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Statistical Analyses of Hydrologic System 

Components and Simulation of Edwards 

Aquifer Water-Level Response to Rainfall 

Using Transfer-Function Models, 

San Antonio Region, Texas 

By Lisa D. Miller and Andrew J. Long 

U.S. Department of the Interior

U.S. Geological Survey

In cooperation with the San Antonio Water System 

Scientific Investigations Report 2006–5131
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Meyers, Director

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

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Although this report is in the public domain, permission must be secured from the individual copyright owners to

reproduce any copyrighted materials contained within this report.

Suggested citation:

Miller, L.D., and Long, A.J., 2006, Statistical analyses of hydrologic system components and simulation of Edwards

aquifer water-level response to rainfall using transfer-function models, San Antonio region, Texas: U.S. Geological

Survey Scientific Investigations Report 2006–5131, 20 p., 1 appendix.
iii

Contents

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

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

Statistical Analyses of Hydrologic System Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Correlation Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Hydrographic Analyses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Simulation of Water-Level Response to Rainfall Using Transfer-Function Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Effective Rainfall Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Parameter Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Simulated Water Levels at Three Wells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Bexar County Index Well (AY–68–37–203) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Hill Country Village Well (AY–68–29–103) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

Medina County FM 1796 Well (TD–69–38–601) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Discussion of Transfer-Function Model Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

References Cited . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Appendix 1—Daily Water-Level Data for Seven Wells Used in Analysis (online version only) 

available at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . http://pubs.usgs.gov/sir/2006/5131/

Figures

1. Map showing Trinity and Edwards aquifers and Edwards aquifer recharge zone, confined 

zone, and site locations in the San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2. Diagrammatic north-northwest-to-south-southeast section showing hydrogeologic 

framework and generalized ground-water-flow directions, Edwards Plateau to Gulf 

Coastal Plain, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3–5. Graphs showing: 

3. Daily maximum water levels at selected wells and daily mean springflow at 

Comal Springs relative to daily maximum water levels at Bexar County index well 

(AY–68–37–203), Edwards aquifer, San Antonio region, Texas, September 1986– 

December 2002 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4. Daily maximum water levels at selected wells and daily mean springflow at Comal 

Springs, Edwards aquifer, San Antonio region, Texas, September 1986–December 2002 . . . . . 9

5. Water-level response to rainfall events for Bexar County index well (AY–68–37–203), 

Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

6. Map showing flow units of the Edwards aquifer, San Antonio region, Texas, and well 

catchment areas for Bexar County index well, Hill Country Village well, and Medina 

County FM 1796 well . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

7. Graph showing calibrated transfer-function models for Bexar County index well 

(AY–68–37–203), Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
iv

8. Hydrograph showing measured and simulated water level for Bexar County index well 

(AY–68–37–203), Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

9. Graph showing calibrated transfer-function models for Hill Country Village well 

(AY–68–29–103), Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

10. Hydrograph showing measured and simulated water level for Hill Country Village well 

(AY–68–29–103), Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

11. Graph showing calibrated transfer-function models for Medina County FM 1796 well 

(TD–69–38–601), Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

12. Hydrograph showing measured and simulated water level for Medina County FM 1796 

well (TD–69–38–601), Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

Tables

1. Site name, site identifier, and period of record for selected well, spring, rainfall, and stream 

sites in or associated with the Edwards aquifer, San Antonio region, Texas . . . . . . . . . . . . . . . . . . . . . . . . 5

2. Spearman's rho correlation coefficients for daily maximum water levels at Bexar County 

index well (AY–68–37–203) lagged from 0 to 16 days and daily maximum water levels at 

selected wells and daily mean springflow at Comal Springs, Edwards aquifer, San Antonio 

region, Texas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3. Estimated parameters for transfer-function models developed for selected wells in the 

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

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).
Statistical Analyses of Hydrologic System 

Components and Simulation of Edwards 

Aquifer Water-Level Response to Rainfall 

Using Transfer-Function Models, 

San Antonio Region, Texas 

By Lisa D. Miller and Andrew J. Long

Abstract 

In 2003 the U.S. Geological Survey, in cooperation with 

the San Antonio Water System, did a study using historical data 

to statistically analyze hydrologic system components in the 

San Antonio region of Texas and to develop transfer-function 

models to simulate water levels at selected sites (wells) in the 

Edwards aquifer on the basis of rainfall. Water levels for two 

wells in the confined zone in Medina County and one well in the 

confined zone in Bexar County were highly correlated and 

showed little or no lag time between water-level responses. 

Water levels in these wells also were highly correlated with 

springflow at Comal Springs. Water-level hydrographs for 

35 storms showed that an individual well can respond differently to similar amounts of rainfall. Fourteen water-levelrecession hydrographs for a Medina County well showed that 

recession rates were variable. Transfer-function models were 

developed to simulate water levels at one confined-zone well 

and two recharge-zone wells in response to rainfall. For the 

confined-zone well, 50 percent of the simulated water levels are 

within 10 feet of the measured water levels, and 80 percent of 

the simulated water levels are within 15 feet of the measured 

water levels. For one recharge-zone well, 50 percent of the 

simulated water levels are within 5 feet of the measured 

water levels, and 90 percent of the simulated water levels 

are within 14 feet of the measured water levels. For the other 

recharge-zone well, 50 percent of the simulated water levels 

are within 14 feet of the measured water levels, and 90 percent 

of the simulated water levels are within 27 feet of the measured 

water levels. The transfer-function models showed that 

(1) the Edwards aquifer in the San Antonio region responds differently to recharge (effective rainfall) at different wells; and 

(2) multiple flow components are present in the aquifer. If simulated long-term system response results from a change in the 

hydrologic budget, then water levels would be difficult to simulate accurately. 

Introduction

The Edwards aquifer is the major source of water for more 

than 1.5 million people in the San Antonio, Texas, area and provides nearly all of the water used for industrial, military, irrigation, and public supplies. San Antonio’s public water supply 

needs are in competition with those of farmers and ranchers 

west of the city. Withdrawals from the aquifer to meet the city’s 

needs are a threat to the continuation of flows at Comal Springs, 

the largest spring in the southwestern United States, and San 

Marcos Springs. Both springs supply downstream users, sustain 

federally listed endangered species, and support local economies through tourism. An Edwards aquifer management plan 

(San Antonio Water System, 2006) has been implemented to, 

among several objectives, ensure continuous springflow at 

Comal Springs. The plan restricts water use on the basis of 

specific ground-water levels of the Edwards aquifer at an index 

well in Bexar County (Bexar County index well). To effectively 

manage the Edwards aquifer on a day-to-day basis, the San 

Antonio Water System (SAWS) would like to be able to simulate water-level response on the basis of measurable and readily 

available data, such as rainfall. 

In 2003 the U.S. Geological Survey (USGS), in cooperation with SAWS, did a study using historical data to statistically 

analyze relations among Edwards aquifer water levels, springflows, rainfall, and streamflow in the San Antonio region of 

Texas and to develop models to simulate water levels at selected 

sites (wells) in the Edwards aquifer on the basis of rainfall.

