U.S. Department of the Interior

U.S. Geological Survey

Circular 1376

Groundwater Resources Program

Streamflow Depletion by Wells—Understanding 

and Managing the Effects of Groundwater 

Pumping on Streamflow
Cover. A, U.S. Geological Survey streamgage along the Watauga River near Sugar Grove, North Carolina. Photograph by 

J. Curtis Weaver, U.S. Geological Survey. B, Colorado River above Nortons Landing, Arizona. Photograph by Michael Collier. C, Circular 

irrigation system, Parshall, Colorado. Photograph by Michael Collier. D, Great Egret, Upper San Pedro Basin, Arizona. Photograph by 

Bob Herrmann. Background photograph Republican River below McCook, Nebraska. Photograph by Michael Collier.

A

B

C

D
Streamflow Depletion by Wells—Understanding 

and Managing the Effects of Groundwater 

Pumping on Streamflow

By Paul M. Barlow and Stanley A. Leake 

Wyoming Pond on the Wood River, Pawcatuck River Basin, Rhode Island. 

Photograph by Robert F. Breault, U.S. Geological Survey

Groundwater Resources Program

Circular 1376

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Barlow, P.M., and Leake, S.A., 2012, Streamflow depletion by wells—Understanding and managing the effects of 

groundwater pumping on streamflow: U.S. Geological Survey Circular 1376, 84 p. 

(Also available at http://pubs.usgs.gov/circ/1376/.)

Library of Congress Cataloging-in-Publication Data

Barlow, Paul M.

 Streamflow depletion by wells: understanding and managing the effects of groundwater pumping on streamflow / 

by Paul M. Barlow and Stanley A. Leake.

 p. cm. -- (Circular ; 1376)

 Understanding and managing the effects of groundwater pumping on streamflow

 Includes bibliographical references.

 ISBN 978-1-4113-3443-4 (alk. paper)

 1. Streamflow. 2. Stream measurements. 3. Groundwater--Management. 4. Wells. I. Leake, S. A. II. Geological 

Survey (U.S.) III. Title. IV. Title: Understanding and managing the effects of groundwater pumping on streamflow. V. 

Series: U.S. Geological Survey circular ; 1376. 

 GB1207.B373 2012

 628.1’12--dc23

 2012038485
iii

Foreword 

Groundwater provides drinking water for millions of Americans and is the primary source of 

water to irrigate cropland in many of the Nation’s most productive agricultural regions. Withdrawals in many aquifers throughout the United States have led to significant groundwater-level 

declines, resulting in growing concerns about sustainability and higher pumping costs. The U.S. 

Geological Survey’s (USGS) Groundwater Resources Program has been instrumental in documenting groundwater declines and in developing groundwater-flow models for use in sustainably managing withdrawals.

Groundwater withdrawals also can lead to a reduction in streamflow, affecting both human uses 

and ecosystems. The first clear articulation of the effects of groundwater pumping on surface 

water was by the well-known USGS hydrologist C.V. Theis. In a paper published in 1940 entitled 

"The Source of Water Derived from Wells," Theis pointed out that pumped groundwater initially 

comes from reductions in aquifer storage. As pumping continues, the effects of groundwater 

withdrawals can spread to distant connected streams, lakes, and wetlands through decreased 

rates of discharge from the aquifer to these surface-water systems. In some settings, increased 

rates of aquifer recharge also occur in response to pumping, including recharge from the connected surface-water features. Associated with this decrease in groundwater discharge to 

surface waters is an increased rate of aquifer recharge. Pumping-induced increased inflow to 

and decreased outflow from an aquifer is now called "streamflow depletion" or "capture."

Groundwater discharge is a significant component of streamflow, with groundwater contributing as much as 90 percent of annual streamflow volume in some parts of the country. In order 

to effectively manage the entire water resource for multiple competing uses, hydrologists and 

resource managers must understand the effects (magnitude, timing, and locations) of groundwater pumping on rivers, streams, springs, wetlands, and groundwater-dependent vegetation.

This circular, developed as part of the USGS Groundwater Resources Program, presents concepts relating to streamflow depletion, methods for quantifying depletion, and common misconceptions regarding depletion. Approaches for monitoring, understanding, and managing 

streamflow depletion also are described. The report is written for a wide audience interested in 

the development, management, and protection of the Nation's water resources.

The Groundwater Resources Program provides objective scientific information and develops the 

interdisciplinary understanding necessary to assess and quantify the availability of the Nation's 

groundwater resources. Detailed assessments of regional aquifers have been completed in 

seven of the Nation’s major aquifers, with several additional assessments ongoing or planned. 

The research and understanding developed through this program for issues such as streamflow 

depletion can provide the Nation’s water-resource managers with the tools and information 

needed to manage this important natural resource.

Jerad D. Bales

Associate Director for Water (Acting)

U.S. Geological Survey
iv
v

Contents

Foreword ........................................................................................................................................................iii

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

Characteristics of Groundwater Systems and Groundwater Interactions with Streamflow............2

Streamflow Response to Groundwater Pumping...................................................................................11

Time Response of Streamflow Depletion During Pumping..........................................................11

Distribution of Streamflow Depletion Along Stream Reaches....................................................21

Variable and Cyclic Pumping Effects...............................................................................................26

Multiple Wells and Basinwide Analyses ........................................................................................29

Pumped Wells and Recharge Wells ................................................................................................33

Streamflow Depletion and Water Quality .......................................................................................35

Common Misconceptions about Streamflow Depletion .......................................................................39

Aquifer Recharge and Development of Water Resources ..........................................................39

Depletion and the Rates and Directions of Groundwater Flow ..................................................40

Depletion after Pumping Stops.........................................................................................................42

Effects of Confining Layers on Depletion........................................................................................46

Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells.......50

Field Techniques .................................................................................................................................50

Analytical and Numerical Modeling ...............................................................................................54

Analytical Models of Streamflow Depletion by Wells ........................................................54

Numerical Models of Streamflow Depletion by Wells ........................................................60

Response Functions and Capture Maps................................................................................66

Management of Streamflow Depletion ..........................................................................................73

Conclusions...................................................................................................................................................76

Acknowledgments.......................................................................................................................................78

References Cited..........................................................................................................................................78

 Boxes

A—Hydraulic Diffusivity ..................................................................................................................8

B—Ways to Express Streamflow Depletion ..............................................................................16

C—Glover’s Analytical Solution and Jenkins’ Stream Depletion Factor (SDF)....................56

Facing page: Rio Grande near Velarde, New Mexico. (Photograph by Michael Collier)
vi

Conversion Factors and Datum

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft)

mile (mi)

0.3048

1.609

meter (m)

kilometer (km)

Area

acre

square foot (ft2

)

square inch (in2

)

square mile (mi2

)

4,047

 0.09290

6.452

 2.590

square meter (m2

)

square meter (m2

)

square centimeter (cm2

)

square kilometer (km2

) 

Volume

acre-foot (acre-ft)

cubic foot (ft3

)

gallon (gal)

million gallons (Mgal)

1,233

0.02832

 3.785

 3,785

cubic meter (m3

)

cubic meter (m3

) 

liter (L) 

cubic meter (m3

)

Flow rate

acre-foot per year (acre-ft/yr)

cubic foot per second (ft3/s)

cubic foot per day (ft3

/d)

cubic foot per second per mile 

[(ft3

/s)/mi]

cubic foot per second per square 

mile [(ft3

/s)/mi2]

foot per second (ft/s)

foot per day (ft/d)

foot per day per foot [(ft/d)/ft]

foot squared per day (ft2

/d) 

inch per year (in/yr)

gallon per minute (gal/min)

million gallons per day (Mgal/d)

0.001233

 0.02832

 0.02832

0.01760

 0.01093

 0.3048

0.3048

1

0.09290

25.4

 0.06309

 0.04381

cubic hectometer per year (hm3

/yr)

cubic meter per second (m3

/s)

cubic meter per day (m3

/d)

cubic meter per second per 

kilometer [(m3

/s)/km]

cubic meter per second per square 

kilometer [(m3

/s)/km2]

meter per second (m/s)

meter per day (m/d)

meter per day per meter [(m/d)/m]

meter squared per day (m2

/d)

millimeter per year (mm/yr)

liter per second (L/s)

cubic meter per second (m3

/s)

The following additional conversions for acre-foot per year (acre-ft/yr) are based on 365.25 days 

per year:

1 cubic foot per second (ft3/s) is equal to 724.5 acre-ft/yr

1 million gallons per day (Mgal/d) is equal to 1,121.0 acre-ft/yr

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

°F=(1.8×°C)+32

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

°C=(°F–32)/1.8

*Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times 

foot of aquifer thickness [(ft3/d)/ft2]ft. In this report, the mathematically reduced form, foot 

squared per day (ft2

/d), is used for convenience. 

Altitude, as used in this report, refers to distance above the vertical datum.
Streamflow Depletion by Wells—Understanding 

and Managing the Effects of Groundwater 

Pumping on Streamflow

By Paul M. Barlow and Stanley A. Leake

Introduction

Groundwater is an important source of water for many 

human needs, including public supply, agriculture, and 

industry. With the development of any natural resource, 

however, adverse consequences may be associated with its 

use. One of the primary concerns related to the development of 

groundwater resources is the effect of groundwater pumping 

on streamflow. Groundwater and surface-water systems are 

connected, and groundwater discharge is often a substantial 

component of the total flow of a stream. Groundwater 

pumping reduces the amount of groundwater that flows to 

streams and, in some cases, can draw streamflow into the 

underlying groundwater system. Streamflow reductions (or 

depletions) caused by pumping have become an important 

water-resource management issue because of the negative 

impacts that reduced flows can have on aquatic ecosystems, 

the availability of surface water, and the quality and aesthetic 

value of streams and rivers.

Scientific research over the past seven decades has 

made important contributions to the basic understanding of 

the processes and factors that affect streamflow depletion 

by wells. Moreover, advances in methods for simulating 

groundwater systems with computer models provide powerful 

tools for estimating the rates, locations, and timing of 

streamflow depletion in response to groundwater pumping 

and for evaluating alternative approaches for managing 

streamflow depletion. The primary objective of this report is to 

summarize these scientific insights and to describe the various 

field methods and modeling approaches that can be used to 

understand and manage streamflow depletion. A secondary 

objective is to highlight several misconceptions concerning 

streamflow depletion and to explain why these misconceptions 

are incorrect.

Lower Colorado River and adjacent farmland in the Yuma, Arizona, area. Diversion structure in upper right is Morelos Dam, the main 

point of delivery of water to Mexico. The “Law of the River” recognizes that water can be withdrawn from the Colorado River by 

“underground pumping.” (Photograph by Andy Pernick, Bureau of Reclamation)
2 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Characteristics of Groundwater 

Systems and Groundwater Interactions 

with Streamflow

This section provides brief descriptions of several terms 

and concepts that contribute to an understanding of streamflow 

depletion by wells. For a more extensive discussion of these 

concepts, the reader is referred to texts on groundwater, 

hydrogeology, and hydrology by Freeze and Cherry (1979), 

Linsley and others (1982), Heath (1983), Domenico and 

Schwartz (1990), and Fetter (2001). 

Aquifers and Groundwater Flow

The pores, fractures, and other voids that are present in 

the sediments and rocks that lie close to the Earth’s surface 

are partially to completely filled with water. In most locations, 

an unsaturated zone in which both water and air fill the voids 

exists immediately beneath the land surface (fig. 1). At greater 

depths, the voids become fully saturated with water. The top 

of the saturated zone is referred to as the water table, and the 

water within the saturated zone is groundwater.

Although voids beneath the water table are filled with 

water, the ability of subsurface materials to store and transmit water varies substantially. The term aquifer refers to 

subsurface deposits and geologic formations that are capable 

of yielding usable quantities of water to a well or spring, 

whereas a confining layer (or confining bed, such as illustrated 

in figure 1) refers to a low-permeability deposit or geologic 

formation that restricts the movement of groundwater (Heath, 

1983). An aquifer can refer to a single geologic layer (or unit), 

a complete geologic formation, or groups of geologic formations (Freeze and Cherry, 1979). 

Most aquifers are classified as either confined or unconfined. A confined aquifer is one that lies between two confining layers, whereas an unconfined aquifer is one in which the 

uppermost boundary is the water table (fig. 1). Unconfined 

aquifers are often referred to as water-table aquifers, and both 

terms are used interchangeably in this report. As illustrated in 

figure 1, unconfined aquifers typically are located near land 

surface and confined aquifers are located at depth. Because of 

their proximity to land surface and associated surface waters, 

unconfined aquifers are often of interest in problems concerning streamflow depletion by wells; however, pumping from 

confined aquifers also can cause depletion. The fact that flow 

paths exist from deep confined aquifers upward to shallow 

aquifers means that changes in water levels from pumping 

(that is, drawdown) in deep confined aquifers also propagate to 

shallow aquifers with connected streams. An additional term, 

“leaky aquifer,” is sometimes used to refer to an aquifer that 

receives inflow from adjacent low-permeability beds, although 

it is actually the adjacent beds that leak water to the aquifer 

(Freeze and Cherry, 1979).

In many areas of the United States, groundwater systems 

are composed of a vertical sequence of aquifers in which an 

upper, unconfined aquifer is underlain by a series of one or 

more confining beds and confined aquifers, such as is illustrated in figure 1. In many other areas, however, the groundwater system consists of a single, often unconfined, aquifer 

underlain by geologic formations, such as crystalline rock, 

whose permeabilities are so low that the formation can be 

assumed to be impermeable to groundwater flow. Aquifers of 

this type are used throughout the report to illustrate many of 

the factors that affect streamflow depletion by wells.

Unsaturated

zone

Pumped well

Recharge area

Stream

 Discharge area

Days

Years

Years

Days

Centuries

Millennia

Confining bed

Confining bed

Confined

aquifer

Unconfined

aquifer

Confined

aquifer

Water table

Figure 1. Groundwater 

flow paths in a multi-aquifer 

groundwater system. 

Groundwater flows from 

recharge areas at the water 

table to discharge locations 

at the stream and well. The 

residence time of groundwater 

can range from days to 

millennia (modified from Winter 

and others, 1998).
Characteristics of Groundwater Systems and Groundwater Interactions with Streamflow 3

0

0

1 MILE

1 KILOMETER

200

180

170

160

150

140

130

110

120

100

90

190

A

B

EXPLANATION C

Water table

Line of equal hydraulic head, in feet

Direction of groundwater flow

90 Water level

Land surface

Unsaturated zone

Piezometer

260

240

220

200

180

160

140

120

100

80

60

40

20

0

Open interval

Feet above reference datum

Water table

Figure 2. Distribution of hydraulic-head contours (groundwater levels) showing groundwater-flow directions in a vertical section of a 

hypothetical water-table aquifer. Groundwater levels are measured in piezometers, which are a type of observation well having a very 

short, open interval to the aquifer at the bottom of the well. The head measurements at the group of three piezometers completed at 

different depths at location C indicate downward groundwater flow at that location, whereas head measurements at the piezometers at 

locations B and A indicate lateral and upward flow at those locations, respectively (modified from Winter and others, 1998). 

Groundwater moves continuously through aquifers from 

areas of groundwater recharge to areas of groundwater discharge. Such flow is illustrated by the flow paths in figure 1. 

The upper, unconfined aquifer shown in figure 1 is recharged 

by water that infiltrates across the land surface and then moves 

downward through the unsaturated zone to the water table to 

become groundwater. The source of groundwater recharge 

typically is precipitation (rain or melted snow) but can also 

originate from anthropogenic sources such as infiltration 

of irrigation return flow and septic-system wastewater. The 

accretion of water at the top of the saturated zone causes the 

water table to rise, and as a result, the saturated thickness 

of the unconfined aquifer increases. As recharge diminishes 

or ceases, the water table will decline and the saturated 

thickness decrease. 

Groundwater commonly discharges to streams and wells, 

as illustrated in figure 1, but it can also discharge to springs, 

lakes, and ponds; to estuaries and directly to oceans; and by 

evaporation and plant transpiration in low-lying areas where 

the water table lies close to land surface, such as in wetlands 

or near streams. The residence time of water in a groundwater 

system can range from days to a few years for water recharged 

close to discharge boundaries, to millennia for water that travels along deep flow paths through low-permeability materials.

Directions of groundwater flow are determined from 

measurements of the altitude of groundwater levels made 

in wells. The water-level altitudes must be determined relative to a common datum plane, such as the National Geodetic 

Vertical Datum of 1929 (commonly referred to as “sea level;” 

Heath, 1983). Groundwater levels are equivalent to hydraulic 

heads and reflect the total potential energy of the groundwater 

system at the point of measurement. In a manner similar to 

flow in other potential fields (such as in electrical or thermal 

systems), groundwater flows from locations of higher potential 

energy to locations of lower potential energy and, therefore, in 

the direction of decreasing hydraulic head (fig. 2). 

The rate of groundwater flow in a particular direction is 

dependent on the hydraulic conductivity of the aquifer, which 

is described in the next section, and the gradient of the hydraulic head in the direction of interest. The hydraulic gradient, 

which is equal to the change in head over a unit distance, can 

be determined from pairs of water-level measurements or 

from water-level contours drawn for a horizontal or vertical section of an aquifer. The hydraulic gradient between the 

130 and 120 feet (ft) contours shown in figure 2, for example, 

is approximately 10 feet per mile, as determined by the 

change in hydraulic head between the two contours divided 

by the approximate distance between the contours along the 

flow line.
Groundwater systems are referred to as being in either 

a steady-state or a transient condition (fig. 3). A steady-state 

system is one in which groundwater levels and flow rates 

within and along the boundaries of the system are constant 

with time, and the rate of storage change within the flow 

system is zero. A transient system is one in which groundwater 

levels and flow rates change with time and are accompanied 

by changes in groundwater storage. Transient conditions occur 

in response to changes in flow rates along the boundaries 

of a groundwater system, such as short-term and long-term 

fluctuations in recharge rates, or changes in flow rates at points 

within a groundwater system, such as fluctuations in pumping 

rates. Although steady-state flow conditions, such as illustrated 

in figure 3A, rarely occur for real-world hydrologic conditions, 

it is often acceptable to assume that steady-state conditions 

exist if the fluctuations in water levels and storage changes 

are relatively small or if there is an interest in an evaluation 

of the long-term average condition of the flow system. 

Many studies of regional aquifer systems, for example, are 

conducted with the assumption that steady-state conditions 

occurred prior to large-scale groundwater development. 

During the predevelopment period, average rates of natural 

recharge and discharge to the aquifers are assumed to have 

been in long-term balance. Another term that is sometimes 

used to refer to the state of a groundwater system is dynamic 

equilibrium (or steady-oscillatory; Maddock and Vionnet, 

1998), in which water levels and flow rates are variable over a 

period of time (such as a year) but vary in a pattern that is the 

same from one period to the next (fig. 3C).

Hydraulic Properties of Aquifers, Confining Layers, and 

Streambed Sediments

The flow and storage of water in a groundwater system 

depend strongly on the hydraulic properties of the aquifers 

and confining layers that make up the system. These properties, which are summarized in table 1, also affect the timing, 

locations, and rates of streamflow depletion.

Hydraulic conductivity, often denoted by the symbol K, is 

a property that describes the rate of flow of a volume of water 

through a unit area of aquifer under a unit gradient of hydraulic head (Heath, 1983). The measurement units of K are length 

per time, such as feet per day (ft/d). The value of hydraulic 

conductivity at a particular location depends on the characteristics of the porous material, such as the size and arrangement 

of the pores and fractures, and the density and viscosity of 

the water within the porous material. Hydraulic-conductivity 

98

99

100

101

102

103

104

0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10

0 1 2 3 4 5 6 7 8 9 10

98

99

100

101

102

103

104

A. Steady state B. Transient

98

99

100

101

102

103

104

C. Dynamic equilibrium

Groundwater level, in feet above reference datum

Time, in years

Time, in years

4 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Figure 3. Hydrologic conditions at a hypothetical observation well at which groundwater-level measurements indicate the state of 

the groundwater system. A, Steady-state system: Groundwater levels at the well do not change during the 10-year period. B, Transient 

system: Groundwater levels fluctuate with time, with the highest water levels generally occurring in the early spring and lowest water

levels in the late summer and fall. C, System in dynamic equilibrium: Groundwater levels fluctuate throughout the year but in a pattern 

that is the same from one year to the next.
Characteristics of Groundwater Systems and Groundwater Interactions with Streamflow 5

Table 1. Aquifer properties that influence the timing of streamflow depletion.

Aquifer property Symbol 

used Units Definition Application

Saturated thickness b Length The vertical thickness of the sediments in which 

pores are fully saturated Any aquifer system

Hydraulic conductivity K Length/time Rate of groundwater flow per unit area under a unit 

hydraulic gradient Any aquifer system

Transmissivity T Length2

/time Rate of groundwater flow per unit width under a 

unit hydraulic gradient ( T = K × b)

Aquifer systems dominated 

by horizontal flow

Volume of water released from or taken into storage 

Specific storage Ss 1/length per unit volume of aquifer per unit change in Confined aquifers

head 

Volume of water released from or taken into storage 

Storage coefficient S Dimensionless per unit surface area of aquifer per unit change in Confined aquifers

head normal to that surface ( S = S × b) s

Ratio of volume of water drainable by gravity from 

Specific yield Sy Dimensionless saturated aquifer material to the total volume of 

that material

Unconfined aquifers

Hydraulic diffusivity D Length2

/time Ratio of the transmissivity to the storage properties 

of an aquifer: T/S, K/S , or T/S s y

Aquifer systems dominated 

by horizontal flow

values have a range of more than 12 to 13 orders of magnitude 

and are relatively large (~1 to 10,000 ft/d) for the unconsolidated sands and gravels and karstic limestones that typically 

constitute aquifers and relatively small (~1 × 10–8 to 0.1 ft/d) 

for clays, silts, and shales that typically constitute confining 

layers (Freeze and Cherry, 1979; Heath, 1983).

