow opening within an extensive, complex 

barrier-fault system. More detailed structural mapping has complicated the interpretation of faults, and no structural restriction 

of flow is apparent coincident with the steeper gradient. Waterlevel maps show a complex, poorly defined flow pattern in central Uvalde County, probably reflecting structural complexity in 

this area that is further complicated by volcanic intrusions. 

From central Uvalde County, ground water flows southward 

and downdip toward southeastern Uvalde and southwestern 

Medina Counties. Worthington (2004, fig. 21) hypothesized the 

presence of conduits along this southeastward flow path partially within a syncline at the base of the Edwards aquifer. However, spatial and temporal data density is inadequate to accurately define the flow characteristics of this important region of 

the aquifer. Wells without measurable drawdown occur in disproportionate numbers near Leona Springs and along a zone 

trending northwestward from Leona Springs (Hovorka and 

others, 2004). Details of the connectivity of flow through this 

area are unclear; however, a network of conduits is inferred 

from the drawdown data.

Simulation of Ground-Water Flow

A conceptual model of the Edwards aquifer in the San 

Antonio region was formulated on the basis of an understanding 

of the hydrogeologic setting, aquifer characteristics, distribution and amount of recharge and discharge, and aquifer boundaries, as described by Lindgren and others (2004). A numerical 

model of ground-water flow, the conduit-flow Edwards aquifer 

model, was constructed on the basis of the conceptual model of 

the aquifer. The conceptual model and the numerical model for 

the diffuse-flow Edwards aquifer model are the same as those 

for the conduit-flow Edwards aquifer model (Lindgren and 

others, 2004), with the exception of the hydraulic conductivity 

distribution as described in the section “Hydraulic Conductivity 

Distribution Developed for Diffuse-Flow Edwards Aquifer 

Model.” 

Two types of simulations were done for the diffuse-flow 

Edwards aquifer model—a steady-state simulation that represents long-term average conditions when inflows to and outflows from the flow system are equal and a transient simulation 

that includes changes in ground-water storage over time.

Numerical Model Description

The FORTRAN computer-model code MODFLOW 

(McDonald and Harbaugh, 1988; Harbaugh and McDonald, 

1996; Harbaugh and others, 2000), a modular finite-difference 

ground-water-flow code developed by the USGS, was used 

to simulate ground-water flow in the Edwards aquifer. The 

Edwards aquifer model uses the Basic, Output Control, 

Block-Centered-Flow, Recharge, Well, Horizontal-Flow 

Barrier, Drain, River, and LMG (numerical solver) modules, or 

MODFLOW packages, to simulate ground-water flow in the 

Edwards aquifer. The software Groundwater Vistas was used as 

a pre- and post-processor to facilitate data entry and allow analysis of model output (Environmental Simulations, Inc., 2002). 

A number of simplifying assumptions about the Edwards aquifer and boundary-condition specifications were required to 

mathematically represent the aquifer. For the original Edwards 

aquifer model (Lindgren and others, 2004), it was assumed that 

conduits could be represented in the model by narrow (one-cellwide) zones with large hydraulic conductivities. This assumption was not incorporated in the diffuse-flow Edwards aquifer 

model, and conduit locations are not explicitly identified and 

simulated as one-cell-wide zones. However, hydrogeologic 

characteristics such as narrow grabens might result in narrow 

zones of comparatively high hydraulic conductivity.

A description of the model includes the structure and 

hydraulic properties of the aquifer, the boundary conditions 

imposed, and the stresses on the aquifer. Pertinent hydraulic 

and hydrologic characteristics of the aquifer for appropriate 

cells within the grid are needed to solve the governing partialdifferential equation. Specific input properties required for 

the model include (1) active and inactive cells, (2) altitudes 

of the top and bottom of the layer, (3) fault locations and horizontal conductance, (4) horizontal hydraulic conductivity, 

(5) storativity, (6) river stage and riverbed (streambed) conductance, (7) hydraulic head and conductance of general-head 

boundary, (8) recharge rates, (9) ground-water withdrawal 

rates, (10) drain elevation and conductance, and (11) initial 

hydraulic heads. The properties for the diffuse-flow Edwards 

aquifer model are the same as for the original Edwards aquifer 

model, with the exception of the modified horizontal hydraulic 

conductivity. See Lindgren and others (2004) for a detailed discussion of the construction of the original Edwards aquifer 

model and the model properties.
Simulation of Ground-Water Flow 11

Numerical ground-water-flow models of karst aquifers 

commonly require appreciable increases in measured hydraulic 

conductivity (upscaling) to make simulated hydraulic heads and 

springflows match measured hydraulic heads and springflows 

(Halihan and others, 2000; Scanlon and others, 2002; Hovorka 

and others, 2004). Hydraulic conductivity in a heterogeneous 

medium depends on the scale at which it is defined (scaling 

effect) (Painter and others, 2002). Single-well-based hydraulic 

conductivity measurements require upscaling to apply to areas 

the size of model cells. In a porous medium, upscaling generally 

is not needed and the geometric-mean hydraulic conductivity 

derived from aquifer tests can be used for aquifer simulations. 

However, for the Edwards aquifer there is a pronounced scaling 

effect, and hydraulic conductivities higher than those measured 

are needed to accurately simulate measured heads and springflows. Worthington (2004, fig. 11) demonstrated that the scaling effect for the Edwards aquifer is similar to that of other karst 

aquifers and, on the basis of this similarity, concluded that 

the Edwards aquifer has a well-developed conduit network. 

Upscaling in a numerical ground-water-flow model can be 

accomplished either by distribution of high permeability 

through a wide (multiple cells) zone (Klemt and others, 1979; 

Maclay and Land, 1988; Scanlon and others, 2002) or by addition of a smaller number of discrete, large-aperture conduits 

(Worthington, 2004). The diffuse-flow Edwards aquifer model 

incorporates upscaling by distribution of high permeability 

through a wide (multiple cells) zone, rather than by addition of 

a smaller number of discrete, large-aperture conduits.

The initial zoned hydraulic conductivity distribution for 

the diffuse-flow Edwards aquifer model comprised 29 zones 

and was derived primarily from (1) estimates of relative transmissivities for the recharge zone made by Maclay and Small 

(1984) on the basis of available geologic, hydrochemical, and 

hydrologic information, (2) the hydraulic conductivity distribution developed by Painter and others (2002) for the confined 

freshwater zone, and (3) geologic structure and geochemical 

information for the HHC zones. These factors were previously 

discussed in the “Hydraulic Conductivity and Transmissivity” 

section of the report. 

Numerical Model Calibration

Model calibration is the process in which initial estimates 

of aquifer properties, stresses (recharge), and boundary conditions are adjusted until simulated hydraulic heads and flows 

acceptably match measured water levels and flows. Regarding 

flows, for the Edwards aquifer model, comparisons were made 

between measured and simulated springflows for Comal, 

San Marcos, Leona, San Antonio, and San Pedro Springs. 

Calibration and evaluation of the ground-water-flow model 

were conducted for steady-state (1939–46) and for transient 

(1947–2000) conditions. No storage terms are included in 

the steady-state simulation because change in storage in the 

aquifer is assumed to be zero. Transient simulations incorporate 

the storage property of the aquifer and are time-dependent. 

Changes in storage in the aquifer occur when the amount of 

water entering the aquifer and the amount of water leaving the 

aquifer are not equal.

During calibration of the diffuse-flow Edwards aquifer 

model, only the simulated hydraulic conductivity distribution 

was modified. All other properties were held constant at the 

same values as those used in the conduit-flow Edwards aquifer 

model. The input data incorporate refinements to published 

and unpublished data on hydraulic conductivity and transmissivity. The calibrated final distribution of hydraulic conductivity results from trial-and-error calibration. During calibration, the hydraulic conductivity data were adjusted (within 

ranges of variability in measured values) to minimize differences between measured and simulated hydraulic heads and 

springflows.

The calibration targets for the diffuse-flow Edwards 

aquifer model are the same as for the conduit-flow Edwards 

aquifer model and include measured water levels in wells 

and springflows. The water-level targets include (1) the averages of a series of measurements of water levels in multiple 

wells for a specified time period (steady-state calibration targets); (2) single measurements of water levels in multiple wells 

within a comparatively short time period, producing an areal 

distribution of hydraulic heads (potentiometric-surface map); 

and (3) a series of measurements of water level within a single 

well over time (hydrograph). Similarly, the springflow targets 

include (1) the median value of a series of measurements of 

springflow for a single spring for a specified time period 

(steady-state calibration target) and (2) a series of measurements of springflow for a single spring over time (transient calibration target; hydrograph). See Lindgren and others (2004) for 

a more detailed discussion of the calibration targets.

Steady-State Simulation

The steady-state calibration period for the diffuse-flow 

Edwards aquifer model was 1939–46, as it was for the conduitflow Edwards aquifer model (Lindgren and others, 2004). 

Although hydrologic conditions in the Edwards aquifer have 

fluctuated temporally and spatially depending on the associated 

distributions of recharge and water use, long-term averages 

of recharge, discharge, and water-level data were compiled 

for a near-predevelopment (pre-1947) period to represent 

hydraulic equilibrium, or steady-state conditions. The period 

1939–46 was chosen because (1) irrigation development was 

minimal, (2) average rainfall for the period was near the 30-year 

(1961–90) normal rainfall (National Oceanic and Atmospheric 

Administration, National Climatic Data Center, 1992), and 

(3) sufficient water-level and springflow information was 

available.

For the steady-state calibration, 144 wells were used as the 

calibration targets (pl. 1; table 1 at end of report). In addition to 

water levels in wells, median springflows for Comal, San Marcos, Leona, San Antonio, and San Pedro Springs for 1939–46 

were used as targets for the steady-state calibration. The median 
12 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

springflows are 332, 152, 19, 10, and 6 cubic feet per second 

(ft3/s) for Comal, San Marcos, Leona, San Antonio, and San 

Pedro Springs, respectively.

The steady-state simulation for the diffuse-flow Edwards 

aquifer model was calibrated by varying the configuration of 

the simulated hydraulic conductivity zones and the magnitude 

of the simulated hydraulic conductivities within those zones. 

The revisions to the initial simulated hydraulic conductivity distribution, as a result of the steady-state calibration, included 

1. Changes in the magnitude of simulated hydraulic conductivities and the areal extent of some zones in the southern 

part of the Barton Springs segment of the aquifer (northern Hays County), 

2. Increases in the simulated hydraulic conductivities for 

areas near streambeds in the recharge zone and 

predominantly decreases in the simulated hydraulic 

conductivities for the areas away from streambeds in the 

recharge zone, 

3. Changes in the magnitude of simulated hydraulic 

conductivities and the areal extent of some zones in the 

northern part of the confined freshwater zone of the 

aquifer, 

4. Increases in the hydraulic conductivities for some zones 

in the confined freshwater zone of the aquifer in eastern 

Uvalde and western Medina Counties, 

5. Decreases in the simulated hydraulic conductivities for 

the freshwater/saline-water transition zone, and 

6. Decreases in the simulated hydraulic conductivities for 

the HHC zone, delineated in the central part of the 

aquifer in Medina and Bexar Counties, that corresponds 

with the zones of high transmissivity mapped by Maclay 

and Land (1988, fig. 19). 

Revisions were made to the configuration of some of the 

simulated hydraulic conductivity zones and to the simulated 

hydraulic conductivities for parts of the recharge zone of the 

Edwards aquifer. Hydraulic conductivity zones were delineated 

for the areas near streambeds in the recharge zone and assigned 

a value of 500 ft/d to better match measured hydraulic heads in 

and near the recharge zone. Maclay and Small (1984) hypothesized that solution channels within the Edwards aquifer might 

be oriented parallel to the courses of streams recharging the 

Edwards aquifer and that vertical solution channels are well 

developed below segments of stream courses in the recharge 

zone. Also, some of the initial hydraulic conductivity zones 

were further subdivided, and the hydraulic conductivities 

decreased to 10 ft/d for much of the recharge zone—in particular for the northern part and areas of zero or small saturated 

thickness. As discussed in Lindgren and others (2004), the simulated aquifer thickness in parts of the recharge zone includes 

Trinity aquifer rocks, which have lower hydraulic conductivity 

than those of the Edwards aquifer.

Revisions were made to the configuration of some of the 

simulated hydraulic conductivity zones and to the simulated 

hydraulic conductivities for parts of the confined freshwater 

zone of the aquifer. In particular, revisions were made in the 

northern part of the confined freshwater zone of the aquifer. 

For example, a hydraulic conductivity zone with a value of 10 

ft/d was expanded in north-central Medina County, and the 

hydraulic conductivity of two zones in north-central Bexar 

County was increased to 1,500 ft/d and the areal extent of the 

zones was enlarged. These revisions were made to obtain a better match between measured and simulated hydraulic heads 

in and near the recharge zone. Other changes to the hydraulic 

conductivity distribution in the confined freshwater zone of 

the aquifer included (1) increases in hydraulic conductivities 

to 2,000–7,500 ft/d for some zones in eastern Uvalde and western Medina Counties, in particular the elongate south- and 

southeast-trending zones, and (2) the addition of a zone with a 

hydraulic conductivity of 2,000 ft/d specified for the area to the 

north, northwest, and northeast of Comal Springs.

Revisions were made to the configuration of the simulated 

hydraulic conductivity zones and to the simulated hydraulic 

conductivities for the freshwater/saline-water transition zone. 

The hydraulic conductivity for the HHC zone delineated along 

the freshwater/saline-water interface was decreased from 

20,000 to 10,000 ft/d in Uvalde and Medina Counties. In Bexar 

County, the initially single HHC zone was divided into two 

zones with hydraulic conductivities of 12,500 and 15,000 ft/d. 

The area between the 1,000- and 3,000-mg/L dissolved solids 

concentration lines, initially delineated as a single zone 

with a hydraulic conductivity of 500 ft/d, also was divided 

into multiple zones with varying hydraulic conductivities. 

A new zone was delineated and the hydraulic conductivity was 

(1) decreased to 250 ft/d for the area in Uvalde, northeastern 

Zavala, and northwestern Frio Counties, (2) decreased to 

100 ft/d in north-central Frio, eastern Medina, northwestern 

Atascosa, and western Bexar Counties, (3) maintained at 

500 ft/d in eastern Bexar County, and (4) increased to 1,100 ft/d 

in western Comal County (southwest of Comal Springs).

In addition to the changes for the HHC zone delineated 

along the freshwater/saline-water interface, revisions were 

made to the configuration of the simulated hydraulic conductivity zones and to the simulated hydraulic conductivities for other 

HHC zones. The HHC zone initially delineated as a single zone 

in the central part of the aquifer in Medina and Bexar Counties 

(corresponding with the zones of high transmissivity mapped 

by Maclay and Land [1988, fig. 19]) was divided into two zones 

with hydraulic conductivities of 10,000 and 12,500 ft/d, 

decreased from an initial value of 20,000 ft/d. Also, a third zone 

was delineated in the immediate vicinity of Comal Springs and 

an increased hydraulic conductivity of 50,000 ft/d assigned. 

Numerical ground-water-flow models for both the San Antonio 

(Maclay and Land, 1988) and Barton Springs (Scanlon and 

others, 2002) segments of the Edwards aquifer assigned the 

highest hydraulic conductivities to zones nearest to the major 

springs. The hydraulic conductivity for the HHC zone west of 

San Marcos Springs was maintained at 20,000 ft/d, whereas the 

hydraulic conductivity for the HHC zone between Comal and 

San Marcos Springs was decreased to 12,500 ft/d. An additional 
Simulation of Ground-Water Flow 13

HHC zone, with a hydraulic conductivity of 20,000 ft/d, was 

added eastward from San Marcos Springs. 

The steady-state simulation calibration results include a 

comparison of simulated hydraulic heads and springflows with 

average measured water levels and median measured springflows for 1939–46. The calibrated steady-state simulation generally reproduces the spatial distribution of measured water levels. Simulated hydraulic heads were within 30 ft of measured 

water levels at 130 of the 144 wells used as calibration targets 

for the steady-state simulation (table 1). The difference was 

less than 20 ft at 122 of the 144 wells. The largest difference 

between measured and simulated hydraulic heads was 116.9 ft 

for a well west of the Guadalupe River near the recharge zone 

in Comal County. Six of the 14 residuals greater than 30 ft occur 

in wells in and near the recharge zone (unconfined conditions). 