Previous statistical regression analyses of hydrologic 

variables for the Edwards aquifer have been made by Puente 
2 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

(1976), Asquith and Jennings (1993), and Tomasko and others 

(2001). Puente (1976) developed equations using simple linear 

regression to estimate daily, monthly, and annual water levels 

and springflow. Asquith and Jennings (1993) developed statistical models to estimate annual springflow at Comal Springs 

and annual water levels for the Bexar County index well. 

Tomasko and others (2001) examined stream-discharge, waterlevel, and spring-discharge response to high rainfall during 

October 1998. Some statistical relations developed in these previous studies might be useful in estimating missing water-level 

record; however, they are unable to simulate changes in water 

levels on the basis of readily available data. 

The purpose of this report is to (1) briefly describe statistical analyses used to investigate the relations among Edwards 

aquifer water levels, springflows, rainfall, and streamflow in 

the San Antonio region of Texas, and (2) describe lumpedparameter transfer-function models developed to simulate 

water-level response at three wells in the Edwards aquifer on 

the basis of rainfall. Two of the wells, one in the recharge zone 

(outcrop) of the Edwards aquifer and one in the confined zone, 

are in Bexar County; and one well is in the recharge zone in 

Medina County. Hydrologic data collected by the USGS, 

Edwards Aquifer Authority, and National Weather Service 

(NWS) in Uvalde, Medina, Bexar, and Comal Counties were 

used in the analyses. All well (daily water-level) data used in the 

analyses are in the appendix (online version only, available at 

http://pubs.usgs.gov/sir/2006/5131/). The rainfall data are 

available from the National Climatic Data Center (National 

Climatic Data Center, 2006). The spring and stream data are 

available from the USGS (U.S. Geological Survey, 2001).

The Edwards aquifer in the San Antonio region (fig. 1) is 

composed of extensively faulted, fractured, and cavernous 

limestone and dolomite of Early Cretaceous age (Maclay, 

1995). The Edwards aquifer in the San Antonio region consists 

of the Georgetown Formation and the Edwards Group or their 

stratigraphic equivalents. These formations crop out within the 

Edwards Plateau and the Balcones fault zone and underlie the 

Gulf Coastal Plain (fig. 2). The Del Rio Clay and overlying 

units form the upper confining unit of the Edwards aquifer, 

and the Trinity aquifer beneath the Edwards, because of its low 

permeability relative to that of the Edwards aquifer, acts as a 

lower confining unit. The Edwards aquifer ranges in thickness 

from about 400 to 800 feet and averages about 550 feet. The 

thickness increases toward the west and south (Maclay, 1995, 

p. 16). 

Most of the recharge to the Edwards aquifer occurs west of 

Bexar County and is from direct infiltration of rainfall and 

streamflow losses in the recharge zone (fig. 1). After entering 

the aquifer in the recharge zone, water moves into the confined 

zone and then east to points of discharge in Bexar County 

(mostly public-supply wells) and northeast, essentially parallel 

to the northeast-trending faults of the Balcones fault zone into 

Comal and Hays Counties, where it is withdrawn from wells 

and discharged by springs. Additional recharge to the Edwards 

aquifer occurs in the recharge zone in northern Bexar County 

and southern Comal and Hays Counties.

Statistical Analyses of Hydrologic System 

Components

A brief summary of the statistical analyses used in this 

study to investigate the relations between ground-water-level 

and springflow data for parts of the Edwards aquifer, and associated rainfall and streamflow data, is discussed in this section. 

Techniques used consist of determination of correlation coefficients between water levels at wells, and between water levels 

at wells and springflows; hydrographic analyses (including 

storm and recession analyses); and linear regression. Table 1 

lists the ground-water, rainfall, and surface-water sites used in 

this analysis. 

Correlation Coefficients

Spearman’s rho correlation coefficients (Helsel and 

Hirsch, 1992) were computed using long-term concurrent daily 

maximum water levels at selected wells in the Edwards aquifer 

and daily mean springflow at Comal Springs. Specifically, each 

time series (for example, water levels from the Bexar County 

index well) was lagged from 0 to 450 days in 1-day intervals 

against each other time series (for example, Comal Springs 

springflow). Correlation coefficients for daily maximum water 

levels at the Bexar County index well lagged from 0 to 16 days 

and those of selected wells and daily mean Comal Springs 

springflow are shown in table 2. 

Daily maximum water levels at the Bexar County index, 

City of Castroville, and Medina County index wells were highly 

correlated. The highest correlations between water levels at 

these wells were computed using lag times of 0 to 2 days, indicating little or no time between water-level responses (table 2). 

Figure 3 shows daily maximum water levels for selected wells 

and daily mean springflow for Comal Springs relative to daily 

maximum water levels at the Bexar County index well. Water 

levels in these wells also were highly correlated with springflow 

at Comal Springs. Springflow at Comal Springs was most 

highly correlated with water levels at the Bexar County index 

well. The highest correlation coefficient of .9728 was obtained 

by lagging water levels at the Bexar County index well by 2 

days (that is, water-level changes at the Bexar County index 

well today are most related to springflow at Comal Springs 2 

days in the future). Water levels at the Medina County FM 1796 

and Quihi wells also were highly correlated (correlation coefficient for zero lag = .9379).

Lag times between water levels at the Bexar County index 

well and water levels at wells in the recharge (unconfined) zone 

of the Edwards aquifer (Hill Country Village, Medina County 

FM 1796, and Quihi wells) were much longer than lag times 

between water levels at wells in the confined zone of the aquifer 

(City of Castroville, Medina County index, and Uvalde County 

index wells). For example, lag times between water levels at the 

Bexar County index well and Hill Country Village well and 

between the Bexar County index well and Quihi well were 
Statistical Analyses of Hydrologic System Components 3 Figure 1. Trinity and Edwards aquifers and Edwards aquifer recharge zone, confined zone, and site locations in the San Antonio region, Texas. 0 30 60 MILES 15 45 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 83 Zone 14

0 120 240 MILES

TEXAS

LOCATION MAP

BEXAR

ATASCOSA

COUNTY

WILSON

COUNTY MEDINA

COUNTY

ZAVALA COUNTY

UVALDE COUNTY

REAL

COUNTY

KERR COUNTY

BANDERA

COMAL

COUNTY

COUNTY

KENDALL

COUNTY

COUNTY

HAYS

COUNTY

TRAVIS

COUNTY

FRIO COUNTY

GUADALUPE

COUNTY

CALDWELL

BASTROP

COUNTY

COUNTY

GONZALES

COUNTY

BLANCO

COUNTY GILLESPIE

COUNTY

EDWARDS

COUNTY

KINNEY

COUNTY

MAVERICK

COUNTY

Austin

San Antonio

Kerrville

New Braunfels

Seguin

San

Marcos Lockhart

Uva dl e

Bastrop

Pleasanton

Pearsall

Eagle Pass

Floresville

Boerne

Gonzales

Crystal City

Blanco

Helotes

Brackettville

Freder cksburg i

Dripping Springs

Castroville Sabinal

Bandera

Rockspr ngs i

Leakey

Hondo

Jourdanton

Johnson City

Lacoste

Sabinal River

o H odn Creek

te lo e H er Cs ek

!