An aquifer in which the values of hydraulic conductivity 

differ from one location to another is said to be heterogeneous, 

whereas one in which the hydraulic conductivity is everywhere the same is said to be homogeneous. Although no natural aquifer is strictly homogeneous with respect to K, aquifer 

response to stress may in some cases be represented using a 

homogeneous equivalent K. For example, alluvial aquifers 

commonly include discontinuous beds of clay of low K distributed within sand of higher K. Even though the contrast in 

the hydraulic conductivity between the clay and sand may be 

orders of magnitude, the response to pumping may be approximated using a homogeneous K if the distribution of clay beds 

is uniform throughout the aquifer. 

Unless specified differently, K refers to hydraulic conductivity in the horizontal direction. A more specific designation of horizontal hydraulic conductivity is Kh

, and, similarly, 

vertical hydraulic conductivity commonly is designated as 

Kv. Because of the presence of low-permeability interbeds 

can be expressed as the product of the hydraulic conductivity 

and saturated thickness at that location: . Because 

the water table of an unconfined aquifer rises and falls in 

response to hydraulic stresses, such as recharge and pumping, the saturated thickness and transmissivity also vary in 

response to the changing water table. This complication is 

often of little consequence for thick aquifers where watertable fluctuations are relatively small, but may be important 

near pumping wells where water-table declines are a significant fraction of the initial saturated thickness. In such situations, and also in the case where pumping wells draw water 

from deep within an unconfined aquifer, vertical components 

of groundwater flow may be too large to ignore and the 

concept of transmissivity less useful.

The dominant process by which water is released from 

storage differs substantially between confined and unconfined 

systems (Heath, 1983). In confined aquifers and confining 

layers, water is released from storage by compression of 

the matrix of solid materials that form the deposit and by 

expansion of the water contained within the pores of the 

deposit. The storage capacities of confined aquifers and 

confining units are described by the hydraulic properties 

of specific storage (Ss

 ) and storage coefficient (S), which 

are related by saturated thickness: . The storage 

properties of confined aquifers and confining units are 

relatively small; typical values of the storage coefficient of 

confined aquifers range from 5 × 10–5 to 5 × 10–3 (Freeze and 

Cherry, 1979). In contrast, the primary component of storage 

T K= ×b

in many aquifers, Kh can be greater than Kv by a factor of 

10 or more.

For groundwater systems that are dominated by horizontal flow, the transmissivity (T) at each location in an aquifer 

S S b = ×s
6 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

in an unconfined aquifer (or a confining layer that contains 

a water table) is drainage of water stored in the pores of the 

aquifer that is released as the water table declines. Water is 

also released from unconfined aquifers by compression of the 

aquifer matrix and expansion of the water, but these sources 

of stored water are small compared to drainage at the water 

table and typically are ignored. The storage capacity of an 

unconfined aquifer is described by its specific yield (Sy

 ). The 

specific yields of unconfined aquifers are much larger than the 

storage coefficients of confined aquifers, typically between 

0.01 and 0.30 (Freeze and Cherry, 1979).

Another hydraulic property that is not widely used 

in groundwater studies but has relevance to streamflow 

depletion is aquifer hydraulic diffusivity (D), which relates the 

transmissive and storage properties of an aquifer. Because of 

its importance to the timing and rates of streamflow depletion, 

it is described in detail in Box A.

Hydraulic properties of streambed and streambank materials may be different from those of the underlying aquifer or 

confining layer. The properties that are most important to the 

flow of water across the streambed and streambank materials 

are the hydraulic conductivity (Ks

 ) and thickness (ds ) of the 

streambed sediments. In most analyses, the storage properties 

of these sediments are considered to be negligible.

Groundwater and Streamflow

Streams and rivers are commonly the primary locations 

of groundwater discharge, and groundwater discharge is 

often the primary component of streamflow. Groundwater 

is discharged through saturated streambed and streambank 

sediments, or permeable bedrock adjacent to the stream, where 

the altitude of the water table is greater than the altitude of 

the stream surface (fig. 4A). Conversely, streamflow seeps 

into the underlying groundwater system where the altitude of 

the stream surface is greater than the altitude of the adjoining 

water table (fig. 4B). Stream reaches that receive groundwater 

discharge are called gaining reaches and those that lose water 

to the underlying aquifer are called losing reaches. The rate 

at which water flows between a stream and adjoining aquifer 

depends on the hydraulic gradient between the two water 

bodies and also on the hydraulic conductivity of geologic 

materials that may be located at the groundwater/surface-water 

interface. A thick, silty streambed, for example, will tend to 

reduce the rate of flow between a stream and aquifer compared 

to a thin, sandy or gravelly streambed. In some cases, 

however, discharge from the aquifer to the stream is controlled 

by the rate at which groundwater must leave the aquifer. In 

this situation, the presence of a thick, silty streambed will 

tend to increase the hydraulic gradient between a stream and 

10

11

12

13

14

15

0 0.5 1.0 1.5 2.0

Streamflow, in cubic feet 

per second

River mile

Gaining reach

Flow direction

Unsaturated zone

Water table

Shallow aquifer

A. Gaining stream

Losing reach

Flow direction

Water table Unsaturated zone

B. Losing stream

EXPLANATION

C. Gaining and losing reaches

Figure 4. A, Gaining stream reaches receive water from the groundwater system, whereas, B, losing reaches lose water to the 

groundwater system. C, Streamflow increases along the gaining reaches of a river and streamflow decreases along the losing reaches 

of a river when there is no direct surface-water runoff to the river (parts A and B modified from Winter and others, 1998).
A

B

Flow direction

Water table

Unsaturated zone

Water table

Unsaturated zone

Figure 5. Disconnected stream reaches are separated from the 

groundwater system by an unsaturated zone. In A, streamflow is a 

source of recharge to the underlying groundwater system, but in 

B, streamflow and groundwater recharge have ceased (modified 

from Winter and others, 1998).

aquifer compared to the presence of a thin, sandy or gravelly 

bed, but will not affect the total amount of groundwater that is 

discharged to the stream. 

The graph in figure 4C illustrates the effects of gaining 

and losing conditions on streamflow during a period of no 

direct surface-water runoff to the river. The graph shows that 

the rate of streamflow increases along gaining reaches and 

decreases along losing reaches. The graph also demonstrates 

that a stream can have both gaining and losing reaches 

simultaneously. Moreover, because precipitation rates, 

pumping rates, and other hydrologic stresses vary with 

time, it is possible for a particular stream reach to switch 

from a gaining to a losing condition or from a losing to a 

gaining condition from one period of time to the next. 

Losing reaches occur under conditions in which the 

underlying sediments are fully saturated, as shown in 

figure 4B, or for conditions in which the sediments are 

unsaturated, as shown in figure 5A. A losing stream reach 

that is underlain by an unsaturated zone is said to be disconnected from the underlying aquifer (Winter and others, 1998). 

Some stream reaches are ephemeral (that is, they periodically 

become dry), and, as a consequence, flows between the stream 

and underlying aquifer may periodically cease (fig. 5B).

The sources of water to streams are generally recognized 

to result from four processes (Linsley and others, 1982): 

precipitation that falls directly onto a stream, which is a 

relatively small component of total streamflow; surface 

runoff (or overland flow) that travels over the land surface 

Characteristics of Groundwater Systems and Groundwater Interactions with Streamflow 7

Groundwater discharge from a basaltic-rock aquifer adjacent to the Metolius River, Deschutes River Basin, Oregon. 

Photograph by David Stannard, U.S. Geological Survey
8 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

 Box A: Hydraulic Diffusivity

Two of the most important factors that control the timing 

and rates of streamflow depletion are distance of the pumping well from connected surface waters and the hydraulic 

diffusivity of the aquifer. Distance to surface waters is easily 

understood, but hydraulic diffusivity is a less familiar property. Hydraulic diffusivity, D, is defined for confined aquifers 

as D = T/S, where T and S are the more familiar properties of 

transmissivity and storage coefficient, respectively. 

The concept of aquifer diffusivity is strictly applicable to 

settings where water-level declines (drawdowns) from groundwater pumping propagate horizontally—but not vertically—

to connected streams and other surface-water features. This 

condition implies that the saturated thickness of the aquifer 

remains constant over time, which is not the case for unconfined aquifers where the water table falls in response to pumping. Nevertheless, it is often acceptable to assume that changes 

in saturated thickness caused by pumping are relatively small 

(for example, less than 10 percent of the predevelopment 

saturated thickness) and that vertical groundwater-flow components within the aquifer are small compared to horizontal 

components. Under these assumptions, the hydraulic diffusivity of an unconfined aquifer is defined with respect to specific 

yield, Sy

, as D = T/Sy .

Hydraulic stresses propagate faster through aquifers with 

higher values of hydraulic diffusivity than through aquifers with lower values of hydraulic diffusivity. It is important to understand that it is the ratio of T and S (or Sy ) that 

controls the timing of depletion and not the values of T and S

individually. For example, the rate of depletion at any given 

time caused by a pumping well in a system with a transmissivity of 10,000 feet squared per day (ft2

/d) and a storage 

coefficient of 0.01 would be the same as in a system with a 

transmissivity of 1,000 ft2

/d and a storage coefficient of 0.001, 

assuming all other factors are equal. As illustrated in table A–1 

for representative confined and unconfined aquifers with equal 

transmissivity, the hydraulic diffusivity of confined aquifers 

is typically several orders of magnitude greater than that for 

unconfined aquifers. This difference results from the much 

larger storage capacity of the unconfined aquifer (as represented by the value of specific yield) compared to that of the 

confined aquifer (as represented by the storage coefficient). 

Higher values of hydraulic diffusivity increase the speed 

at which responses to stresses such as pumping propagate 

through an aquifer to connected streams. Streamflow depletion therefore generally will occur much more rapidly in 

confined aquifers than in unconfined aquifers (fig. A–1). Each 

of the responses shown in figure A–1 illustrates the slower and 

damped response to a pumping stress in an unconfined aquifer 

with a relatively low hydraulic diffusivity compared to the 

faster response to the same stress in a confined aquifer with 

a relatively high hydraulic diffusivity. The responses shown 

in the figure are characteristic of streamflow depletion from 

pumping, but hydraulic diffusivity similarly affects groundwater-level responses to stresses other than pumping, such as 

recharge and changes in surface-water stage.

A final point concerning the propagation of hydraulic 

stresses within an aquifer is that the rate of propagation of 

a hydraulic perturbation is not the same as the velocity with 

which a volume of groundwater actually travels through an 

aquifer or the associated residence time of groundwater in the 

aquifer. Groundwater movement is nearly always substantially 

slower than the propagation of hydraulic stresses through most 

types of aquifers, particularly those that are the source of most 

large-scale groundwater withdrawals.

Table A–1. Example transmissivity, storage property, and resulting hydraulic diffusivity of a confined and unconfined aquifer. 

[Saturated thickness (b) of both aquifers is 100 feet, hydraulic conductivity (K) is 100 feet per day, and specific storage (Ss  ) is 1 × 10–6 feet–1; –, not applicable]

Aquifer type

Transmissivity

(K × b)

[feet squared per day]

Storage coefficient

(Ss × b)

[dimensionless]

Specific yield 

[dimensionless]

Hydraulic diffusivity

[feet squared per day]

Confined 10,000 0.0001 – 1 × 108

Unconfined 10,000 –1 0.1 1 × 105

1

Although storage changes related to the product of Ss and b apply in unconfined aquifers, this property can be ignored in analyses of responses to 

pumping if the product is much smaller than specific yield.
Characteristics of Groundwater Systems and Groundwater Interactions with Streamflow 9

Aquifer with large value 

 of diffusivity

Aquifer with small value 

 of diffusivity

EXPLANATION

Time Time

Stress Stress Stress

Stress to aquifer Response some distance

from the applied stress

Response Response Response

A. Steady following an instantaneous change

B. Episodic

C. Cyclic

Figure A–1. Groundwater-system response to different types of stresses for two values of hydraulic diffusivity—a 

relatively large value representative of confined aquifers and a relatively small value representative of unconfined aquifers. 

Stresses to the aquifer could be pumping at a well or recharge to an aquifer. The responses shown are characteristic 

streamflow-depletion responses to pumping, but also could be water-level responses to pumping or recharge. For the 

hypothetical situation shown, the pumping stresses and streamflow-depletion responses would be in units of volume per 

time (such as cubic feet per second). Other types of stresses and resulting responses could have different measurement 

units; for example, recharge rates typically are reported in units of length per time (such as inches per year) and water 

levels in units of length (such as feet). [Rates of streamflow depletion were calculated by using a computer program 

described in Reeves (2008); hydraulic diffusivity of confined and unconfined aquifers are 100,000 and 10,000 feet squared per 

day, respectively.]
10 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Month

1

10

100

1,000

Flow, in cubic feet per second

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

Total streamflow

Base flow

EXPLANATION

Figure 6. Total streamflow and the estimated base-flow component of streamflow for the Hunt River near East Greenwich, Rhode 

Island, 2001. Temporally varying rates of precipitation, evaporation, and plant transpiration within the watershed result in highly variable 

rates of daily and seasonal streamflow conditions. During periods of streamflow decline, such as occurred from mid April to mid May, 

streamflow consists nearly entirely of base flow. The direct-runoff component of streamflow is the difference between total streamflow 

and base flow. (Data available from U.S. Geological Survey National Water Information System Web Interface, http://waterdata.usgs.

gov/nwis; base flow estimated by the PART computer program documented in Rutledge, 1998.)

to a stream channel; interflow (or subsurface storm flow) 

that moves through the upper soil layers to a stream channel; 

and groundwater discharge, which is commonly referred 

to as base flow. Surface runoff and interflow are important 

during storm events, and their contributions typically 

are combined into a single term called the direct-runoff 

component of streamflow. Groundwater on the other hand 

is most important for sustaining the flow of a stream during 

periods between storms and during dry times of the year.

The proportion of streamflow that is contributed by 

groundwater discharge varies across physiographic and 

climatic settings (Winter and others, 1998). Base-flow 

contributions can be estimated for some streams by analysis 

of streamflow hydrographs, such as is illustrated for the Hunt 

River in Rhode Island (fig. 6). During periods of streamflow 

decline (recession) that follow storms, streamflow in the 

river consists nearly entirely of groundwater discharge, but 

groundwater discharge also contributes to streamflow during 

and shortly after periods of high flow. The average long-term 

base-flow component of the Hunt River was estimated to be 

nearly 81 percent of the total flow in the river (Barlow and 

Dickerman, 2001). This large contribution of groundwater 

discharge is typical for rivers of the Northeastern United 

States that are underlain by highly permeable sand and gravel 

deposits that facilitate high rates of groundwater recharge and 

low rates of direct runoff. The contribution of groundwater 

discharge to streamflow is lower for basins underlain by lesspermeable materials.
Streamflow Response to Groundwater 

Pumping

This section describes the fundamental processes and factors that affect the timing, rates, and locations of streamflow 

depletion. Unless otherwise stated, two important assumptions 

are made throughout this discussion—first, that the stream and 

underlying aquifer remain hydraulically connected by a continuous saturated zone, and second, that the stream does not 

become dry. These assumptions may not be valid for extreme 

cases of large-scale groundwater development and limited 

streamflow where groundwater levels have been drawn down 

below the bottom of the streambed. When the stream cannot 

supply the quantity of water pumped, the stream may eventually lose all of its water to the aquifer and become ephemeral. 

Even if flow remains in the stream, once groundwater levels decrease below the streambed, an unsaturated zone may 

develop near the locations of pumping that disconnects the 

groundwater and surface-water systems, at which time the 

flow rate between the groundwater and surface-water systems in the affected areas will no longer respond to pumping. 

Brunner and others (2011) provide a summary of several of 

the issues related to disconnected systems and the factors that 

influence the dynamics of disconnection; Su and others (2007) 

and Zhang and others (2011) provide examples of the effects 

of pumping on the formation of disconnected systems. 

Time Response of Streamflow Depletion During 

Pumping

As stated by Theis (1940) in his seminal work on the 

source of water derived from wells, knowledge of the influence of time is fundamental to understanding the effects 

of groundwater development on aquifers and hydraulically 

connected surface waters. When a well begins to pump water 

from an aquifer, groundwater levels around the well decline, 

creating what is called a “cone of depression” in the water 

levels around the well. These water-level declines are largest 

at the well and decrease to effectively zero decline at some 

radial distance from the well (fig. 7). The hydraulic gradient that is established within the cone of depression forces 

water to move from the aquifer into the well. Initially, all of 

the water pumped by the well comes from water stored in 

the aquifer. The cone of depression generally deepens and 

expands laterally with increased pumping time. Because the 

hydraulic diffusivity of confined aquifers is relatively large, 

the cone of depression that forms around a well in a confined 

aquifer expands rapidly away from a well. In contrast, because 

the hydraulic diffusivity of unconfined aquifers is relatively 

small, the cone of depression around a well pumping from an 

unconfined aquifer expands slowly outward from the well.

The release of water from aquifer storage continues 

to be the only source of water to the well until the cone of 

depression reaches one or more areas of the aquifer from 

which water can be captured. Captured water consists of two 

possible sources—a reduction in the natural discharge (or 

outflow) rate of groundwater from the aquifer or an increase in 

the natural or artificial recharge (or inflow) rate to the aquifer. 

The primary sources of captured discharge are groundwater 

that would otherwise have flowed to streams, drains, lakes, or 

oceans, as well as reductions in groundwater evapotranspiration in low-lying areas such as riparian zones and wetlands. 

Figure 7C illustrates the capture of groundwater that would 

otherwise have discharged to the bounding stream. Groundwater discharge to the stream is reduced because groundwater 

levels at the stream-aquifer boundary have been lowered 

by pumping, which reduces the hydraulic gradient from the Photograph by David E. Burt, Jr., U.S. Geological Survey

Streamflow Response to Groundwater Pumping 11

Groundwater pumped for 

flood irrigation of a rice field. 

Groundwater withdrawals from 

the Mississippi River alluvial 

aquifer to support agriculture 

in the Mississippi Delta region 

have resulted in groundwaterlevel declines and reductions 

in groundwater discharge to 

many Delta streams (Barlow 

and Clark, 2011). 
12 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Land surface

Water table

Unconfined aquifer

Confining unit

B Q

Land surface

Water table

Unconfined aquifer

Confining unit

C Q

Stream

Land surface

Water table

Unconfined aquifer

Confining unit

A

Land surface

Water table

Unconfined aquifer

Confining unit

D Q

Figure 7. Effects of pumping from a hypothetical water-table aquifer that discharges to a stream. A, Under 

natural conditions, recharge at the water table is equal to discharge at the stream. B, Soon after pumping 

begins, all of the water pumped by the well is derived from water released from groundwater storage. C, As 

the cone of depression expands outward from the well, the well begins to capture groundwater that would 

otherwise have discharged to the stream. D, In some circumstances, the pumping rate of the well may be 

large enough to cause water to flow from the stream to the aquifer, a process called induced infiltration 

of streamflow. Streamflow depletion is equal to the sum of captured groundwater discharge and induced 

infiltration (modified from Heath, 1983; Alley and others, 1999). [Q, pumping rate at well]
Streamflow Response to Groundwater Pumping 13

EXPLANATION

Streamflow without pumping

Streamflow with pumping

0

5

10

15

20

25

30

35

40

45

0 30 60 90 120 150 180

Streamflow, in cubic feet per second

Time, in days

Figure 8. Effects of groundwater pumping on a hypothetical streamflow hydrograph. Top curve shows daily streamflow without 

pumping at a nearby well. Lower curve shows daily streamflow with pumping from a well located near the stream at a rate of 2.0 million 

gallons per day (about 3.1 cubic feet per second) beginning at day 30. After about day 60, the total decrease in streamflow each day is 

equal to the pumping rate of the well. 

aquifer to the stream; however, there is no reversal in the 

gradient toward the stream, and the stream remains gaining. 

An example of captured recharge is induced leakage from 

streams, drains, or lakes. For example, if the reductions in 

groundwater levels near a hydraulically connected stream 

are large enough, the hydraulic gradient at the stream-aquifer 

interface will be reversed, and streamflow will be induced to 

flow into the aquifer toward the well (fig. 7D). This process 

is referred to as induced infiltration of streamflow and results 

in the stream becoming losing within the reach of stream in 

which the gradient has been reversed. Captured groundwater 

discharge to streams and induced infiltration of streamflow 

both result in reductions in the total amount of streamflow; as 

a result, the two processes are combined into the single term 

streamflow depletion. Reductions in streamflow that result 

from pumping at a hypothetical well are illustrated for a representative streamflow hydrograph in figure 8. The lower curve 

on the graph illustrates that streamflow continues to rise and 

fall in response to precipitation events, but the rates of streamflow are lower than those that would occur in the absence of 

pumping. For the hypothetical conditions shown, the amount 

of streamflow reduction at any point in time is equal to the 

pumping rate of the well after about 60 days of pumping.

The time response of the sources of water to a hypothetical well is illustrated by the curves in figure 9. For this 

example aquifer, the only sources of water to the well are 

groundwater released from aquifer storage and streamflow 

depletion in a nearby stream. Groundwater storage is the 

primary source of water to the well soon after pumping 

begins, but its contribution to the well’s withdrawal declines 

with time. The time at which more than half of the pumping 

rate of the well is supplied by streamflow depletion is designated on the figure as the time to reach a depletion-dominated 

supply (tdds  

). If the well pumps for an extended period of time, 

the source of water pumped by the well will be entirely from 

depletion, with no further contributions from groundwater 

storage. When this occurs, water levels no longer decline in 

response to pumping, the cone of depression does not expand 

any further, and the aquifer is in a new state of equilibrium in 

which the pumping rate of the well is equal to the amount of 

streamflow depletion. The time that is required for a new state 

of equilibrium to be attained has been called the “time to full 

capture” and can range from a matter of days to decades and 

even centuries (Bredehoeft and Durbin, 2009; Walton, 2010). 