Residuals greater than 30 ft also occur in the confined freshwater zone of the aquifer at three wells in southern Hays 

County, at two wells southwest of the Bexar County index well, 

and at one well each in southern Comal and eastern Medina 

Counties. The goodness-of-fit between measured and simulated 

hydraulic heads was quantified using the mean absolute difference, mean algebraic difference, and root-mean-square (RMS) 

error. The mean absolute difference between measured and simulated hydraulic heads, computed as the sum of the absolute 

values of the differences divided by the number of wells, is 

11.3 ft (table 2, at end of report). The mean algebraic difference 

between measured and simulated hydraulic heads, computed as 

the algebraic sum of the differences divided by the number of 

wells, is 1.5 ft, which indicates that positive differences were 

approximately balanced by negative differences. The graph of 

simulated relative to measured hydraulic heads (fig. 3) indicates 

little bias in the steady-state simulation results. 

Figure 3. Simulated relative to measured hydraulic heads, steady-state simulation, conduit-flow and diffuse-flow Edwards aquifer 

models, San Antonio region, Texas. 

400 600 800 1,000 1,200 1,400

MEASURED HYDRAULIC HEAD, IN FEET ABOVE NGVD 29

400 600 800 1,000 1,200 1,400

MEASURED HYDRAULIC HEAD, IN FEET ABOVE NGVD 29

400

600

800

1,000

1,200

1,400

SIMULATED HYDRAULIC HEAD,

IN FEET ABOVE NGVD 29

400

600

800

1,000

1,200

1,400

SIMULATED HYDRAULIC HEAD,

IN FEET ABOVE NGVD 29

Conduit-flow model

Diffuse-flow model

Line of equal value

Line of equal value
14 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

The RMS error is derived from the residuals between the 

measured and simulated hydraulic heads, as given in the following equation:

, (1)

where

RMS is the root-mean-square error [L],

n is the number of calibration points,

hm is the measured hydraulic head at point i [L], and

hs is the simulated hydraulic head at point i [L].

The RMS error for the 144 target wells of the calibrated steadystate simulation is 20.9 ft (table 2). This error represents about 

3 percent of the total measured head difference across the model 

area (650 ft). For comparison, calibration guidelines adopted by 

the TWDB Groundwater Availability Modeling (GAM) program specify that the RMS error should be less than 10 percent 

of the total head difference across the model area (Texas Water 

Development Board, 2004).

The simulated diffuse-flow-model springflows for 

Comal and San Marcos Springs for the calibrated steady-state 

simulation are within about 2.4 and 15 percent of the median 

springflows for the two springs, respectively (table 3, at end of 

report). GAM calibration guidelines specify that simulated 

flows, such as springflow or stream-aquifer leakage, should be 

within 10 percent of the measured flows. The combined simulated springflows for San Antonio and San Pedro Springs were 

31 percent greater than the measured springflows. However, the 

simulated flows probably reflect local hydrogeologic conditions. Little local-scale data were available for calibration of 

these two relatively small springs. The simulated springflow for 

Leona Springs was about twice the measured springflow. However, this discrepancy is reasonable because the reported discharge for Leona Springs might not account for all the discharge 

from the Edwards aquifer to the Leona gravels (Green, 2004).

Transient Simulation

The transient simulation includes changes in ground-water 

storage over time that result from pumping and other hydraulic 

stresses. The distribution of aquifer storativity resulted, therefore, from the calibration of the transient simulation for the 

original Edwards aquifer model. For the diffuse-flow Edwards 

aquifer model, however, only the hydraulic conductivity distribution was changed during model calibration, as indicated previously. Simulations for steady-state and transient calibration 

were run sequentially, and adjustments were made to the appropriate input data until the final versions of both simulations 

were numerically consistent (residuals minimized for steadystate and transient simulations using the same model properties) 

representations of the Edwards aquifer flow system. 

The transient calibration period for the original Edwards 

aquifer model was 1947–2000. The transient simulation used 

648 monthly stress periods and a single time step per stress 

period. Multiple time steps (as many as 10) per stress period 

were used initially, but the number of time steps used was found 

to have no effect on the model results. Therefore, to minimize 

the length of the transient-simulation run times, only one time 

step per stress period subsequently was used.

The transient calibration targets included both a series of 

measurements over time of water level within a single well 

(hydrograph) and synoptic sets of water levels in multiple wells 

within comparatively short time periods. Synoptic sets of water 

levels in multiple wells during periods of below-normal 

(drought) and above-normal rainfall were selected to maximize 

the range of hydrologic conditions included in the transient calibration. The period of below-normal rainfall selected was 

August 1956, during the 1950s drought, when the lowest water 

levels of record were recorded. Water-level measurements for 

May–November 1956 were included as targets for the drought 

period to have a greater number and better areal distribution of 

wells with measurements; however, most of the water-level 

measurements were for August 1956. Therefore, the simulated 

hydraulic heads for the corresponding (August 1956) model 

stress period (stress period 117) were used to calculate the 

hydraulic head residuals. For the drought period, 171 wells 

were used as transient calibration targets (pl. 1; table 4, at end 

of report). The period of above-normal rainfall selected was 

November 1974–July 1975, a period of near record-high water 

levels in wells. Although most of the water-level measurements 

were for February 1975, the expansion of the time period of 

water-level measurements used was necessary to have a greater 

number and areal distribution of wells. The simulated hydraulic 

heads for the model stress period corresponding with February 

1975 (stress period 339) were used to calculate the hydraulic 

head residuals. For the above-normal rainfall period, 169 wells 

were used as transient calibration targets (pl. 1; table 5, at end 

of report). 

In addition to water levels in wells, springflows for Comal, 

San Marcos, Leona, San Antonio, and San Pedro Springs were 

used as calibration targets for the transient model calibration. 

Springflows for time periods that lack measurements were estimated by interpolation or from relations between springflows 

and water levels at nearby index wells.

The transient simulation for the diffuse-flow Edwards 

aquifer model was calibrated by varying the simulated hydraulic conductivities. Minor adjustments to the simulated hydraulic 

conductivities were needed during the transient calibration, particularly in the recharge zone. Calibration of the transient simulation for periods of greatly above-normal rainfall and recharge 

necessitated increases in hydraulic conductivities for parts of 

the recharge zone to avoid simulated hydraulic heads above 

land surface during these periods. This increase of hydraulic 

conductivities was most prevalent in Kinney, Uvalde, and 

Medina Counties. The final calibrated hydraulic conductivity 

distribution for the diffuse-flow Edwards aquifer model used 

for the steady-state and transient conditions is shown in 

figure 4. The distribution comprises 38 zones with hydraulic 

conductivities ranging from 3 to 50,000 ft/d.

RMS 1

n

-- hm hs ( ) – 2

i i = 1

n

∑

0.5

=
Figure 4. Simulated distribution of hydraulic conductivity for calibrated diffuse-flow Edwards aquifer model, San Antonio region, Texas. 

EXPLANATION

Hydraulic conductivity, in feet per day

33.54.5 8 10 11 15 20 25 3539 40 45 50 75 100 150 200 250 300

320 450 500 600 700 800 1,000 1,100 1,236 1,5002,000 5,000 7,500 10,000 12,500 15,000 20,000 50,000

Spring

100 ̊20'30" 99 ̊50'15" 99 ̊20' 98 ̊49'45" 98 ̊19'30" 

28 ̊59'

29 ̊29'15"

29 ̊59'30"

30 ̊29'45"

0 20 3

10

EDWARDS

KERR

REAL

KINNEY

BANDERA

KENDALL

GILLESPIE BLANCO

TR

HAYS

COMAL

WILSON

BEXAR

ATASCOSA

FRIO

MAVERICK ZAVALA

UVALDE

MEDINA

Las Moras Springs

Leona Springs

San Pedro Springs

San Antonio Springs

Comal S

Hueco Sp
16 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 5. Simulated relative to measured hydraulic heads for (A) August 1956 (stress period 117) and (B) February 1975 (stress period 

339), transient simulation, conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, Texas. 

400 600 800 1,000 1,200 1,400

MEASURED HYDRAULIC HEAD, IN FEET ABOVE NGVD 29

400 600 800 1,000 1,200 1,400

MEASURED HYDRAULIC HEAD, IN FEET ABOVE NGVD 29

400

600

800

1,000

1,200

1,400

SIMULATED HYDRAULIC HEAD,

IN FEET ABOVE NGVD 29

400

600

800

1,000

1,200

1,400

SIMULATED HYDRAULIC HEAD,

IN FEET ABOVE NGVD 29

A. Drought conditions, August 1956

Conduit-flow model

Diffuse-flow model

Line of equal value

Line of equal value

The final transient simulation generally reproduces the 

spatial distribution of measured water levels for the periods of 

drought and above-normal rainfall. Quantitative measures of 

goodness-of-fit between measured and simulated hydraulic 

heads (mean absolute difference, mean algebraic difference, 

and RMS error) were computed for the periods of drought and 

above-normal rainfall. The closest-match simulated hydraulic 

heads for the period of drought (May–November 1956) were 

within 30 ft of measured water levels at 141 of the 171 wells for 

which water-level data were available (table 4). The difference 

was less than 20 ft at 131 of the 171 wells. Differences were 

greater than 100 ft for five of the wells, and the largest difference was 175.8 ft for a well in the recharge zone in Medina 

County. All five of these wells are in or near the recharge zone 

in Medina and Uvalde Counties. Residuals greater than 30 ft 

occurred predominantly in wells in and near the recharge zone 

and in isolated individual wells in the confined freshwater zone 

of the aquifer in northeastern Kinney, central and eastern 

Uvalde, north-central and eastern Bexar, and southern Hays 

Counties. The isolated individual wells with large residuals 

generally are near wells with smaller (less than 30 ft) residuals; 

therefore, the large residuals are anomalous and might be 

caused by local hydrogeologic conditions not represented in the 

diffuse-flow Edwards aquifer model. The mean absolute difference between measured and simulated hydraulic heads is 

20.5 ft. The corresponding mean algebraic difference is -8.1 ft, 
Simulation of Ground-Water Flow 17

which might indicate a small bias toward simulated hydraulic 

heads too low relative to measured hydraulic heads during the 

period of drought. The graph of simulated relative to measured 

hydraulic heads indicates little bias in the simulation results for 

the period of drought (fig. 5). The RMS error is 33.4 ft (table 2) 

This error represents about 5 percent of the total measured head 

difference across the model area (712 ft). 

The final transient simulation generally reproduces the 

spatial distribution of measured water levels for the period of 

above-normal rainfall. The closest-match simulated hydraulic 

heads for the period of above-normal rainfall (November 

1974–July 1975) were within 30 ft of measured water levels 

at 138 of the 169 wells for which water-level data were available (table 5). The difference was less than 20 ft at 125 of the 

169 wells. Differences were greater than 100 ft for two wells, 

and the largest difference was 103.3 ft for a well in the recharge 

zone in Uvalde County. Wells with residuals greater than 

30 ft occur predominantly in and near the recharge zone. Isolated individual wells with relatively large residuals (greater 

than 30 ft) occur in central and south-central Uvalde, central 

and north-central Bexar, and southern Hays Counties. The 

mean absolute difference between measured and simulated 

hydraulic heads is 17.2 ft (table 2). The corresponding mean 

algebraic difference is 0.5 ft, which indicates that positive 

differences were approximately balanced by negative differences. The graph of simulated relative to measured hydraulic 

heads indicates little bias in the simulation results for the 

period of above-normal rainfall (fig. 5). The RMS error is 

25.8 ft (table 2). This error represents about 4 percent of the 

total measured head difference across the model area (663 ft).

Figure 5. Continued. 

400 600 800 1,000 1,200 1,400

MEASURED HYDRAULIC HEAD, IN FEET ABOVE NGVD 29

400 600 800 1,000 1,200 1,400

MEASURED HYDRAULIC HEAD, IN FEET ABOVE NGVD 29

400

600

800

1,000

1,200

1,400

SIMULATED HYDRAULIC HEAD,

IN FEET ABOVE NGVD 29

400

600

800

1,000

1,200

1,400

SIMULATED HYDRAULIC HEAD,

IN FEET ABOVE NGVD 29

Conduit-flow model

Diffuse-flow model

B. Above-normal rainfall conditions, February 1975

Line of equal value

Line of equal value
18 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

As indicated by the mean algebraic difference between 

simulated and measured hydraulic heads (-8.1 ft), the model 

might tend to simulate lower-than-measured hydraulic heads 

during periods of drought. On the basis of the RMS errors and 

the mean algebraic differences, the model provides a reasonable, conservative simulation of water levels for varying hydrologic conditions.

 The transient calibration results also include a comparison 

of simulated springflows and hydraulic heads with a series 

of measurements of springflow and of water levels within individual wells over time (hydrograph). Selected hydrographs 

comparing measured and simulated hydraulic heads for 11 of 

12 target wells with long-term water-level measurements and 

springflows for five springs are included in this report. The 12 

target wells are distributed throughout the model area (pl. 1) and 

are representative of the results of the transient simulation. The 

transient simulation for 1947–2000 acceptably reproduces measured fluctuations in hydraulic heads over time in the Edwards 

aquifer (figs. 6–8). The match between measured and simulated 

hydraulic heads generally is closer for wells completed in the 

confined zone of the aquifer than for those in and near the 

recharge zone. The RMS error ranged from 6.3 to 30.4 ft in 

12 wells with water-level measurements for varying periods 

during 1947–2000 (table 6, at end of report), and these errors 

represent 5.0 to 31.3 percent of the range in water-level fluctuations of each of those wells. The three wells with RMS errors 

greater than 20 ft are all in Hays County. The smallest RMS 

error (6.3 ft) was for well 6823701 in the confined freshwater 

zone of the aquifer in Comal County, and the largest (30.4 ft) 

was for well 6702103 in the confined freshwater zone of the 

aquifer in Hays County (table 6).

Generally acceptable agreement also was obtained 

between measured and simulated flow at springs (figs. 9, 10). 

The RMS errors for Comal, San Marcos, Leona, San Antonio, 

and San Pedro Springs ranged from 348,280 cubic feet per day 

(ft3

/d) (4.0 ft3/s) for San Pedro Springs to 3,448,867 ft3/d 

(39.9 ft3

/s) for San Antonio Springs (table 6). The RMS errors 

for the five springs, as a percentage of the range of discharge 

fluctuations measured at the springs, varied from 7.2 percent 

for San Marcos Springs and 8.1 percent for Comal Springs 

to 28.8 percent for Leona Springs. The mean algebraic differences between simulated and measured spring discharges are 

-127,334 ft3/d (-1.5 ft3/s) and 543,298 ft3/d (6.3 ft3/s) for Comal 

and San Marcos Springs, respectively, indicating that positive 

differences were approximately balanced by negative differences (table 6). Simulated high discharges during the 1970s and 

1990s for Comal Springs and during the late 1960s for San 

Marcos Springs are lower than the measured high discharges 

(fig. 9), whereas during other periods of measured high flows, 

the simulated and measured discharges generally are in close 

agreement. The recessions in simulated flows for San Marcos 

Springs generally are more gradual than are those in the 

measured data, and for some time periods the simulated low 

discharges of the recessions do not match the measured low 

discharges. Therefore, the simulated springflows tend to overestimate the measured springflows during many low-flow 

periods, resulting in the positive mean algebraic difference for 

San Marcos Springs (table 6). The simulated spring discharge 

for Leona Springs often is greater than the measured discharge 

during periods of zero or low discharge and is anomalously high 

following the very large recharge events of the early 1990s 

(fig. 10). However, as noted at the end of the previous section, 

reported discharge for Leona Springs might appreciably underestimate the actual discharge because of unmeasured discharge 

from the Edwards aquifer to the Leona gravels. The simulated 

spring discharges for San Antonio Springs tend to overestimate 

the measured discharges and for San Pedro Springs tend to 

underestimate the measured discharges during peak discharge 

periods (fig. 10). In general, the model reasonably simulates 

springflows for different hydrologic conditions; the match is 

closer for Comal and San Marcos Springs than for the smaller 

springs (Leona, San Antonio, and San Pedro Springs).