!Comal Springs

San Marcos Springs

! !

!

!

!

!

Uvalde County ni dex

YP–69–50–302

City of Castroville

TD–68–41–301 Medina County FM 1796 TD–69–38–601

Bexar County index

AY–68–37–203

Medina County index

TD–69–47–306

Hill Country Village

AY–68–29–103

Hondo Creek near Tarpley

08200000

Helotes Creek at Helotes

08181400

Sabinal River near Sabinal

08198000

Quihi

TD

!

–69–40–102

!

!

Trinity aquifer outcrop—Modified from

Ashworth and Hopkins, 1995

Edwards aquifer outcrop

(recharge [unconf ni ed] zone)

—Modified

from Ashworth and Hopkins, 1995

Edwards aquifer subcrop

(confined zone)—Downdip

boundary from Schultz, 1994

Balcones fault zone

Site, name, and identifier or State well

number (table 1)

U.S. Geological Survey streamflow

Well

U.S. Geological Survey springflo

w

Hondo Creek near Tarpley

08200000

Bexar County index

AY–68–37–203

EXPLANATION

Comal Springs

99°00'

97°00'

29°00'

30°00'

100°00'

98°00'

San Antonio International Airport
4 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall Figure 2. Diagrammatic north-northwest-to-south-southeast section showing hydrogeologic framework and generalized ground-water-flow directions, Edwards Plateau to Gulf Coastal Plain, San Antonio region, Texas (modified from Barker and Ardis, 1996, plates 1 and 3). Balcones fault zone Edwards aquifer recharge zone Catchment area Gillespie County Kendall County Bexar County Atascosa County EXPLANATIONUPPER CONFINING UNIT EDWARDS AQUIFER UNCONFINED CONFINED TRINITY AQUIFER APPROXIMATE FRESHWATER/SALINE- WATER INTERFACE FAULT—Arrows indicate direction LIMESTONE SAND PALEOZOIC ROCKS GENERALIZED DIRECTION OF GROUND-WATER FLOW of movement Balcones escarpment EDWARDS PLATEAU GULF COASTAL PLAIN NOT TO SCALEHILL COUNTRY NNW SSE

Trinity Group

Trinity

Group

Del Rio Clay and overlying units

Trinity Group

Edwards Group (remnants)

Trinity Group

Hammett Shale

Georgetown Formation

and Edwards Group

Georgetown Formation

and Edwards Group
Statistical Analyses of Hydrologic System Components 5

about 45 and 310 days, respectively; whereas, lag times for 

wells in the confined zone of the aquifer (City of Castroville, 

Medina County index, and Uvalde County index wells) ranged 

from 0 to about 14 days. 

Hydrographic Analyses

Hydrographic analyses were done to obtain relations 

between rainfall and water-level changes and to characterize 

water-level-recession curves during periods of no rainfall. 

Water-level hydrographs were generated for 35 storms for the 

Bexar County index well and the City of Castroville well. Fourteen water-level-recession hydrographs were generated for the 

Medina County index well. 

Average basinwide rainfall for the 35 storms ranged from 

0.17 to 2.18 inches. The time to peak water level, the monthly 

Palmer drought severity index (National Weather Service 

Climate Prediction Center, 2005), and daily total rainfall and 

daily mean streamflow across the basin were recorded for each 

storm. The Palmer drought severity index uses temperature 

and rainfall information in a formula to characterize dryness. 

It was somewhat useful in approximating long-term antecedent 

conditions.

Figure 4 shows hydrographs of water levels at the 

Bexar County index, City of Castroville, and Medina County 

index wells, and springflow at Comal Springs. Long-term water 

levels for these wells are very similar; however, short-term 

fluctuations (water-level changes over days or weeks) can be 

quite different. In general for the 35 storms analyzed, water 

levels peaked sooner at the Bexar County index well than at the 

City of Castroville well. 

Visual examination of the water-level hydrographs 

showed that an individual well can respond differently to similar amounts of rainfall. For example, figure 5 shows two different responses at the Bexar County index well to approximately 

the same amount of rainfall. The water level rose about 6 feet 

during one event (event 1), whereas the water level rose only 

0.5 foot during another event (event 2). The Palmer drought 

severity index indicated below-normal moisture during event 1 

(6-foot water-level rise) and above-normal moisture during 

event 2 (0.5-foot water-level rise). The average water level at 

the Bexar County index well during event 1 was 644.25 feet 

above NGVD 29 and during event 2 was 680.41 feet above 

NGVD 29. Average 7-day streamflows were computed at 

selected USGS streamflow sites within the well catchment 

area (defined later) during each event. Streamflow was lower 

across the basin during event 1 than during event 2. For 

Table 1. Site name, site identifier, and period of record for selected well, spring, rainfall, and stream sites in or associated with the 

Edwards aquifer, San Antonio region, Texas.

[Most sites have periods of missing daily records. USGS, U.S. Geological Survey; EAA, Edwards Aquifer Authority; --, not available or not applicable; NWS, 

National Weather Service] 

Site name Site 

type Agency Siteidentifier

State well

number

Period of record

used in analysis

Bexar County index Well USGS/EAA 292845098255401 AY–68–37–203 June 1963–Dec. 2002

Hill Country Village Well USGS/EAA 293522098291201 AY–68–29–103 Nov. 1957–Dec. 2002

City of Castroville Well USGS/EAA 292117098524701 TD–68–41–301 May 1950–Dec. 2002

Medina County FM 1796 Well USGS/EAA 292618099165901 TD–69–38–601 July 1957–Dec. 2002

Medina County index Well USGS/EAA 292045099081801 TD–69–47–306 Sept. 1986–Dec. 2002

Quihi Well EAA -- TD–69–40–102 June 1994–Dec. 2002 

Uvalde County index Well USGS/EAA 291237099471201 YP–69–50–302 Dec. 1949–Dec. 2002

Comal Springs at New Braunfels, Tex. Spring USGS 08168710 -- Oct. 1932–Dec. 2002

Boerne Rainfall NWS 410902 -- July 1897–Dec. 2002

Hondo Rainfall NWS 414254 -- Jan. 1900–Dec. 2002

Hondo Airport Rainfall NWS 414256 -- Mar. 1975–Dec. 2002

Kerrville Rainfall NWS 414780 -- Jan. 1897–Dec. 2002

Rio Medina Rainfall NWS 417628 -- Aug. 1922–Dec. 2002

Sabinal Rainfall NWS 417873 -- Sept. 1903–Dec. 2002

Tarpley Rainfall NWS 418845 -- Oct. 1937–Dec. 2002

Helotes Creek at Helotes, Tex. Stream USGS 08181400 -- June 1968–Dec. 2002

Hondo Creek near Tarpley, Tex. Stream USGS 08200000 -- Aug. 1952–Dec. 2002

Sabinal River near Sabinal, Tex. Stream USGS 08198000 -- Oct. 1942–Dec. 2002
6 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

Figure 3. Daily maximum water levels at selected wells and daily mean springflow at Comal Springs relative to daily maximum water 

levels at Bexar County index well (AY–68–37–203), Edwards aquifer, San Antonio region, Texas, September 1986–December 2002.