In some aquifers, however, a new equilibrium may never be 

reached if the total pumping rate from the aquifer exceeds the 

rate at which water can be captured. In other aquifers, the time 

to reach full capture, as expressed as 100 percent of the pumping rate of the well, is so long that for practical purposes it is 

not meaningful. In those cases, it may be preferable to define 

full capture as a value somewhat less than 100 percent, such as 

99 percent or 95 percent.

The factors that control the time response of streamflow 

depletion to pumping are the geologic structure, dimensions, 

and hydraulic properties of the groundwater system; the locations and hydrologic conditions along the boundaries of the 

groundwater system, including the streams; and the horizontal 

and vertical distances of wells from the streams. The effects 

of these factors will be illustrated in different ways throughout 

this report, beginning with a discussion of two of the most 

important variables—the distance of a pumping well from 

a nearby stream and the hydraulic diffusivity of an aquifer. 
14 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Storagedominated 

supply Depletion-dominated supply

Water from storage

Water from streamflow depletion

0

50

100

Percentage of groundwater pumping rate

t dds Pumping time

Figure 9. Relation of storage 

change and streamflow 

depletion as sources of 

pumped groundwater through 

time for a hypothetical well. 

Initially, the source of water 

(or supply) to the well is 

dominated by reductions 

in aquifer storage. At later 

times, streamflow depletion 

is the dominant source of 

supply. The condition of more 

than half of the pumping rate 

coming from streamflow 

depletion is designated as 

depletion-dominated supply, 

and variable t

dds is the time 

to reach the condition of 

depletion-dominated supply for 

a particular pumping location.

Jenkins (1968a, b) introduced a term that is widely applied in 

streamflow-depletion problems called the “stream depletion 

factor” (or SDF) to quantify the relation between these two 

variables. The stream depletion factor for a well pumping at a 

particular location in an aquifer is defined as

where d is the shortest distance between the pumped well and 

nearby stream, and D is the hydraulic diffusivity of the aquifer. 

Values of SDF have units of time. 

For a given pumping location, the value of SDF is a relative measure of how rapidly streamflow depletion occurs in 

response to a new pumping stress. Streamflow depletion will 

occur relatively quickly in response to pumping from wells 

with a low value of SDF and relatively slowly in response 

to wells with a high value of SDF. A high value of hydraulic 

diffusivity, for example, will result in a relatively low value 

of SDF and, as described and illustrated in Box A, a relatively 

fast response of streamflow depletion to pumping. The effects 

of well distance on streamflow depletion are illustrated in 

figure 10 for two hypothetical wells pumping from the same 

aquifer. Because well A is located much farther from the 

stream than well B, the time necessary for the cone of depression formed by pumping at well A to reach the stream is much 

longer than that for well B, and as a result, groundwaterstorage depletion is a source of water to the well for a longer 

period of time. In contrast, the cone of depression formed by 

pumping at well B reaches the stream much sooner than that 

, SDF d

D =

2

for well A, and streamflow depletion becomes the primary 

source of water to the well much sooner than for well A. 

The presence of streambed and streambank sediments 

that impede the flow of water at the stream-aquifer interface 

also can affect the response of streamflow to pumping 

(fig. 11). These bed sediments often consist of fine-grained 

deposits and organic materials that have a lower hydraulic 

conductivity (permeability) than the surrounding aquifer 

materials. The effect of these sediments is to extend the time to 

full capture and to reduce the amount of streamflow depletion 

that occurs at any given time relative to a condition in which 

the low-permeability sediments are absent. For example, for 

the simulated conditions shown in the graph in figure 11, 

65 percent of the water withdrawn by the well after 60 days 

of pumping consists of streamflow depletion for the condition 

with no resistance to flow at the stream-aquifer interface, 

whereas only 53 percent of the well’s withdrawal rate consists 

of streamflow depletion after 60 days of pumping for the 

condition in which streambed and streambank materials with 

lower permeability than the aquifer are present at the streamaquifer interface.

Conditions that do not affect the timing of depletion also 

are worth noting. First, in most aquifer systems, the timing 

of streamflow depletion is independent of the pumping rate 

at the well. If the pumping does not cause system changes 

such as large reductions in aquifer thickness or the drying 

up of streams or wetlands, depletion at any given time is 

proportional to the pumping rate. Depletion, therefore, can 

be expressed as a fraction (or percentage) of the pumping 

rate at a well, as described in Box B. Moreover, the fraction 
Streamflow Response to Groundwater Pumping 15

Well A

Stream

When pumping

starts: 

After 10 years

of pumping:

After 50 years

of pumping:

Relative amount of groundwater

pumping rate coming from

streamflow depletion

Relative amount of groundwater

pumping rate coming from aquifer

storage (falling water table) 

B

A 0 0

0.2

0.4

0.6

0.8

1.0

Streamflow depletion, as fraction 

of pumping rate

Well B

Well A

Time, in years

10 20 30 40 50

A

B

Well B

Figure 10. A, Sources of pumped groundwater at two hypothetical well locations for pumping times of 10 and 50 years. B, Streamflow 

depletion is a much larger source of water to well B than to well A during the 50-year pumping period because well B is much closer to 

the stream (modified from Leake and Haney, 2010).

Saturated zone

Unsaturated zone

Water table

Water table Sediments

Unsaturated zone

Stream with streambed and streambank sediments 

less permeable than surrounding aquifer sediments.

Stream with streambed and streambank sediments 

the same as the aquifer sediments.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120

Time, in days

No streambank or streambed

 sediments present

Streambank and streambed

Streamflow depletion, as fraction

 sediments present

of pumping rate

Figure 11. Streamflow depletion resulting from a well pumping 500 feet from a stream at a rate of 250 gallons per minute. The presence 

of streambed and streambank materials with lower permeability than the surrounding aquifer reduces the amount of streamflow 

depletion during the 120 days of pumping. [Rates of streamflow depletion were calculated by using a computer program described 

in Reeves (2008); hydraulic diffusivity of aquifer is 10,000 feet squared per day and streambed leakance, which represents resistance 

between the stream and aquifer, is 200 feet.]
16 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

 Box B: Ways to Express Streamflow Depletion

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 40 80 120 160 200 240 280 320 360

Streamflow depletion, in cubic

feet per second

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 40 80 120 160 200 240 280 320 360

Time, in days

Streamflow depletion, as fraction of

pumping rate

A

B

Figure B–1. Streamflow depletion resulting from pumping at a 

well located 250 feet from a stream. The well is pumped at a rate 

of 1 million gallons per day (about 1.55 cubic feet per second). In 

graph A, streamflow depletion is expressed as a rate, in cubic feet 

per second; in graph B, depletion is expressed as a fraction of the 

pumping rate at the well, which is a dimensionless quantity. [Rates 

of streamflow depletion were calculated by using a computer 

program described in Reeves (2008); hydraulic diffusivity of the 

aquifer is 10,000 feet squared per day.]

Different approaches are used to quantitatively express 

the effects of groundwater pumping on streamflow. Some of 

these approaches are described and illustrated here to provide 

background for the discussions in the remainder of the report.

Change in streamflow rate

The most common way to describe streamflow depletion has been to report the change in the instantaneous flow 

rate of the stream, which is expressed in units of volume of 

streamflow per unit of time, such as cubic feet per second 

(ft3

/s), million gallons per day (Mgal/d), or acre-foot per year 

(acre-ft/yr). A related approach is to report the rate of streamflow depletion as a fraction of the pumping rate of the well, 

which is a dimensionless quantity. 

These two approaches are illustrated in figure B–1, where 

rates of streamflow depletion are shown for a pumping rate 

of 1.0 Mgal/d at a well located 250 feet from a stream. The 

streamflow depletion that results from pumping the well is 

shown in units of cubic feet per second, which is the unit most 

often used in reporting streamflow. In these units, the pumping 

rate of the well is 1.55 ft3

/s, and the rate of streamflow depletion caused by pumping at the well is shown in the top graph 

of figure B–1 to approach this rate asymptotically. The bottom 

graph shows streamflow-depletion rates as a fraction of the 

pumping rate at the well for the same pumping conditions. In 

this case, the reporting unit is dimensionless, and the curve on 

the graph asymptotically approaches a value of 1.0. 

Cumulative volume of streamflow depletion

Another approach used to describe streamflow depletion is the cumulative (or total) volume of streamflow that 

occurs over a specified period of time. In this approach, the 

units used are volumes of streamflow that are depleted, such 

as cubic feet, million gallons, or acre-feet. Because rates of 

streamflow depletion change over time, in order to calculate 

the total volume depleted over a period of time it is necessary 

to sum the volumes of depletion that occur over shorter time 

intervals within the full period of interest. For example, if one 
Streamflow Response to Groundwater Pumping 17

wants to determine the total volume of depletion over a 1-year 

period, an approach would be to sum the individual volumes 

of depletion that occur each day. These volumes could be 

calculated by multiplying the daily rates of streamflow depletion by the 1-day time interval. Volumes of depletion also can 

be expressed as a dimensionless fraction of the total volume of 

water pumped over the period of interest.

These concepts are illustrated in figure B–2 for the same 

pumping conditions described for figure B–1. Because the 

pumping rate at the well is constant at 1.0 Mgal/d, the cumulative amount of groundwater pumped increases linearly with 

time and is equal to 360 Mgal at the end of the 360-day pumping period (top curve in fig. B–2A). However, as shown in 

the graph, at any particular time, the total volume of streamflow depletion is less than the total volume of water pumped 

because of the delayed effect of the response of the stream to 

pumping at the well. The volume of streamflow depletion as a 

dimensionless fraction of total groundwater pumped is shown 

in the bottom graph of figure B–2. It should be noted that the 

dimensionless curve shown in the bottom graph of figure B–2 

is not equal to the dimensionless curve in figure B–1 because 

the underlying responses (that is, rates of streamflow depletion 

as opposed to volumes of streamflow depletion) are different.

A closer look at where depletion occurs

Some situations may require detailed analyses of individual stream reaches subject to depletion. This is particularly 

true if depletion-related changes in water chemistry or temperature are of concern or if a goal is to maintain a minimum 

base flow in a critical stream reach. For these analyses, depletion can be reported as the instantaneous rate of depletion per 

unit length of stream, such as in units of cubic feet per second 

per mile. Detailed reach-by-reach estimates of depletion can 

be calculated with numerical groundwater-flow models to 

gain insight into where pumping-induced infiltration from 

the stream to the aquifer might occur. An example of such an 

analysis is shown in figure 15A.

A

B

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Time, in days

0

40

80

120

160

200

240

280

320

360

0 40 80 120 160 200 240 280 320 360

0 40 80 120 160 200 240 280 320 360

Cumulative volume, in million gallons

Volume pumped

Cumulative volume of streamflow depletion,

as fraction of volume pumped at the well

Volume of streamflow depletion

Figure B–2. Cumulative volume of streamflow depletion resulting 

from pumping at a well located 250 feet from a stream. The 

well is pumped at a rate of 1 million gallons per day. In graph 

A, streamflow depletion is expressed as the total (cumulative) 

volume of depletion that has occurred since the initiation of 

pumping, in million gallons; in graph B, the cumulative volume 

of depletion is expressed as a fraction of the cumulative volume 

of groundwater pumped at the well, which is a dimensionless 

quantity. [Volumes of streamflow depletion were calculated from 

the rates of streamflow depletion shown in figure B–1.] 
Annaquatuck

River

Hunt

River

MASSACHUSETTS

RHODE

ISLAND

CONNECTICUT

Study

area

0

0 10 MILES

10 KILOMETERS

0

0.2

0.4

0.6

0.8

1.0

0 30 60 90 120 150 180 210 240 270 300 330 360

Streamflow depletion, as

fraction of pumping rate 

Time, in days

Well 3A pumping

Well NK9 pumping

Well NK6 pumping

Stratified deposits

Till and bedrock

Basin boundary

Aquifer boundary

General direction of

 groundwater flow

Water-supply well

 and identifier

EXPLANATION

41o37’30”

71o32’30”

71o27’30”

41o32’30”

0

0

0.5

0.5

1 MILE

1 KILOMETER

18 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Figure 12. Streamflow depletion for three wells pumping from the unconfined-aquifer system of the Hunt River Basin, Rhode Island

(map and streamflow-depletion data modified from Barlow and Dickerman, 2001).

of streamflow depletion computed for one pumping rate 

also can be applied to other pumping rates that do not cause 

substantial changes to the aquifer system. As noted in a later 

section of the report, the timing of depletion is also independent of rates and directions of groundwater flow in most aquifers. This means that depletion as a net effect on streamflow 

is the same whether a stream is gaining or losing, that features 

such as groundwater flow lines and divides have no influence 

on depletion, and that transient events such as changes in river 

stage or rates of aquifer recharge do not affect the timing of 

depletion by a pumping well (Leake, 2011).

Case studies from aquifers in the Eastern and Western 

United States illustrate the large differences in the timing of 

streamflow depletion that result from the variability in the 

scale of the two aquifer systems, proximity of the pumping 

wells to streams, and differences in the geology and hydraulic 

properties of the two aquifers. The case study from the Eastern 

United States is the 40 square mile (mi2

) stream-aquifer 

system of the Hunt River Basin of Rhode Island (fig. 12). The 

aquifer is typical of many of the glacially derived aquifers of 

the Northeastern United States that consist of stratified, unconsolidated sand and gravel sediments that are hydraulically 

connected to shallow streams, lakes, and ponds. The sediments 

were deposited by glacial meltwater within generally narrow 

river valleys bounded laterally and at depth by glacial till and 

bedrock. The sand and gravel deposits can have very high 

values of transmissivity, even though they are often no more 

than 100 to 150 ft thick at the deepest part of the valley. The 

aquifers typically are unconfined and have substantial storage 

capacities. Water-supply wells frequently are placed close to 

the streams where the valley depth and aquifer transmissivity 

are greatest. Thus, the distance from the wells to the groundwater-discharge boundaries at the streams is often less than a 

few hundred feet.
COCHIS COUNTY

?

Well A

Well B

Time, in years

0 10 20 30 40 50 60 70 80 90 100

1.0

0.8

0.6

0.4

0.2

0

Streamflow depletion, as

fraction of pumping rate 

EXPLANATION

Extent of silt and clay layer

San Pedro Riparian National

 Conservation Area

Extent of active part of

 model layer 4

Hypothetical well location

 and identifier

A

C

B A

0

0

10 KILOMETERS

10 MILES

30’

31°45’

110o30’

15’

31°

15’ 110°

? ? ? ?

Rio Los Fresnos

San Pedro River

Babocomari River

UNITED STATES

MEXICO

River

San edro P

ARIZONA

Model area

Tucson

Sierra Vista

Subwatershed

Upper San

Pedro Basin

Modified from Pool and Dickinson (2007)

HUACHUCA

MOUNTAINS

Bisbee

Fort

Huachuca Sierra

Vista

Tombstone

ARIZONA,

UNITED STATES

SONORA, 

MEXICO

Streamflow Response to Groundwater Pumping 19

Figure 13. Streamflow depletion for hypothetical well locations A and B pumping from the Upper San Pedro Basin aquifer system, 

southern Arizona (modified from Leake, Pool, and Leenhouts, 2008.) [Well C is discussed later in the report.]

The distribution of water-supply wells in the Hunt River 

Basin is typical of wells in these river-valley aquifers (fig. 12). 

The majority of the wells are clustered along the Hunt and 

Annaquatucket Rivers, where the transmissivities of the 

aquifer are largest (Barlow and Dickerman, 2001). Nearly all 

of the wells are within about 500 ft of a stream from which 

groundwater that would otherwise have discharged to the 

stream is captured or streamflow is drawn into the aquifer 

by the process of induced infiltration. Because of the close 

proximity of the wells to the streams and the relatively high 

transmissivity of the aquifer near the wells, the time response 

of streamflow depletion to pumping is relatively fast, as 

illustrated by the streamflow-depletion curves calculated by a 

numerical groundwater-flow model of the basin for three wells 

that pump near the Hunt River (fig. 12). Each of the three 

wells captures more than 90 percent of its withdrawal from 

streamflow depletion within 180 days of the start of pumping, 

and the time to reach a depletion-dominated supply is less than 

50 days for each well.

In contrast to the narrow and relatively shallow alluvialvalley aquifer settings of the Northeast, many aquifers of the 

Western United States extend over hundreds to thousands 

of square miles and are hundreds of feet thick. An example 

groundwater system of the West is that within the Upper San 

Pedro Basin that extends from northern Sonora, Mexico, into 

southern Arizona (fig. 13). The watershed covers an area of 

about 1,700 mi2. Groundwater discharge sustains perennial 

reaches in the San Pedro River and tributaries, as well as 

narrow bands of groundwater-dependent vegetation adjacent 

to streams. The riparian area provides year-round habitat for 

aquatic and terrestrial wildlife species, and also is an important 

corridor for birds migrating between Mexico and the United 

States. The San Pedro Riparian National Conservation Area, 

managed by the Bureau of Land Management, was established 

in 1988 to protect and enhance this desert ecosystem. 
20 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

The primary aquifer within the Upper San Pedro Basin 

comprises thick alluvial deposits that occupy a structural basin 

that lies between rocks in the surrounding mountains (Pool 

and Dickinson, 2007; Leake, Pool, and Leenhouts, 2008). 

The basin-fill deposits are subdivided into upper, highly 

permeable and lower, less permeable parts that are collectively 

as much as 1,700 ft thick. An extensive silt and clay layer that 

vertically spans parts of the upper and lower basin fill separates the aquifer into deep confined and shallow unconfined 

sections. The areal extent of the silt and clay layer is shown 

in figure 13. Groundwater within the Upper San Pedro Basin 

generally flows from recharge areas near the mountains to 

areas near the San Pedro River where it discharges to the 

stream and springs or is evaporated or transpired by riparian 

vegetation. A portion of the groundwater flow is intercepted 

upgradient from the streams by pumped wells.

Graphs of streamflow depletion for two wells pumping 

within the San Pedro Basin in figure 13 illustrate the large 

difference in response times for pumping from this system 

compared to that of the Hunt River Basin. Response times 

for streamflow depletion in the San Pedro River Basin are 

measured in years and decades, whereas those for the Hunt 

River are measured in days and months. For example, in 

contrast to wells pumping in the Hunt River Basin, the time 

required to reach depletion-dominated supply is about 5 years 

for well A and nearly 90 years for well B. The long response 

times for the San Pedro Basin result from the relatively large 

distances of hypothetical wells A and B from the San Pedro 

River (about 1.5 miles (mi) for well A and 6 mi for well B) 

and the specific characteristics of the groundwater system of 

the San Pedro River Basin, including its large areal extent, 

the thickness of the basin-fill sediments, and the presence of 

the silt and clay confining unit, all of which increase the time 

during which the wells draw from aquifer storage. These long 

response times have implications to monitoring and managing 

streamflow depletion in these aquifer settings—a topic that 

will be discussed later in the report. 

The discussion in this section on the time response of 

streamflow depletion to pumping is based on concepts of the 

source of water to pumped wells that have been presented 

in literature over a period of more than 70 years, including 

those by Theis (1940), Lohman (1972), Bredehoeft and others 

(1982), Heath (1983), Alley and others (1999), Bredehoeft 

(2002), and Bredehoeft and Durbin (2009). These concepts are 

also relevant to the related topics of groundwater budgets and 

groundwater sustainability.

San Pedro River below Hereford, Arizona. The riparian zone 

along the river provides abundant food, water, and cover for 

hundreds of species of birds, including the Vermilion Flycatcher. 

(Background photograph by Michael Collier)

Photograph by Bob Herrmann
Streamflow Response to Groundwater Pumping 21

Distribution of Streamflow Depletion Along 

Stream Reaches

The cone of depression that forms around a well extends 

outward in all directions from the well, and, as a result, 

groundwater pumping affects streams and stream reaches that 

are both upgradient to and downgradient from the location of 

withdrawal. Some stream reaches will be affected more than 

others, depending on the distance of the well from the reach 

and the three-dimensional distribution and hydraulic properties of the geologic materials that compose the groundwater 

system and adjoining streambeds. Steep hydraulic gradients at 

the stream-aquifer interface created by the pumping may cause 

some stream reaches to become losing, while other reaches 

remain gaining. Streamflow depletion increases in the downstream direction of a basin, and if depletion is the only source 

of water to the pumped well, the rate of depletion over time 

will tend to approach the pumping rate of the well in the direction of the outflow point (or points) of the basin.

These concepts are illustrated by the results of numerical 

simulations for two different aquifers, the first a hypothetical 

groundwater system representative of river-valley aquifers of 

the Northeastern United States and the second a real-world 

aquifer in northern Arizona. The hypothetical system consists 

of a single stream that receives groundwater discharge along 

its entire length from a hydraulically connected unconfined 

aquifer (fig. 14; based on Barlow, 1997). The unconsolidated 

sand and gravel deposits that fill the valley range in saturated 

thickness from about 40 ft along the boundaries of the valley 

to a maximum of about 100 ft in the center of the valley. For 

simplicity, the hydraulic properties of the aquifer and streambed sediments are homogeneous. The aquifer is bounded at 

depth by impermeable bedrock. The primary source of water 

to the groundwater system is recharge at the water table, but 

groundwater also flows into the river valley from the surrounding uplands and along the northern boundary of the 

simulated area. Groundwater leaves the system primarily as 

discharge to the stream but also along the southern boundary 

of the simulated area. 

The rate of groundwater discharge to the stream is 

constant along its entire length in the absence of pumping 

(fig. 15A), which results in a linear increase in streamflow 

from zero cubic foot per second (ft3

/s) at the upstream end of 

the simulated basin to 6.1 ft3/s at the outflow point of the basin 

(fig. 15B). The uniform rate of groundwater discharge to the 

stream results from the symmetry of the system and assumed 

homogeneity of the hydraulic properties of the aquifer and 

streambed materials.