Water Budget

In addition to hydraulic heads, the water budget for the 

model is computed for each stress period. A water budget in 

the context of the model is an accounting of inflow to, outflow 

from, and storage change in the aquifer. For steady-state 

conditions, inflow (sources) to the aquifer equals outflow 

(discharges) from the aquifer. For transient conditions, changes 

in storage likely occur. For a balanced transient water budget—that is, total sources equal total discharges equal total 

flow through the aquifer—positive changes (gains) in storage 

must be included as discharges, and negative changes (losses) 

in storage must be included as sources. Sources of water to 

the Edwards aquifer include (1) recharge from leakage from 

streams and infiltration of rainfall in the recharge zone and 

(2) inflow through the northern and northwestern aquifer 

boundaries. Also, a small amount of leakage from the Colorado 

River to the aquifer occurs during periods of low water levels. 

Discharge from the Edwards aquifer includes (1) springflow 

(drain discharge), (2) withdrawals by wells, and (3) leakage to 

the Colorado River from the aquifer.

Steady-State Simulation

The steady-state simulation water budget indicates that 

recharge accounts for 93.6 percent of the sources of water to the 

Edwards aquifer, and inflow through the northern and northwestern model boundaries contributes 6.4 percent (table 7, at 

end of report). Most of the flow into the model area through the 

northern and northwestern model boundaries occurs through the 

northern boundary (87.9 percent). The largest discharges from 

the Edwards aquifer in the steady-state simulation water budget 

are springflow (73.4 percent) and withdrawals by wells (25.7 

percent) (table 7). Discharge from the aquifer to the Colorado 

River (as stream-aquifer leakage) is a minor component of the 

steady-state budget (0.9 percent).
Simulation of Ground-Water Flow 19

Transient Simulation

In the simulated water budget for the transient simulation 

for 1956 (table 7), positive changes (gains) in storage for stress 

periods are included as discharges, and negative changes 

(losses) in storage are included as sources. This convention is 

consistent with making the water budget (total sources equal 

total discharges equal total flow through the aquifer) balance. 

The 1956 water budget represents drought conditions.

The principal source of water to the Edwards aquifer 

(excluding change in storage) for the transient simulation is 

recharge, constituting about 60 percent of the sources of water 

to the Edwards aquifer during 1956 (table 7). Inflow through 

the northern and northwestern model boundaries contributed a 

relatively small amount of water. Subsurface inflow through 

the northern and most of the northwestern model boundaries 

was simulated as a constant flux, and therefore no variation 

occurs on a monthly and annual basis. Although the amount of 

water contributed by boundary inflow was relatively small, it 

constituted about 40 percent of the sources (excluding change 

in storage) to the aquifer during 1956, because of the greatly 

reduced recharge during this drought period. A very small 

amount of leakage from the Colorado River to the aquifer 

occurred during 1956. This leakage occurred because hydraulic 

heads in the aquifer, although generally above river stage, are 

below river stage during periods of low water levels in the 

aquifer.

The principal discharges from the Edwards aquifer for the 

transient simulation are springflow and withdrawals (pumpage) 

(table 7). During 1956, representing drought conditions, the 

greatest discharge was withdrawals (pumpage) (76.1 percent), 

followed by springflow (23.2 percent); this is the reverse of 

steady state for which the greatest discharge is springflow, followed by withdrawals (pumpage). During 1956 and for steadystate, discharge from the aquifer to the Colorado River is a small 

component of the budget. Withdrawals (pumpage) was the largest budget component (excluding change in storage) during 

1956, with low rainfall resulting in low recharge and increased 

pumpage. In contrast, for steady-state the much greater rainfall 

and corresponding greater recharge (steady-state recharge 

about 9.6 times greater than in 1956) resulted in pumpage being 

a proportionately smaller component of the budget. Springflow 

was the largest discharge from the aquifer for steady state, much 

greater than in 1956 (by a factor of about 4.9), because of higher 

water levels in the aquifer. Water levels in the aquifer depend 

on both recharge and pumpage. Steady-state pumpage was 

approximately one-half of the pumpage during 1956, and 

recharge was greater by a factor of 9.6, which resulted in higher 

water levels. 

During 1956, the change in storage (net water released 

from storage) was much greater than recharge, accounting 

for 75.0 percent of the total flow (including change in storage) 

compared to 15.0 percent for recharge (table 7). The amount 

and percentage of water released from storage is large during 

1956 (drought conditions) because recharge is small and 

more water is required from storage to meet the pumpage 

demand. During 1956, the largest net releases from storage 

occurred during June–August, the period of largest withdrawals 

by wells and comparatively low recharge. No net addition to 

storage occurred during 1956, which indicated the aquifer was 

being depleted of water during the entire year. 

Comparison of Simulations

Hydraulic heads and springflows simulated by the diffuseflow Edwards aquifer model for selected observation wells and 

springs were compared to the corresponding hydraulic heads 

and springflows simulated by the conduit-flow Edwards aquifer 

model. Both the steady-state and transient simulated hydraulic 

heads and springflows were used for the comparisons. The 

results of the comparison between the simulated hydraulic 

heads and springflows for the diffuse-flow Edwards aquifer 

model and the conduit-flow Edwards aquifer model are shown 

in hydrographs for selected observation wells and springs 

(figs. 11, 12) and summarized in table 6. The mean absolute difference, mean algebraic difference, and RMS error of the residuals for the diffuse-flow Edwards aquifer model and the conduit-flow Edwards aquifer model are tabulated. These statistics 

are used as quantitative measures of the goodness-of-fit 

between the measured and simulated hydraulic heads and 

springflows.

The mean absolute difference and the RMS error of the 

residuals for hydraulic heads for the diffuse-flow Edwards 

aquifer model are appreciably smaller than those for the conduit-flow Edwards aquifer model for the three synoptic waterlevel time periods (steady state, drought, and above-normal 

rainfall) (table 2). The RMS errors for the conduit-flow 

Edwards aquifer model are 27, 76, and 30 percent greater than 

for the diffuse-flow Edwards aquifer model for the steady-state, 

drought, and above-normal rainfall synoptic time periods, 

respectively. The improved statistical match between the simulated and measured hydraulic heads also is evident from a 

comparison of the graphs of simulated relative to measured 

hydraulic heads, as indicated by less deviation from the match 

line (line of equal value) of the data in the graphs for the diffuseflow Edwards aquifer model (figs. 3, 5). The improvements in 

the match between simulated and measured hydraulic head 

were for wells predominantly in or near the recharge zone of 

the aquifer. The improvements were achieved primarily by 

adjustments to the configuration of hydraulic conductivity 

zones and the assigned hydraulic conductivities for the hydraulic conductivity zones in and near the recharge zone. The 

general pattern of lower simulated hydraulic heads for the diffuse-flow Edwards aquifer model than for the conduit-flow 

Edwards aquifer model is indicated by the consistently lower 

mean algebraic differences for the diffuse-flow Edwards aquifer model for all three synoptic water-level time periods 

(table 2).
20 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 6. Measured and simulated water levels (hydraulic heads) for Edwards aquifer wells in (A) Uvalde County and (B) Medina 

County, diffuse-flow Edwards aquifer model, San Antonio region, Texas. 

DATE

DATE

1/1/1947

1/1/1949

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ALTITUDE, IN FEET 

ABOVE NGVD 29

ALTITUDE, IN FEET

ABOVE NGVD 29

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Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Hydraulic head

Hydraulic head

A

Well 6950302 (Uvalde County index well J–27)

(South-central Uvalde County; see plate 1 for location)

Well 6945401

(East-central Uvalde County; see plate 1 for location)
Simulation of Ground-Water Flow 21

Figure 6. Continued.

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

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1/1/19551/1/1957

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ALTITUDE, IN FEET 

ABOVE NGVD 29

ALTITUDE, IN FEET

ABOVE NGVD 29

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Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Hydraulic head

Hydraulic head

B

Well 6946701

(Southwest Medina County; see plate 1 for location)

Well 6841301

(East-central Medina County; see plate 1 for location)
22 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 7. Measured and simulated water levels (hydraulic heads) for Edwards aquifer wells in Bexar County, diffuse-flow Edwards 

aquifer model, San Antonio region, Texas.

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/19591/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

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1/1/1973

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1/1/1981

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1/1/1949

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1/1/19751/1/1977

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DATE

DATE

DATE

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

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ALTITUDE, I

N FEET 

ABO

VE 

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VD 29

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N FEET 

ABO

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Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Hydraulic head

Hydraulic head

Hydraulic head

Well 6837203 (Bexar County index well J–17)

(Central Bexar County; see plate 1 for location)

Well 6845102

(South-central Bexar County; see plate 1 for location)

Well 6830211

(Northeast Bexar County; see plate 1 for location)
Simulation of Ground-Water Flow 23

The simulated steady-state springflows for the diffuseflow Edwards aquifer model and the conduit-flow Edwards 

aquifer model are generally similar (table 3). The differences 

are 3 ft3

/s for San Marcos and San Pedro Springs, 2 ft3/s for 

Comal Springs, and approximately zero for Leona and San 

Antonio Springs. The differences are 0.6 and 2.0 percent of the 

median steady-state springflows for Comal and San Marcos 

Springs, respectively. 

For the transient simulation, the mean absolute difference 

and RMS error of the residuals for the diffuse-flow Edwards 

aquifer model are smaller than those for the conduit-flow 

Edwards aquifer model for six of the 12 target wells with longterm water-level measurements (table 6). Conversely, those 

statistics for the diffuse-flow Edwards aquifer model are larger 

than those for the conduit-flow Edwards aquifer model for six 

of the 12 target wells. The largest reductions in the RMS error 

for the diffuse-flow Edwards aquifer model occurred for two 

wells in Bexar County (-11.1 and -8.0 ft). The largest increases 

in the RMS error occurred for two wells in Hays County (15.0 

and 15.1 ft). In Comal, Medina, and Uvalde Counties the differences in the RMS errors are 7.2 ft or less and are equally distributed between reductions and increases. The mean algebraic 

differences for the three target wells in Hays County for the 

diffuse-flow Edwards aquifer model are higher than those for 

the conduit-flow Edwards aquifer model (table 6), indicating a 

general increase in hydraulic heads. In contrast, the mean algebraic differences for the three target wells in Bexar County are 

lower for the diffuse-flow Edwards aquifer model, indicating a 

general decrease in hydraulic heads. The mean algebraic differences for the target wells in Comal, Medina, and Uvalde Counties are equally distributed between reductions and increases for 

the diffuse-flow Edwards aquifer model compared to those of 

the conduit-flow Edwards aquifer model. Hydrographs also 

illustrate the differences between measured and simulated 

hydraulic heads and springflows for the diffuse-flow Edwards 

aquifer model compared to those of the conduit-flow Edwards 

aquifer model. The hydrographs for the Bexar County index 

well (6837203) and the Uvalde County index well (6950302) 

generally illustrate lower water levels simulated by the diffuseflow Edwards aquifer model than those simulated by the 

conduit-flow Edwards aquifer model (fig. 11).

The residual statistics (mean absolute difference and RMS 

error of the residuals) in some cases are not a complete measure 

of the goodness-of-fit between the measured and simulated 

hydraulic heads. The hydrograph for the Bexar County index 

well indicates that the conduit-flow Edwards aquifer model 

might be more responsive to the magnitude of fluctuations in 

measured water levels than the diffuse-flow Edwards aquifer 

model (fig. 11), although the residual statistics for the diffuseflow Edwards aquifer model are similar to those for the conduitflow Edwards aquifer model (table 6). The simulated peaks in 

the hydrograph for the Bexar County index well for the diffuseflow Edwards aquifer model generally are lower than for the 

conduit-flow Edwards aquifer model. During the periods of 

highest water levels (periods of highest precipitation and 

recharge) and largest peaks in the hydrograph, the differences in 

simulated heads between the two models are greater than for 

periods with lower peaks in the hydrograph. 

The goodness-of-fit between measured and simulated 

springflows, as indicated by the statistics in table 6 and the 

hydrographs of Comal and San Marcos Springs in figure 12, 

is similar for Comal, San Marcos, and Leona Springs for the 

diffuse-flow Edwards aquifer model and the conduit-flow 

Edwards aquifer model. The mean absolute difference and 

RMS error were lower for Comal and Leona Springs and 

minimally higher for San Marcos Springs for the diffuse-flow 

Edwards aquifer model. The RMS errors for Comal and Leona 

Springs were 15.6 and 21.3 percent less, respectively, whereas 

the RMS error for San Marcos Springs was 3.3 percent greater. 

The differences in simulated springflows between the diffuseflow Edwards aquifer model and the conduit-flow Edwards 

aquifer model are greatest during the periods of greatest springflows (fig. 12). The RMS errors for San Antonio and San Pedro 

Springs were appreciably greater, 80.2 and 51.0 percent, 

respectively, for the diffuse-flow Edwards aquifer model 

(table 6). The appreciable increases in the RMS errors for San 

Antonio and San Pedro Springs might be caused by the movement of large volumes of water through a broader HHC zone, as 

opposed to the one-cell-wide conduits for the conduit-flow 

Edwards aquifer model. San Antonio and San Pedro Springs are 

relatively distant from the simulated one-cell-wide conduits in 

the conduit-flow Edwards aquifer model, but they are within an 

HHC zone in the diffuse-flow Edwards aquifer model. The 

mean algebraic differences indicate that the springflows are less 

for all the springs, except San Antonio Springs, for the diffuseflow Edwards aquifer model compared to those for the conduitflow Edwards aquifer model. This, coupled with the observation that greater differences occur during the periods of greatest 

springflows, might indicate that the diffuse-flow Edwards aquifer model is somewhat less responsive than the conduit-flow 

Edwards aquifer model.

The simulated water budgets for the diffuse-flow Edwards 

aquifer model are similar to those for the conduit-flow Edwards 

aquifer model. For the steady-state simulation, the largest differences in percentage of total sources or discharges for a budget component are 0.3 percent for two discharges, springflow 

and stream-aquifer leakage (table 7). For 1956 during the 

transient simulation, the largest differences in percentage of 

total sources or discharges for a budget component are an 

increase of 1.8 percent for withdrawals (pumpage) (increase of 

749.7 acre-feet per year [acre-ft/yr]) and a decrease of 2.0 percent for springflow (decrease of 10,732.1 acre-ft/yr). In addition, the magnitude (decrease of 10,497.6 acre-ft/yr) and percentage (decrease of 0.9 percent) for the net change in storage 

(net loss of water from storage) were less for the diffuse-flow 

Edwards aquifer model. The relatively small increase in withdrawals (pumpage) for the diffuse-flow Edwards aquifer model 

was due to fewer model cells going dry in response to the simulated drought conditions and the deactivation of wells in those 

dry model cells. 
24 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 8. Measured and simulated water levels (hydraulic heads) for Edwards aquifer wells in (A) Comal County and (B) Hays County, 

diffuse-flow Edwards aquifer model, San Antonio region, Texas. 

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

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1/1/1985

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1/1/1989

1/1/1991

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1/1/2001

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DATE

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

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1/1/1963

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Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Hydraulic head

Hydraulic head

A

Well 6823701

(South-central Comal County; see plate 1 for location)

Well 6816801

(Comal County; between Comal and San Marcos Springs; see plate 1 for location)

The largest change in terms of the magnitude of water 

budget components was the decrease of about 10,730 acre-ft/yr 

in springflow for the diffuse-flow Edwards aquifer model 

compared to springflow for the conduit-flow Edwards aquifer 

model (table 7). This decrease in springflow (a water budget 

discharge) was largely offset by the smaller net loss of water 

from storage (a water budget source) of about 10,500 acre-ft/yr 

(table 7). The decrease in springflow for the diffuse-flow 

Edwards aquifer model compared to that for the conduitflow Edwards aquifer model might be due to the general pattern 

of lower simulated hydraulic heads for the diffuse-flow 

Edwards aquifer model compared to that for the conduitflow Edwards aquifer model, indicated by the lower mean algebraic differences for the diffuse-flow Edwards aquifer model 

(table 2). Smaller springflows for all the springs, except San 

Antonio Springs, for the diffuse-flow Edwards aquifer model 

compared to springflows for the original Edwards aquifer 

model also are indicated by the lower mean algebraic differences for the diffuse-flow Edwards aquifer model as compared 

to the differences for the conduit-flow Edwards aquifer model 

(table 6). 
Simulation of Ground-Water Flow 25

Figure 8. Continued. 