610 640 650 660 670 680 690 700 71 620 630 0

640

660

680

700

720

740

750

630

650

670

690

710

730

ALTITUDE AT BEXAR COUNTY INDEX WELL, IN FEET ABOVE NGVD 29

ALTITUDE, IN FEET ABOVE NGVD 29

City of Castroville well (TD–68–41–301)

610 630 650 670 690 620 640 660 680 700 710

670

690

710

730

750

660

680

700

720

740

ALTITUDE AT BEXAR COUNTY INDEX WELL, IN FEET ABOVE NGVD 29

ALTITUDE, IN FEET ABOVE NGVD 29

Hill Country Village well (AY–68–29–103)
Statistical Analyses of Hydrologic System Components 7

Figure 3. Continued.

610 630 650 670 690 710 620 640 660 680 700

0

100

200

300

400

500

550

50

150

250

350

450

ALTITUDE AT BEXAR COUNTY INDEX WELL, IN FEET ABOVE NGVD 29

SPRINGFLOW, IN CUBIC FEET PER SECOND

Comal Springs (08168710)

610 630 650 670 690 620 640 660 680 700 710

620

670

720

770

645

695

745

795

ALTITUDE AT BEXAR COUNTY INDEX WELL, IN FEET ABOVE NGVD 29

ALTITUDE, IN FEET ABOVE NGVD 29

Medina County index well (TD–69–47–306)
8 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

Table 2. Spearman’s rho correlation coefficients for daily maximum water levels at Bexar County index well (AY–68–37–203) lagged 

from 0 to 16 days and daily maximum water levels at selected wells and daily mean springflow at Comal Springs, Edwards aquifer, San 

Antonio region, Texas.

[Bexar County index well_LAG#, number of days water levels at Bexar County index well were lagged (example: LAG1 = 1-day lag); first number presented in 

table is Spearman’s rho correlation coefficient; second number presented in table is number of x-y pairs used to compute correlation] 

City of Castroville well

(TD–68–41–301)

Medina County index well

(TD–69–47–306)

Uvalde County index well

(YP–69–50–302)

Comal Springs 

(08168710)

Bexar County index well_LAG0 .9736 .9636 .8054 .9720

13,092 5,806 10,121 14,651

Bexar County index well_LAG1 .9740 .9636 .8066 .9726

13,091 5,806 10,120 14,650

Bexar County index well_LAG2 .9738 .9629 .8076 .9728

13,090 5,806 10,119 14,649

Bexar County index well_LAG3 .9732 .9618 .8085 .9725

13,089 5,806 10,118 14,648

Bexar County index well_LAG4 .9722 .9604 .8094 .9721

13,088 5,806 10,117 14,647

Bexar County index well_LAG5 .9711 .9587 .8100 .9714

13,087 5,806 10,116 14,646

Bexar County index well_LAG6 .9697 .9568 .8106 .9705

13,086 5,806 10,115 14,645

Bexar County index well_LAG7 .9681 .9547 .8111 .9694

13,085 5,806 10,114 14,644

Bexar County index well_LAG8 .9664 .9526 .8115 .9681

13,084 5,806 10,113 14,643

Bexar County index well_LAG9 .9645 .9503 .8117 .9666

13,083 5,806 10,112 14,642

Bexar County index well_LAG10 .9625 .9479 .8118 .9650

13,082 5,806 10,111 14,641

Bexar County index well_LAG11 .9603 .9455 .8118 .9633

13,081 5,806 10,110 14,640

Bexar County index well_LAG12 .958 .9432 .8119 .9615

13,080 5,806 10,109 14,639

Bexar County index well_LAG13 .9556 .9408 .8120 .9597

13,079 5,806 10,108 14,638

Bexar County index well_LAG14 .9532 .9383 .8121 .9578

13,078 5,806 10,107 14,637

Bexar County index well_LAG15 .9507 .9358 .8120 .9558

13,077 5,806 10,106 14,636

Bexar County index well_LAG16 .9482 .9333 .8118 .9537

13,076 5,806 10,105 14,635
Statistical Analyses of Hydrologic System Components 9

example, during event 1, the streamflows at Sabinal River near 

Sabinal (USGS 08198000), Hondo Creek near Tarpley (USGS 

08200000), and Helotes Creek at Helotes (USGS 08181400) 

were 13, 4, and 0.01 cubic feet per second, respectively; 

whereas, the average streamflows at these sites during event 2 

were 54, 39, and 8 cubic feet per second, respectively.

Water-level-recession hydrographs were generated to indicate whether recession rates were similar during periods of no 

rainfall at a given well and whether a simple relation could be 

developed to simulate water-level response to no rainfall. 

Recession hydrographs were isolated by choosing periods with 

no rainfall for at least 10 to 14 days and declining water levels. 

Analyses of 14 recession hydrographs for the Medina County 

index well showed that recession rates were variable. Average 

recession rates ranged from about 0.11 to 1.22 feet per day. The 

difference in recession rates could be caused by factors such as 

season, antecedent condition, and aquifer depth. These hydrographic analyses underscore the need to incorporate antecedent 

conditions in any model to simulate water levels.

Linear Regression

Linear regression equations were developed to estimate 

water levels at selected wells using data available on a near 

real-time basis, such as water levels from nearby wells, rainfall, 

and streamflow. The monthly Palmer drought severity index 

also was used as an independent variable in the regressions. 

Simple linear regression was done using water levels at one well 

to simulate water levels at another well on the basis of lag times 

determined from the correlation analyses. Simple linear regression also was done using water levels at a selected well and rainfall at nearby gages or streamflow from nearby streams. MultiFigure 4. Daily maximum water levels at selected wells and daily mean springflow at Comal Springs, Edwards aquifer, San Antonio 

region, Texas, September 1986–December 2002.

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

YEAR

500

550

600

650

700

750

800

ALTITUDE, IN FEET ABOVE NGVD 29

0

100

200

300

400

500

600

700

SPRINGFLOW, IN CUBIC FEET PER SECOND

Bexar County index well (AY–68–37–203)

City of Castroville well (TD–68–41–301)

Medina County index well (TD–69–47–306)

Comal Springs (08168710)

EXPLANATION
10 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

ple linear regression was used to try to improve the equations 

developed using one variable. Variables used in the multiple 

linear regressions comprise water levels at selected wells, rainfall, streamflow, and monthly Palmer drought severity index. 

Rainfall and streamflow were not used in the same equations 

because these two variables were correlated.