The effects of pumping at three well locations are evaluated for steady-state flow conditions; that is, for conditions 

in which groundwater levels are no longer declining, aquiferstorage depletion is no longer occurring, and streamflow 

depletion is the only source of water to the wells. The three 

wells are located midway between the northern and southern boundaries of the system at distances of 300 ft (well A), 

700 ft (well B), and 1,400 ft (well C) from the stream (fig. 14). 

fig 14

0

0 300 900 METERS

1,000 3,000 FEET

40

50

60

70

80

90

C B A

A

EXPLANATION

Water-table altitude, in feet

Groundwater-flow direction

Well and identifier

90

Stream

A

B

N

Figure 14. A, Cross section of a hypothetical river-valley aquifer 

with a shallow stream. B, Plan view of the water-table altitude and 

groundwater-flow directions in the aquifer with no pumping at the 

three wells. The stream receives groundwater discharge along its 

entire length (modified from Barlow, 1997).
22 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

0

1

2

3

4

5

6

7

0 2,000 4,000 6,000 8,000 10,000 12,000

Streamflow and streamflow depletion, in cubic feet per second

Distance along stream, in feet

B

Well A pumping

Well B pumping

Well C pumping

-7

-5

-3

-1

1

3

5

7

0 2,000 4,000 6,000 8,000 10,000 12,000

Seepage rate at stream, in cubic feet

per second per length of stream (x 10-4)

Distance along stream, in feet

A

Pumping

rate

Pumping

rate

Streamflow without

pumping

Streamflow

with pumping

Streamflow

depletion EXPLANATION

Groundwater-discharge rate to stream without pumping

Groundwater 

 discharge

Induced infiltration

of the stream shown in figure 14B: In the absence of pumping, the stream receives groundwater discharge at a uniform rate along its 

entire length. Pumping from wells A and B, which are located 300 feet and 700 feet from the stream, respectively, cause induced infiltration along part of the stream, whereas pumping at well C, which is located 1,400 feet from the stream, does not. Reaches that are gaining coincide with locations of groundwater discharge, whereas reaches that are losing coincide with locations of induced infiltration.

B, Streamflow and streamflow depletion along the stream: In the absence of pumping, there is a linear increase in streamflow along the 

entire stream length. With pumping, streamflow depletion increases in the downstream direction and approaches the pumping rate of 

each well (1.55 cubic feet per second), regardless of the distance of each well from the stream. The results shown in these graphs are 

for steady-state flow conditions. Well locations are shown in figure 14. (Results from models documented in Barlow, 1997.)

Figure 15. A, Rates of groundwater discharge (positive values) and induced infiltration (negative values) along the 12,000-foot reach 

Each well is pumped independently of the others at a rate 

of 1 million gallons per day (Mgal/d; 1.55 ft3

/s) in three 

separate simulations. 

The graph in figure 15A shows the distribution and rates 

of streambed seepage along the stream for pumping at the 

three wells. Seepage rates greater than zero indicate groundwater discharge to the stream and gaining streamflow conditions, whereas seepage rates less than zero indicate induced 

infiltration of streamflow into the aquifer and losing streamflow conditions. The graph indicates that changes in streambed 

seepage rates are not confined to the reach of the stream that 

is immediately opposite to the wells (that is, at 6,000 ft along 

the stream), but instead extend both upgradient to and downgradient from the wells. The graph also indicates that inducedinfiltration rates are largest for the well closest to the stream 

(well A) and decrease as the distance of the pumped well from 

the stream increases.

The graphs in figure 15B demonstrate that streamflow 

depletion also occurs in both the upgradient and downgradient directions from the pumped wells and that the amount of 

depletion asymptotically approaches the pumping rate of each 

well (1.55 ft3

/s) in the downstream direction, regardless of the 

distance of the pumped well from the stream. This results from 

the fact that for the conditions simulated (including the steadystate flow conditions) there are no other sources of water to 

the wells. As a consequence, all of the water pumped by each 

well must come from streamflow depletion, either as captured 

groundwater discharge or induced infiltration.

The change in the groundwater-discharge rates to the 

stream and resulting changes to streamflow that occur in 

response to pumping at the wells can be explained by the distribution of groundwater-level declines (drawdowns) that form 

around each pumped well (fig. 16). Because well A is closest 

to the stream, the drawdowns created at the well are larger 
Streamflow Response to Groundwater Pumping 23

1.0

1.5

2.0

2.5

3.0

0.50.5

0.50.5

1.01.0

1.01.0

1.51.5

2.02.0

2.52.5

3.03.0

0.5 0.5

0.5 0.5

1.0

1.01.0

1.5

1.51.5

2.0

2.02.0

2.5

2.52.5

3.0

3.03.0

A

A

A B

C

Stream Stream

1,000 FEET

300 METERS

0

0

EXPLANATION

Groundwater-level

 decline, in feet

Well and identifier

0.50.5

Figure 16. Groundwater-level declines (drawdowns) in the aquifer caused by, A, pumping at well A, and, B, pumping at well C. Well 

locations are shown in figure 14. (Results from models documented in Barlow, 1997.)

at the stream-aquifer boundary than those that are created by 

pumping at well C. As a result, the hydraulic gradients at the 

stream boundary and resulting rates of induced infiltration 

are largest for pumping at well A and smallest for pumping 

at well C. The symmetry of the seepage and streamflowdepletion rates shown in figure 15 results from the symmetry 

of the drawdown curves around each well, which results from 

the straight boundaries along the modeled aquifer and of the 

stream and the uniformity of the simulated aquifer sediments.

The real-world example considered here is from a 

study of the C aquifer in northeastern Arizona. Groundwater 

discharge from the C aquifer supports threatened and endangered fish species in some reaches of the Little Colorado 

River and its tributaries (Leake and others, 2005). The aquifer 

is named for the Coconino Sandstone, which is the principal water-bearing unit of the aquifer. The primary discharge 

area for the C aquifer in the Little Colorado River Basin is a 

series of springs in the lower reaches of the Little Colorado 

River, including Blue Spring. Discharge also occurs along 

various reaches of the tributaries to the Little Colorado River, 

such as the lower reaches of Clear and Chevelon Creeks 

(fig. 17); base-flow measurements made around the time of the 

C-aquifer study indicate groundwater discharge rates of about 

5.6 and 2.7 ft3/s, respectively, to the two reaches.

The C aquifer is the most productive aquifer in the Little 

Colorado River Basin and an important source of water for 

many users (Leake and others, 2005). Increased withdrawals 

from the aquifer have been proposed from a cluster of 

wells just south of Leupp, Arizona, to meet increased future 

demands (fig. 17). A numerical model of change in groundwater flow in the aquifer was developed to evaluate the potential effects of future withdrawals on groundwater discharge to 

perennial reaches in the Chevelon and Clear Creek drainages 

and to the Little Colorado River in the area below Blue Spring 

(fig. 17). Two withdrawal scenarios were simulated for a 

101-year period that included 51 years of withdrawals followed by 50 years of no withdrawals. Scenario A simulates 

a nearly constant withdrawal rate of about 9.0 ft3/s [about 

6,500 acre-feet per year (acre-ft/yr)], and scenario B simulates 

a more complicated pumping pattern with a maximum withdrawal rate of about 15.9 ft3

/s (11,500 acre-ft/yr; fig. 18). 

The time distribution of streamflow depletion is shown 

for all stream reaches in figure 19A and for only the lower 

Clear and Chevelon Creek reaches in figure 19B. All of the 

depletion curves shown in the figure indicate a gradual, 

steady increase in the streamflow-depletion rates for both 

scenarios, even though the withdrawal schedule for scenario B 

is quite variable. This damping of the pumping variability 

results from the large distances of the wells from the stream 

reaches of interest and from the diffusivity of the aquifer. 

Total streamflow depletion for all reaches at the end of the 

51-year pumping period is about 0.31 ft3/s for scenario A 

and 0.37 ft3/s for scenario B (fig. 19A). Of the total depletion 

shown in figure 19A for the two scenarios, nearly all of the 
Clear

Creek

Chevelon

Creek

Little

Colo r ado River

Blue Spring

Clear

Creek

Blue Spring

Chevelon

Creek

Little

Colo r ado River

Colorado 

River

Flagstaff Flagstaff

Winslow

Leupp

Flagstaff Flagstaff

Area of

pumping

Base from U.S. Geological Survey digital data, 

1:100,000, 1980, Lambert Conformal Conic projection 

Standard parallels 2930' and 4530', Central meridian–11130'

112° 111°

36°

35°

0

0 25 MILES

25 KILOMETERS

EXPLANATION

Boundary of active model area

Perennial stream reach

Intermittent stream

Existing well used in scenarios

 to compute streamflow depletion

Phoenix

Santa Fe

Albuquerque

ARIZONA

NEW MEXICO

Active model 

area

Area Flagstaff

shown

24 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Figure 17. Locations of perennial stream reaches and some of the wells simulated in proposed withdrawal scenarios for the C aquifer, 

northeastern Arizona (modified from Leake and others, 2005).

depletion occurs in the two reaches that are closest to the 

pumping center, lower Clear Creek, which is about 25 mi from 

the wells, and lower Chevelon Creek, which is about 34 mi 

from the wells (fig. 19B). 

The results shown in figure 19 indicate that the rates of 

depletion in all stream reaches after 51 years of pumping are 

relatively small compared to the maximum pumping rates 

for each scenario. For example, for scenario A, streamflowdepletion rates are 0.26 ft3

/s for lower Clear Creek and 

0.05 ft3/s for lower Chevelon Creek at the end of the pumping period (fig. 19B), yet the maximum pumping rate at the 

well cluster is about 9.0 ft3/s for this scenario. These results 

indicate that nearly all of the water pumped by the wells during the pumping period is derived from reductions in aquifer 

storage and that the system is far from reaching a new steadystate condition.

The responses shown in the figure also indicate that 

streamflow depletion continues long after pumping stops. 

This results from the fact that the withdrawal locations are 

far from the perennial stream reaches—recovery from shutting off withdrawals takes time to reach distant parts of the 

outward-propagating cone of depression (Leake and others, 

2005). Maximum streamflow-depletion rates for all reaches 

taken together (fig. 19A) occur at about year 95 for both withdrawal scenarios, about 44 years after pumping stops. For the 

lower Chevelon Creek reach, however, maximum depletion 

occurs even later in time, near the end of the 101-year simulation period (fig. 19B). Residual pumping effects on streamflow depletion are discussed in more detail in the section 

“Depletion after Pumping Stops” in the chapter on common 

misconceptions about streamflow depletion.
Streamflow Response to Groundwater Pumping 25

Withdrawal rate, in cubic feet per second

0

2

4

6

8

10

12

14

16

18

2000 2010 2020 2030 2040 2050 2060 2070

Year

Scenario A

Scenario B

EXPLANATION

Figure 18. Withdrawal scenarios simulated for the C aquifer, 

northeastern Arizona (modified from Leake and others, 2005).

0.4

Total streamflow depletion, in cubic feet per second

0.3

0.2

0.1

0.7

0.6

0.5

0

Time, in years since start of pumping Time, in years since start of pumping

0 10 20 30 40 50 60 70 80 90 100 110

Scenario

B

Scenario A

0.4

0.3

0.2

0.1

0.6

0.5

0

Lower Chevelon Creek

Lower Clear Creek

0 10 20 30 40 50 60 70 80 90 100 110

Scenario

B

Scenario A

Scenario A

Scenario B

A

B

Total depletion

for all stream

reaches

Pumping stops 

Pumping stops

Figure 19. Streamflow depletion as a function of time for two scenarios of groundwater pumping from the C aquifer, northeastern 

Arizona. A, All stream reaches. B, The lower Clear and Chevelon Creeks. Withdrawals in both scenarios stop at the end of year 51, 

indicated by the vertical red lines (modified from Leake and others, 2005).

Lower Clear Creek near Winslow, Arizona. (Photograph by Robert 

J. Hart, U.S. Geological Survey)
Variable and Cyclic Pumping Effects

Previous sections of this report have focused primarily 

on streamflow depletion for conditions in which pumping 

occurs at a single rate for an extended period of time. More 

commonly, however, pumping schedules vary with time, 

either in response to changing water-supply demands or for 

maintenance and overall operation of the water-supply system. 

Pumping schedules can vary on hourly and daily bases in 

response to short-term fluctuations in demands and over 

longer-term cycles in response to factors such as seasonal 

and annual climate variability and irrigation demands. Two 

examples of the effects of variable and cyclic pumping on 

streamflow depletion are described for two different watersupply settings—a well that pumps to meet daily fluctuations 

in public-supply demands and one that pumps on a seasonal 

pumping and nonpumping cycle to meet irrigation demands. 

The examples demonstrate that the overall effect of the 

diffusive properties of an aquifer are to dampen the variability 

and amplitude (range) of the pumping rates, such that the 

resulting rates of streamflow depletion are less variable and 

smaller in amplitude.

Groundwater withdrawals for primarily domestic and 

commercial uses in the Ipswich River Basin in eastern 

Massachusetts have caused substantial depletions of 

streamflow during summer low-flow periods (Zarriello and 

Ries, 2000). In the past, these depletions stressed aquatic 

communities and caused fish and mussel kills during dry 

years (Armstrong and others, 2001; Glennon, 2002). Pumping 

rates at one of the water-supply wells in the basin during a 

9-year period illustrate the variability in withdrawals that 

occur in response to fluctuations in water-supply demands, 

which are generally highest during the spring and summer 

but then decrease during the fall and winter (fig. 20). 

Photograph by David Armstrong, U.S. Geological Survey

26 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Pool and dry river bed along the Ipswich River, Reading, Massachusetts, September 2005. 
Streamflow Response to Groundwater Pumping 27

1989 1990 1991 1993 1994 1995 1996

0

0.2

Calculated streamflow

 depletion

Specified daily pumping 

 rate at well

Year

0.4

0.6

0.8

1.0

1.2

1992 1997

Pumping rate and streamflow depletion, 

in cubic feet per second

EXPLANATION

Figure 20. Daily pumping rates and model-calculated streamflow depletion for a well pumping about 500 feet from the Ipswich River, 

Massachusetts (modified from Barlow, 2000).

Rates of streamflow depletion in the Ipswich River that result 

from the daily pumping schedule also are shown in the figure 

and were calculated with an analytical model of streamflow 

depletion (Jenkins, 1968a; Barlow, 2000). As can be seen in 

figure 20, the range and variability of calculated streamflowdepletion rates are much less than those for the pumping rates 

at the well. The factors that cause reductions in the amplitude 

and variability of the pumping rates that are represented in the 

analytical model are the distance of the well from the river 

(about 500 ft) and the hydraulic diffusivity of the aquifer. 

Calculated streamflow depletion also exhibits an upward trend 

during the 9-year period, which is consistent with the upward 

trend in groundwater withdrawals. 

Groundwater is a source of irrigation water to some of 

the most productive agricultural areas of the country, including California’s Central Valley and the High Plains area of 

the Midwest. The hydrogeologic setting of many agricultural 

areas is often a river-valley system consisting of one or more 

streams that are in hydraulic connection with a shallow, 

unconfined aquifer. Pumping rates from these aquifers are 

largest during the irrigation season but then decrease sharply 

during the remainder of the year. The effect of cyclic pumping on streamflow depletion has been the subject of much 

research, and the remaining discussion draws on contributions by Jenkins (1968a), Wallace and others (1990), Darama 

(2001), Chen and Yin (2001), Kendy and Bredehoeft (2006), 

Bredehoeft and Kendy (2008), and Bredehoeft (2011a). An 

example of the effects of cyclic pumping at a hypothetical 

agricultural supply well placed at various distances from a 

stream is described here and is similar to examples of cyclic 

pumping provided by Bredehoeft and Kendy (2008) and 

Bredehoeft (2011a).

The annual pumping cycle for the hypothetical agricultural supply well is illustrated in the top graph of figure 21. 

The well withdraws water from an extensive, unconfined 

aquifer that is bounded on one side by a single river. Pumping to meet irrigation demands occurs from June through 

August of each year; the irrigation season is then followed by 

a 9-month period of no withdrawals. The effects of this annual 

pumping cycle on streamflow depletion are illustrated for a 

15-year period of pumping at three wells located at different 

distances from the river—300 ft, 1,000 ft, and 3,000 ft. The 

total volume of water pumped at the well during each irrigation season is 365 Mgal. When averaged over the full year, 

the withdrawal rate at the well is 1.0 Mgal/d (about 1.5 ft3

/s), 

but because withdrawals only occur during the 3-month 

(92-day) period, the actual pumping rate is nearly 4 Mgal/d 

(about 6.1 ft3

/s) during the irrigation season (fig. 21A). For 

comparison, streamflow depletions resulting from the cyclic 

pumping pattern are contrasted with those resulting from a 

constant pumping rate at the well for the entire 15-year period 

of 1.0 Mgal/d. 
28 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

0

1

2

3

4

5

6

7

A. Pumping rate at well

0

1

2

3

4

5

6

7

B. Depletion for well pumping at 300 feet

0

1

2

3

4

5

6

7

Streamflow depletion, in cubic feet per second 

C. Depletion for well pumping at 1,000 feet

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Time, in years

D. Depletion for well pumping at 3,000 feet

Pumping rate, in cubic feet 

per second

Figure 21. Patterns of streamflow depletion for both seasonal and constant pumping rates. A, The constant pumping rate, shown 

by the black line, is 1 million gallons per day (1.55 cubic feet per second); the seasonal pumping rate, shown by the magenta line, is 

approximately 4 million gallons per day (6.14 cubic feet per second) during June, July, and August. Depletion rates are shown for a 

well pumping at, B, 300 feet; C, 1,000 feet; and D, 3,000 feet from the river. Streamflow-depletion rates for the constant pumping rate 

are shown by the solid black lines and for the seasonal pumping rate by the magenta lines. The hydraulic diffusivity of the aquifer is 

10,000 feet squared per day. [Rates of streamflow depletion were calculated by using a computer program described in Reeves (2008).]
Streamflow Response to Groundwater Pumping 29

The cyclic-pumping schedule results in cyclic patterns of 

streamflow depletion in the river, although the timing, rates, 

and range of depletion depend on the distance of the well 

from the river (fig. 21). The amplitude of the annual depletion 

rates is largest when the well is placed close to the river (that 

is, fig. 21B) but is substantially reduced as the distance of the 

well from the river is increased (fig. 21C and D). As noted 

by Jenkins (1968a), as the distance of the well from the river 

increases, the cyclic pumping pattern has an effect on streamflow depletion that closely resembles the constant pumping 

pattern. This effect is illustrated in the figure by contrasting 

the patterns of streamflow depletion for pumping at distances 

of 300 and 3,000 ft from the river. For pumping at 300 ft, the 

annual range of depletion in the 15th year is 5.0 ft3

/s, whereas 

it is only 0.4 ft3

/s for pumping at a distance of 3,000 ft from 

the river. The figure also shows that for a constant rate of 

pumping at each well, streamflow-depletion rates asymptotically approach the pumping rate at each well (1.5 ft3

/s), 

although this constant rate of depletion is attained much more 

slowly as the distance of the well from the river is increased. 

In contrast, depletions that result from the cyclic-pumping 

schedules asymptotically approach a condition of annual 

dynamic equilibrium, and this condition is attained most 

slowly for pumping at a distance of 3,000 ft from the river. 

The maximum rate of depletion for the well at 300 ft 

occurs on August 31 of each year, the last day of pumping, 

and the minimum depletion rate occurs on May 31, just before 

the well begins to pump for the new irrigation season. In 

contrast, for pumping at a distance of 3,000 ft, the maximum 

rate of depletion in the first year does not occur until 

December 21, more than 3 months after the irrigation period 

ends; the minimum depletion rate in the first year occurs on 

July 12 and 13, about half-way through the new irrigation 

season. In later years, the maximum rate of depletion for 

pumping at this well shifts to December 1—still 3 months into 

the non-irrigation season—and the minimum depletion shifts 

to July 18–19. The dependence of the timing of the maximum 

and minimum depletion rates on the distance of the well 

from the river has important implications to the management 

of streamflow depletion, which will be discussed later in 

the report.

For some time after the initiation of pumping, groundwater storage is the primary source of water to the well, and 

on an annual basis, the volume of depletion is less than the 

annual volume withdrawn (365 Mgal). With time, however, 

the annual volume of depletion approaches the annual volume 

pumped at the well, regardless of the distance of the well 

from the river or the pattern of withdrawal (constant or cyclic; 

Wallace and others, 1990; Darama, 2001; Bredehoeft, 2011a). 

The time required for the annual volume of depletion to equal 

the annual volume pumped increases with distance of the well 

from the river. In addition to the distance of the well from 

the river, the time required for the system to reach a new 

equilibrium is also a function of the hydraulic diffusivity 

of the aquifer and the width of the river valley (Butler and 

others, 2001; Miller and others, 2007; Bredehoeft, 2011a). 

In summary, the effect of cyclic pumping close to a 

stream is highly variable depletion through time, with a maximum that may approach the maximum pumping rate during 

periods of pumping. In contrast, the effect of cyclic pumping 

at greater distances from a stream is less-variable depletion 

through time, with maximum depletion that may only be 

slightly greater than the long-term average pumping rate.

Multiple Wells and Basinwide Analyses

The focus of this report thus far has been on the effects 

on streamflow depletion caused by individual wells pumping at different locations within a groundwater system. 

Typically, however, multiple wells withdraw water simultaneously from locations distributed throughout a groundwater 

basin. Many groundwater basins in the United States have 

hundreds and in some cases thousands of wells from which 

water is withdrawn. Considered individually, these wells 

may have small effects on streamflow, but when evaluated 

together on the scale of an entire basin, these wells can have 

substantial effects on streamflow. Moreover, basinwide 

groundwater development typically occurs over a period 

of several decades, and the resulting cumulative effects on 

streamflow depletion may not be fully realized for many 

years. As a result of the large number of wells and complex history of development, it is often necessary to take a 

basinwide perspective to assess the effects of groundwater 

withdrawals on streamflow depletion.

Such an approach was taken in a study of the effects 

of groundwater development on streamflow in the 

Elkhorn and Loup River Basins of central Nebraska (fig. 22). 