Well 5858101

(Eastern Hays County; see plate 1 for location)

Well 5857903

(Hays County; edge of recharge zone; see plate 1 for location)

1/1/1947

1/1/1949

1/1/1951

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DATE

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690

ALTITUDE, I

N FEET ABO

VE 

N

G

VD 29

Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Hydraulic head

Hydraulic head

B
26 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 9. Measured and simulated springflows for (A) Comal Springs and (B) San Marcos Springs, 1947–2000, diffuse-flow Edwards 

aquifer model, San Antonio region, Texas. 

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

DATE

DATE

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

1/1/2001

1/1/2001

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

40,000,000

45,000,000

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

40,000,000

45,000,000

0

0

SPRI

NGFLOW, I

N CUBIC FEET PER DAY SPRI

NGFLOW, I

N CUBIC FEET PER DAY

Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

A. Comal Springs

B. San Marcos Springs

Springflow

Springflow

Model Limitations

All numerical ground-water-flow models are simplifications of the real system and, therefore, have limitations. 

Limitations generally result from assumptions used to develop 

the conceptual and numerical models, limitations in the quality 

and quantity of the input data, and scale at which the model can 

be applied. In addition, a combination of input to the model 

different from that used in the calibrated simulations could produce the same result; the solution is non-unique. A summary of 

important limitations and uncertainties associated with conceptual and numerical models, input data, and scale of application 

is given in the text box on page 29. Lindgren and others (2004) 

contains a more detailed discussion of the model limitations. 
Simulation of Ground-Water Flow 27

Figure 10. Measured and simulated springflows for (A) Leona Springs, (B) San Antonio Springs, and (C) San Pedro Springs, 1947–2000, 

diffuse-flow Edwards aquifer model, San Antonio region, Texas. 

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

DATE

DATE

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

1/1/2001

1/1/2001

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/19751/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

DATE

1/1/2001

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

7,000,000

8,000,000

9,000,000

10,000,000

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

3,000,000

SPRI

NGFLOW, I

N CUBIC FEET PER DAY SPRI

NGFLOW, I

N CUBIC FEET PER DAY SPRI

NGFLOW, I

N CUBIC FEET PER DAY

Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Measured

Simulated

EXPLANATION

Springflow

Springflow

Springflow

A. Leona Springs

B. San Antonio Springs

C. San Pedro Springs
28 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 11. Measured and simulated water levels (hydraulic heads) for (A) Bexar County index well (J–17, 6837203) and (B) Uvalde 

County index well (J–27, 6950302), 1947–2000, conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, Texas. 

DATE

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

1/1/2001

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

DATE

1/1/2001

600

610

620

630

640

650

660

670

680

690

700

710

ALTITUDE, I

N FEET ABO

VE 

N

G

VD 29

810

820

830

840

850

860

870

880

890

900

910

920

930

ALTITUDE, I

N FEET ABO

VE 

N

G

VD 29

Measured

Simulated by conduit-flow

Edwards aquifer model

EXPLANATION

Hydraulic head

Simulated by diffuse-flow

Edwards aquifer model

Measured

Simulated by conduit-flow

Edwards aquifer model

EXPLANATION

Hydraulic head

Simulated by diffuse-flow

Edwards aquifer model

A. Well 6837203

(Bexar County index well J–17; see plate 1 for location)

B. Well 6950302

(Uvalde County index well J–27; see plate 1 for location)

An additional limitation results from the calibration 

technique, trial-and-error calibration, that was used for both the 

conduit-flow Edwards aquifer model and the diffuse-flow 

Edwards aquifer model. Manual trial-and-error adjustment of 

input data does not give information on the degree of uncertainty in the final input data selection (confidence intervals 

on input data estimates cannot be determined), nor does it guarantee the statistically best solution. Also, the trial-and-error 

process is influenced by the modeler’s expertise and biases and 

is therefore a subjective solution. An alternative calibration 

technique is an automated statistically-based solution of the 

inverse problem, generally called parameter estimation. Parameter estimation quantifies the uncertainty in estimates of input 

data and gives the statistically most appropriate solution for the 

given input data, provided it is based on an appropriate statistical model of errors (Anderson and Woessner, 1992). However, 

the use of parameter estimation was beyond the scope of the 

study of this report. 
Simulation of Ground-Water Flow 29

Summary of important limitations and uncertainties associated with conceptual and numerical models, 

input data, and scale of application

1. Assumptions for conceptual and numerical models

a. Use of a distributed, porous media model to simulate flow in a karst system results in

• Inability to simulate rapid, potentially turbulent flow in conduits

• Inability to simulate travel times for contaminants in the aquifer system

b. Discretization of the model grid

• Vertical: one model layer

• Horizontal: relatively coarse cell size

c. Temporal discretization for transient simulation

• Monthly stress periods

d. Representation of boundary conditions

• Placement of the southern model boundary at the 10,000-mg/L dissolved solids concentration line

• Use of a constant-flux boundary condition for the northern model boundary for the transient 

simulation

• Assumption that the effectiveness of a fault as a barrier to flow is proportional to the fault 

displacement

2. Limitations of input data

a. Datasets based on scanty information for some parameters and in some areas

• Parameters and data based on scanty information: (1) storativity distribution and (2) water-level data

• Area with scanty information: (1) recharge zone, (2) Kinney County, and (3) south of the 1,000-mg/L 

dissolved solids concentration line

b. Data of uncertain accuracy that warrants further analysis

• Recharge

• Withdrawals by wells

• Location and characteristics of high-permeability zones or conduits

3. Scale of application

a. The Edwards aquifer model is regional in scale, and therefore its application to local, site-specific issues is not 

appropriate
30 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Figure 12. Measured and simulated springflows for (A) Comal Springs and (B) San Marcos Springs, 1947–2000, conduit-flow and 

diffuse-flow Edwards aquifer models, San Antonio region, Texas.

DATE

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

1/1/2001

1/1/1947

1/1/1949

1/1/1951

1/1/1953

1/1/1955

1/1/1957

1/1/1959

1/1/1961

1/1/1963

1/1/1965

1/1/1967

1/1/1969

1/1/1971

1/1/1973

1/1/1975

1/1/1977

1/1/1979

1/1/1981

1/1/1983

1/1/1985

1/1/1987

1/1/1989

1/1/1991

1/1/1993

1/1/1995

1/1/1997

1/1/1999

DATE

1/1/2001

SPRI

NGFLOW, I

N CUBIC FEET PER DAY SPRI

NGFLOW, I

N CUBIC FEET PER DAY

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

40,000,000

45,000,000

0

5,000,000

10,000,000

15,000,000

20,000,000

25,000,000

30,000,000

35,000,000

40,000,000

45,000,000

Measured

Simulated by conduit-flow

Edwards aquifer model

EXPLANATION

Springflow

Simulated by diffuse-flow

Edwards aquifer model

Measured

Simulated by conduit-flow

Edwards aquifer model

EXPLANATION

Springflow

Simulated by diffuse-flow

Edwards aquifer model

A. Comal Springs

B. San Marcos Springs

Summary

A numerical ground-water-flow model (hereinafter, the 

conduit-flow Edwards aquifer model) of the karstic Edwards 

aquifer in south-central Texas was completed as part of a study 

conducted during 2000–2003 by the U.S. Geological Survey 

(USGS) and The University of Texas at Austin, Bureau of Economic Geology, in cooperation with the U.S. Department of 

Defense and the Edwards Aquifer Authority. The conceptualization that served as the basis for the conduit-flow Edwards 

aquifer model emphasizes conduit development and conduit 

flow, and included simulating conduits as one-cell-wide, continuously connected features. Uncertainties regarding the 

degree to which conduits pervade the Edwards aquifer and 

influence ground-water flow, as well as uncertainties inherent 

in simulating conduits as one-cell-wide, continuously connected features, raised the question of whether a model based on 

the conduit-flow conceptualization was the optimum model for 

the Edwards aquifer. Accordingly, a model with a hydraulic 

conductivity distribution without conduits was considered. To 

develop an alternative, non-conduit or diffuse-flow hydraulic 

conductivity distribution for the Edwards aquifer model, the 
Summary 31

USGS, in cooperation with the San Antonio Water System, conducted a study during 2004–05. 

Calibration of the Edwards aquifer model with the alternative hydraulic conductivity distribution (hereinafter, the diffuse-flow Edwards aquifer model) included changes to the simulated hydraulic conductivity distribution only. All other 

properties were held constant at the same values used in the 

conduit-flow Edwards aquifer model. The hydraulic conductivity distribution for the diffuse-flow Edwards aquifer model, 

based primarily on a conceptualization in which flow in the 

aquifer predominantly is through a network of numerous small 

fractures and openings, includes 38 zones with hydraulic conductivities ranging from 3 to 50,000 ft/d. The initial hydraulic 

conductivity distribution for the diffuse-flow Edwards aquifer 

model was derived primarily from (1) estimates of relative 

transmissivities made by Maclay and Small (1984), based on 

available geologic, hydrochemical, and hydrologic information, 

for the recharge zone; (2) the hydraulic conductivity distribution developed by Painter and others (2002) for the freshwater 

confined zone; and (3) geologic structure and geochemical 

information used to delineate zones of high hydraulic conductivity. The final calibrated distribution of hydraulic conductivity results from the outcome of trial-and-error calibration, by 

varying the configuration of some of the simulated hydraulic 

conductivity zones and the simulated hydraulic conductivities. 

Calibration and evaluation of the diffuse-flow (and the 

conduit-flow) Edwards aquifer model were conducted for 

steady-state (1939–46) and transient (1947–2000) conditions. 

Simulated hydraulic heads were within 30 ft of measured water 

levels at 130 of 144 wells used as targets for the steady-state 

simulation. The difference was less than 20 ft at 122 of the 144 

wells. The RMS error for the calibrated steady-state simulation 

is 20.9 ft. This error represents about 3 percent of the total head 

difference across the model area. The simulated springflows for 

Comal and San Marcos Springs for the calibrated steady-state 

simulation were within 2.4 and 15 percent of the median springflows for the two springs, respectively. 

The transient calibration period for the diffuse-flow 

Edwards aquifer model was 1947–2000, with 648 monthly 

stress periods, the same as for the conduit-flow Edwards aquifer 

model. The closest-match simulated hydraulic heads for a 

period of drought (May–November 1956) for the calibrated 

transient simulation were within 30 ft of measured water levels 

at 141 of the 171 wells for which water-level data were available. The difference was less than 20 ft at 131 of the 171 wells. 

The RMS error is 33.4 ft, which represents about 5 percent of 

the total head difference across the model area (712 ft). The 

closest-match simulated hydraulic heads for a period of abovenormal rainfall (November 1974–July 1975) for the calibrated 

transient simulation were within 30 ft of measured water levels 

at 138 of the 169 wells for which water-level data were available. The difference was less than 20 ft at 125 of the 169 wells. 

The RMS error is 25.8 ft, which represents about 4 percent of 

the total head difference across the model area. 

The RMS error ranged from 6.3 to 30.4 ft in 12 target wells 

with long-term water-level measurements for varying periods 

during 1947–2000 for the calibrated transient simulation for the 

diffuse-flow Edwards aquifer model, and these errors represent 

5.0 to 31.3 percent of the range in water-level fluctuations of 

each of those wells. The three wells with RMS errors greater 

than 20 ft are all in Hays County. The RMS errors for the five 

major springs in the San Antonio segment of the aquifer for the 

calibrated transient simulation, as a percentage of the range of 

discharge fluctuations measured at the springs, varied from 

7.2 percent for San Marcos Springs and 8.1 percent for Comal 

Springs to 28.8 percent for Leona Springs. The simulated spring 

discharges for San Antonio Springs tend to overestimate the 

measured discharges and for San Pedro Springs tend to underestimate the measured discharges during peak discharge 

periods.

In addition to hydraulic heads, the water budget for the 

model is computed for each stress period. A water budget in the 

context of the model is an accounting of inflow to, outflow 

from, and storage change in the aquifer. The steady-state 

simulation water budget indicates that recharge accounts for 

93.6 percent of the sources of water to the Edwards aquifer, 

and inflow through the northern and northwestern model 

boundaries contributes 6.4 percent. The largest discharges from 

the Edwards aquifer in the steady-state simulation water budget 

are springflow (73.4 percent) and withdrawals by wells (25.7 

percent).

The principal source of water to the Edwards aquifer 

(excluding change in storage) for the transient simulation is 

recharge, constituting about 60 percent of the sources of water 

to the Edwards aquifer during 1956, a drought period. Although 

the amount of water contributed by boundary inflow was relatively small, it constituted about 40 percent of the sources 

(excluding change in storage) to the aquifer during 1956, 

because of the greatly reduced recharge during this drought 

period. The principal discharges from the Edwards aquifer for 

the transient simulation during 1956 were withdrawals (pumpage) (76.1 percent), followed by springflow (23.2 percent). 

During 1956, the change in storage (net water released from 

storage) was much greater than recharge, accounting for 75.0 

percent of the total flow (including change in storage) compared 

to 15.0 percent for recharge. The amount and percentage of 

water released from storage is large during 1956 (drought conditions) because recharge is small and more water is required 

from storage to meet the pumpage demand. 

Hydraulic heads and springflows simulated by the diffuseflow Edwards aquifer model for selected observation wells and 

springs were compared to the corresponding hydraulic heads 

and springflows simulated by the conduit-flow Edwards aquifer 

model. The mean absolute difference and the RMS error of the 

residuals for hydraulic heads for the diffuse-flow Edwards aquifer model are appreciably smaller than those for the conduitflow Edwards aquifer model for the three synoptic water-level 

time periods (steady state, drought, and above-normal rainfall). 

The RMS errors for the conduit-flow Edwards aquifer model 

are 27, 76, and 30 percent greater than those for the diffuse-flow 

Edwards aquifer model for the steady-state, drought, and 

above-normal rainfall synoptic time periods, respectively. The 
32 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

improvements in the match between simulated and measured 

hydraulic head were predominantly for wells in or near the 

recharge zone of the aquifer. The general pattern of lower simulated hydraulic heads for the diffuse-flow Edwards aquifer 

model compared to that for the conduit-flow Edwards aquifer 

model is indicated by the consistently lower mean algebraic differences for the diffuse-flow Edwards aquifer model for all 

three synoptic water-level time periods. 

The simulated steady-state springflows for the diffuseflow Edwards aquifer model and the conduit-flow Edwards 

aquifer model generally are similar. Differences are 0.6 and 2.0 

percent of the median steady-state springflows for Comal and 

San Marcos Springs, respectively. For the transient simulation, 

the mean absolute difference and RMS error of the residuals for 

the diffuse-flow Edwards aquifer model are smaller than those 

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

target wells with long-term water-level measurements and 

larger for the six other wells. The largest reductions in the RMS 

error for the diffuse-flow Edwards aquifer model occurred for 

two wells in Bexar County (-11.1 and -8.0 ft). The largest 

increases in the RMS error occurred for two wells in Hays 

County (15.0 and 15.1 ft). The hydrographs for the Bexar 

County index well (6837203) and the Uvalde County index well 

(6950302) generally illustrate lower water levels simulated by 

the diffuse-flow Edwards aquifer model than those simulated 

by the conduit-flow Edwards aquifer model. 

The goodness-of-fit between measured and simulated 

springflows is similar for Comal, San Marcos, and Leona 

Springs for the diffuse-flow Edwards aquifer model and the 

conduit-flow Edwards aquifer model. The RMS errors for 

Comal and Leona Springs were 15.6 and 21.3 percent less, 

respectively, whereas the RMS error for San Marcos Springs 

was 3.3 percent greater for the diffuse-flow Edwards aquifer 

model compared to the conduit-flow Edwards aquifer model. 

The RMS errors for San Antonio and San Pedro Springs were 

appreciably greater, 80.2 and 51.0 percent, respectively, for the 

diffuse-flow Edwards aquifer model. The mean algebraic differences indicate that the springflows are less for all the springs, 

except San Antonio Springs, for the diffuse-flow Edwards aquifer model compared to those for the conduit-flow Edwards 

aquifer model. This, coupled with the observation that greater 

differences occur during the periods of greatest springflows, 

might indicate that the diffuse-flow Edwards aquifer model is 

somewhat less responsive than the conduit-flow Edwards aquifer model.