Water-level equations with the highest coefficients of 

determination (r2

) (the fraction of the variation in simulated 

water levels accounted for by the variation in the explanatory 

variables) are shown below: 

 WLHillCountry = (WLBexarCo_Lag45)(0.8910)

+ (SA Prec60) (0.4997) 

+ 99.5469, (1)

r

2 = .7072, 

Residual standard error = 9.217 on 13,630 degrees of freedom, 

p-value (attained significance 

level) < .0001; and 

WLMedinaFM = (WLMedinaCo_Lag85)(1.0437) + 131.5623, (2)

r

2 = .7742, 

Residual standard error = 14.74 on 4,114 degrees of freedom, 

p-value < .0001, 

where 

WLHillCountry is water level, in feet above NGVD 29, at 

the Hill Country Village well;

WLBexarCo_Lag45 is water level, in feet above NGVD 29, at 

the Bexar County index well lagged 

45 days;

SA Prec60 is sum of the previous 60 days of daily 

total rainfall, in inches, at San Antonio 

International Airport;

WLMedinaFM is water level, in feet above NGVD 29, at 

the Medina County FM 1796 well;

WLMedinaCo_Lag85 is water level, in feet above NGVD 29, at 

the Medina County index well lagged 

85 days.

Figure 5. Water-level response to rainfall events for Bexar County index well (AY–68–37–203), Edwards aquifer, San Antonio region, 

Texas.

123456 7

DAYS

0

1

2

3

4

5

6

WATER-LEVEL CHANGE, IN FEET 

San Antonio International Airport rainfall = 1.28 inches

Average area rainfall = 0.93 inch

San Antonio International Airport rainfall = 1.44 inches

Average area rainfall = 1.01 inches

Event 1

Event 2
Simulation of Water-Level Response to Rainfall Using Transfer-Function Models 11

Observed water levels in the Edwards aquifer show both 

short-term (hours or days) and long-term (days, weeks, or 

months) response to rainfall. Although there are some relatively 

high coefficients of determination, the regression equations 

might not adequately take into account both the short- and longterm variation in water levels. For this reason, transfer-function 

models were developed to simulate water-level response at 

three wells to rainfall. 

Simulation of Water-Level Response to 

Rainfall Using Transfer-Function Models

Transfer functions, often called unit hydrographs, are commonly used in watershed modeling. The transfer-function 

approach requires few assumptions about the properties and 

boundary conditions of the system, because the properties 

affecting the response are lumped into a single transfer function 

determined on the basis of measured hydrologic time-series 

data. The shape of the transfer function characterizes the system 

response to an input signal. In this application, the system 

response is the water-level change and the input signal is effective rainfall; that is, the amount of rainfall passing through the 

root zone that recharges the aquifer.

The following sections describe the methods used to 

develop the transfer-function models and the results obtained. 

The methods comprise estimation of effective rainfall, convolution, and parameter estimation. The results are simulated water 

levels at three wells. 

Effective Rainfall Estimation

The amount of rainfall during the last few days before a 

particular rainfall event partly determines the fraction of rainfall 

that passes through the root zone. High humidity and cool temperatures during wet periods might decrease evapotranspiration 

(ET) rates. The method of Jakeman and Hornberger (1993) is 

used to compute an antecedent rainfall index, , which weights 

the daily rainfall by the rainfall of previous days. The weight is 

scaled exponentially backward in time and is computed by 

; 

; (3)

where

i is the time step, in days; 

c is a normalizing parameter to limit si

 to values between 

0 and 1; and 

κ is a coefficient that weights the influence of antecedent 

conditions. 

Effective daily rainfall, ui

, is then estimated by

, (4)

where

 is the total daily rainfall, in inches. 

When discussing the hydraulic-head (water-level) 

response, the term “effective rainfall” is used in this report to 

describe the fraction of total rainfall that recharges an aquifer by 

direct infiltration. For this analysis, it is assumed that most rainfall on the recharge zone of the Edwards aquifer recharges the 

aquifer by direct infiltration.

Convolution

A transfer-function model also can be called a linear system. In this approach, the water-level response to effective rainfall is described by the convolution integral,

, (5)

where

 is the time series of water level (response function);

 is the time series of recharge (forcing function or 

signal);

 is a transfer function; 

is the delay time from forcing function to response; 

and 

 is the derivative of time (Dooge, 1973; Singh, 

1988). 

If time steps of equal duration are used, the discrete form of 

equation 5 is 

 i = 0, 1, 2, ..., N (6)

The transfer function represents the component of 

the response function that results from a single pulse of the 

forcing function . Thus, the transfer function can be thought 

of as the superposition of multiple transfer functions resulting 

from multiple pulses of the forcing function, where each of the 

transfer functions is scaled by the magnitude of the corresponding pulse. The transfer function also represents the statistical 

distribution of response travel times for a single point in space 

for any single pulse of the forcing function, the peak of which 

establishes the travel time for the peak response. The total 

length of time of the transfer function establishes the length of 

time that the effects of a pulse remain. 

The transfer function is assumed to be stationary in time at 

any single point in space. If transfer functions are estimated 

along a series of points in space, each located a farther distance 

from the forcing function’s location, then that series of transfer 

functions will begin with a short duration and high peak and 

progressively acquire longer durations with lower peaks. This 

series would be similar to the propagation of a wave. 

si

si cri 1 κ–1 ( ) – s = + i – 1

c ri 1 κ–1 ( ) – ri – 1 1 κ–1 ( ) – 2

r = [ ] + + i – 2 + ...

i = 012 ,,, , ... N;

0 si > > 1

ui ri

s = i

ri

y t( ) h t( ) – τ x()τ τ d o

i = ∫

y t( )

x( ) τ

h t( ) – τ

( ) t – τ

dt

yi hi j – xj

j = 0

i

= ∑

hi j – ( )

yi ( )

xj
12 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

The transfer function is propagated through the system 

similarly to the propagation of a wave and thus can change as it 

moves through the system, depending on the distance traveled 

and media heterogeneity. One unique advantage of transferfunction models is that multiple flow components can be 

detected by using multiple transfer functions. In this approach, 

each transfer function is assumed to represent a distinct component of flow. Long and Putnam (2004) used this method to 

simulate transport in a karst aquifer using oxygen-18 (18O) 

data and concluded that there were three distinct components 

of flow—conduit flow, diffuse flow, and delayed flow. The 

conduit-flow component responded quickest, followed by the 

diffuse-flow component, and then the delayed-flow component. 

White and White (2001) indicate that the Edwards aquifer also 

has three distinct components of flow.

A lognormal distribution is similar to karst springflow 

hydrographs in response to storms and is therefore assumed to 

approximate the true transfer function of a karst hydraulic 

response. The lognormal distribution also is computationally 

efficient and is defined by only two parameters: the mean and 

variance. 

Parameter Estimation

Effective rainfall and measured daily maximum water levels were input into the parameter estimation program PEST 

(Doherty, 2002). Parameters comprising the mean ( ), variance 

( ), and scalar component ( ) of each transfer function and 

the effective rainfall coefficient ( ) were estimated using 

PEST. The scalar component represents the relative fraction of 

flow for each of the three distinct components—conduit, diffuse, and delayed flow. PEST minimizes the sum of the squared 

weighted residuals between measured and computed values by 

adjusting model parameters in an iterative process. Parameter 

sensitivities are determined by calculating the derivatives of all 

observations with respect to all parameters. 