Groundwater withdrawals from thousands of wells in these 

basins are used to irrigate crops, and the number of acres 

irrigated with groundwater has risen sharply since the 1940s 

(fig. 23; Peterson and others, 2008; Stanton and others, 

2010). Withdrawals in the basins occur from the High Plains 

aquifer, with most of the wells located outside of the largely 

undeveloped Sand Hills region (Peterson and others, 2008). 

Total groundwater withdrawals within the areas shown in 

figure 22 averaged about 1,700 Mgal/d in 2005.

Groundwater pumping has had substantial effects on 

streamflow throughout the Elkhorn and Loup River Basins. 

These effects are illustrated by the cumulative reductions in 

groundwater discharge (base flow) to selected river reaches 

within the basins, as determined by use of a groundwater 

model of the area (fig. 24). Depletions were relatively small 

prior to 1970, but have increased sharply since then as the 

number of wells and total amount of withdrawals have 
30 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Boundary of

study area

Boundary of

active model

102° 98°

42°

41°

0

0

10

10

20

20

30

30

40 MILES

40 KILOMETERS

South Loup River

Loup River

Platte River

Elkhorn River

EXPLANATION

Boundary of Sand Hills region

Streamflow point identified in figure 24

 Upper Elkhorn River

 South Loup River

 Loup River downstream

Location of one or more wells simulated in model

Study area

Boundary of Sand Hills region

0

0

50 MILES

50 KILOMETERS

Figure 22. Locations of simulated pumping wells in parts of the Elkhorn and Loup River Basins, Nebraska, 2009. Locations of 

streamflow points identified in figure 24 are also shown (modified from Stanton and others, 2010).

increased. The effects of pumping have been largest for the 

lower reaches of the Loup River Basin, most likely because 

streams in those areas are in close proximity to extensive areas 

of irrigation (Peterson and others, 2008).

The basinwide effects of pumping in the Elkhorn and 

Loup River Basins over a period of several decades are 

representative of conditions that occur in groundwater basins 

throughout the United States. However, for the purpose of 

illustrating the underlying physical processes that occur when 

multiple wells pump from a groundwater system, it is useful to 

focus on just a few wells that withdraw water from a relatively 

simple aquifer system. As an example, the effects of a phased 

groundwater-development program in which three wells are 

developed over a 15-year period are evaluated by use of the 

hypothetical system described in the previous section of the 

report, in which a single stream is bounded by an areally 

extensive aquifer. Development within the hypothetical 

system is assumed to progress over time from areas closest to 

the stream to those distant from the stream: well A, which is 

located 300 ft from the stream, begins pumping in year 1; well 

B, located 1,000 ft from the stream, begins pumping in year 6; 

and well C, located 3,000 ft from the stream, in year 11. Each 

well pumps at a constant rate of 1 Mgal/d (1.55 ft3

/s), such 

that the total rate of pumping is 1 Mgal/d for the first 5 years 
Streamflow Response to Groundwater Pumping 31

1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1,400,000

1,600,000

1,800,000

2,000,000

2,200,000

2,400,000

Surface-water-irrigated acres

Groundwater-irrigated acres

Yearly estimated acres

EXPLANATION

Year

Figure 23. Estimates of 

acres of cropland irrigated 

by groundwater and surface 

water, 1940 through 2005, 

Elkhorn and Loup River Basins, 

Nebraska (modified from 

Stanton and others, 2010).

Figure 24. Model-calculated 

cumulative reductions in 

stream base flow caused 

by groundwater pumping, 

Elkhorn and Loup River Basins, 

Nebraska, 1940 through 2005. 

Locations of streamflow points 

shown in figure 22 (modified 

from Peterson and others, 2008).

−50,000

50,000

0

150,000

100,000

250,000

200,000

350,000

300,000

450,000

400,000

550,000

500,000

650,000

600,000

750,000

700,000

1940 1950 1960 1970 1980 1990 2000 2010

Cumulative reduction in stream base flow, in acre-feet

Upper Elkhorn River

South Loup River

Loup River downstream

EXPLANATION

Year
32 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

0 5 10 15

0 5 10 15

Time, in years

0

1

2

3

1

0

2

3

3

2

1

0

4

5

Total pumping rate, in cubic feet per second 

0

1

2

3

4

5

Streamflow depletion rate, in cubic feet per second 

A

B

Well A pumping

Wells A and B

pumping

All wells pumping

EXPLANATION

Total depletion

Depletion for pumping at 

 well A only

Depletion for pumping at 

 well B only

Depletion for pumping at 

 well C only

Total pumping rate, in million gallons per day Streamflow depletion rate, in million gallons per day 

Figure 25. A, Total pumping rates. B, Streamflow-depletion rates for three wells pumping at a constant rate of 1 million gallons per 

day (1.55 cubic feet per second) for different lengths of time. Well A, located 300 feet from the stream, pumps for 15 years; well B, 

1,000 feet from the stream, pumps from years 6 through 15; well C, 3,000 feet from the stream, pumps from years 11 through 15. [Rates of 

streamflow depletion were calculated by using a computer program described in Reeves (2008).]

of development, 2 Mgal/d for the middle 5-year period, and 

3 Mgal/d for the last 5 years (fig. 25A).

Figure 25B shows streamflow depletion that occurs 

in response to pumping at each well individually, as well 

as the cumulative effects of pumping at all wells. The 

individual effects of pumping at each well are shown by 

the lower three curves in the figure, which indicate that 

streamflow depletion asymptotically approaches the pumping 

rate of each well, 1.55 ft3

/s (1.0 Mgal/d), regardless of the 

distance of the well from the stream. The cumulative effects 

of pumping at the wells, which are shown by the top curve 

on the graph, are additive—total depletion approaches a 

value of 1.55 ft3

/s for pumping at well A only, a value of 

3.10 ft3/s (2.0 Mgal/d) for pumping at wells A and B, and a 

value of 4.65 ft3/s (3.0 Mgal/d) for pumping at all three wells, 

although the time at which this depletion rate would be fully 

realized occurs several years after the 15-year time frame 

evaluated here.
Streamflow Response to Groundwater Pumping 33

Pumped Wells and Recharge Wells

The practice of artificial recharge of water into aquifers 

is becoming an increasingly important component of many 

water-resource management programs. Artificial recharge 

is used as an alternative to surface-water reservoirs to store 

excess surface water and as a means to augment streamflows. Methods for artificially recharging an aquifer include 

direct injection by wells and infiltration by gravity in basins 

or ponds at the land surface. When water is injected into an 

aquifer at a recharge well, groundwater levels near the well 

increase, and groundwater flows outward from the resulting area of mounded water. If the aquifer is bounded by a 

stream, the rate of groundwater discharge to the stream will 

increase, and the timing and rate of streamflow accretion 

will be equal, but opposite in sign, to the timing and rate of 

streamflow depletion caused by pumping at the same location and rate (as long as the system responds linearly to 

pumping, which is discussed in the section on “Superposition Models”). This scenario is illustrated by the first two 

Braided channel of the Platte 

River, Nebraska. 

Photograph by Michael Collier
34 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Pumping and streamflow depletion 

0 120 240 360 480 600 720

rates, in cubic feet per second 

A. Pumping only

0

Recharge and streamflow accretion 

0 120 240 360 480 600 720

rates, in cubic feet per second 

Time, in days

B. Recharge only

0.1

0.3

0.5

0.7

0 120 240 360 480 600 720

Pumping/recharge and streamflow depletion/

accretion rates, in cubic feet per day

Time, in days

C. Pumping followed by recharge

-0.1

-0.2

-0.3

-0.4

-0.5

-0.6

-0.7

-0.1

-0.3

-0.5

-0.7

EXPLANATION

Pumping or injection rate

Streamflow depletion or accretion

Figure 26. Injection of water into a recharge well increases streamflow, and the timing and rates of streamflow accretion are equal, 

but opposite in sign, to those of streamflow depletion caused by pumping. A, A well located 500 feet from a stream is pumped at a rate 

of 250 gallons per minute (0.56 cubic foot per second) for 720 days. B, The same well is recharged at a rate of 250 gallons per minute for 

720 days. C, The well is pumped for 120 days, followed by a 120-day period of recharge. [Rates of streamflow depletion and accretion 

were calculated by using a computer program described in Reeves (2008).]

graphs in figure 26, which contrast streamflow depletion 

caused by pumping at a well located 500 ft from a stream 

at a rate of 250 gallons per minute (gal/min; fig. 26A) with 

streamflow accretion caused by recharging the aquifer at the 

same well at a rate of 250 gal/min (fig. 26B). The shape of 

the streamflow-depletion and streamflow-accretion curves 

are mirror images of one another, and each curve tends 

asymptotically toward the pumping or recharge rate of the 

well (±0.56 ft3/s or ±250 gal/min). Because depletion has 

been represented as a positive quantity throughout this report, 

streamflow accretion is shown as a negative quantity in the 

figure, although it should be apparent that artificial recharge 

has a positive effect on streamflow. The results shown in the 

figure are based on the important assumption that the mound 

of groundwater that is formed by injection at the recharge 

well remains below land surface; should the mound reach land 

surface, surface-water runoff may occur, resulting in less water 

available for groundwater discharge to the stream.

Graph C in figure 26 illustrates the effects of a 120-day 

pumping period followed by a 120-day recharge period at 

the same well. As described in the previous section of the 

report for the case of multiple wells pumping from an aquifer, 

the combined effects of the pumping and recharge cycle on 

streamflow are additive. As a result, the period of streamflow 

depletion caused by pumping is followed by a period of 

streamflow accretion caused by recharge; ultimately, sometime 

after recharge ends, the effects of pumping and recharge at the 

well diminish to zero. 
Streamflow Response to Groundwater Pumping 35

Streamflow Depletion and Water Quality

One of the important concerns associated with 

streamflow depletion by wells is the effect of reduced 

groundwater discharge on the quality of affected surface 

waters. Groundwater discharge affects the chemistry of 

surface water and plays an important role in regulating 

stream temperature, which is a critical water-quality property 

in determining the overall health of an aquatic ecosystem 

(Baron and others, 2002; Hayashi and Rosenberry, 2002; 

Stonestrom and Constantz, 2003; Risley and others, 2010). 

Because groundwater-temperature fluctuations are 

relatively small compared to daily and seasonal streamflowtemperature fluctuations, groundwater discharge at a 

nearly constant temperature provides a stable-temperature 

environment for fish and other aquatic organisms. Average 

shallow groundwater temperature at a particular location is 

approximately equal to mean annual air temperature, and, 

as a result, groundwater discharge is typically warmer than 

the receiving streamflow during the winter and cooler than 

the receiving streamflow during the summer. Groundwater 

discharge provides cool-water environments that protect 

fish from excessively warm stream temperatures during 

the summer, and conversely, relatively warm groundwater 

discharge can protect against freezing of the water during 

the winter (Hayashi and Rosenberry, 2002). Stark and others 

(1994) and Risley and others (2010) provide examples of 

the effects of pumping on stream temperatures. The work of 

Risley and others (2010) illustrates how reductions in the rates 

of groundwater discharge to streams caused by pumping can 

warm stream temperatures during the summer and cool stream 

temperatures during the winter.

For many issues related to the quantity of streamflow 

depletion, such as water-rights administration and instreamflow needs to sustain aquatic habitats, the distinction between 

the two components of depletion—captured groundwater 

discharge and induced infiltration of streamflow—is generally 

not of interest. For water-quality concerns, however, the 

relative contribution of captured groundwater discharge 

and induced infiltration have important implications to the 

resulting quality of the streamflow, groundwater, and pumped 

water. Where groundwater pumping is large enough to cause 

induced infiltration of streamflow, the quality of the induced 

surface water will affect the quality of water in the underlying 

aquifer and possibly that of the pumped wells themselves. 

Infiltrated surface water that has been contaminated by 

chemical pollutants or biological constituents such as Giardia 

lamblia and Cryptosporidium, therefore, can be a source of 

contamination to a groundwater system, potentially having 

adverse effects to the health of people ingesting water 

from the contaminated groundwater supply. The amount of 

surface-water contamination entering a water-supply well 

will depend on several factors, including the natural ability 

of the streambank and aquifer materials to filter contaminants 

from the polluted water (Bourg and Bertin, 1993; Macler, 

1995). Natural “bank filtration” of surface-water contaminants 

as they move from a stream to a pumped well involves 

geochemical and biological processes that remove nutrients, 

organic carbon, and microbes from the contaminated water 

(National Research Council, 2008; Farnsworth and Hering, 

2011). Numerous field studies of the distribution, transport, 

and fate of chemical and biological constituents within 

contaminated and uncontaminated aquifers have been done 

to establish hydraulic connections between surface-water 

sources and pumped groundwater and to test the effectiveness 

of bank filtration and other natural processes for reducing 

contaminant concentrations. Examples of these types of 

studies are available for many areas of Europe and the United 

States (Farnsworth and Hering, 2011), including Ohio (Sheets 

and others, 2002), Missouri (Kelly, 2002; Kelly and Rydlund, 

2006), and Oregon (McCarthy and others, 1992).

Groundwater-temperature measurements can be an 

effective method to demonstrate the hydraulic connection 

that exists between groundwater and surface-water systems 

and to trace surface-water infiltration in groundwater systems 

(Stonestrom and Constantz, 2003; Anderson, 2005; Constantz, 

2008). An example of the use of temperature measurements 

to demonstrate a hydraulic connection between surface 

water and pumped wells is provided by the results of a 

study conducted in 1960–61 along the Mohawk River near 

Schenectady, New York (fig. 27), where the aquifer consists 

of highly permeable sand and gravel deposits. Groundwater 

pumped from two well fields near the river averaged about 

20 Mgal/d during the study period, with about 90 percent 

of the pumping occurring from the well field furthest from 

the river (Winslow, 1962). The temperature of the river on 

the measurement date (September 7, 1961) was 77 degrees 

Fahrenheit (°F), which was nearly 30 °F warmer than the 

average temperature of the groundwater in areas unaffected by 

induced infiltration. The warm river water, which was drawn 

into the aquifer by pumping at the production wells, became 

progressively cooler with distance from the river as it mixed 

with the cold groundwater. 
36 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

75 70 65

55

60

65

70

55

60

65

70

0

0 100 200 300 METERS

500 1,000 FEET

Groundwater-temperature

contour, in degrees Fahrenheit (°F) 

Pumped well

EXPLANATION

Aquifer

Rock

55

Rotterdam 

well field

Schenectady

well field

Mohawk River (77 °F)

Lock

Figure 27. Groundwater-temperature contours in the vicinity of two well fields near the Mohawk River, New York, on September 7, 

1961. Contours are based on measurements of groundwater temperature made at 60 observation wells. Temperature of the river on that 

date was 77 degrees Fahrenheit (modified from Winslow, 1962).

Some of the factors that affect the relative contributions 

of captured groundwater discharge and induced infiltration 

can be illustrated by one of the hypothetical stream-aquifer 

systems described previously and shown in figure 14. Several steady-state and transient simulations were done with 

the numerical model of the stream-aquifer system for pumping at a rate of 1.0 Mgal/d at wells located 100 ft, 300 ft, 

700 ft, and 1,400 ft from the stream. Steady-state conditions 

were simulated to illustrate the maximum effects of pumping on streamflow. The long-term average recharge rate to the 

aquifer of 26.0 inches per year (in/yr) also was varied in these 

simulations to include a 25-percent increase in the recharge 

rate (32.5 in/yr) and a 25-percent decrease in the recharge rate 

(19.5 in/yr). For each simulation, the resulting rates of total 

streamflow depletion, captured groundwater discharge, and 

induced infiltration were determined at the outflow point of 

the basin (that is, the most downstream location on the stream 

in figure 14). 

Results for the steady-state simulations are shown in 

figure 28. As shown by the uppermost curve in the figure, the 

total amount of streamflow depletion at the outflow point of 

the basin is the same for all of the simulations (and equal to 

the 1.0 Mgal/d pumping rate at each of the wells), regardless of either the distance of the well from the stream or the 

recharge rate to the aquifer. This results from the fact that at 

equilibrium, when aquifer storage is no longer a source of 

water to the wells, all of the water pumped by the wells must 

result in decreased streamflow, either by captured groundwater 

discharge or by induced infiltration. In contrast, the relative 

contributions of captured discharge and induced infiltration 

are a function of both the distance of the well from the stream 

and the recharge rate to the aquifer. As the well distance 
Streamflow Response to Groundwater Pumping 37

0

0.2

0.4

0.6

0.8

1.0

1.2

100 300 500 700 900 1,100 1,300

Flow rate, in million gallons per day

Well distance from stream, in feet

EXPLANATION

Orange: High recharge rate

Light blue: Moderate recharge rate

 Dark blue: Low recharge rate 

Total streamflow depletion for all recharge rates

Captured discharge

Induced infiltration

Figure 28. Rates of streamflow depletion, captured groundwater discharge, and induced infiltration at the outflow point of a basin for 

steady-state pumping conditions at wells located 100, 300, 700, and 1,400 feet from a stream. Each well is pumped independently of the 

others at a rate of 1.0 million gallons per day in 12 separate simulations. Three rates of recharge were simulated: a high recharge rate 

(32.5 inches per year), a moderate recharge rate (26.0 inches per year), and a low recharge rate (19.5 inches per year). Total streamflow 

depletion is equal to the sum of captured discharge and induced infiltration. As shown by the results along the top (pink) curve, at steady 

state, the total rate of streamflow depletion at the basin outflow point is equal to the pumping rate of each well and is independent of 

both the distance of each well from the stream and the recharge rate to the aquifer. Rates of captured groundwater discharge (middle 

three curves) and induced infiltration (bottom three curves), however, are a function of both well distance from the stream and recharge 

rate to the aquifer. (Results from numerical model shown in figure 14 of this report and documented in Barlow, 1997.)

from the stream increases, the proportion of induced infiltration decreases. Similarly, as the recharge rate to the aquifer 

increases, the proportion of induced infiltration also decreases. 

Note that at a well distance of 1,400 ft, the rate of induced 

infiltration for all recharge rates is essentially zero. These 

results illustrate that for some stream-aquifer systems, such as 

the extensive systems found in the Midwestern and Western 

United States in which pumping occurs miles from a stream, 

induced infiltration may not occur, and the water-quality concerns associated with streamflow depletion will be focused on 

the effects of reduced groundwater discharge on the thermal 

and water-quality conditions of the receiving streams. The 

results of additional simulations for transient-flow conditions 

were consistent with the steady-state simulations; specifically, the rate of recharge affects the relative contributions of 

captured discharge and induced infiltration but does not affect 

the total rate of streamflow depletion.

Other factors also affect the relative proportion of captured discharge and induced infiltration. These factors include 

the pumping rate of the well (with greater rates of induced 

infiltration occurring for higher pumping rates), the direction of groundwater flow in the aquifer prior to pumping, the 

distribution of aquifer boundaries near the well (including 

the presence of impermeable boundaries and other streams), 

the hydraulic properties of the aquifer and streambank materials, and the penetration depths of the pumped well and stream 

into the aquifer (Newsom and Wilson, 1988; Morrissey, 1989; 

Wilson, 1993; Conrad and Beljin, 1996; Chen, 2001; Chen and 

Yin, 2001; Chen and Shu, 2002; Chen and Chen, 2003; Chen 

and Yin, 2004; Gannett and Lite, 2004). 
38 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

70

60

0

0 300 METERS

1,000 FEET

60

70

Stream

60

EXPLANATION

Particle pathline

Simulated altitude of

 water table, in feet

Model cell in which

 pumped well is located

60

Zone of 

induced 

throughflow

Figure 29. Pumping at the well located 300 feet from the stream at a rate of 1.0 million gallons per day 

causes induced infiltration of streamflow. More than 80 percent of the induced streamflow is captured 

by the well, but some of the induced streamflow returns to the stream through a zone of “induced 

throughflow” (Newsom and Wilson, 1988; model results from Barlow, 1997).

Several of these factors also affect the proportion of 

induced infiltration that actually flows to and is discharged 

by a well. Figure 29 shows the flow paths of water particles 

that have been drawn into the aquifer by pumping at the well 

300 ft from the stream at the steady-state rate of 1.0 Mgal/d 

(for the average recharge rate of 26.0 in/yr). As shown by the 

flow paths, some of the water that has been drawn into the 

aquifer actually returns to the stream downgradient from the 

well and does not reach the well. Newsom and Wilson (1988) 

refer to the area in which induced infiltration flows back to 

the stream as the “zone of induced throughflow.” The figure 

illustrates that the rate of stream infiltration is not the same 

as the rate of infiltrated streamflow that is actually pumped 

at the well. The ability to quantify the relative contributions 

of captured discharge and induced infiltration to the source 

of water pumped by a well, or the concentrations of chemical constituents in the well or adjoining aquifer, requires 

analysis techniques that are more advanced than those used 

to quantify streamflow-depletion rates only. These techniques 

include computer programs that track water particles through 

a simulated aquifer, such as illustrated by the flow paths 

shown in figure 29 that were calculated by use of MODPATH (Pollock, 1994), or solute-transport codes that simulate 

movement of chemical constituents within a groundwaterflow system (for example, the computer programs documented 

by Konikow and others, 1996, or Zheng and Wang, 1999).
Common Misconceptions about Streamflow Depletion 39

Common Misconceptions about 

Streamflow Depletion

An understanding of the basic concepts of streamflow 

depletion is needed to properly assess the effects of groundwater withdrawals on connected surface water and areas of 

evapotranspiration. Important concepts relating to depletion 

are available throughout this report and also in other literature, 

beginning with the paper, “The Source of Water Derived from 

Wells,” by Theis (1940). In spite of these sources of information, misconceptions regarding factors controlling depletion 

are sometimes evident in analyses of depletion. This discussion highlights the following common misconceptions related 

to streamflow depletion.

Misconception 1. Total development of groundwater 

resources from an aquifer system is 

“safe” or “sustainable” at rates up to the 

average rate of recharge.

Misconception 2. Depletion is dependent on the rate and 

direction of water movement in the 

aquifer.

Misconception 3. Depletion stops when pumping ceases.