The simulated water budgets for the diffuse-flow Edwards 

aquifer model are similar to those for the conduit-flow Edwards 

aquifer model. For the steady-state simulation, the largest differences in percentage of total sources or discharges for a budget component are 0.3 percent for two discharges, springflow 

and stream-aquifer leakage. For 1956 for the transient simulation, the largest differences in percentage of total sources or 

discharges for a budget component are an increase of 1.8 percent for withdrawals (pumpage) (increase of 749.7 acre-ft/yr) 

and a decrease of 2.0 percent for springflow (decrease of 

10,732.1 acre-ft/yr). In addition, the magnitude (decrease of 

10,497.6 acre-ft/yr) and percentage (decrease of 0.9 percent) for 

the net change in storage (net loss of water from storage) were 

less for the diffuse-flow Edwards aquifer model. 

The largest change in terms of the magnitude of water budget components was the decrease of about 10,730 acre-ft/yr in 

springflow for the diffuse-flow Edwards aquifer model compared to springflow for the conduit-flow Edwards aquifer 

model. This decrease in springflow (a water budget discharge) 

was largely offset by the smaller net loss of water from storage 

(a water budget source) of about 10,500 acre-ft/yr. The decrease 

in springflow for the diffuse-flow Edwards aquifer model compared to that for the conduit-flow Edwards aquifer model might 

be due to the general pattern of lower simulated hydraulic heads 

for the diffuse-flow Edwards aquifer model compared to that 

for the conduit-flow Edwards aquifer model.

References 

Abbott, P.L., and Woodruff, C.M., Jr., 1986, Geologic history 

of the Edwards aquifer [abs.]: Geological Society of America 

Abstracts with Programs, v. 18, no. 6, p. 521. 

Anderson, M.P., and Woessner, W.W., 1992, Applied groundwater modeling—Simulation of flow and advective transport: San Diego, Calif., Academic Press, 381 p.

Birk, Steffen, Bauer, Sebastian, Liedl, Rudolf, and Sauter, 

Martin, 2003, Coupling a pipe-network to MODFLOW to 

predict the evolution of karst aquifers in Poeter, E.P., Zheng, 

C., Hill, M.C., and Doherty, John, eds., MODFLOW and 

more 2003—Understanding through modeling, Golden, 

Colo., September 16–19, 2003, Proceedings: Colorado 

School of Mines, p. 65–69.

Environmental Simulations, Inc., 2002, Guide to using Groundwater Vistas: Reinholds, Pa., Environmental Simulations, 

Inc., 266 p.

Garza, Sergio, 1968, Aquifer characteristics from well-field 

production records, Edwards Limestone, San Antonio area, 

Texas: Tucson, University of Arizona, Masters Thesis, 46 p.

George, W.O., 1952, Geology and ground-water resources of 

Comal County, Texas: U.S. Geological Survey WaterSupply Paper 1138, 126 p.

Green, R.T., 2004, Geophysical survey to determine the depth 

and lateral extent of the Leona aquifer and evaluation of 

discharge through the Leona River floodplain, south of 

Uvalde, Texas: Contract report to Edwards Aquifer Authority, 17 p.

Groschen, G.E., 1996, Hydrogeologic factors that affect the 

flowpath of water in selected zones of the Edwards aquifer, 

San Antonio region, Texas: U.S. Geological Survey Water 

Resources Investigations Report 96–4046, 73 p.

Halihan, Todd, Mace, R.E., and Sharp, J.M., 2000, Flow in the 

San Antonio segment of the Edwards aquifer—Matrix, fractures, or conduits?, in Sasowsky, I.D., and Wicks, C.M., 

Groundwater flow and contaminant transport in carbonate 

aquifers: Brookfield, Vt., A.A. Balkema, p. 129–146.
References 33

Harbaugh, A.W., and McDonald, M.G., 1996, User’s documentation for MODFLOW–96, an update to the U.S. Geological 

Survey modular finite-difference ground-water flow model: 

U.S. Geological Survey Open-File Report 96–485, 56 p.

Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G., 

2000, MODFLOW–2000, the U.S. Geological Survey modular ground-water model—User guide to modularization 

concepts and the ground-water flow process: U.S. Geological 

Survey Open-File Report 00–92, 121 p.

Holt, C.L.R., Jr., 1959, Geology and ground-water resources of 

Medina County, Texas: U.S. Geological Survey WaterSupply Paper 1422, 213 p. [Also published as Texas Board of 

Water Engineers Bulletin 5601, 278 p., 1956.]

Hovorka, S.D., Mace, R.E., and Collins, E.W., 1998, Permeability structure of the Edwards aquifer, south Texas—Implications for aquifer management: Austin, University of Texas, 

Bureau of Economic Geology Report of Investigations 250, 

55 p.

Hovorka, S.D., Phu, T., Nicot, J.P., and Lindley, A., 2004, 

Refining the conceptual model for flow in the Edwards 

aquifer—Characterizing the role of fractures and conduits in 

the Balcones fault zone segment: Contract report to Edwards 

Aquifer Authority, 53 p.

Klemt, W.B., Knowles, T.R., Edler, G.R., and Sieh, T.W., 1979, 

Ground-water resources and model applications for the 

Edwards (Balcones fault zone) aquifer in the San Antonio 

region: Texas Water Development Board Report 239, 88 p.

Knowles, Leel, Jr., O’Reilly, A.M., and Adamski, J.C., 2002, 

Hydrogeology and simulated effects of ground-water 

withdrawals from the Floridan aquifer system in Lake 

County and in the Ocala National Forest and vicinity, northcentral Florida: U.S. Geological Survey Water-Resources 

Investigations Report 2002–4207, 140 p.

Liedl, R., Sauter, M., Hückinghaus, D., Clemens, T., and 

Teutsch, G., 2003, Simulation of the development of karst 

aquifers using a coupled continuum pipe flow model: Water 

Resources Research, v. 39, no. 3, p. 1,057–1,067.

Lindgren, R.J., Dutton, A.R., Hovorka, S.D., Worthington, 

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34 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

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Table 1 35

Table 1

Table 1. Steady-state simulation target wells and residuals for the conduit-flow and diffuse-flow Edwards aquifer models, San Antonio 

region, Texas—Continued. 

Conduit-flow Edwards aquifer model Diffuse-flow Edwards

Measured (Lindgren and others, 2004) aquifer model TWDB Latitude Longitude water County Simulated Simulated well ID (DD.MMSS) (DD.MMSS) level Residual Residual water level water level (feet) (feet) (feet) (feet) (feet)

7038601 Kinney 100.2569 29.4392 1,216 1,188.7 -27.3 1,203.4 -12.6

7038903 Kinney 100.2731 29.4122 1,211 1,189.7 -21.3 1,185.8 -25.2

7038906 Kinney 100.2833 29.3792 1,141 1,123.2 -17.8 1,137.9 -3.1

7045502 Kinney 100.4250 29.3136 1,109 1,105.6 -3.4 1,105.3 -3.7

7045602 Kinney 100.4125 29.3269 1,099 1,106.1 7.1 1,105.5 6.5

7046101 Kinney 100.3428 29.3436 1,116 1,108.2 -7.8 1,110.3 -5.7

7046302 Kinney 100.2622 29.3367 1,079 1,073.0 -6.0 1,087.7 8.7

7046901 Kinney 100.2667 29.2703 1,044 1,042.6 -1.4 1,045.0 1.0

7047402 Kinney 100.2431 29.3236 1,072 1,052.1 -19.9 1,073.2 1.2

7047802 Kinney 100.2078 29.2631 999 989.1 -9.9 999.7 .7

7048701 Kinney 100.1139 29.2911 964 928.7 -35.3 967.6 3.6

6935601 Uvalde 99.6297 29.4311 898 920.2 22.2 904.3 6.3

6935804 Uvalde 99.7017 29.3950 1,009 927.2 -81.8 1,012.1 3.1

6941701 Uvalde 99.9711 29.2603 917 889.8 -27.2 923.9 6.9

6943204 Uvalde 99.6744 29.3628 881 885.4 4.4 870.0 -11.0

6943404 Uvalde 99.7367 29.3042 859 871.0 12.0 859.0 0

6943604 Uvalde 99.6586 29.2933 888 861.9 -26.1 804.6 -83.4

6944705 Uvalde 99.6028 29.2644 763 808.2 45.2 792.9 29.9

6950302 Uvalde 99.7867 29.2103 870 872.0 2.0 871.1 1.1

6950304 Uvalde 99.7531 29.2294 870 871.7 1.7 867.6 -2.4

6950609 Uvalde 99.7825 29.1875 867 871.1 4.1 871.1 4.1

6825708 Medina 98.9772 29.5153 885 858.3 -26.7 884.4 -.6

6825912 Medina 98.8881 29.5017 782 788.0 6.0 841.9 59.9

6833101 Medina 98.9839 29.4747 824 823.8 -.2 824.4 .4

6833107 Medina 98.9764 29.4644 841 804.6 -36.4 779.9 -61.1

6833208 Medina 98.9269 29.4658 822 759.7 -62.3 783.7 -38.3

6833209 Medina 98.9253 29.4764 824 782.6 -41.4 825.2 1.2

6833210 Medina 98.9356 29.4858 849 826.2 -22.8 870.2 21.2

6833211 Medina 98.9500 29.4744 846 766.2 -79.8 773.3 -72.7

6833303 Medina 98.9025 29.4981 837 800.5 -36.5 844.3 7.3

6833503 Medina 98.9431 29.4519 728 741.3 13.3 729.7 1.7

6833604 Medina 98.8881 29.4219 705 722.3 17.3 709.5 4.5

6834106 Medina 98.8528 29.4917 754 745.8 -8.2 761.5 7.5

6834706 Medina 98.8661 29.4153 698 720.2 22.2 707.9 9.9

6841605 Medina 98.9011 29.3139 703 715.2 12.2 704.7 1.7

6842224 Medina 98.8189 29.3592 677 711.1 34.1 696.7 19.7

6842226 Medina 98.8244 29.3656 659 712.0 53.0 697.8 38.8

6842504 Medina 98.8147 29.3094 691 708.7 17.7 700.9 9.9

6938602 Medina 99.2725 29.4328 824 789.2 -34.8 831.5 7.5

6939507 Medina 99.1947 29.4531 827 805.2 -21.8 825.8 -1.2

6939903 Medina 99.1336 29.4042 760 776.5 16.5 761.4 1.4

6940405 Medina 99.1022 29.4347 768 789.8 21.8 768.2 .2

6945601 Medina 99.4089 29.3328 761 760.3 -.7 768.7 7.7

6946701 Medina 99.3525 29.2639 754 750.1 -3.9 762.6 8.6

6947514 Medina 99.1989 29.2922 812 740.9 -71.1 747.5 -64.5

6954401 Medina 99.3342 29.1864 755 743.1 -11.9 757.5 2.5

6822701 Bexar 98.3739 29.6517 749 724.7 -24.3 748.2 -.8

6822702 Bexar 98.3489 29.6250 663 684.8 21.8 670.6 7.6

Table 1. Steady-state simulation target wells and residuals, conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, 

Texas. 

[Measured and simulated water levels in altitude above National Geodetic Vertical Datum of 1929. TWDB, Texas Water Development Board; ID, identification 

number; DD.MMSS, degrees.minutes/seconds; residual, simulated water level minus measured water level; mean absolute difference, sum of absolute values of 

residuals divided by number of wells; mean algebraic difference, algebraic sum of residuals divided by number of wells; RMS error, root-mean-square error] 
36 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

6826901 Bexar 98.7536 29.5236 734 740.6 6.6 728.0 -6.0

6827514 Bexar 98.6803 29.5619 724 793.9 69.9 727.2 3.2

6827515 Bexar 98.6747 29.5575 723 763.6 40.6 720.9 -2.1

6827701 Bexar 98.7356 29.5122 702 730.2 28.2 708.8 6.8

6827702 Bexar 98.7267 29.5036 698 720.5 22.5 699.9 1.9

6828201 Bexar 98.5797 29.5942 715 789.1 74.1 721.5 6.5

6828507 Bexar 98.5514 29.5422 679 701.4 22.4 678.9 -.1

6828704 Bexar 98.6008 29.5250 701 688.4 -12.6 698.4 -2.6

6829207 Bexar 98.4267 29.6164 688 716.5 28.5 680.3 -7.7

6829411 Bexar 98.4847 29.5642 674 688.6 14.6 671.4 -2.6

6829502 Bexar 98.4500 29.5708 674 683.8 9.8 669.9 -4.1

6829604 Bexar 98.4094 29.5511 668 667.4 -.6 668.0 0

6829605 Bexar 98.3872 29.5500 668 663.3 -4.7 667.1 -.9

6829815 Bexar 98.4242 29.5031 682 670.0 -12.0 668.7 -13.3

6829916 Bexar 98.4078 29.5103 669 669.1 .1 668.3 -.7

6830101 Bexar 98.3553 29.5919 667 663.5 -3.5 664.3 -2.7

6830612 Bexar 98.2889 29.5431 670 651.9 -18.1 664.5 -5.5

6830706 Bexar 98.3706 29.5083 667 667.1 .1 667.6 .6

6830801 Bexar 98.3139 29.5175 671 657.7 -13.3 666.0 -5.0

6835202 Bexar 98.6906 29.4889 691 707.9 16.9 694.6 3.6

6835312 Bexar 98.6558 29.4717 690 700.5 10.5 686.4 -3.6

6835807 Bexar 98.7075 29.3778 685 696.7 11.7 686.3 1.3

6836113 Bexar 98.5861 29.4664 671 689.1 18.1 677.7 6.7

6836505 Bexar 98.5461 29.4531 674 684.4 10.4 675.2 1.2

6836506 Bexar 98.5711 29.4297 676 685.9 9.9 676.2 .2

6836606 Bexar 98.5072 29.4328 668 680.7 12.7 672.9 4.9

6836706 Bexar 98.6242 29.4061 682 691.6 9.6 680.8 -1.2

6836709 Bexar 98.6244 29.3822 675 689.2 14.2 675.9 .9

6836713 Bexar 98.5992 29.3878 673 686.8 13.8 675.4 2.4

6836812 Bexar 98.5819 29.4094 673 686.8 13.8 675.4 2.4

6836813 Bexar 98.5667 29.3922 675 684.7 9.7 674.9 -.1

6836910 Bexar 98.5225 29.4011 674 682.3 8.3 673.9 -.1

6836930 Bexar 98.5314 29.3939 675 683.1 8.1 674.2 -.8

6837114 Bexar 98.4900 29.4703 672 675.8 3.8 671.3 -.7

6837126 Bexar 98.4692 29.4653 681 671.4 -9.6 670.4 -10.6

6837204 Bexar 98.4272 29.4717 675 674.2 -.8 669.9 -5.1

6837407 Bexar 98.4633 29.4364 671 678.4 7.4 671.7 .7

6837408 Bexar 98.4789 29.4267 671 679.7 8.7 672.2 1.2

6837409 Bexar 98.4956 29.4183 616 680.7 64.7 672.8 56.8

6837411 Bexar 98.4894 29.4278 659 680.1 21.1 672.5 13.5

6837517 Bexar 98.4303 29.4386 623 676.5 53.5 670.7 47.7

6837606 Bexar 98.4108 29.4456 677 675.5 -1.5 670.1 -6.9

6837707 Bexar 98.4928 29.4006 675 683.2 8.2 673.0 -2.0

6837715 Bexar 98.4889 29.3983 666 683.2 17.2 673.0 7.0

6837716 Bexar 98.4878 29.4142 665 680.6 15.6 672.7 7.7

6842314 Bexar 98.7825 29.3706 692 705.9 13.9 694.1 2.1

6842315 Bexar 98.7611 29.3739 689 702.9 13.9 692.0 3.0

6843108 Bexar 98.7272 29.3528 688 698.9 10.9 689.6 1.6

6843611 Bexar 98.6636 29.3264 673 693.1 20.1 679.9 6.9

6843812 Bexar 98.6839 29.2806 679 695.8 16.8 686.3 7.3

6843813 Bexar 98.6700 29.2703 688 695.1 7.1 685.1 -2.9

Table 1. Steady-state simulation target wells and residuals for the conduit-flow and diffuse-flow Edwards aquifer models, San Antonio 

region, Texas—Continued. 