Simulated Water Levels at Three Wells 

Transfer-function models were determined for three wells 

in the Edwards aquifer: the Bexar County index well, Hill 

Country Village well, and Medina County FM 1796 well. These 

transfer-function models were developed using daily maximum 

water levels and effective rainfall (estimated recharge). Daily 

maximum water levels were used to develop the models 

because long-term records were available. Effective rainfall 

was estimated from daily total rainfall recorded at an NWS 

rainfall site located within or near each well catchment area. 

Figure 6 shows the well catchment areas for Bexar County 

index, Hill Country Village, and Medina County FM 1796 

wells. A well catchment area is assumed to be one of four flow 

units (or part of a flow unit) of the Edwards aquifer in the San 

Antonio region, as defined by Maclay and Land (1988, fig. 22, 

table 4), in which the well is located. The water-level datum 

used in the models was the base of the aquifer, which is better 

suited to transfer-function models than is NGVD 29. Water 

levels, however, are reported here in terms of feet above NGVD 

29. The approximate altitude of the base of the aquifer at each 

well was estimated from well logs.

Bexar County Index Well (AY–68–37–203)

The Bexar County index well (AY–68–37–203) is within 

the city of San Antonio in the confined zone of the Edwards 

aquifer. Transfer-function models were developed using daily 

maximum water levels from June 4, 1963, to December 31, 

2002, at the Bexar County index well and daily total rainfall 

from January 1, 1920, to December 31, 2002, at the NWS rainfall site at Hondo (414254) (fig. 6). During the period, water 

levels at the well ranged from 622.66 to 703.31 feet above 

NGVD 29 and daily total rainfall at Hondo ranged from 0 to 

9.15 inches. Missing daily total rainfall at Hondo was estimated 

directly from daily total rainfall at NWS rainfall site Hondo Airport (414256). If daily total rainfall was missing at both Hondo 

and Hondo Airport, daily total rainfalls at NWS sites Sabinal 

(417873), Tarpley (418845), and Rio Medina (417628) were 

averaged to estimate daily total rainfall at Hondo.

Three transfer-function models were used to simulate 

water-level response to effective rainfall at the Bexar County 

index well. Table 3 shows the estimated parameters for the 

transfer-function models. The first function peaks at about 2 

months, the second function peaks at about 9 years, and the 

third function peaks at about 27 years (fig. 7). Measured and 

simulated water levels at the Bexar County index well (fig. 8) 

were compared. Fifty percent of the simulated water levels are 

within 10 feet of the measured water levels, and 80 percent of 

the simulated water levels are within 15 feet of the measured 

water levels. 

Hill Country Village Well (AY–68–29–103)

The Hill Country Village well is in northern Bexar County 

in the recharge zone of the Edwards aquifer. Transfer-function 

models were developed using daily maximum water levels from 

November 15, 1957, to December 31, 2002, at the Hill Country 

Village well and daily total rainfall at the NWS rainfall site 

Boerne (410902) (fig. 6) from January 1, 1920, to December 31, 

2002. During the period, water levels at the well ranged from 

668.32 to 747.67 feet above NGVD 29 and daily total rainfall at 

Boerne ranged from 0 to 8.93 inches. Missing daily total rainfall 

at Boerne was estimated directly from daily total rainfall at 

either NWS rainfall sites Kerrville (414780), Bulverde 

(411215), or Fair Oaks Ranch (413038).

Two transfer-function models were used to simulate 

water-level response to effective rainfall at the Hill Country 

Village well. Table 3 lists the estimated parameters for transferfunction models. The first function peaks at about 6 months, and 

the second function peaks at about 16 years (fig. 9). Because the 

relation between effective rainfall and water-level response at 

the Hill Country Village well appeared to change over time, a 

μ

σ

2

α

κ
Simulation of Water-Level Response to Rainfall Using Transfer-Function Models 13 Figure 6. Flow units of the Edwards aquifer, San Antonio region, Texas, and well catchment areas for Bexar County index well, Hill Country Village well, and Medina County FM 1796 well. 0 30 60 MILES 15 45

BEXAR

ATASCOSA

COUNTY

WILSON

COUNTY MEDINA

COUNTY

ZAVALA COUNTY

UVALDE COUNTY

REAL

COUNTY

KERR COUNTY

BANDERA

COMAL

COUNTY

COUNTY

KENDALL

COUNTY

COUNTY

HAYS

COUNTY

TRAVIS

COUNTY

FRIO COUNTY

GUADALUPE

COUNTY

CALDWELL

BASTROP

COUNTY

COUNTY

GONZALES

COUNTY

BLANCO

COUNTY GILLESPIE

COUNTY

EDWARDS

COUNTY

KINNEY

COUNTY

MAVERICK

COUNTY

Sabinal River

o H odn Creek

et ol e H re Cs ke

EXPLANATION

Catchment areaBexar County index wellHill Country Village wellMedina County FM 1796 wellEdwards aquifer flow unit—FromMaclay and Land, 1988, fig. 22, table 4National Weather Service rainfall site,name, and identifierWell site, name, and State well number

!!

Hondo

414254

Bexar County indexAY–68–37–203

Western-southern flow unit

South-central flow unit

Eastern flow unit

North-central flow unit

!

!

!

Bexar County index

AY–68–37–203

Medina County FM 1796

TD–69–38–601

Hill Country Village

AY–68–29–103

! ! !

!

!

!

!

Kerrville

414780

Boerne

410902

Rio Medina

417628

Tarpley

418845

Sabinal

417873

Hondo Airport

414256

Hondo

414254

!

Bulverde

411215 !

Fair Oaks Ranch

413038

99°00'

97°00'

29°00'

30°00'

100°00'

98°00'

Base modified from U.S. Geological Survey digital dataScales 1:250,000 (county boundaries) and 1:2,000,000 (hydrography)Universal Transverse Mercator projection, Datum NAD 83Zone 14
14 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

Figure 7. Calibrated transfer-function models for Bexar County index well (AY–68–37–203), Edwards aquifer, San Antonio region, Texas.

Figure 8. Measured and simulated water level for Bexar County index well (AY–68–37–203), Edwards aquifer, San Antonio region, 

Texas.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

YEARS

0

0.5

1.0

1.5

2.0

2.5

WATER-LEVEL CHANGE, IN FEET PER INCH OF

EFFECTIVE RAINFALL PER DAY

Transfer function 1

Transfer function 2

Transfer function 3

1960 1965 1970 1975 1980 1985 1990 1995 2000 2003

YEAR

600

620

640

660

680

700

720

740

WATER LEVEL, IN FEET ABOVE NGVD 29

Measured water level

Simulated water level
Simulation of Water-Level Response to Rainfall Using Transfer-Function Models 15

Table 3. Estimated parameters for transfer-function models developed for selected wells in the Edwards aquifer, San Antonio region, 

Texas. 

[μi, mean; σ2

i

, standard deviation; αi, function scale coefficient; κ, effective rainfall coefficient; c, normalizing factor to limit the antecedent rainfall 

index between 0 and 1; --, not applicable] 

1 See figure 7 for Bexar County index well; figure 9 for Hill Country Village well; figure 11 for Medina County FM 1796 well.

2 Confidence limits provide only an indication of parameter uncertainty—they rely on a linearity assumption, which might not extend as far in parameter

space as the confidence limits themselves—see PEST manual (Doherty, 2002).