Misconception 4. Pumping groundwater exclusively below 

a confining layer will eliminate the 

possibility of depletion of surface water 

connected to the overlying groundwater 

system.

Although most of the concepts needed to clear up these misconceptions are presented in other sections, further discussion 

and examples are given here. 

Aquifer Recharge and Development of Water 

Resources

There has been a tendency in parts of the United States to 

view groundwater development in an aquifer to be “sustainable” or “safe” when the overall rate of groundwater extraction 

does not exceed the long-term average rate of recharge to the 

aquifer. Conversely, development is considered to be unsustainable or unsafe when groundwater extraction rates exceed 

the average recharge rate. The rationale behind this concept is 

that long-term extraction beyond the average recharge rate will 

result in ongoing net depletions in storage that will eventually 

deplete the aquifer to the extent that continued pumping is no 

longer feasible. These views of sustainability, however, do not 

directly recognize the effects of withdrawals on outflow from 

an aquifer, which often occur through groundwater discharge 

to surface-water features and through evapotranspiration.

In the paper “Groundwater—The Water-Budget Myth,” 

Bredehoeft and others (1982) explained that in an undeveloped 

aquifer, long-term average natural recharge is balanced by 

long-term average natural discharge. They show that if water 

is pumped from the aquifer at a given rate, that rate will be 

offset by the sum of an increase in the rate of recharge to the 

aquifer, decrease in the rate of discharge from the aquifer, 

and increase in the rate of removal of water from storage 

in the aquifer. With time, the rate of removal of water from 

storage change diminishes and the pumping rate is balanced 

by the sum of pumping-induced increased recharge and 

decreased discharge.

Most recharge to aquifers occurs through percolation of 

a portion of precipitation from the land surface, through an 

unsaturated zone, to the water table. In more humid areas, this 

recharge can be widely distributed over the surface area of an 

aquifer, and in more arid areas, this recharge can be focused 

in locations such as beneath arroyos where infrequent runoff 

events cause a movement of water through the unsaturated 

zone. In either case, however, the process of natural recharge 

through the unsaturated zone is unaffected by a pumped well. 

On the contrary, one situation in which pumping can increase 

recharge occurs in areas in which the water table is at the 

land surface (fig. 30A). Drawdown from pumping can result 

in infiltration and recharge that would have otherwise run off 

because of a lack of available space for storage beneath the 

land surface (fig. 30B). Another situation in which pumping 

can increase recharge is when recharge occurs from direct 

movement of water from surface-water bodies to the aquifer, 

such as for a naturally losing stream; this type of increased 

recharge is a form of induced infiltration.

Discharge from aquifers, on the other hand, commonly 

occurs through direct movement of groundwater into surfacewater bodies and through evaporation and transpiration by 

plants that use groundwater. Groundwater pumping reduces 

the movement of water into surface-water features by decreasing the natural hydraulic gradients to these features. Pumping 

furthermore reduces evaporation and transpiration by lowering 

the water table below the land surface and roots of plants that 

use groundwater.

In spite of several possible cases in which pumping can 

increase recharge to an aquifer, most recharge is unaffected 

by pumping. Therefore, increases in recharge from pumping 

often can be considered to be small or zero. In this case, the 

pumping rate eventually will be approximately balanced by 

decreases in discharge. For this reason, Bredehoeft and others 

(1982) concluded that the magnitude of sustained groundwater 

pumping generally depends only on how much of the natural 

discharge can be captured. Although there may be physical limits to the amount of water that can be captured, lower 

limits to capture may exist for other reasons. For example, 

certain levels of instream flow may be required to sustain 

aquatic ecosystems, and capture or depletion of surface water 

that diminishes flow below those limits may not be permitted under some regulatory systems. Similarly, depletion that 

reduces the availability of surface-water flow for holders of 

surface-water rights may not be permitted in some areas. For 

further discussions of sustainability of groundwater resources, 

see Alley and others (1999), Alley and Leake (2004), and 

Gleeson and others (2012).
40 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

A B

Runoff

Well

Runoff

Runoff

Recharge

Runoff

Aquifer Aquifer

Figure 30. One way in which groundwater pumping can increase recharge to an aquifer. A, If the water table is at land surface, 

surface runoff cannot infiltrate because of a lack of available subsurface storage space. B, The addition of a pumped well that lowers 

the water table allows runoff to infiltrate and recharge the aquifer.

Depletion and the Rates and Directions of 

Groundwater Flow

A common misunderstanding regarding streamflow 

depletion is that the rates, locations, and timing of depletion 

are dependent on the pre-pumping rates and directions of 

groundwater flow in an aquifer. As indicated previously, 

depletion is the sum of pumping-induced increased inflow to 

the aquifer and decreased outflow from the aquifer. Provided 

that sufficient surface water is available to meet the pumping 

demand, a new steady-state condition will eventually be 

reached in which the rate of storage change is zero and the 

entire pumping rate can be accounted for as increased recharge 

and decreased discharge. It is important to understand that 

depletion is independent of the natural, pre-pumping rates of 

recharge and discharge. The concept that the rate of recharge 

does not affect the rate of depletion was demonstrated 

previously (fig. 28), where it was also noted that the recharge 

rate does affect the individual components of depletion—

captured groundwater discharge and induced infiltration. 

Maddock and Vionnet (1998) extended these concepts to show 

that even with seasonally varying recharge and discharge, 

temporal patterns of recharge and discharge do not enter into 

calculations of depletion. 

Timing and locations of depletion are affected, however, 

by aquifer properties and system geometry. In a system with 

predominantly horizontal flow, the progression from a storagedominated to a depletion-dominated supply of pumped water 

is controlled by hydraulic diffusivity (Box A) and distance 

between pumping locations and connected surface-water and 

groundwater-evapotranspiration areas or other groundwaterdischarge areas. In settings in which vertical components of 

groundwater flow are important, distributions of vertical and 

horizontal hydraulic conductivity, specific storage, specific 

yield, and aquifer thickness, in addition to well distance from 

the stream, are the key properties that control the timing 

of depletion.

As long as aquifer transmissivity and storage properties 

are the same in each case, total depletion (in contrast to the 

individual components of captured discharge and induced 

infiltration) at any given time would be the same for cases 

with natural pre-pumping flow from the stream to the aquifer 

(fig. 31A), from the aquifer to the stream (fig. 31B), or 

with no flow between the aquifer and the stream (fig. 31C). 

Furthermore, relative amounts of depletion in multiple streams 

are the same regardless of the existence of a divide between 

the streams (fig. 31D), natural flow from one stream to another 

(fig. 31E), or with no flow between the streams (fig. 31F).

The independence of depletion and rates and directions 

of groundwater flow in most systems allows calculation of 

depletion by a number of different methods. These methods 

include analytical solutions, superposition models, and 

groundwater-flow models (see “Analytical and Numerical 

Modeling” section). In using either analytical solutions or 

superposition models, the natural rates and directions of 

groundwater flow are ignored.
Common Misconceptions about Streamflow Depletion 41

A B C

D E F Well Well

Well

Well

Groundwaterdivide

WellWell

Stream 1Stream 2Stream 1Stream 2Stream 1Stream 2

StreamStreamStream

Aquifer

Aquifer

Aquifer

Aquifer

Aquifer

Aquifer

Direction of groundwater flow

 before pumping

EXPLANATION

Figure 31. Position of a pumped well in relation to a stream or streams for configurations of various pre-pumping groundwaterflow patterns. As long as aquifer properties are the same in each case, depletion of the steam by the pumping well would be the 

same with, A, pre-pumping flow away from the stream; B, pre-pumping flow toward the stream; or, C, no pre-pumping flow. Similarly, 

relative amounts of depletion in adjacent streams are unaffected by a groundwater divide with, D, pre-pumping flow toward each 

stream; E, pre-pumping flow from one stream to the other; or, F, no flow between streams. 
42 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Depletion after Pumping Stops

When a well begins to pump, water is removed from 

storage around the well, creating a cone of depression. As 

discussed previously, the cone of depression expands and can 

increase recharge to and discharge from the aquifer. If a well 

pumps groundwater for a period of time and then pumping 

ceases, groundwater levels will begin to recover and the cone 

of depression created by the pumping will gradually fill, with 

water levels eventually reaching positions that existed before 

pumping started (fig. 32). During the time that the cone of 

depression is filling, groundwater that otherwise would have 

flowed to streams instead goes into aquifer storage; thus, 

streamflow depletion is ongoing, even though pumping has 

ceased. The factors that control the rate of recovery are the 

same as those that affect the rate of groundwater-level declines 

in response to pumping—the geology, dimensions, and 

hydraulic properties of the groundwater system; the locations 

EXPLANATION

Volume of cone of depression

 refilled since pumping 

 stopped

Land surface

Water table

Unconfined aquifer

Confining unit

Land surface

Water table

Unconfined aquifer

Confining unit

Stream

Land surface

Water table

Unconfined aquifer

Confining unit

A

C

B

Q

Figure 32. Residual effects of streamflow depletion after pumping stops. A, Prior to the well being shut down, the pumping rate at the 

well is balanced by decreases in aquifer storage and by streamflow depletion, which consists of captured groundwater discharge and 

induced infiltration of streamflow. B, After pumping stops, groundwater levels begin to recover, and water flows into aquifer storage to 

refill the cone of depression created by the previous pumping stress. C, Eventually, the system may return to its pre-pumping condition 

with no additional changes in aquifer storage or streamflow depletion. [Q, pumping rate at well]
Common Misconceptions about Streamflow Depletion 43

and hydrologic conditions along the boundaries of the 

groundwater system, including the streams; and the horizontal 

and vertical distance of the well from the stream.

Some key points relating to depletion from a well or 

wells that pump and then stop pumping are as follows:

1. Maximum depletion can occur after pumping stops, 

particularly for aquifers with low diffusivity or for large 

distances between pumping locations and the stream.

2. Over the time interval from when pumping starts until the 

water table recovers to original pre-pumping levels, the 

volume of depletion will equal the volume pumped.

3. Higher aquifer diffusivity and smaller distances between 

the pumping location and the stream increase the 

maximum rate of depletion that occurs through time, 

but decrease the time interval until water levels are fully 

recovered after pumping stops.

4. Lower aquifer diffusivity and larger distances between the 

pumping location and the stream decrease the maximum 

rate of depletion that occurs through time, but increase the 

time interval until water levels are fully recovered after 

pumping stops.

5. Low-permeability streambed sediments, such as those 

illustrated in figure 11, can extend the period of time 

during which depletion occurs after pumping stops.

6. In many cases, the time from cessation of pumping until 

full recovery can be longer than the time that the well 

was pumped.

Most of these concepts are illustrated by a hypothetical 

example of pumping in a desert basin with a through-flowing 

river (fig. 33). The basin is 20 mi wide and 40 mi long with 

a well-connected river entering the basin at the northeast 

corner, running along the east side of the basin, and exiting 

at the southeast corner of the basin. Mountain-front recharge 

of 500 acre-ft/yr is uniformly distributed along the western 

boundary of the basin. Hydraulic conductivity is 50 ft/d and 

aquifer thickness is about 500 ft, resulting in a transmissivity of about 25,000 ft2

/d. Specific yield is 0.2. The effects 

of pumping at two possible well locations are shown in 

figure 34—well 1 is 5 mi from the river, and well 2 is 10 mi 

from the river. Pumping at either well is at a rate of 600 acreft/yr for a period of 50 years, after which pumping ceases. The 

purpose of this analysis is to better understand the effects of 

pumping at these locations individually, not simultaneously.

Depletion was calculated by using a groundwaterflow model. The U.S. Geological Survey (USGS) computer 

program MODFLOW–2005 (Harbaugh, 2005) was used with 

a single layer with 40 rows and 40 columns of finite-difference 

cells. Cell dimensions in the east-west direction are 2,640 ft 

and in the north-south direction are 5,280 ft. A steady-state 

solution was run prior to simulating pumping. In that solution, the gradient of the river resulted in inflow to the aquifer 

at a rate of 1,795 acre-ft/yr from the upper part of the river. 

River

River stage

= 101.8 feet

River stage

= 85 feet

Aquifer properties

Hydraulic conductivity — 50 feet per day

Aquifer thickness — ~500 feet

Transmissivity — ~25,000 feet squared per day

Specific yield — 0.2

Natural inflow from river

= 1,795 acre-feet per year

Natural outflow to river

= 2,295 acre-feet per year

Well 1

0 5 10 MILES

0 5 10 KILOMETERS

Well 2

5 miles

10 miles

Natural mountain-front recharge, totaling 500 acre-feet per year

N

Figure 33. Hypothetical desert-basin aquifer with a throughflowing river along the east side of the basin. In separate 

analyses, water is pumped at locations of well 1 and well 2 at a 

rate of 600 acre-feet per year for 50 years.

That inflow, plus 500 acre-ft/yr of mountain-front recharge 

resulted in 2,295 acre-ft/yr of outflow from the aquifer to the 

lower part of the river. With this flow pattern, pumping at 

either location will increase the inflow from the river to the 

aquifer and decrease the outflow from the aquifer to the river. 

Pumping cannot, however, increase the specified amount of 

mountain-front recharge. For cases of pumping at each well 

location, 50 years of pumping was followed by 100 years 

of recovery.

Results for pumping at the location of well 1 are shown 

in the upper three graphs in figure 34. Pumping causes inflow 

from the river to increase from 1,795 acre-ft/yr to a maximum 

of 2,009 acre-ft/yr at a time of 50 years. In the 100 years 

that follow, inflow from the river gradually decreases to 
44 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Pumping stops

Pumping stops

A–1

A–2

A–3

B–1

B–2

B–3

0

0 10 20 30 40 50 60

Time, in years since start of pumping

Inflow from river with well 1 pumping

Outflow to river with well 1 pumping

Increased inflow

from river

Decreased outflow

to river

Increased

inflow from river

Decreased

outflow to river

Increased inflow

from river

Decreased

outflow to river

Increased inflow

from river

Decreased outflow

to river

Total depletion with well 1 pumping

Inflow from river with well 2 pumping

Outflow to river with well 2 pumping

Total depletion with well 2 pumping

Flow rate or total depletion rate, in acre-feet per year Flow rate or total depletion rate, in acre-feet per year

70 80 90 100 110 120 130 140 150

40

80

120

160

200

240

280

0

50

100

150

200

250

300

350

400

450

2,100

2,140

2,180

2,220

2,260

2,300

1,780

1,820

1,860

1,900

1,940

1,980

2,050

2,100

2,150

2,200

2,250

2,300

1,800

1,850

1,900

1,950

2,000

2,050

Figure 34. Inflow from the river, outflow to the river, and total depletion rate with well 1 pumping (upper three graphs) and with well 2 

pumping (lower three graphs). Well locations in relation to the river are shown in figure 33.
Common Misconceptions about Streamflow Depletion 45

1,813 acre-ft/yr. Additional time would be required to a 

full recovery of an inflow value of 1,795 acre-ft/yr. Similarly, pumping causes outflow to the river to decline from 

2,295 acre-ft/yr to 2,090 acre-ft/yr at a time of 50 years. In the 

100 years that follow with no pumping, outflow increases to 

2,270 acre-ft/yr. For any given time, the sum of the increase 

in inflow from the river and decrease in outflow to the river is 

the total depletion from pumping. That value begins at zero, 

reaches a maximum of 419 acre-ft/yr at 50 years, and diminishes to 43 acre-ft/yr at 150 years.

Results for pumping at the location of well 2 are shown 

in the lower three graphs in figure 34. Pumping causes inflow 

from the river to increase from 1,795 acre-ft/yr to a maximum 

of 1,908 acre-ft/yr at a time of 54 years (4 years after pumping stops). In the 96 years that follow, inflow from the river 

gradually decreases to 1,828 acre-ft/yr. Similarly, pumping 

causes outflow to the river to decline from 2,295 acre-ft/yr 

to 2,131 acre-ft/yr at a time of 53 years. In the 97 years that 

follow with no pumping, outflow increases to 2,250 acre-ft/

yr. Total depletion increases from zero to a maximum of 

278 acre-ft/yr at 53 years and diminishes to 78 acre-ft/yr at 

150 years.

In pumping at either location, 30,000 acre-ft of water 

is pumped over the 50-year period of pumping (fig. 35). 

For pumping at the location of well 1, total depletion in 

the 50-year period of pumping was 15,412 acre-ft, which 

means that nearly half of the total volume of depletion 

(30,000 acre-ft) will occur after pumping stops. In contrast, 

the total volume depleted in 50 years from pumping at the 

location of well 2 is 7,390 acre-ft, which means that about 

three-fourths of the total volume of depletion will occur after 

pumping stops. For pumping at either location, ultimate depletion of 30,000 acre-ft has not occurred in the 150-year period 

shown (fig. 35), but the trend in the depletion-volume curves 

is toward that ultimate value.

Most of the six key points listed previously are illustrated by this example. For pumping at the location of well 2, 

the maximum depletion rate occurred 3 years after pumping stopped. The time interval between the end of pumping 

and the time of maximum depletion rate will increase with 

increasing distance between pumping location and connected 

surface-water features. In the case of the C-aquifer analysis 

presented previously in the report (figs. 17–19), pumped wells 

were more than 20 mi from connected surface-water features. 

Maximum depletion in that analysis was computed to occur 

about 44 years after pumping stopped (fig. 19; Leake and others, 2005). In addition, the example in this section shows that 

pumping at either location can both increase inflow from the 

river and decrease outflow to the river. The sum of these two 

components is depletion, which represents the total reduction 

in surface-water flow at any given time.

0

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

5,000

10,000

15,000

20,000

25,000

35,000

30,000

Cumulative volume, in acre-feet

Time, in years since start of pumping

Depletion volume for 

pumping at well 1

Depletion volume for pumping at well 2

Volume pumped

Pumping stops

Figure 35. Cumulative volume pumped and cumulative volume of streamflow depletion for pumping at wells 1 and 2. Well locations in 

relation to the river are shown in figure 33. 
46 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Effects of Confining Layers on Depletion

Various geologic features that act as conduits or barriers 

to groundwater flow can affect the timing of depletion from 

groundwater pumping and also can affect which streams are 

affected by the pumping. Confining layers within or adjacent 

to aquifers are the most common type of geologic feature 

that potentially affect timing and locations of depletion. 

Here the term “confining layers” is used to refer to horizontal 

or nearly horizontal beds of clay, silt, or other geologic strata 

that have substantially lower hydraulic conductivity than 

adjacent aquifer material. In unconsolidated sediments that 

typically are a part of stream-aquifer systems, aquifer material 

generally consists of sand and gravel, and confining material 

generally consists of silt and clay. Confining layers may be 

laterally discontinuous or they may form laterally extensive 

barriers that separate adjacent aquifers. Drawdown from 

a pumped well propagates more rapidly in coarse-grained 

aquifer material than in confining layers, and in most cases 

confining layers between pumping locations and streams 

slow down the progression of depletion in comparison to 

equivalent aquifer systems without confining layers. It is 

not reasonable, however, to expect that pumping beneath an 

extensive confining layer will eliminate depletion. Water does 

move vertically from one aquifer to another through confining 

layers, and drawdown from pumping can propagate through 

confining layers as well. Also, the effective storage coefficient 

in confined aquifers (beneath confining layers) commonly 

Groundwater from aquifers 

beneath the Colorado Plateau 

is shown discharging at Fossil 

Springs in north-central 

Arizona. 

Photograph by Stanley Leake, U.S. Geological Survey
Common Misconceptions about Streamflow Depletion 47

is 2–4 orders of magnitude less than in shallow unconfined 

aquifers with storage properties dominated by specific yield. 

Smaller storage coefficients result in faster lateral propagation 

of drawdown from pumping locations to distant edges of 

confining layers or locations where drawdown can more easily 

propagate upward. The argument that pumping beneath a 

confining layer eliminates the possibility of depletion implies 

that the pumped aquifer is without any vertical or lateral 

connection to aquifer material that is connected to surface 

water. The existence of gradients of water levels in confined 

aquifers, however, is evidence that the aquifers receive water 

from and discharge water to vertically adjacent aquifers. 

Drawdown from pumping also can propagate to these adjacent 

aquifers. The timing of depletion in systems with extensive 

confining layers is best understood using numerical models of 

groundwater flow.

 Discontinuous confining layers between pumping 

locations and connected streams can either slow down or 

speed up the progression of depletion, depending on the 

configurations of the confining layers in relation to connected 

streams and pumping locations. These effects are illustrated 

using a finite-difference model of the hypothetical basinfill aquifer shown in figure 36. The aquifer is 30 mi wide, 

45 mi long, and 600 ft thick. A river connected to the upper 

part of the aquifer is present along the center of the basin. 

Horizontal and vertical hydraulic conductivity, specific yield, 

and specific storage for coarse sediments and confining clay 

layers (fig. 36D) are within ranges of values for these types of 

sediments in real aquifer systems. The larger storage property, 

specific yield, applies only at the upper boundary of the 

system where lowering of the water table causes pore spaces 

to drain. In the aquifer below the water table, a much smaller 

storage property consisting of the product of specific storage 

and aquifer thickness accounts for storage changes from 

compressibility of water and the matrix of solids that makes up 

the aquifer. Three cases with different configurations of clay 

layers in the aquifer are shown in figure 36B. In Cases 2 and 3, 

clay layers are 5 percent of the total aquifer thickness and are 

near the vertical center of the aquifer.

Horizontal dimensions of finite-difference cells were 

1,575 ft in each direction, resulting in 101 columns and 

151 rows to simulate the basin width and length, respectively. 

Twenty layers, each with a thickness of 30 ft, were used to 

simulate the entire aquifer thickness. Depletion fractions 

from pumping at four locations in section A–A' at a rate of 

1,000 ft3/d for 25 years were computed using the superposition modeling approach with MODFLOW–2005 

(Harbaugh, 2005).

Comparison of depletion curves for the three cases and 

four pumping locations (fig. 37) yields some insights into the 

range of effects of clay layers on depletion. The first result 

to note is that even with no clay layer present, depletion 

from pumping at depth in some locations progresses faster 

than depletion from pumping near the top of the aquifer. 