TWDB

well ID County Latitude

(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
Table 1 37

6844220 Bexar 98.5714 29.3494 676 686.7 10.7 675.4 -0.6

6844221 Bexar 98.5692 29.3458 673 686.8 13.8 675.4 2.4

6844222 Bexar 98.5719 29.3436 675 687.0 12.0 675.5 .5

6844223 Bexar 98.5678 29.3431 676 686.9 10.9 675.4 -.6

6844405 Bexar 98.6100 29.3050 671 690.6 19.6 677.3 6.3

6844602 Bexar 98.5378 29.3294 655 686.3 31.3 674.9 19.9

6845102 Bexar 98.4972 29.3742 660 683.9 23.9 673.6 13.6

6815904 Comal 98.1625 29.7503 640 634.7 -5.3 635.7 -4.3

6816703 Comal 98.0928 29.7531 601 611.1 10.1 613.5 12.5

6816704 Comal 98.1097 29.7639 612 632.9 20.9 618.5 6.5

6816801 Comal 98.0528 29.7861 594 594.5 .5 602.7 8.7

6816804 Comal 98.0628 29.7778 608 598.4 -9.6 605.3 -2.7

6822301 Comal 98.2578 29.7119 677 713.5 36.5 667.7 -9.3

6822303 Comal 98.2517 29.7133 662 710.2 48.2 659.2 -2.8

6822502 Comal 98.2964 29.6975 670 722.7 52.7 676.5 6.5

6822503 Comal 98.3161 29.6844 701 720.9 19.9 686.3 -14.7

6822601 Comal 98.2858 29.6772 657 701.6 44.6 661.2 4.2

6822803 Comal 98.3225 29.6392 666 689.1 23.1 672.1 6.1

6822804 Comal 98.3306 29.6311 673 685.2 12.2 670.0 -3.0

6823101 Comal 98.2106 29.7403 668 657.2 -10.8 647.8 -20.2

6823102 Comal 98.2250 29.7261 767 661.0 -106.0 650.1 -116.9

6823206 Comal 98.1819 29.7483 659 636.7 -22.3 639.4 -19.6

6823209 Comal 98.1792 29.7206 635 644.7 9.7 642.5 7.5

6823210 Comal 98.2078 29.7147 643 647.5 4.5 647.3 4.3

6823212 Comal 98.1728 29.7433 637 633.9 -3.1 638.4 1.4

6823220 Comal 98.2081 29.7419 668 648.7 -19.3 647.1 -20.9

6823306 Comal 98.1528 29.7464 630 633.7 3.7 634.9 4.9

6823308 Comal 98.1453 29.7475 631 633.7 2.7 633.5 2.5

6823309 Comal 98.1347 29.7183 625 640.3 15.3 637.8 12.8

6823507 Comal 98.1989 29.6889 641 658.0 17.0 647.7 6.7

6823604 Comal 98.1633 29.6700 638 622.4 -15.6 633.9 -4.1

6823705 Comal 98.2378 29.6344 652 635.4 -16.6 649.4 -2.6

6824106 Comal 98.1133 29.7344 620 636.1 16.1 631.7 11.7

6830216 Comal 98.3286 29.6203 671 678.2 7.2 663.2 -7.8

6830313 Comal 98.2572 29.6167 619 639.6 20.6 654.3 35.3

5857301 Hays 97.8903 30.0936 621 607.7 -13.3 650.7 29.7

5858101 Hays 97.8422 30.0836 589 598.5 9.5 614.2 25.2

5858104 Hays 97.8486 30.1042 589 583.8 -5.2 592.3 3.3

5858703 Hays 97.8542 30.0278 579 600.0 21.0 630.1 51.1

6701307 Hays 97.8869 29.9675 569 588.9 19.9 604.7 35.7

6701702 Hays 97.9650 29.8958 577 594.5 17.5 592.8 15.8

6701807 Hays 97.9192 29.9008 574 587.6 13.6 588.1 14.1

6702103 Hays 97.8725 29.9889 579 589.4 10.4 615.4 36.4

6709102 Hays 97.9758 29.8508 577 588.0 11.0 590.9 13.9

6816605 Hays 98.0042 29.8289 566 588.6 22.6 593.9 27.9

Statistics:

Mean absolute difference 19.4 11.3

Mean algebraic difference 4.5 1.5

RMS error 26.5 20.9

Table 1. Steady-state simulation target wells and residuals for the conduit-flow and diffuse-flow Edwards aquifer models, San Antonio 

region, Texas—Continued. 

TWDB

well ID County Latitude

(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
38 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Table 3

Table 2. Comparison of the residuals for hydraulic heads, by synoptic water-level time period (steady-state, below-normal rainfall 

[drought], and above-normal rainfall), conduit-flow and diffuse-flow Edwards aquifer models, San Antonio region, Texas. 

[residual, simulated water level minus measured water level; MAE (mean absolute difference), sum of absolute values of residuals divided by number of wells; 

ME (mean algebraic difference), algebraic sum of residuals divided by number of wells; RMS, root-mean-square error] 

Table 3. Measured and simulated springflows for steady-state simulation, conduit-flow and diffuse-flow Edwards aquifer models, San 

Antonio region, Texas.

[Simulated, model-computed springflow for steady-state simulation]

Synoptic

time

period

Hydraulic-head residuals

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004) Diffuse-flow Edwards aquifer model

MAE ME RMS MAE ME RMS

Steady state 19.4 4.5 26.5 11.3 1.5 20.9

Drought 31.6 -7.6 58.7 20.5 -8.1 33.4

Above-normal rainfall 23.5 3.5 33.5 17.2 .5 25.8

Year

Springflow

(cubic feet per second)

Comal

Springs

San Marcos

Springs

Leona

Springs

San Antonio

Springs

San Pedro

Springs

Mean Median Mean Median Mean Median Mean Median Mean Median

 Measured

1939 297 301 98 103 21 20 4 0 5 4

1940 275 274 107 107 18 18 0 0 3 3

1941 340 339 182 170 21 23 28 29 9 9

1942 346 333 153 135 26 27 29 23 9 8

1943 337 325 133 134 21 20 13 10 7 6

1944 342 331 183 178 11 10 11 8 6 6

1945 357 342 189 176 11 13 23 16 8 7

1946 356 358 181 173 3 2 16 9 7 6

Mean (1939–46) 332 326 153 147 16 17 16 12 7 6

Median (1939–46) 341 332 167 152 20 19 14 10 7 6

 Simulated

Conduit-flow Edwards aquifer 

model 

342 172 40 16 8

Diffuse-flow Edwards aquifer 

model 

340 175 40 16 5
Table 4 39

Table 4. Transient simulation target wells and residuals for drought conditions, conduit-flow and diffuse-flow Edwards aquifer models, 

San Antonio region, Texas—Continued.

Conduit-flow Edwards aquifer model Diffuse-flow Edwards

Measured (Lindgren and others, 2004) aquifer model TWDB Latitude Longitude water

well ID County Simulated Simulated (DD.MMSS) (DD.MMSS) level Residual Residual water level water level (feet) (feet) (feet) (feet) (feet)

7038501 Kinney 100.3083 29.4328 1,221 1,186.5 -34.5 1,183.5 -37.5

7038901 Kinney 100.2606 29.4114 1,158 1,186.5 28.5 1,180.8 22.8

7038906 Kinney 100.2833 29.3792 1,137 1,181.3 44.3 1,134.5 -2.5

7045502 Kinney 100.4250 29.3136 1,109 1,122.0 13.0 1,105.1 -3.9

7045602 Kinney 100.4125 29.3269 1,095 1,105.6 10.6 1,105.3 10.3

7046901 Kinney 100.2667 29.2703 1,034 1,106.0 72.0 1,033.0 -1.0

7047101 Kinney 100.2108 29.3572 1,058 1,039.8 -18.2 1,093.1 35.1

7047201 Kinney 100.1750 29.3636 1,011 1,063.0 52.0 1,092.8 81.8

7047301 Kinney 100.1461 29.3417 979 1,041.9 62.9 1,039.8 60.8

7047303 Kinney 100.1617 29.3531 979 977.4 -1.6 1,058.3 79.3

7047501 Kinney 100.1711 29.3206 926 1,009.9 83.9 1,024.5 98.5

6933601 Uvalde 99.8972 29.4264 1,231 980.9 -250.1 1,080.0 -151.0

6933901 Uvalde 99.8783 29.3936 1,119 941.9 -177.1 1,014.8 -104.2

6935701 Uvalde 99.7461 29.3917 979 911.0 -68.0 960.2 -18.8

6935804 Uvalde 99.7017 29.3950 934 879.2 -54.8 923.4 -10.6

6935901 Uvalde 99.6456 29.3869 717 862.6 145.6 769.5 52.5

6937401 Uvalde 99.4908 29.4575 799 826.0 27.0 764.6 -34.4

6941101 Uvalde 99.9606 29.3442 1,001 729.9 -271.1 976.3 -24.7

6941701 Uvalde 99.9711 29.2603 839 913.5 74.5 885.1 46.1

6941903 Uvalde 99.9089 29.2603 840 843.5 3.5 862.6 22.6

6942101 Uvalde 99.8561 29.3419 929 830.6 -98.4 902.0 -27.0

6942603 Uvalde 99.7550 29.3083 800 854.2 54.2 807.9 7.9

6942604 Uvalde 99.7708 29.3125 801 816.6 15.6 814.0 13.0

6942911 Uvalde 99.7614 29.2883 802 818.5 16.5 809.1 7.1

6942912 Uvalde 99.7758 29.2661 814 816.4 2.4 813.8 -.2

6943106 Uvalde 99.7389 29.3550 847 816.8 -30.2 811.7 -35.3

6943204 Uvalde 99.6744 29.3628 791 822.9 31.9 794.3 3.3

6943404 Uvalde 99.7367 29.3042 790 821.9 31.9 799.6 9.6

6943406 Uvalde 99.7494 29.3083 776 814.2 38.2 805.6 29.6

6943501 Uvalde 99.6906 29.3292 769 815.9 46.9 784.6 15.6

6943911 Uvalde 99.6500 29.2892 755 811.4 56.4 720.7 -34.3

6944705 Uvalde 99.6028 29.2644 662 796.3 134.3 708.2 46.2

6945401 Uvalde 99.4681 29.3192 666 727.8 61.8 688.7 22.7

6950101 Uvalde 99.8506 29.2406 833 678.6 -154.4 838.6 5.6

6950202 Uvalde 99.7981 29.2372 818 821.6 3.6 819.6 1.6

6950204 Uvalde 99.8247 29.2203 821 817.9 -3.1 824.3 3.3

6950302 Uvalde 99.7867 29.2103 818 819.0 1.0 818.1 .1

6950305 Uvalde 99.7550 29.2261 813 817.0 4.0 814.1 1.1

6950306 Uvalde 99.7522 29.2322 808 816.1 8.1 812.2 4.2

6950406 Uvalde 99.8667 29.1806 824 816.1 -7.9 840.1 16.1

6950507 Uvalde 99.8289 29.1861 820 819.0 -1.0 826.8 6.8

6950609 Uvalde 99.7825 29.1875 819 818.0 -1.0 819.2 .2

6950612 Uvalde 99.7533 29.1789 822 816.5 -5.5 815.5 -6.5

6950901 Uvalde 99.7739 29.1664 814 813.2 -.8 818.8 4.8

6950902 Uvalde 99.7669 29.1653 840 815.8 -24.2 817.7 -22.3

6951407 Uvalde 99.7475 29.1819 827 815.0 -12.0 815.1 -11.9

6952401 Uvalde 99.6250 29.1972 758 812.4 54.4 703.6 -54.4

Table 4

Table 4. Transient simulation target wells and residuals for drought conditions, conduit-flow and diffuse-flow Edwards aquifer models, 

San Antonio region, Texas.

[Measured and simulated water levels in altitude above National Geodetic Vertical Datum of 1929. TWDB, Texas Water Development Board; ID, identification 

number; DD.MMSS, degrees.minutes/seconds; residual, simulated water level minus measured water level; mean absolute difference, sum of absolute values of 

residuals divided by number of wells; mean algebraic difference, algebraic sum of residuals divided by number of wells; RMS error, root-mean-square error]
40 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

6826702 Medina 98.8556 29.5122 614 708.6 94.6 653.4 39.4

6833303 Medina 98.9025 29.4981 783 637.6 -145.4 665.7 -117.3

6833604 Medina 98.8881 29.4219 628 660.7 32.7 625.0 -3.0

6841202 Medina 98.9297 29.3353 615 633.0 18.0 625.8 10.8

6841301 Medina 98.8797 29.3544 627 635.5 8.5 624.7 -2.3

6841403 Medina 98.9886 29.3203 640 631.8 -8.2 627.9 -12.1

6842504 Medina 98.8147 29.3094 626 639.2 13.2 621.2 -4.8

6932702 Medina 99.0939 29.5258 976 628.1 -347.9 800.2 -175.8

6932801 Medina 99.0797 29.5350 979 775.5 -203.5 835.7 -143.3

6938904 Medina 99.2653 29.3833 690 789.5 99.5 674.2 -15.8

6939507 Medina 99.1947 29.4531 740 676.0 -64.0 717.7 -22.3

6939903 Medina 99.1336 29.4042 659 703.2 44.2 670.8 11.8

6940101 Medina 99.1228 29.4906 775 679.2 -95.8 741.0 -34.0

6940405 Medina 99.1022 29.4347 673 737.7 64.7 676.1 3.1

6940901 Medina 99.0008 29.4094 637 688.8 51.8 629.4 -7.6

6945601 Medina 99.4089 29.3328 663 640.1 -22.9 680.0 17.0

6946601 Medina 99.2786 29.3319 659 674.3 15.3 668.3 9.3

6946701 Medina 99.3525 29.2639 659 661.8 2.8 674.9 15.9

6947301 Medina 99.1600 29.3597 634 665.9 31.9 640.2 6.2

6947402 Medina 99.2097 29.3331 642 652.8 10.8 657.7 15.7

6948402 Medina 99.1069 29.3247 636 656.3 20.3 634.8 -1.2

6954401 Medina 99.3342 29.1864 659 648.6 -10.4 673.3 14.3

6955202 Medina 99.2006 29.2269 640 661.0 21.0 659.4 19.4

6822702 Bexar 98.3489 29.6250 620 649.5 29.5 608.5 -11.5

6826804 Bexar 98.7978 29.5242 638 620.1 -17.9 631.1 -6.9

6826901 Bexar 98.7536 29.5236 632 632.6 .6 617.2 -14.8

6827515 Bexar 98.6747 29.5575 653 628.9 -24.1 611.6 -41.4

6827608 Bexar 98.6442 29.5436 644 500.6 -143.4 611.7 -32.3

6827702 Bexar 98.7267 29.5036 625 637.7 12.7 614.0 -11.0

6828201 Bexar 98.5797 29.5942 686 622.7 -63.3 608.0 -78.0

6828507 Bexar 98.5514 29.5422 620 600.2 -19.8 603.0 -17.0

6828705 Bexar 98.6247 29.5014 623 591.9 -31.1 605.9 -17.1

6828908 Bexar 98.5350 29.5183 621 594.8 -26.2 605.2 -15.8

6829207 Bexar 98.4267 29.6164 681 594.6 -86.4 610.8 -70.2

6829304 Bexar 98.4106 29.5975 623 608.1 -14.9 601.6 -21.4

6829411 Bexar 98.4847 29.5642 641 602.8 -38.2 602.9 -38.1

6829508 Bexar 98.4203 29.5775 619 571.2 -47.8 604.9 -14.1

6829604 Bexar 98.4094 29.5511 616 601.4 -14.6 604.8 -11.2

6829701 Bexar 98.4636 29.5369 617 602.1 -14.9 604.9 -12.1

6829709 Bexar 98.4617 29.5028 623 591.6 -31.4 604.6 -18.4

6829916 Bexar 98.4078 29.5103 636 599.8 -36.2 604.6 -31.4

6829917 Bexar 98.4078 29.5100 616 604.0 -12.0 604.6 -11.4

6830101 Bexar 98.3553 29.5919 617 604.0 -13.0 604.9 -12.1

6830404 Bexar 98.3606 29.5456 610 607.3 -2.7 604.7 -5.3

6830513 Bexar 98.3222 29.5475 617 607.5 -9.5 604.7 -12.3

6830514 Bexar 98.3194 29.5789 623 607.0 -16.0 604.7 -18.3

6830612 Bexar 98.2889 29.5431 618 606.4 -11.6 604.7 -13.3

6830707 Bexar 98.3706 29.5083 618 606.8 -11.2 604.7 -13.3

6830801 Bexar 98.3139 29.5175 616 608.4 -7.6 604.7 -11.3

6830802 Bexar 98.3139 29.5175 615 607.5 -7.5 604.7 -10.3

Table 4. Transient simulation target wells and residuals for drought conditions, conduit-flow and diffuse-flow Edwards aquifer models, 

San Antonio region, Texas—Continued.