Parameter Description

Transfer

function

number1

Value

Estimated 95-percent confidence limits2

Sensitivity Relative

sensitivity Lower limit Upper limit

Bexar County index well AY–68–37–203 (292845098255401)

Effective rainfall

μ1 Conduit response 1 6.56 6.43 6.70 1.36 1.11

σ2

1 2.44 2.29 2.60 .19 .07

α1 1,667.1 1,499.2 1,853.7 1.91 6.14

μ2 Diffuse response 2 8.34 8.30 8.38 4.95 4.56

σ2

2 .27 .24 .29 .19 .11

α2 2,963.9 2,349.2 3,739.5 3.12 10.85

μ3 Delayed response 3 9.32 9.30 9.33 17.63 17.09

σ2

3 .14 .14 .14 .74 .63

α3 8,689.3 7,331.2 10,298.9 10.50 41.35

κ Effective rainfall coefficient 1,245.4 1,044.8 1,484.6 15.06 46.61

c Normalizing factor .008 -- -- -- --

Hill Country Village well AY–68–29–103 (293522098291201)

Effective rainfall

μ1 Conduit response 1 6.08 6.05 6.11 1.38 1.08

σ2

1 .92 .9 .95 .12 .004

α1 1,091.1 1,020.3 1,166.9 1.35 4.09

μ2 Diffuse response 2 9.40 9.34 9.45 7.65 7.45

σ2

2 .73 .66 .82 .24 .03

α2 1,986.6 1,730.5 2,280.5 1.72 5.69

μ3 Delayed response -- -- -- -- -- --

σ2

3 -- -- -- -- --

α3 -- -- -- -- --

κ Effective rainfall coefficient 1,002.6 919.0 1,093.8 2.90 8.70

c Normalizing factor .0091 -- -- -- --

Medina County FM 1796 well TD-69-38-601 (292618099165901

Effective rainfall

μ1 Conduit response 1 6.28 6.20 6.36 4.86 3.88

σ2

1 1.30 1.22 1.39 .48 .05

α1 2,634.0 2,358.0 2,942.4 4.05 13.84

μ2 Diffuse response 2 8.03 8.01 8.04 8.55 7.73

σ2

2 .39 .37 .41 .35 .14

α2 3,698.8 3,368.8 4,061.3 5.27 18.80

μ3 Delayed response 3 9.95 9.95 9.95 65.0 64.9

σ2

3 .01 .01 .01 .24 .46

α3 2,359.5 2,164.9 2,571.7 2.44 8.23

κ Effective rainfall coefficient 273.2 247.5 301.7 5.46 13.40

c Normalizing factor .025 -- -- -- --
16 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

multiplication factor was used to obtain a better match between 

measured and simulated water levels. As a result, effective 

rainfall was decreased at a constant rate starting on January 1, 

1940. The multiplication factor on that day was 1.0 and 

decreased linearly until January 1, 2003, at which time the 

factor was 0.64. The cause of this change in the relation 

between effective rainfall and water-level response is not 

known. It might be related to land- or water-use changes within 

the catchment area or nonlinearities in the aquifer such as 

changes in aquifer properties with depth in the aquifer. Measured and simulated water levels at the Hill Country Village 

well (fig. 10) were compared. Fifty percent of the simulated 

water levels are within 5 feet of the measured water levels, and 

90 percent of the simulated water levels are within 14 feet of the 

measured water levels.

Medina County FM 1796 Well (TD–69–38–601)

The Medina County FM 1796 well is in northwestern 

Medina County in the recharge zone of the Edwards aquifer. 

Transfer-function models were developed using daily maximum water levels from July 8, 1957, to December 31, 2002, 

at the Medina County FM 1796 well and daily total rainfall 

from January 1, 1920, to December 31, 2002, at the NWS 

rainfall site Hondo (414254) (fig. 6). During the period, 

water levels at the well ranged from 733.70 to 942.00 feet 

above NGVD 29, and daily total rainfall at Hondo ranged from 

0 to 9.15 inches. Missing daily total rainfall at Hondo was estimated directly from daily total rainfall at NWS rainfall site 

Hondo Airport (414256). If daily total rainfall was missing at 

both Hondo and Hondo Airport, daily total rainfalls at NWS 

sites Sabinal (417873), Tarpley (418845), and Rio Medina 

(417628) were averaged to estimate daily total rainfall at 

Hondo.

Three transfer-function models were used to simulate 

water-level response to effective rainfall at the Medina County 

FM 1796 well. Table 3 lists the estimated parameters for transfer-function models. The first function peaks at about 5 months, 

the second function peaks at about 6 years, and the third function peaks at about 57 years (fig. 11). Measured and simulated 

water levels at the Medina County FM 1796 well were compared (fig. 12). Fifty percent of the simulated water levels are 

within 14 feet of the measured water levels, and 90 percent of 

the simulated water levels are within 27 feet of the measured 

water levels.

Figure 9. Calibrated transfer-function models for Hill Country Village well (AY–68–29–103), Edwards aquifer, San Antonio region, Texas.

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85

YEARS

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

WATER-LEVEL CHANGE, IN FEET PER INCH OF

EFFECTIVE RAINFALL PER DAY 

Transfer function 1

Transfer function 2
Simulation of Water-Level Response to Rainfall Using Transfer-Function Models 17

Figure 10. Measured and simulated water level for Hill Country Village well (AY–68–29–103), Edwards aquifer, San Antonio region, 

Texas.

Figure 11. Calibrated transfer-function models for Medina County FM 1796 well (TD–69–38–601), Edwards aquifer, San Antonio region, 

Texas.

640

660

680

700

720

740

760

780

WATER LEVEL, IN FEET ABOVE NGVD 29

Measured water level

Simulated water level

1960 1965 1970 1975 1980 1985 1990 1995 2000 2003

YEAR

1955

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80

YEARS

0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

WATER-LEVEL CHANGE, IN FEET PER INCH OF

EFFECTIVE RAINFALL PER DAY 

Transfer function 1

Transfer function 2

Transfer function 3
18 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

Discussion of Transfer-Function Model Results

The transfer-function models showed that (1) the Edwards 

aquifer in the San Antonio region responds differently to effective rainfall at different wells, and (2) multiple flow components 

are present in the aquifer, likely of the type reported by Long 

and Putnam (2004), as described in the “Convolution” section; 

that is, conduit flow, diffuse flow, and delayed flow (table 3). 

Each of the three wells for which water levels were simulated had different transfer-function models. All three wells 

(one confined zone and two recharge zone) had short-term 

transfer functions that peaked from 2 to 6 months, which might 

indicate a flow component with conduit response; and intermediate-term functions that peaked from 6 to 16 years, which 

might indicate a flow component with diffuse response. The 

Bexar County index well and Medina County FM 1796 well had 

long-term functions that peaked at about 27 and 57 years, 

respectively, which might indicate a flow component with 

delayed response. A long-term transfer function was not used to 

simulate water levels at the Hill Country Village well. The longterm effect at the Hill Country Village well probably was 

accounted for by decreasing effective rainfall at a constant rate 

starting on January 1, 1940, and continuing to January 1, 2003. 