For example, with no clay layer, depletion progresses slightly 

faster from pumping at depth (fig. 37B) than from pumping 

nearer to the water table (fig. 37A). This difference occurs 

because vertical hydraulic conductivity is much lower than the 

horizontal hydraulic conductivity. Drawdown from pumping 

at depth can propagate more easily laterally toward the river 

location than to the overlying water table where the specific 

yield value can result in large storage-change values that slow 

the propagation of the cone of depression. 

The existence of a clay layer under the river (Case 2) 

greatly slows depletion for the deep pumping location nearer 

to the river (fig. 37D). The clay layer restricts direct 

propagation of drawdown upwards to the river. Drawdown 

must propagate laterally around the edge of the clay layer and 

then back to the river. This case is similar to the situation in 

the Upper San Pedro Basin in Arizona, where a silt and clay 

layer underlies the stream at most locations (fig. 13).

 The existence of clay layers along the margins of the 

valley (Case 3) substantially speeds up the depletion for the 

pumping location beneath that layer (fig. 37B). The clay 

layer speeds up depletion from underlying pumping because 

it creates a confined aquifer zone that restricts propagation 

of drawdown to the water table and, with a small storage 

coefficient, allows relatively rapid propagation of drawdown 

to the edge of the clay layer. 

In summary, confining layers and other geologic features 

are complexities that can affect the timing of depletion from 

groundwater pumping. If features have a lower hydraulic 

conductivity than that of aquifer material, the feature can 

slow down the progress of depletion through time. In some 

cases, such as is shown in figure 37B, the feature may speed 

up the progress of depletion. For systems with multiple 

aquifers separated by confining layers, or for aquifers with 

discontinuous confining layers and other heterogeneities, 

numerical flow modeling approaches are needed to better 

understand the timing of depletion.
48 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

3 × 101

3 × 10–3

3 × 10–1

3 × 10–5

6 × 10–7

6 × 10–7

2 × 10–1

2 × 10–1

A

A’ 45 miles

River

30 miles

600 feet

Coarse sediments

No clay layers are present

Coarse sediments

Clay layers

Horizontal hydraulic

conductivity, in feet

per day

Vertical hydraulic

conductivity, in feet

per day

Specific storage,

in per foot

Specific yield,

dimensionless

A clay layer is present over one-third of

the basin width, underlying the river

Clay layers are present along the margins

of the basin, but not under the river

Case 1

D. Aquifer properties

C. Geometry of section A–A’

B. Configurations of clay layers for Cases 1, 2, and 3

A. Model dimensions and location of section A–A’

Case 2 Case 3

Clay layers

A C

B D

Extent of clay in Case 3 Extent of clay in Case 2

A A’

River

Pumping location

0

0 5 10 15

300

600

Feet above reference datum

Distance, in miles

Vertical section

shown in part C

EXPLANATION

Figure 36. A, Hypothetical basin-fill aquifer used to illustrate possible effects of discontinuous clay layers on timing of depletion 

in the river as a function of vertical and horizontal locations of pumping. B, Configurations of clay layers are shown for three cases. 

C, Depletion in vertical section A–A’ is shown in figure 37 for pumping locations A, B, C, and D. D, Aquifer properties are within the range 

of values typical of basin-fill aquifers, with a horizontal-to-vertical hydraulic conductivity ratio of 100:1. Clay layers in Cases 2 and 3 

increase restrictions to vertical flow in parts of the aquifer.
Common Misconceptions about Streamflow Depletion 49

Case 1, no clay layer

A. Pumping location A C. Pumping location C

B. Pumping location B D. Pumping location D

Case 2, clay layer beneath river

Case 3, clay layers along margins of valley

0

0

0.2

0.4

0.6

0.8

1.0

0

0.2

0.4

0.6

0.8

1.0

10 20 30

Time, in years since start of pumping

Streamflow depletion, as fraction of pumping rate

40 50 0 10 20 30 40 50

EXPLANATION

Figure 37. Computed depletion at pumping locations A, B, C, and D in vertical section A–A’ shown in figure 36C. For A, shallow distant 

pumping location A, either configuration of clay layers slows depletion in comparison to case 1. For B, deep distant pumping location B, 

pumping below the clay layer at the valley margins (Case 3) produces substantially more rapid depletion than in the case with no clay 

layers. For C, shallow close pumping location C, configurations of clay layers change depletion from the case of no clay layer by a minor 

amount. For D, deep close pumping location D, the clay layer beneath the river (Case 2) substantially slows the process of depletion.
50 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Approaches for Monitoring, 

Understanding, and Managing 

Streamflow Depletion by Wells

This section describes approaches for determining the 

effects of pumping on streamflow. These approaches fall into 

two broad categories: collection and analysis of field data and 

analytical and numerical modeling. Additionally, this section 

describes approaches that are used for managing streamflow depletion, which build on both an understanding of the 

underlying processes that affect the response of streamflow to 

pumping as well as the application of techniques for modeling 

these processes.

Field Techniques

Quantification of streamflow depletion using fieldmeasurement techniques first requires that changes in flow 

between the stream and aquifer can be measured or estimated. 

The measurement technique must have the capability to 

resolve changes in streamflow that occur over a stream reach 

that may be affected by a well or wells. Such changes can 

most likely be detected when groundwater pumping is a 

substantial fraction of the available streamflow and when 

enough time has elapsed since pumping began for depletion 

to occur. A second requirement is that there must be a way 

to separate pumping-induced changes in streamflow from 

changes in flow caused by other stresses such as climatedriven variations in recharge and stream stage. Changes in 

groundwater/surface-water interactions not related to pumping 

can be as large as or larger than pumping-induced changes. 

Separating pumping-driven effects from other effects in field 

data may require comprehensive analysis of the coupled 

groundwater/surface-water system. 

Field techniques for determination of streamflow 

depletion can be grouped into the following general 

approaches, which are described in greater detail by 

Stonestrom and Constantz (2003), Rosenberry and LaBaugh 

(2008), and Constantz (2008): 

1. Direct measurement of streamflow,

2. Point measurements of flow across the streambed, or

3. Measurement of other types of data that indicate the 

direction or quantity of flow between a stream and 

adjoining aquifer. 

The second approach includes seepage meters placed at 

specific points in the stream channel (Rosenberry and 

LaBaugh, 2008). Many of the additional data types in the 

third approach also focus on specific point measurements in a 

stream channel but also include methods that monitor larger 

areas of a stream reach. These approaches employ water levels 

measured at observation wells or streambed piezometers, 

measurements of temperature in the stream and streambed, 

analysis of geochemical constituents or tracers, and geophysical studies of the stream-aquifer system. Field methods that 

detect changes in flow between an aquifer and a stream over 

a long reach are more likely to be successful in detecting 

depletion from pumping than methods that focus on specific 

locations along a stream channel. For that reason, this discussion will be limited to direct measurement of streamflow to 

detect depletion. 

Direct measurements of streamflow are used to determine 

streamflow changes that occur either at a particular stream 

location over time or at a particular time at two or more locations along a stream. Repeated streamflow measurements at a 

single site such as a streamgaging station can detect changes 

in flow over time that are driven by all processes, including 

depletion by groundwater pumping. Streamflow measurements 

made simultaneously at two or more sites along a stream are 

known as “seepage runs” and are indicative of streamflow 

gains or losses in the reaches between measurement locations. Detection of depletion using seepage runs requires that 

two or more measurements be made during a period in which 

substantial streamflow depletion may occur. 

The identification of streamflow depletion from streamflow measurements is complicated by a number of factors. 

First, the rate of depletion must be large enough to be detected 

by the streamgaging instrumentation, and significantly 

greater than the accuracy of the streamflow measurement. 

Each streamflow measurement made by USGS personnel, for 

example, is given a rating of “excellent,” “good,” “fair,” or 

“poor,” depending on the hydrologic and hydraulic conditions 

in which the measurement was made (Turnipseed and Sauer, 

2010). As defined by the USGS, an “excellent” rating is one in 

which the accuracy of the measurement is judged to be ±2 percent of the measured flow, a “good” rating is one with an accuracy of ±5 percent, a “fair” rating ±8 percent, and a “poor” 

rating greater than ±8 percent. As an example of the effects 

of streamflow-measurement accuracy, a streamflow-depletion 

rate of 1.6 ft3/s (1.0 Mgal/d) could not be accurately detected 

using the USGS rating system for a stream with a measured 

flow of 100 ft3/s, even if the streamflow measurement had 

been rated as “excellent.” This is because the depletion rate of 

1.6 ft3/s is less than the 2.0 ft3/s accuracy of the measurement. 

A related complicating factor is the effect that the aquifer 

has on delaying the time of arrival and on damping the range 

of streamflow-depletion rates caused by pumping at a well. 

Many of the examples provided in previous sections of this 

report, such as that for the Upper San Pedro Basin of Arizona 

(fig. 13), have demonstrated that it may take several years, if 

not decades, for a pumping stress to be manifested in a stream. 

The propensity of the aquifer to delay and damp a particular 

pumping stress can make it extremely challenging, if not 

impossible, to monitor streamflow depletion in some field settings or to differentiate streamflow depletion caused by pumping at a particular well or well field from depletion caused by 

other short-term or long-term stresses to the aquifer (Zlotnik, 

2004; Bredehoeft, 2011b).
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 51

Left, streamgage on the Snake 

River, near Moran, Wyoming. 

(Photograph from U.S. 

Geological Survey files) 

Above, seepage meters and in-stream piezometers deployed in 

the Shingobee River, Minnesota, to understand directions and 

rates of water movement between the stream and the underlying 

groundwater system. (Photograph by Donald O. Rosenberry, U.S. 

Geological Survey) 

Streamflow measurement on Fish Creek, Teton County, Wyoming. 

(Photograph by Jerrod D. Wheeler, U.S. Geological Survey)
52 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

COLORADO

OKLAHOMA

KANSAS

OKLAHOMA

TEXAS

TEXAS

High Plains Aquifer

Beaver−North Canadian

River Basin study area

Beaver Rive r

OKLAHOMA

NEW MEXICO

North Canadian River

37°

104°

35°

104°

37°

98°

35°

98°

0

0

50

50

100 MILES

100 KILOMETERS

Guymon

Oklahoma

City

EXPLANATION

Well 363033101440701

Beaver River near Guymon, Oklahoma,

 streamgage location

Beaver–North Canadian River Basin 

 study area

In light of these challenges, techniques for monitoring 

streamflow depletion have been limited to two general 

approaches. In the first, short-term field tests lasting several 

hours to several months are done to determine local-scale 

effects of pumping from a specific well or well field on 

streams that are in relatively close proximity to the location 

of withdrawal. In the second, evaluations are made of 

hydrologic and climatic data collected over a period of many 

years to determine whether changing streamflow conditions 

can be correlated to long-term, basinwide development 

of groundwater resources (Wahl and Tortorelli, 1997; 

Sophocleous, 2000; Fleckenstein and others, 2004; and 

Prudic and others, 2006). Analyses of this type typically use 

statistical techniques to identify and explain long-term trends 

in streamflow conditions. 

Short-term tests to determine local-scale effects of 

pumping are done for two primary purposes. The first is to 

determine the effects of an existing production well (or well 

field) on specific stream reaches or, conversely, to determine 

the quantity (and often the quality) of surface water captured 

by a well. Examples of these types of studies are provided by 

Myers and others (1996) for a site in Kansas and Dudley and 

Stewart (2006) for a site in Maine, and by several studies cited 

previously related to bank filtration. The second purpose is to 

Figure 38. Location of the Beaver–North Canadian River Basin, western Oklahoma (modified from Wahl and Tortorelli, 1997).

improve the general scientific understanding of the geologic 

and hydrogeologic controls on streamflow depletion or to test 

the predictive ability of analytical and numerical models to 

determine streamflow depletion under actual field conditions. 

Field studies such as these typically make use of multiple 

data types to provide a comprehensive picture of how streamaquifer systems respond to pumping. Experimental studies of 

this type include those described by Sophocleous and others 

(1988), Christensen (2000), Hunt and others (2001), Nyholm 

and others (2002, 2003), Hunt (2003b), Kollet and Zlotnik 

(2003), Fox (2004), and Lough and Hunt (2006).

An example of a study in which long-term changes in 

streamflow were correlated with groundwater development 

is provided for the Beaver–North Canadian River Basin of 

western Oklahoma (fig. 38). The basin is underlain by the 

High Plains aquifer, which is one of the most productive 

aquifer systems of the United States. Groundwater levels 

have declined in many parts of the High Plains aquifer in 

response to large-scale development of groundwater for 

irrigation that began in the 1940s (McGuire and others, 2003). 

These declines are illustrated by water levels measured in 

an observation well in western Oklahoma since the 1950s 

(fig. 39A). The study was undertaken in response to concerns 

about streamflow reductions that seemed to be occurring in the 
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 53

1930 1940 1950 1960 1970 1980 1990 2000

180

220

190

200

210

Depth to water, in feet

0

1930 1940 1950 1960 1970 1980 1990 2000

Streamflow, acre-feet

0

1930 1940 1950 1960 1970 1980 1990 2000

Base flow, acre-feet

Water Year

150,000

100,000

50,000

A

B

C

6,000

4,000

2,000

EXPLANATION

Depth to water

Well 363033101440701

EXPLANATION

Streamflow

10-year moving average

EXPLANATION

Base flow

10-year moving average

Figure 39. Long-term hydrologic data for the Beaver–North Canadian River Basin, western Oklahoma. A, Groundwater levels in 

an observation well in Texas County (1956–95). B, Total annual volume of streamflow and, C, base flow for the Beaver River near 

Guymon, Oklahoma (1938–93; modified from Wahl and Tortorelli, 1997). Location of observation well and streamgaging station shown 

in figure 38. 

North Canadian River, which at the time of the study was the 

source of about half of the public-water supply for Oklahoma 

City (Wahl and Tortorelli, 1997). 

Several sources of hydrologic and climatic data were 

analyzed as part of the study, including the measured volume 

of annual streamflow and estimated volume of annual base 

flow at several USGS streamgaging stations in the basin. 

The data were divided into an “early” period (ending in 

1971), representing conditions before groundwater levels 

had declined substantially, and a “recent” period (1978–94), 

reflecting the condition of declining groundwater levels 

(Wahl and Tortorelli, 1997). Statistical tests of the data showed 

that the total volume of annual streamflow measured at most 

of the streamgaging stations in the basin had decreased from 

the early to recent periods, even though precipitation records 

for the area showed no corresponding changes. Groundwater 

discharge to streams in the basin had also undergone 

significant changes, with substantial reductions documented 

at some of the streamgaging stations. These trends are 

illustrated by streamflow data and base-flow estimates for 

the Beaver River at Guymon, Oklahoma (fig. 39B and C). 

Overall, the observed reductions in streamflow throughout the 

basin correlated well with long-term declines in groundwater 

levels that occurred in response to increased pumping 
54 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

for irrigation, although other factors such as changes in 

farming and conservation practices in the basin also may 

have had an effect on the changes in streamflow (Wahl 

and Tortorelli, 1997). 

Statistical studies such as these can be used in general 

to evaluate the large-scale effects of basinwide pumping on 

streamflow reductions. They cannot, however, account for the 

specific effects of pumping at individual wells, nor can they 

help with understanding how specific management actions 

might affect future depletion. Such analyses require the use of 

analytical or numerical models.

Analytical and Numerical Modeling

Analytical and numerical modeling methods are the 

most widely applied approaches for estimating the effects of 

groundwater pumping on streamflow. The two approaches 

use different mathematical techniques to solve the partial 

differential equation of groundwater flow (or change 

in groundwater flow). The groundwater-flow equation 

mathematically describes the distribution of hydraulic heads 

(or drawdowns) throughout a groundwater system over time. 

Analytical models are limited to the analysis of idealized 

conditions in which many of the complexities of the real 

groundwater system are either ignored or approximated 

by use of simplifying assumptions. These simplifications 

typically include representation of the three-dimensional 

flow system by a one- or two-dimensional system, idealized 

boundary conditions such as perfectly straight streams, and 

homogeneous aquifer materials. In contrast, numerical models 

are capable of simulating fully three-dimensional flow in 

groundwater systems that are horizontally and vertically 

heterogeneous and have complex boundary conditions. 

Although both modeling approaches have been widely 

used, numerical models provide the most robust approach 

for determining the rates, locations, and timing of streamflow depletion by wells. Nevertheless, because analytical 

models have received substantial application and continue 

to be the subject of much research, a brief review of the 

history and scope of analytical solutions for analysis of 

streamflow depletion is provided. Different approaches for 

numerical-modeling analyses of streamflow depletion also 

are described and provide background for the discussions on 

streamflow-depletion response functions, capture maps, and 

management approaches. 

Analytical Models of Streamflow Depletion 

by Wells 

Several analytical solutions to the groundwater-flow 

equation have been developed to determine time-varying 

rates of streamflow depletion caused by pumping. Analytical 

solutions are based on highly simplified representations of 

field conditions that are necessary to develop mathematical 

solutions to the groundwater-flow equation. Although these 

solutions are highly simplified representations of real-world 

field conditions, they can provide insight into the several 

factors that affect streamflow depletion and can be used as an 

initial estimate of the effects of a particular well on a nearby 

stream. Partly because they require less site-specific data to 

implement than do numerical models, analytical models have 

been used by a number of States as the basis for making watermanagement regulatory decisions (Sophocleous and others, 

1995; Miller and others, 2007; Reeves and others, 2009). 

Figure 40A illustrates a hypothetical stream-aquifer 

system that is representative of many river-valley aquifers 

of the United States. A single well pumps from the aquifer 

and captures streamflow from the adjoining major stream 

and perhaps also from tributaries to the stream. The aquifer 

is underlain by sediments having a lower permeability 

than the aquifer (such as glacial till) and then by relatively 

impermeable bedrock.

Many, if not most, streams penetrate only a small fraction 

of the saturated thickness of the adjoining aquifer, such as 

illustrated for the stream in figure 40A. This condition is 

referred to as a partially penetrating stream, and both the 

stream and the well in figure 40A partially penetrate the 

aquifer. Partially penetrating streams and pumped wells can 

create complicated three-dimensional flow patterns in the 

vicinity of the wells and streams and can result in water being 

captured by the wells from parts of the aquifer that are on the 

opposite side of the streams from the wells. 

A simplified representation of the hypothetical rivervalley aquifer is shown in figure 40B. The conceptualization 

of the stream-aquifer-well system forms the basis for the 

development of the simplest and most widely applied 

analytical solution of streamflow depletion, which was 

developed independently and in somewhat different forms 

by Theis (1941) and Glover and Balmer (1954) and later 

implemented in a set of tables and graphs by Jenkins (1968a). 

The solution is based on several assumptions, including 

representation of the partially penetrating stream by one 

that fully penetrates the aquifer. Other assumptions are that 

(1) the aquifer is confined, homogeneous, underlain by an 

impermeable boundary, and extends to infinity in all directions 

away from the stream; (2) the aquifer is bounded by a single 

stream that is straight and in perfect hydraulic connection with 

the aquifer (that is, there are no resistive streambed sediments 

at the stream-aquifer interface); and (3) a single well pumps 

from the full saturated thickness of the aquifer. The solution 

is frequently applied to unconfined aquifers (as in figure 40) 

when it can be assumed that drawdowns caused by pumping 

at a well are small compared to the initial saturated thickness 

of the aquifer. The solution is sometimes referred to as the 

“Glover solution” or “Jenkins’ approach” and, because it has 

been so widely applied, is discussed in more detail in Box C.
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 55

A B

d

Qw

Qw

d

A A'

EXPLANATION

Aquifer

Low-permeability deposits

Low-permeability bedrock

Stream

Water table

Impermeable boundary

Streambed sediments

Stream surface

Groundwater-flow direction

Pumped well

Plan view

Section A-A’, vertical scale exaggerated

A A'

Figure 40. A, Hypothetical river-valley aquifer with a single pumping well. B, Simplified conceptualization of the same river-valley 

aquifer for the Glover analytical solution. [d is distance from well to nearest stream and Qw is pumping rate at well]
56 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

 Box C: Glover’s Analytical Solution and Jenkins’ Stream Depletion Factor (SDF)

1. The aquifer is homogeneous, isotropic, and extends to infinity away from the stream. 

2. The aquifer is confined, and the transmissivity and saturated thickness of the aquifer do not change with time. 

The solution is also applied to water-table aquifers when it can be assumed that drawdown caused by pumping is small 

compared to the initial saturated thickness of the aquifer.

3. Water is released instantaneously from storage (and there are no delayed-drainage effects characteristic of 

water-table aquifers).

4. The stream that forms a boundary with the aquifer is straight, fully penetrates the thickness of the aquifer, is infinitely 

long, remains flowing at all times, and is in perfect hydraulic connection with the aquifer (that is, no streambed and 

streambed sediments impede flow between the stream and aquifer).

5. The temperature of the stream and aquifer are the same and do not change with time. This assumption is necessary 

because variations in temperature affect the hydraulic conductivity of streambed and aquifer sediments.

6. The well pumps from the full saturated thickness of the aquifer at a constant rate.

The most widely applied analytical solution for determining the effects of pumping on streamflow is one that was developed by Glover and Balmer (1954) that has become known as the Glover solution. The solution is based on a highly simplified 

stream-aquifer-well system illustrated in figure 40B. The full set of assumptions on which the solution is based can be summarized as follows (Jenkins, 1968a):

The assumption that the aquifer is confined (or that the drawdown in a water-table aquifer is small compared to the initial 

saturated thickness of the aquifer) in conjunction with the two assumptions that the stream and well penetrate the full saturated 

thickness of the aquifer imply that groundwater flow in the aquifer is horizontal.