TWDB

well ID County Latitude(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
Table 4 41

6830901 Bexar 98.2669 29.5128 646 607.5 -38.5 604.7 -41.3

6834301 Bexar 98.7789 29.4753 629 607.4 -21.6 620.9 -8.1

6834602 Bexar 98.7900 29.4386 633 628.4 -4.6 621.2 -11.8

6834603 Bexar 98.7586 29.4169 624 627.6 3.6 614.1 -9.9

6835202 Bexar 98.6906 29.4889 624 618.3 -5.7 612.6 -11.4

6835311 Bexar 98.6503 29.4711 626 618.0 -8.0 608.5 -17.5

6835504 Bexar 98.6714 29.4392 620 609.7 -10.3 608.8 -11.2

6835807 Bexar 98.7075 29.3778 620 609.4 -10.6 611.4 -8.6

6835901 Bexar 98.6381 29.4147 617 615.7 -1.3 608.6 -8.4

6835911 Bexar 98.6506 29.3944 626 608.2 -17.8 609.3 -16.7

6836302 Bexar 98.5364 29.4722 621 609.4 -11.6 605.7 -15.3

6836303 Bexar 98.5094 29.4697 589 603.4 14.4 605.4 16.4

6836410 Bexar 98.6236 29.4558 619 602.6 -16.4 607.7 -11.3

6836507 Bexar 98.5442 29.4264 624 606.5 -17.5 605.9 -18.1

6836602 Bexar 98.5022 29.4411 615 610.0 -5.0 605.1 -9.9

6836604 Bexar 98.5411 29.4336 620 610.8 -9.2 605.9 -14.1

6836706 Bexar 98.6242 29.4061 620 609.3 -10.7 608.3 -11.7

6836911 Bexar 98.5314 29.4064 616 608.1 -7.9 605.8 -10.2

6836913 Bexar 98.5197 29.3806 615 612.1 -2.9 606.2 -8.8

6837114 Bexar 98.4900 29.4703 617 613.3 -3.7 605.0 -12.0

6837203 Bexar 98.4322 29.4708 621 602.1 -18.9 604.8 -16.2

6837204 Bexar 98.4272 29.4717 617 608.5 -8.5 604.8 -12.2

6837407 Bexar 98.4633 29.4364 616 608.1 -7.9 604.9 -11.1

6837409 Bexar 98.4956 29.4183 610 610.7 .7 605.1 -4.9

6837512 Bexar 98.4294 29.4383 618 611.3 -6.7 605.1 -12.9

6837513 Bexar 98.4281 29.4400 618 609.2 -8.8 605.1 -12.9

6837514 Bexar 98.4183 29.4344 615 609.0 -6.0 605.1 -9.9

6837606 Bexar 98.4108 29.4456 618 609.5 -8.5 605.0 -13.0

6837707 Bexar 98.4928 29.4006 618 609.6 -8.4 605.9 -12.1

6838109 Bexar 98.3467 29.4664 614 613.0 -1.0 604.8 -9.2

6838301 Bexar 98.2653 29.4725 611 609.0 -2.0 605.8 -5.2

6842314 Bexar 98.7825 29.3706 625 608.2 -16.8 616.3 -8.7

6842315 Bexar 98.7611 29.3739 624 623.0 -1.0 614.9 -9.1

6843205 Bexar 98.6978 29.3456 623 620.6 -2.4 612.1 -10.9

6843404 Bexar 98.7142 29.2961 613 619.4 6.4 616.8 3.8

6843507 Bexar 98.6961 29.2939 622 621.7 -.3 615.6 -6.4

6843605 Bexar 98.6533 29.3269 603 621.0 18.0 608.5 5.5

6843611 Bexar 98.6636 29.3264 617 617.9 .9 609.3 -7.7

6843807 Bexar 98.6719 29.2750 628 618.2 -9.8 613.8 -14.2

6843812 Bexar 98.6839 29.2806 625 620.5 -4.5 615.0 -10.0

6844213 Bexar 98.5614 29.3578 616 621.0 5.0 606.6 -9.4

6844405 Bexar 98.6100 29.3050 614 614.0 0 608.2 -5.8

6845102 Bexar 98.4972 29.3742 605 617.3 12.3 606.1 1.1

6815903 Comal 98.1414 29.7575 618 613.3 -4.7 599.4 -18.6

6815904 Comal 98.1625 29.7503 612 605.2 -6.8 601.5 -10.5

6815906 Comal 98.1597 29.7786 633 606.5 -26.5 617.2 -15.8

6816703 Comal 98.0928 29.7531 593 614.5 21.5 594.7 1.7

6816801 Comal 98.0528 29.7861 578 599.3 21.3 590.2 12.2

6816804 Comal 98.0628 29.7778 596 589.0 -7.0 591.4 -4.6

6822301 Comal 98.2578 29.7119 649 591.8 -57.2 614.8 -34.2

Table 4. Transient simulation target wells and residuals for drought conditions, conduit-flow and diffuse-flow Edwards aquifer models, 

San Antonio region, Texas—Continued.

TWDB

well ID County Latitude(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
42 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

6822601 Comal 98.2858 29.6772 628 640.2 12.2 610.1 -17.9

6823208 Comal 98.1936 29.7347 618 633.5 15.5 603.8 -14.2

6823212 Comal 98.1728 29.7433 618 605.1 -12.9 602.0 -16.0

6823302 Comal 98.1389 29.7161 614 606.1 -7.9 601.3 -12.7

6823306 Comal 98.1528 29.7464 612 605.0 -7.0 600.3 -11.7

6823307 Comal 98.1594 29.7461 616 605.0 -11.0 600.8 -15.2

6823308 Comal 98.1453 29.7475 613 604.9 -8.1 599.8 -13.2

6823310 Comal 98.1253 29.7306 603 605.0 2.0 599.9 -3.1

6823507 Comal 98.1989 29.6889 620 613.4 -6.6 603.9 -16.1

6823701 Comal 98.2164 29.6486 615 611.2 -3.8 604.6 -10.4

6823809 Comal 98.1928 29.6594 588 604.6 16.6 604.4 16.4

6824102 Comal 98.1069 29.7444 610 604.3 -5.7 598.2 -11.8

6830208 Comal 98.3194 29.6097 615 615.3 .3 605.0 -10.0

6830217 Comal 98.3006 29.6181 614 615.1 1.1 605.0 -9.0

6830313 Comal 98.2572 29.6167 576 605.7 29.7 604.6 28.6

5857301 Hays 97.8903 30.0936 596 551.6 -44.4 559.3 -36.7

5857902 Hays 97.8958 30.0083 574 582.1 8.1 576.6 2.6

5857903 Hays 97.8861 30.0381 561 575.9 14.9 564.1 3.1

5858101 Hays 97.8422 30.0836 560 548.3 -11.7 541.7 -18.3

6701307 Hays 97.8869 29.9675 565 584.8 19.8 583.8 18.8

6701701 Hays 97.9639 29.8956 568 586.2 18.2 586.1 18.1

6701808 Hays 97.9194 29.9014 582 585.0 3.0 585.0 3.0

6702103 Hays 97.8725 29.9889 519 584.6 65.6 577.1 58.1

6816301 Hays 98.0214 29.8714 601 589.2 -11.8 603.6 2.6

Statistics:

Mean absolute difference 31.6 20.5

Mean algebraic difference -7.6 -8.1

RMS error 58.7 33.4

Table 4. Transient simulation target wells and residuals for drought conditions, conduit-flow and diffuse-flow Edwards aquifer models, 

San Antonio region, Texas—Continued.

TWDB

well ID County Latitude(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
Table 5 43

Table 5

Table 5. Transient simulation target wells and residuals for above-normal rainfall conditions, conduit-flow and diffuse-flow Edwards 

aquifer models, San Antonio region, Texas—Continued.

Conduit-flow Edwards aquifer model Diffuse-flow Edwards

Measured (Lindgren, 2004) aquifer model TWDB Latitude Longitude water County well ID Simulated Simulated (DD.MMSS) (DD.MMSS) level Residual Residual water level water level (feet) (feet) (feet) (feet) (feet)

7038501 Kinney 100.3083 29.4328 1,240 1,179.8 -60.2 1,169.7 -70.3

7038902 Kinney 100.2617 29.4131 1,183 1,191.1 8.1 1,193.6 10.6

7045505 Kinney 100.4219 29.3106 1,117 1,105.2 -11.8 1,103.3 -13.7

7045603 Kinney 100.4125 29.3278 1,093 1,105.7 12.7 1,103.5 10.5

7046101 Kinney 100.3428 29.3436 1,120 1,100.2 -19.8 1,105.8 -14.2

7046201 Kinney 100.3042 29.3453 1,112 1,094.0 -18.0 1,105.1 -6.9

7046302 Kinney 100.2622 29.3367 1,097 1,071.9 -25.1 1,092.3 -4.7

7046901 Kinney 100.2667 29.2703 1,046 1,043.9 -2.1 1,048.6 2.6

7047501 Kinney 100.1711 29.3206 1,017 991.4 -25.6 1,057.1 40.1

6933901 Uvalde 99.8783 29.3936 1,126 960.7 -165.3 1,022.7 -103.3

6935804 Uvalde 99.7017 29.3950 1,042 970.2 -71.8 1,094.7 52.7

6936601 Uvalde 99.5158 29.4256 829 870.2 41.2 876.5 47.5

6937402 Uvalde 99.4700 29.4411 860 836.9 -23.1 855.2 -4.8

6941101 Uvalde 99.9606 29.3442 1,012 961.8 -50.2 1,028.1 16.1

6941502 Uvalde 99.9483 29.3183 983 937.2 -45.8 991.0 8.0

6941504 Uvalde 99.9336 29.2967 934 918.3 -15.7 971.8 37.8

6941701 Uvalde 99.9711 29.2603 938 904.0 -34.0 933.9 -4.1

6941901 Uvalde 99.8803 29.2850 906 893.1 -12.9 907.9 1.9

6942601 Uvalde 99.7508 29.3150 879 888.3 9.3 878.7 -.3

6942709 Uvalde 99.8625 29.2731 904 892.0 -12.0 902.4 -1.6

6942901 Uvalde 99.7589 29.2544 867 887.0 20.0 876.9 9.9

6942907 Uvalde 99.7533 29.2828 881 887.3 6.3 876.2 -4.8

6943103 Uvalde 99.7100 29.3478 924 899.0 -25.0 892.2 -31.8

6943106 Uvalde 99.7389 29.3550 962 893.5 -68.5 885.4 -76.6

6943202 Uvalde 99.6994 29.3592 948 916.3 -31.7 913.9 -34.1

6943301 Uvalde 99.6503 29.3650 866 904.7 38.7 896.3 30.3

6943603 Uvalde 99.6364 29.2956 811 871.0 60.0 826.1 15.1

6943804 Uvalde 99.6917 29.2767 885 882.9 -2.1 856.1 -28.9

6943902 Uvalde 99.6333 29.2761 886 869.7 -16.3 826.6 -59.4

6943903 Uvalde 99.6508 29.2694 884 877.3 -6.7 829.7 -54.3

6943910 Uvalde 99.6400 29.2503 876 839.4 -36.6 821.9 -54.1

6944301 Uvalde 99.5117 29.3494 808 811.9 3.9 815.9 7.9

6944402 Uvalde 99.5933 29.3297 810 872.3 62.3 825.3 15.3

6944701 Uvalde 99.5942 29.2697 808 827.6 19.6 814.5 6.5

6944703 Uvalde 99.5950 29.2586 810 806.9 -3.1 809.0 -1.0

6944704 Uvalde 99.6108 29.2547 797 821.1 24.1 814.3 17.3

6944804 Uvalde 99.5733 29.2903 813 834.9 21.9 814.3 1.3

6945401 Uvalde 99.4681 29.3192 806 798.5 -7.5 801.4 -4.6

6949302 Uvalde 99.8803 29.2442 902 891.7 -10.3 906.3 4.3

6950101 Uvalde 99.8506 29.2406 900 889.7 -10.3 898.0 -2.0

6950202 Uvalde 99.7981 29.2372 887 887.4 .4 882.6 -4.4

6950204 Uvalde 99.8247 29.2203 887 887.7 .7 885.5 -1.5

6950302 Uvalde 99.7867 29.2103 881 886.2 5.2 880.4 -.6

6950306 Uvalde 99.7522 29.2322 884 886.3 2.3 877.0 -7.0

Table 5. Transient simulation target wells and residuals for above-normal rainfall conditions, conduit-flow and diffuse-flow Edwards 

aquifer models, San Antonio region, Texas.

[Measured and simulated water levels in altitude above National Geodetic Vertical Datum of 1929. TWDB, Texas Water Development Board; ID, identification 

number; DD.MMSS, degrees.minutes/seconds; residual, simulated water level minus measured water level; mean absolute difference, sum of absolute values of 

residuals divided by number of wells; mean algebraic difference, algebraic sum of residuals divided by number of wells; RMS error, root-mean-square error] 
44 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

6950403 Uvalde 99.8367 29.1908 875 886.6 11.6 888.2 13.2

6950408 Uvalde 99.8603 29.2042 886 888.2 2.2 898.0 12.0

6951104 Uvalde 99.7467 29.2358 883 886.3 3.3 875.3 -7.7

6951202 Uvalde 99.6719 29.2331 843 858.6 15.6 830.1 -12.9

6951401 Uvalde 99.7347 29.1786 858 880.3 22.3 876.1 18.1

6951602 Uvalde 99.6600 29.1756 826 837.2 11.2 815.9 -10.1

6952201 Uvalde 99.5781 29.2189 803 795.0 -8.0 800.2 -2.8

6952402 Uvalde 99.6236 29.1986 723 809.5 86.5 806.6 83.6

7040901 Uvalde 100.0075 29.3944 1,078 1,006.0 -72.0 1,065.6 -12.4

6833601 Medina 98.8903 29.4350 738 761.9 23.9 734.0 -4.0

6833604 Medina 98.8881 29.4219 732 756.6 24.6 731.7 -.3

6834506 Medina 98.8128 29.4314 720 758.2 38.2 735.0 15.0

6841301 Medina 98.8797 29.3544 722 742.8 20.8 724.3 2.3

6841305 Medina 98.8897 29.3672 722 746.2 24.2 725.4 3.4

6842106 Medina 98.8536 29.3547 725 741.2 16.2 719.7 -5.3

6842504 Medina 98.8147 29.3094 716 735.2 19.2 718.4 2.4

6849813 Medina 98.9392 29.1650 717 739.0 22.0 737.9 20.9

6937301 Medina 99.3836 29.4664 884 841.4 -42.6 858.7 -25.3

6938601 Medina 99.2831 29.4383 901 850.3 -50.7 889.8 -11.2

6938901 Medina 99.2653 29.4147 858 839.6 -18.4 850.7 -7.3

6938902 Medina 99.2744 29.3756 799 801.0 2.0 788.1 -10.9

6939503 Medina 99.1928 29.4358 869 858.6 -10.4 830.7 -38.3

6939504 Medina 99.1942 29.4503 893 870.0 -23.0 882.1 -10.9

6939505 Medina 99.2025 29.4492 900 872.9 -27.1 899.5 -.5

6940101 Medina 99.1228 29.4906 906 926.5 20.5 948.7 42.7

6940901 Medina 99.0008 29.4094 748 759.6 11.6 734.2 -13.8

6946601 Medina 99.2786 29.3319 784 780.8 -3.2 784.3 .3

6946701 Medina 99.3525 29.2639 793 782.7 -10.3 789.0 -4.0

6946901 Medina 99.2831 29.2836 791 778.2 -12.8 785.1 -5.9

6947204 Medina 99.2067 29.3606 785 785.6 .6 778.2 -6.8

6947302 Medina 99.1639 29.3689 754 773.7 19.7 748.8 -5.2

6947604 Medina 99.1389 29.2969 762 765.0 3.0 748.2 -13.8

6947701 Medina 99.2489 29.2561 797 776.4 -20.6 783.1 -13.9

6948102 Medina 99.0864 29.3508 754 763.8 9.8 736.4 -17.6

6955501 Medina 99.1989 29.1764 783 756.1 -26.9 763.5 -19.5

6956501 Medina 99.0517 29.1736 755 745.8 -9.2 747.0 -8.0

6827505 Bexar 98.6797 29.5600 781 817.7 36.7 769.6 -11.4

6827512 Bexar 98.6831 29.5625 822 837.8 15.8 775.0 -47.0

6828404 Bexar 98.6039 29.5417 721 696.1 -24.9 756.0 35.0

6828507 Bexar 98.5514 29.5422 655 749.4 94.4 699.0 44.0

6828705 Bexar 98.6247 29.5014 707 710.5 3.5 699.2 -7.8

6828901 Bexar 98.5308 29.5389 692 734.0 42.0 685.3 -6.7

6828909 Bexar 98.5261 29.5072 784 712.7 -71.3 683.7 -100.3

6828910 Bexar 98.5381 29.5356 699 738.9 39.9 686.5 -12.5

6829103 Bexar 98.4869 29.5894 709 809.0 100.0 743.3 34.3

6829304 Bexar 98.4106 29.5975 657 716.1 59.1 681.7 24.7

6829506 Bexar 98.4411 29.5736 681 708.1 27.1 678.6 -2.4

6829605 Bexar 98.3872 29.5500 685 679.5 -5.5 674.6 -10.4

Table 5. Transient simulation target wells and residuals for above-normal rainfall conditions, conduit-flow and diffuse-flow Edwards 

aquifer models, San Antonio region, Texas—Continued.