Two possible explanations are hypothesized for the longterm transfer functions for two of the wells (Bexar County index 

and Medina County FM 1796) and for the long-term effect 

accounted for by slowly decreasing effective rainfall for the Hill 

Country Village well: (1) The long-term function represents a 

third and long-term (delayed response) flow component, and 

(2) the long-term function does not represent a true flow component but instead represents a change in the hydrologic budget 

(nonlinearity in the system). Nonlinearities might be related to 

land- or water-use changes within the well catchment area. Differences in aquifer properties at different depths in the aquifer 

also might explain nonlinear responses. As water levels in the 

recharge area change as a result of long-term climatic changes, 

different parts of the aquifer or different thicknesses of the aquifer can become saturated. If, for example, rising water levels 

cause a previously unsaturated part of the aquifer to become saturated, and if the newly saturated part has different properties 

than the originally saturated part, then the response characteristics might change as a result. Hence the simulated long-term 

system response might be reflecting actual long-term nonlinear 

effects. If the long-term system response does indeed result 

from nonlinearity in the hydrologic system, then water levels 

would be more difficult to simulate accurately. Short-term simulations probably are feasible; however, the extent to which 

accurate simulations can be made over time might be subject to 

the degree of understanding of nonlinear effects. 

Figure 12. Measured and simulated water level for Medina County FM 1796 well (TD–69–38–601), Edwards aquifer, San Antonio region, 

Texas.

700

750

800

850

900

950

1,000

WATER LEVEL, IN FEET ABOVE NGVD 29

Measured water level

Simulated water level

1960 1965 1970 1975 1980 1985 1990 1995 2000 2003

YEAR

1955
Summary 19

Other errors or differences between measured and simulated water levels might occur for several reasons. Some might 

be caused by errors in the estimation of effective rainfall. Errors 

in the estimation of effective rainfall might occur because 

(1) rainfall measured at a single site might not represent rainfall 

over the entire well catchment area, (2) recharge beyond the 

catchment area of a well might affect water levels, (3) there are 

rainfall measurement errors, and (4) the method used to estimate effective rainfall simplifies the numerous complexities 

that influence the amount of water reaching the aquifer. In addition, errors could be incurred because the lognormal transfer 

functions are approximations of the true transfer functions. 

Ongoing urbanization also might affect recharge to the aquifer 

in varying degrees over time and might not be reflected adequately in a given transfer-function model. Urbanization also 

probably affects the amount of water being withdrawn from the 

aquifer.

Some of the differences between measured and simulated 

water levels might occur because aquifer pumpage and recharge 

from streamflow losses to the aquifer were not used to develop 

the transfer-function models. These stresses were not included 

because (1) long-term daily pumpage data were not available, 

(2) adequate spatially distributed daily streamflow loss data 

were not available, and (3) it was assumed that most recharge to 

the aquifer occurred during storm events when rainfall and 

streamflow would be closely correlated. Thus rainfall was 

assumed to be a surrogate for streamflow loss. Despite these 

sources of error, the authors believe the models do an adequate 

job, in many cases, of simulating aquifer water-level response 

from rainfall data. 

Summary

In 2003 the U.S. Geological Survey, in cooperation with 

the San Antonio Water System, did a study using historical data 

to statistically analyze hydrologic system components in the 

San Antonio region of Texas and to develop models to simulate 

water levels at selected sites (wells) in the Edwards aquifer on 

the basis of rainfall. This report briefly describes (1) statistical 

analyses used to investigate the relations among Edwards aquifer water levels, springflows, rainfall, and streamflow in the San 

Antonio region, and (2) lumped-parameter transfer-function 

models developed to simulate water-level response at three 

wells in the Edwards aquifer on the basis of rainfall. Two of the 

wells, one in the recharge zone (outcrop) of the Edwards aquifer 

and one in the confined zone, are in Bexar County; and one well 

is in the recharge zone in Medina County.

Statistical techniques used consist of determination of correlation coefficients between water levels at wells, and between 

water levels at wells and springflows; hydrographic analyses 

(including storm and recession analyses); and linear regression. 

Spearman’s rho correlation coefficients were computed using 

long-term concurrent daily maximum water levels at selected 

wells in the Edwards aquifer and daily mean springflow at 

Comal Springs. Water levels for two wells in the confined zone 

in Medina County (Medina County index and City of Castroville) and one well in the confined zone in Bexar County (Bexar 

County index) were highly correlated and showed little or no 

lag time between water-level responses. Water levels in these 

wells also were highly correlated with springflow at Comal 

Springs. 

Water-level hydrographs for 35 storms showed that an 

individual well can respond differently to similar amounts of 

rainfall. Fourteen water-level-recession hydrographs for the 

Medina County index well showed that recession rates were 

variable. Average recession rates ranged from about 0.11 to 

1.22 feet per day. 

Linear regression equations were developed to estimate 

water levels at selected wells using water levels from nearby 

wells, springflow, rainfall, streamflow, and the monthly Palmer 

drought severity index. Because the regression equations might 

not adequately take into account both short-term (hours or days) 

and long-term (days, weeks, or months) variation in water levels, transfer-function models were developed to simulate waterlevel response to rainfall.

Transfer-function models were developed to simulate 

water levels at one confined-zone well and two recharge-zone 

wells in response to rainfall. For the confined-zone well (Bexar 

County index), three transfer-function models were used to 

simulate water levels, with peaks occurring at about 2 months, 

9 years, and 27 years, respectively. Fifty percent of the simulated water levels are within 10 feet of the measured water 

levels, and 80 percent of the simulated water levels are within 

15 feet of the measured water levels. For one recharge-zone 

well (Hill Country Village), two transfer-function models were 

used to simulate water levels, with peaks occurring at about 6 

months and 16 years. To obtain a better match between measured and simulated water levels (the need for which possibly 

was caused by a change in the hydrologic budget [nonlinearity 

in the system]), effective rainfall was decreased at a constant 

rate during the simulation period. Fifty percent of the simulated 

water levels are within 5 feet of the measured water levels, and 

90 percent of the simulated water levels are within 14 feet of the 

measured water levels. For the other recharge-zone well 

(Medina County FM 1796), three transfer-function models 

were used to simulate water levels, with peaks occurring at 

about 5 months, 6 years, and 57 years. Fifty percent of the simulated water levels are within 14 feet of the measured water 

levels, and 90 percent of the simulated water levels are within 

27 feet of the measured water levels. 

The transfer-function models showed that (1) the Edwards 

aquifer in the San Antonio region responds differently to 

recharge (effective rainfall) at different wells; and (2) multiple 

flow components are present in the aquifer. If the simulated 

long-term system response results from a change in the hydrologic budget, then water levels would be difficult to simulate 

accurately. Short-term simulations probably are feasible; however, the extent to which accurate simulations can be made over 

time might be subject to the degree of understanding of nonlinear effects.
20 Statistical Analyses of Hydrologic System Components and Simulation of Edwards Aquifer Water-Level Response to Rainfall 

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Austin, TX 78754–4733

Information regarding water resources in Texas is available at 

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