TWDB

well ID County Latitude

(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
Table 5 45

6829701 Bexar 98.4636 29.5369 690 702.0 12.0 679.2 -10.8

6829811 Bexar 98.4475 29.5136 692 684.2 -7.8 675.5 -16.5

6829913 Bexar 98.3792 29.5306 684 678.6 -5.4 674.5 -9.5

6829914 Bexar 98.4036 29.5075 684 685.0 1.0 675.1 -8.9

6830101 Bexar 98.3553 29.5919 682 682.0 0 672.4 -9.6

6830211 Bexar 98.3278 29.6050 676 692.8 16.8 670.6 -5.4

6830220 Bexar 98.3153 29.6008 660 663.2 3.2 669.1 9.1

6830514 Bexar 98.3194 29.5789 682 663.1 -18.9 670.2 -11.8

6830705 Bexar 98.3667 29.5403 692 677.0 -15.0 674.1 -17.9

6830802 Bexar 98.3139 29.5175 682 670.8 -11.2 673.2 -8.8

6830807 Bexar 98.2956 29.5247 682 667.1 -14.9 672.6 -9.4

6834602 Bexar 98.7900 29.4386 718 756.5 38.5 733.5 15.5

6834603 Bexar 98.7586 29.4169 706 730.6 24.6 708.5 2.5

6835202 Bexar 98.6906 29.4889 706 738.8 32.8 717.0 11.0

6835312 Bexar 98.6558 29.4717 700 727.6 27.6 703.1 3.1

6835807 Bexar 98.7075 29.3778 706 721.0 15.0 699.8 -6.2

6836104 Bexar 98.6006 29.4906 680 709.3 29.3 690.7 10.7

6836105 Bexar 98.6014 29.4875 698 710.0 12.0 690.2 -7.8

6836407 Bexar 98.6239 29.4261 703 714.7 11.7 692.3 -10.7

6837103 Bexar 98.4869 29.4972 681 705.2 24.2 681.3 .3

6837203 Bexar 98.4322 29.4708 687 692.4 5.4 677.8 -9.2

6837409 Bexar 98.4956 29.4183 688 700.1 12.1 681.3 -6.7

6837511 Bexar 98.4292 29.4389 666 695.4 29.4 678.6 12.6

6837606 Bexar 98.4108 29.4456 686 693.7 7.7 677.8 -8.2

6837707 Bexar 98.4928 29.4006 686 703.1 17.1 681.5 -4.5

6843611 Bexar 98.6636 29.3264 691 715.4 24.4 690.1 -.9

6843807 Bexar 98.6719 29.2750 699 717.5 18.5 695.5 -3.5

6844109 Bexar 98.5858 29.3378 662 709.0 47.0 685.1 23.1

6844214 Bexar 98.5481 29.3558 689 705.8 16.8 683.8 -5.2

6845102 Bexar 98.4972 29.3742 677 703.9 26.9 682.2 5.2

6845301 Bexar 98.3994 29.3711 664 695.8 31.8 679.5 15.5

6845901 Bexar 98.3817 29.2564 650 694.3 44.3 678.6 28.6

6815902 Comal 98.1397 29.7592 645 653.2 8.2 639.3 -5.7

6815903 Comal 98.1414 29.7575 641 652.9 11.9 640.5 -.5

6816501 Comal 98.0433 29.7972 597 596.6 -.4 604.6 7.6

6816602 Comal 98.0239 29.7936 601 597.3 -3.7 604.6 3.6

6816701 Comal 98.1044 29.7572 612 637.8 25.8 623.2 11.2

6816703 Comal 98.0928 29.7531 606 615.5 9.5 618.6 12.6

6816801 Comal 98.0528 29.7861 604 597.8 -6.2 606.9 2.9

6816803 Comal 98.0736 29.7697 616 598.3 -17.7 610.7 -5.3

6822301 Comal 98.2578 29.7119 681 763.0 82.0 689.4 8.4

6822501 Comal 98.2931 29.6800 684 755.6 71.6 678.0 -6.0

6822903 Comal 98.2597 29.6267 647 647.6 .6 659.5 12.5

6823101 Comal 98.2106 29.7403 682 684.3 2.3 658.2 -23.8

6823202 Comal 98.2006 29.7111 652 672.1 20.1 657.4 5.4

6823206 Comal 98.1819 29.7483 655 657.2 2.2 649.3 -5.7

6823220 Comal 98.2081 29.7419 682 672.9 -9.1 657.1 -24.9

6823302 Comal 98.1389 29.7161 628 662.3 34.3 648.8 20.8

Table 5. Transient simulation target wells and residuals for above-normal rainfall conditions, conduit-flow and diffuse-flow Edwards 

aquifer models, San Antonio region, Texas—Continued.

TWDB

well ID County Latitude

(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
46 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

6823306 Comal 98.1528 29.7464 650 652.9 2.9 644.1 -5.9

6823701 Comal 98.2164 29.6486 660 638.0 -22.0 650.5 -9.5

6823706 Comal 98.2289 29.6317 656 643.7 -12.3 653.7 -2.3

6823807 Comal 98.1714 29.6658 653 629.1 -23.9 640.0 -13.0

6823808 Comal 98.1819 29.6572 648 632.5 -15.5 643.8 -4.2

6824102 Comal 98.1069 29.7444 609 654.0 45.0 637.2 28.2

6824104 Comal 98.1017 29.7472 616 654.0 38.0 636.9 20.9

6824105 Comal 98.0883 29.7383 636 617.2 -18.8 619.3 -16.7

6830208 Comal 98.3194 29.6097 674 695.9 21.9 670.4 -3.6

6830312 Comal 98.2822 29.6128 657 652.9 -4.1 664.7 7.7

5849911 Hays 97.8894 30.1328 629 594.6 -34.4 671.7 42.7

5857902 Hays 97.8958 30.0083 614 606.3 -7.7 648.1 34.1

5857903 Hays 97.8861 30.0381 587 619.7 32.7 662.5 75.5

5858101 Hays 97.8422 30.0836 637 610.5 -26.5 635.0 -2.0

5858104 Hays 97.8486 30.1042 623 595.9 -27.1 608.9 -14.1

5858406 Hays 97.8558 30.0614 624 620.0 -4.0 653.8 29.8

6701203 Hays 97.9206 29.9619 598 602.7 4.7 620.5 22.5

6701304 Hays 97.8761 29.9844 586 593.5 7.5 631.3 45.3

6701305 Hays 97.8872 29.9675 578 592.9 14.9 620.0 42.0

6701401 Hays 97.9642 29.9500 600 628.6 28.6 631.9 31.9

6701501 Hays 97.9475 29.9236 577 617.3 40.3 607.7 30.7

6701701 Hays 97.9639 29.8956 579 605.6 26.6 596.9 17.9

6701809 Hays 97.9286 29.9119 587 598.5 11.5 594.3 7.3

6702103 Hays 97.8725 29.9889 598 593.6 -4.4 634.5 36.5

6709102 Hays 97.9758 29.8508 580 590.2 10.2 593.0 13.0

6709110 Hays 97.9819 29.8431 590 590.4 .4 593.7 3.7

6808601 Hays 98.0278 29.9458 810 680.0 -130.0 772.2 -37.8

6816301 Hays 98.0214 29.8714 606 640.6 34.6 689.6 83.6

6816605 Hays 98.0042 29.8289 588 590.9 2.9 596.6 8.6

Statistics:

Mean absolute difference 23.5 17.2

Mean algebraic difference 3.5 .5

RMS error 33.5 25.8

Table 5. Transient simulation target wells and residuals for above-normal rainfall conditions, conduit-flow and diffuse-flow Edwards 

aquifer models, San Antonio region, Texas—Continued.

TWDB

well ID County Latitude

(DD.MMSS)

Longitude

(DD.MMSS)

Measured

water

level

(feet)

Conduit-flow Edwards aquifer model

(Lindgren, 2004)

Diffuse-flow Edwards

aquifer model

Simulated

water level

(feet)

Residual

(feet)

Simulated

water level

(feet)

Residual

(feet)
Table 6 47

Table 6

Table 6. Comparison of the residuals for hydraulic heads and springflows for selected observation wells and springs, conduit-flow and 

diffuse-flow Edwards aquifer models, San Antonio region, Texas.

[TWDB, Texas Water Development Board; ID, identification number; residual, simulated water level minus measured water level; MAE (mean absolute 

difference), sum of absolute values of residuals divided by number of wells; ME (mean algebraic difference), algebraic sum of residuals divided by number of 

wells; RMS, root-mean-square error; C, confined conditions at well site; U, unconfined conditions at well site] 

TWDB

well ID

Period of

measurements County Hydrologiccondition

Hydraulic-head residuals

(feet)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

MAE ME RMS MAE ME RMS

6945401 1954–2000 Uvalde C 11.4 .4 14.2 17.2 12.7 19.9

6950302 1947–2000 Uvalde C 11.7 1.7 15.0 11.1 -2.3 13.8

6841301 1950–2000 Medina C 15.9 14.9 17.8 8.5 5.4 10.6

6946701 1947–90 Medina C 10.6 -1.4 13.5 15.1 11.6 17.3

6837203 1947–2000 Bexar C 6.2 1.5 8.0 6.7 -4.4 8.7

6830211 1964–2000 Bexar C/U 12.8 4.8 15.4 5.5 -2.7 7.4

6845102 1950–84 Bexar C 22.3 22.3 23.4 11.1 10.7 12.3

6816801 1947–2000 Comal U 3.4 -.6 5.0 7.0 6.3 7.7

6823701 1947–94 Comal C 6.7 -1.1 8.7 4.4 -2.1 6.3

5857903 1949–85 Hays C/U 8.0 2.1 11.0 18.9 11.8 26.0

5858101 1947–2000 Hays C 26.2 -18.6 29.2 21.0 -15.4 25.9

6702103 1947–77 Hays C 11.1 -8.9 15.3 27.1 27.1 30.4

Spring 

name

Period of

measurements County

Springflow residuals

(cubic feet per day)

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004)

Diffuse-flow Edwards

aquifer model

MAE ME RMS MAE ME RMS

Comal 1947–2000 Comal 3,083,452 577,905 3,967,067 2,654,312 -127,334 3,348,776

San Marcos 1947–2000 Hays 2,145,232 1,296,041 2,691,442 2,209,134 543,298 2,780,848

Leona 1947–2000 Uvalde 2,025,127 1,881,722 2,884,793 1,697,922 1,452,740 2,271,649

San Antonio 1947–2000 Bexar 830,745 -418,464 1,914,358 1,573,585 1,120,551 3,448,867

San Pedro 1947–2000 Bexar 153,317 4,359 230,676 207,910 -199,293 348,280
48 Diffuse-Flow Conceptualization and Simulation of the Edwards Aquifer, San Antonio Region, Texas

Table 7

Table 7. Simulated annual water budget for the steady-state simulation and for 1956 for the transient simulation, conduit-flow and 

diffuse-flow Edwards aquifer models, San Antonio region, Texas.

[Recharge includes leakage from streams through streambeds and infiltration of precipitation in interstream areas. Boundary inflow includes inflow through 

general-head and specified-flow boundary condition cells at northern and northwestern model boundaries. Stream-aquifer leakage is between Edwards aquifer and 

Colorado River at northeastern model boundary. Subtotal comprises source or discharge components exclusive of changes in storage. Total includes changes in 

storage. Negative net change in storage indicates net loss of water from storage (storage accounted for as source). NA, not applicable]

Information regarding water resources in Texas is available at 

http: //tx.usgs.gov/

Budget

component

and time

period

Conduit-flow Edwards aquifer model

(Lindgren and others, 2004) Diffuse-flow Edwards aquifer model Difference

Flow rate

(acre-feet/

year)

Percentage of

total sources

or discharges

Percentage of

subtotal for 

sources or

discharges

Flow rate

(acre-feet/

year)

Percentage of

total sources

or discharges

Percentage

of subtotal for 

sources or

discharges

Percentage of

total sources

or discharges

Sources

Recharge

Steady-state 583,985.9 93.5 NA 585,154.8 93.6 NA 0.1

1956 60,459.5 14.5 60.4 61,111.7 15.0 60.1 .5

Boundary inflow

Steady-state 40,265.3 6.5 NA 40,265.3 6.4 NA -.1

1956 39,457.3 9.5 39.4 40,354.3 9.9 39.7 .4

Stream-aquifer leakage

Steady-state 0 0 NA 0 0 NA 0

1956 179.0 .04 .2 204.2 .05 .2 .01

Subtotal

1956 . . . . . . . . . . 100,095.8 24.1 100.0 101,670.2 25.0 100.0 NA

Total sources

Steady-state . . . . . . . 624,251.2 100.0 NA 625,420.1 100.0 NA NA

1956 . . . . . . . . . . . . 416,036.3 100.0 NA 407,113.1 100.0 NA NA

Discharges

Withdrawals (pumpage)

Steady-state 160,592.5 25.7 NA 160,593.2 25.7 NA 0

1956 309,177.7 74.3 74.3 309,927.4 76.1 76.1 1.8

Springflow

Steady-state 460,169.3 73.7 NA 459,363.9 73.4 NA -.3

1956 104,983.6 25.2 25.2 94,251.5 23.2 23.2 -2.0

Stream-aquifer leakage

Steady-state 3,488.7 .6 NA 5,462.3 .9 NA .3

1956 1,871.4 .4 .4 2,933.0 .7 .7 .3

Subtotal

1956 . . . . . . . . . . 416,032.7 100.0 100.0 407,111.8 100.0 100.0 NA

Total discharges

Steady-state . . . . . . . 624,250.5 100.0 NA 625,419.5 100.0 NA NA

1956 . . . . . . . . . . . . 416,032.7 100.0 100.0 407,111.8 100.0 100.0 NA

Net change in storage

1956 . . . . . . . . . . -315,940.5 75.9 NA -305,442.9 75.0 NA -.9