The Glover solution provides an expression for the total rate of streamflow depletion as a function of time (defined mathematically as Qs 

), and is equal to the product of the pumping rate of the well, Qw, and a mathematical function referred to as the 

complementary error function, erfc( )z : 

Q Q erfc z s w = ( ) . (C1)

Variable z in this equation is equal to ( ) d S ( ) Tt 2 4 , in which d is the shortest distance of the well to the stream, S is the 

storage coefficient of the aquifer (or specific yield, for water-table aquifers), T is the transmissivity of the aquifer, and t is the 

time. Note that the ratio S T is the inverse of the hydraulic diffusivity of the aquifer (D T = S). The solution is illustrated in 

figure C–1A for two wells pumping from an aquifer having a hydraulic diffusivity of 10,000 feet squared per day.

As noted previously in the report, Jenkins (1968a and 1968b) defined the quantity d D2 , which is equivalent to ( ) d S ( ) T 2

in equation C1, as the “stream depletion factor,” or “SDF.” Jenkins’ SDF has the units of time, such as seconds or days, 

depending on the units of time used to express T. Although Jenkins named the constant the stream depletion factor, it might 

alternatively be called a “streamflow-depletion response-time factor” because of its similarity to other types of hydraulic 

response-time constants that have been defined for groundwater systems (Domenico and Schwartz, 1990; Alley and others, 

2002; Sophocleous, 2012). 

For the two wells illustrated in figure C–1C, the SDF of well A is 6.25 days and that of well B is 25 days. Note that as 

either the distance of the well from the stream increases or the hydraulic diffusivity of the aquifer decreases, rates of streamflow 

depletion increase more slowly. Jenkins also noted that for the stream-aquifer conditions modeled by equation C1, the stream 

depletion factor is equal to the time at which streamflow depletion is equal to 28 percent of the volume pumped for a given 

location. This can be seen graphically in figure C–1B, in which the total volume of streamflow depletion for pumping at wells A 

and B is 28 percent (that is, a fraction of 0.28) of the volume pumped at 6.25 days and 25 days, respectively.
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 57

An important aspect of the SDF is that it can be calculated for every location in an aquifer. Wells pumping at the same 

rate and with the same pumping schedule at any location having a particular SDF value will have an equal effect on streamflow depletion, assuming that the conditions for which equation C1 were derived are met. Figure C–1C illustrates a map of 

stream depletion factors for the simplified stream-aquifer system that meets the assumptions underlying equation C1. As an 

example use of the map, any well pumped at a constant rate along the SDF contour equal to 25.0 days will result in a streamflow-depletion rate of about 57 percent of the pumping rate of the well after 40 days of pumping (from figure C–1A, well B 

curve) and a total volume of streamflow depletion equal to about 37 percent of the total volume of water pumped to that time 

(figure C–1B, well B curve).

In many field settings, the conditions required for application of the Glover solution and Jenkins’ SDF mapping approach 

are not fully met, such as for aquifers that are bounded laterally by low-permeability rocks or sediments. In such cases, methods 

have been developed to determine modified SDF values that account for the specific conditions of the particular field setting 

(for example, Jenkins 1968b and 1968c; Hurr, Schneider, and others, 1972; Burns, 1983; and Miller and others, 2007). More 

recently, alternative approaches to the SDF methodology have been developed to map aquifer locations having equal effect on 

streamflow depletion, such as response-function and capture maps.

Stream

EXPLANATION

Line of equal stream depletion

 factor (SDF), in days

Well and identifier

28 percent of volume pumped at well

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 25 50 75 100 125 150 175 200

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 25 50 75 100 125 150 175 200

Time, in days

Streamflow depletion, as fraction 

of pumping rate

Cumulative volume of streamflow 

depletion, as fraction of volume 

pumped at each well

0 250 FEET 6.25

25.00

56.25

100.00

A

A

B

A

C

B

6.25

EXPLANATION

Well A pumped 

Well B pumped

Figure C–1. A, Rate and, B, cumulative volume of streamflow depletion caused by pumping at two wells located 250 feet (well A) and 

500 feet (well B) from a stream. Rates of streamflow depletion were calculated by use of the Glover equation (C1), as implemented in the 

computer program described in Reeves (2008); cumulative volumes were calculated by adding the daily rates of streamflow depletion. 

Each well is pumped independently of the other at a rate of 1 million gallons per day from an aquifer having a hydraulic diffusivity of 

10,000 feet squared per day. C, Contours of stream depletion factor for the aquifer.
A B

C

EXPLANATION

Aquifer

Confining layer

Impermeable boundary

Streambed sediments

Water table or stream surface

Groundwater-flow direction

Qw

Qw

Qw

58 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Figure 41. Alternate conceptualizations of stream-aquifer systems for which analytical solutions have been developed. A, Singlelayer aquifer with a partially penetrating stream. B, Leaky-aquifer system with flow through a low-permeability confining layer from an 

underlying aquifer. C, Leaky-aquifer system with flow from an overlying confining layer (modified from Reeves and others, 2009). [Qw 

is 

pumping rate at well]

Since the initial work of Theis and of Glover and Balmer, 

many additional solutions have been derived to represent more 

realistic field conditions. Glover (1974) presented a solution to 

compute streamflow depletion from a well pumping between 

a stream and a lateral impermeable boundary that is parallel 

to the stream. Such an approach would be needed to represent 

the well pumping between the stream and the impermeable 

edge of the valley shown in figure 40A. Other solutions have 

focused on incorporating the effects of field conditions such as 

are shown in figure 41.

Several authors have demonstrated that the assumptions that a stream is in perfect hydraulic connection with the 

aquifer and extends over the full thickness of the aquifer can 

lead to significant errors in the determination of the timing and 

rates of streamflow depletion (Spalding and Khaleel, 1991; 

Sophocleous and others, 1995; Conrad and Beljin, 1996). 

Hantush (1965) was the first to develop a solution that 

accounted for resistance to flow at the stream-aquifer boundary due to streambed materials having a lower hydraulic conductivity than the adjacent aquifer, although his solution was 

based on a conceptualization of a fully penetrating stream. 

Hunt (1999), Butler and others (2001), Fox and others (2002), 

and Singh (2003) later extended the work of Hantush to 

allow both streambed resistance and partial penetration of the 

stream into the aquifer (fig. 41A). Simulating the stream as 

partially penetrating the aquifer allows for the propagation of 
drawdown under the stream and resulting groundwater-storage 

changes on the side of the stream opposite to the well. An 

important assumption common to all of these approaches is 

that the groundwater level in the aquifer at the stream remains 

above the streambed, such that the stream does not become 

disconnected from the underlying aquifer. 

Additional solutions have been developed to address 

flow conditions along the lower and upper boundaries of the 

aquifer. Zlotnik (2004), Butler and others (2007), and Zlotnik 

and Tartakovsky (2008) developed solutions for leaky-aquifer 

systems in which the pumped aquifer is underlain by a lowpermeability confining layer that restricts flow between the 

pumped aquifer and an underlying high-permeability aquifer 

(fig. 41B). In a separate set of papers, Hunt (2003a, 2008) 

developed analytical solutions for the condition in which the 

affected stream is located within an overlying confining layer 

that provides a source of leakage to the underlying pumped 

aquifer during the early stages of withdrawal (fig. 41C). 

At equilibrium, however, streamflow depletion is the only 

source of water to the well.

Although much work has been done to extend the 

applicability of analytical solutions to conditions that 

are typically found in the field, these solutions remain 

unable to address many of the complicating factors that 

affect streamflow depletion by wells, such as aquifer 

heterogeneity (Sophocleous and others, 1995; Kollet and 

Zlotnik, 2003) and the presence of meandering streams that 

have multiple tributaries. Moreover, even solutions that have 

been developed to represent aquifers having a finite width 

(that is, aquifers bounded laterally by low-permeability 

materials such as shown in figure 40A) are difficult to apply 

because of irregular geometry of lateral boundaries. It is 

the authors’ experience that these three factors—aquifer 

heterogeneity, multiple streams and (or) complex stream 

geometry, and finite-width aquifers with complex geometry—

can have substantial effects on streamflow depletion that limit 

the use of analytical solutions for many practical applications, 

particularly basinwide analyses in which multiple wells pump 

simultaneously. For these conditions, numerical-modeling 

methods are needed. 

Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 59

Winding channel of the Washita River between Anadarko and Chickasha, Oklahoma. 

Photograph by Michael Collier
60 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Numerical Models of Streamflow Depletion by 

Wells

Difficulties in applying analytical approaches to 

streamflow-depletion problems in real-world settings are 

apparent in the diagram of a portion of a stream-aquifer 

system shown in figure 42. Analytical solutions assume 

a single straight stream, yet the system shown includes a 

stream and two tributaries, each with irregular geometry. 

Similarly, analytical solutions would not be able to account 

for effects of the irregular edges of the aquifer. When faced 

with these and other complexities, a numerical-modeling 

approach is needed for analysis of streamflow depletion. 

Numerical groundwater models are the most powerful tools 

for understanding streamflow depletion from groundwater 

pumping. Some of the more common complexities of real 

systems that require a numerical-modeling approach include

• Irregular geometry of lateral and vertical boundaries 

of aquifers.

• Irregular geometry of streams, rivers, and other 

surface-water features.

• Non-uniform (heterogeneous) aquifer properties.

• Complex, time-varying pumping schedules at multiple 

wells or well fields pumping within a basin.

• Nonlinearities, such as boundary conditions and 

aquifer properties that change with changes in 

groundwater levels.

Many of the examples in this report that illustrate various 

aspects of streamflow depletion are derived from groundwater 

models of actual stream-aquifer systems. Investigators in those 

studies chose a numerical-modeling approach, in part because 

of the complexities listed above.

Groundwater-flow models simulate movement of water 

from areas of recharge, through an aquifer or an aquifer 

system, to streams and other features where groundwater 

discharges. Any groundwater-model program can be used to 

Grid layer

number

Area inside of aquifer

Area outside of aquifer Model cell containing portion

 of stream

Model cell containing well

A B

Finite-difference grid

EXPLANATION

Groundwater underflow out

Tributary 1

Tributary 2

Stream

well B

Grid row number

Grid column number

well A

Figure 42. A, Part of a hypothetical stream-aquifer system. B, Representation of that system with a finite-difference model grid 

consisting of 26 rows, 22 columns, and 2 layers of rectangular finite-difference blocks.
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 61

simulate depletion, as long as the program carries out rigorous 

calculations of system water-balance components, including 

inflow to the aquifer, change in storage within the aquifer, 

and outflow from the aquifer. The discussion that follows 

will reference the USGS finite-difference groundwater-model 

program, MODFLOW (McDonald and Harbaugh, 1988; 

Harbaugh, 2005), which is used worldwide to simulate many 

aspects of groundwater flow, including streamflow depletion. 

This type of model uses a grid of rectangular or square blocks 

to represent an aquifer (fig. 42B). In this example, a portion of 

a valley-fill aquifer is represented using a finite-difference grid 

consisting of 26 rows and 22 columns of equally spaced model 

cells. Aquifer properties are represented as being constant in 

each grid cell, and locations of boundaries occur either at the 

center of the cell or along the edges of cells. Use of a regular 

grid of finite-difference cells leads to approximations of locations of features such as the edges of the aquifer, streams, and 

wells (fig. 42B); however, use of a finer finite-difference grid 

will allow more accurate representation of locations of these 

features. In this example, two layers of grid cells were used to 

represent the aquifer in the vertical dimension.

Steady-State Flow Models

Steady-state groundwater models solve for head (groundwater levels) and flow components for the condition in which 

inflow rates balance outflow rates, and the rate of storage 

change in the aquifer is zero. As shown in the example in 

figure 42, inflow components might include recharge to the 

aquifer surface (not shown), lateral inflow from the rocks surrounding the aquifer, and flow from some stream segments to 

the aquifer. Outflow components would include groundwater 

underflow out of the model domain, flow from the aquifer to 

stream segments, and discharge by wells. Ultimate effects of 

pumping on streams (including tributaries) can be computed in 

three steps as follows:

Step 1. Run the model without pumping by a well or 

wells of interest and record model-computed 

flow rates to and from stream segments.

Step 2. Run the model with pumping by a well or wells 

of interest and record model-computed flow 

rates to and from stream segments.

Step 3. Subtract model-computed flow rates in step 2 

from corresponding flow rates in step 1 to get 

net change in flow between the aquifer and 

streams.

If the pumping cannot increase recharge to the aquifer, 

or increase lateral inflow, or decrease underflow out, then the 

total change in flow to and from stream segments will equal 

the total pumping rate. This type of steady-state analysis 

cannot address the timing of depletion but is useful in understanding which features would ultimately be affected by the 

pumping (fig. 43). 

Stream

Stream,

33 gallons per

minute

Tributary 1,

21 gallons per

minute

Tributary 2,

46 gallons per

minute

Ultimate or steady-state depletion

of three surface-water features

well A

Plan view of portion of aquifer around well A (fig. 42). 

In this example, well A is assumed to pump at a rate 

of 100 gallons per minute.

Tributary 1

Tributary 2

Figure 43. Possible ultimate rate of depletion of different surface-water features by pumping well A at a rate of 100 gallons per minute 

until steady-state conditions are reached.
62 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Transient Flow Models

Transient groundwater models solve for head and flow 

components at discrete intervals of time, called “time steps.” 

In these models, head may change with time and the rate 

of change in aquifer storage is a component in model water 

budgets. For the example in figure 42, inflow components to 

the aquifer would be recharge to the aquifer surface, lateral 

inflow from surrounding rocks, flow from some stream segments to the aquifer, and the rate that water is released from 

aquifer storage (the condition that happens when aquifer head 

declines). Outflow components would include groundwater 

underflow out of the model domain, flow from the aquifer to 

stream segments, discharge by wells, and the rate that water 

is going into aquifer storage (the condition that occurs when 

aquifer head rises). The latter condition of water going into 

storage would not occur as a result of pumping, but it is a 

possible condition in part of the model domain if other waterbudget components are varying through time. 

The procedure for computing depletion in transient models uses the same three steps outlined above for steady-state 

models except that these steps must be carried out for each 

time step for which depletion is to be calculated. For example, 

if a transient model uses 10 time steps to simulate 1 year of 

pumping, depletion at a pumping time of 1 year can be calculated by recording flow components at time step 10 in model 

runs with and without pumping, and computing differences in 

corresponding components.

Simulated Features that can be Affected by Groundwater 

Pumping

Although the focus of this report is streamflow depletion, 

many models simulate additional features including rivers, 

lakes, springs, wetlands, and evapotranspiration areas. Evaluation of total effects of pumping involves calculating pumpinginduced changes in inflow to and outflow from the aquifer 

from all relevant features. As opposed to the term “streamflow 

depletion,” total change in pumping-induced inflow to and 

outflow from the aquifer is referred to here as “capture.”

Table 2 lists select MODFLOW packages that can be used to 

simulate features from which capture may occur. 

In the Upper San Pedro groundwater model (fig. 13), outflow to streams, springs, and riparian vegetation is simulated, 

respectively, with the Stream, Drain, and Evapotranspiration 

Packages. For any given pumping location, total capture may 

include reduced outflow to a combination of these features. 

For example, at the location of well C in figure 13, total 

capture consists mostly of streamflow depletion with some 

evapotranspiration capture and no capture of spring discharge 

(fig. 44). Numerical models, such as presented in this example, 

are the only approach to compute capture from different features in a real-world setting. 

Photograph by Michael Collier

Republican River below McCook, Nebraska. The Republican River 

Compact Administration groundwater model is used to assess 

groundwater consumptive use in Kansas, Colorado, and Nebraska 

(http://www.ksda.gov/ interstate_water_issues/content/142). 
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 63

Table 2. Select MODFLOW packages for representing boundary conditions in which pumping may increase inflow to the aquifer or 

decrease outflow from the aquifer.

MODFLOW

package Common uses Possible responses to pumping Comments

Specified head 

(CHD)

Well-connected surfacewater featuresIncreased inflow to aquifer, 

decreased outflow from aquifer

The package sets head in aquifer equal to head in 

connected surface-water feature

General-head 

flow (GHB)

Streams, rivers, other 

surface-water 

features

Increased inflow to aquifer, 

decreased outflow from aquifer

A linear boundary condition in which flow between 

boundary and aquifer is proportional to difference 

between boundary head and aquifer head

Stream (STR) or 

Streamflow 

Routing (SFR)

Streams, rivers Increased inflow to aquifer, 

decreased outflow from aquifer

Can calculate stream stage, keeps track of flow in 

streams, streams may go dry

River (RIV) Rivers, streams that do 

not go dry

Increased inflow to aquifer, 

decreased outflow from aquifer

River stage is specified at each location of cell with 

a river, seepage rate to aquifer becomes steady if 

groundwater level drops below bottom of streambed sediments

Drain (DRN) Agricultural drains, 

springs

Decreased outflow from aquifer Discharge to a simulated drain ceases if groundwater 

level drops below drain altitude

Lake (LAK) Lakes Increased inflow to aquifer, 

decreased outflow from aquifer

Can calculate lake stage, maintains mass balances of 

lakes, lakes may go dry

Evapotranspiration (EVT)Groundwater 

evapotranspiration

Decreased outflow from aquifer Evapotranspiration ceases if groundwater level 

drops below a specified level; evapotranspiration 

is constant with groundwater levels above another 

specified level

Evapotranspiration capture

Streamflow depletion

Total capture = Streamflow depletion + Evapotranspiration capture

Storage

change

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

10 20 30 40 50 60 70 80 90 100

Time, in years since start of pumping

Storage change, capture, or depletion

as fraction of pumping rate

Figure 44. Model-computed 

streamflow depletion, 

evapotranspiration capture, 

and total capture for location 

of hypothetical well C (see 

figure 13) in the Upper San 

Pedro Basin, Arizona.
64 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

In addition to depleting streamflow, groundwater pumping can capture groundwater that otherwise would be used by plants 

(phreatophytes). Riparian trees, shown here, use shallow groundwater along the channel of the Mojave River in California.

Photograph by Michael Collier
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 65

Superposition Models

In the suite of methods available for computing depletion, superposition models are an intermediate approach 

between simple analytical solutions and complex calibrated 

groundwater-flow models. Unlike flow models, superposition 

groundwater models do not simulate natural movement of 

water through an aquifer. Instead of computing head and flow, 

these models directly compute change in head and change 

in flow from an added stress such as pumping. To compute 

streamflow depletion, the initial pre-pumping state of the 

superposition model is to have no flow between the stream and 

the aquifer. After addition of a pumping stress, computed flow 

from a boundary representing a stream is a direct calculation 

of total streamflow depletion. Because the natural flow system 

is not simulated, superposition models cannot determine if 

the depletion represents reduced groundwater discharge to the 

stream, increased flow of water from the stream to the aquifer 

(that is, induced infiltration), or a combination of these two 

components. Regardless, the streamflow depletion computed 

by a superposition model is a direct calculation of the reduced 

availability of surface water in the stream.

Application of the principle of superposition strictly 

applies to groundwater systems that respond linearly to 

stresses such as groundwater pumping (Reilly and others, 

1987). Linearity of response means that changes from the 

added stress do not change the aquifer properties or configuration or function of the boundary conditions. Some examples of 

nonlinear responses include (1) drawdown that causes substantial changes in aquifer saturated thickness and corresponding 

changes in transmissivity, (2) drawing aquifer water levels 

below the base of a streambed so that the stream is no longer 

in direct hydraulic connection with the aquifer, (3) drawing 

water levels down below the evapotranspiration extinction 

depth so that evapotranspiration ceases, and (4) drying up a 

spring or reach of a stream. Many aquifer systems respond 

linearly to some range of lower stresses, and superposition 

can be applied in many mildly nonlinear systems (Reilly and 

others, 1987).

Leake and others (2005) used a superposition modeling 

approach to compute streamflow depletion from proposed 

pumping in the C aquifer in northern Arizona (figs. 17–19). In 

that model, both confined and unconfined areas of the aquifer 

and complex variations in aquifer thickness were represented. 

In contrast, Leake, Greer, and others (2008) computed possible 

depletion of the lower Colorado River using superposition 

models that were representative of aquifer material of uniform 

thickness and aquifer properties. In that application, vertical 

geometry and aquifer properties are treated simplistically as 

they would be in an analytical solution, yet all complexities 

of horizontal aquifer and river geometry are represented in 

greater detail than would be possible by an analytical solution. These types of superposition models can be constructed 

faster and at less expense than more complex numerical flow 

models and are useful in gaining an initial understanding of 

the possible timing of depletion. For details on how to set up 

a groundwater model to compute changes using superposition, see Reilly and others (1987). Durbin and others (2008) 

present methods of representing nonlinear boundaries in 

superposition models.

Simulating the Effects of Other Boundary Conditions on 

Streamflow Depletion

In addition to boundary conditions representing surfacewater features and evapotranspiration (table 2), models can 

simulate the effects of no-flow or specified-flow boundaries 

at appropriate locations. For example, the area outside of 

the aquifer depicted in figure 42 may be crystalline rocks 

of low permeability. If interchange of water between these 

rocks and the aquifer is insignificant, the lateral edges of the 

aquifer shown in the figure could be represented as a no-flow 

boundary. Alternately, if some mountain-block recharge to the 

aquifer occurs through these rocks, the interface could be represented as a specified-flow boundary. Whether this boundary 

is represented as no flow or specified flow, the presence of 

impermeable or low-permeability rocks tends to speed up the 

timing of streamflow depletion because drawdown and storage 

change from pumping cannot extend beyond the boundary.

Ideally, all model boundaries should represent physical 

features such as the edge of the aquifer or a surface-water 

boundary. In some cases, it is impractical to construct a model 

that extends to all physical boundaries. In the example shown 

in figure 42, the area of interest may be around wells A and B, 

but the aquifer may extend a great distance down the valley 

from this area. Using the model domain shown in figure 42, an 

“artificial” boundary must be implemented to represent flow 

out of the model domain along model row 26, columns 2–17 

in layer 1 and columns 4–8 in layer 2. Options for representing artificial boundaries at this location include (1) specified 

flow―that is, estimated downvalley flow is input for each 

boundary cell and the model will compute head at these cells, 

(2) specified head―that is, head is set to the estimated water 

level for each boundary cell, and the model will compute 

flow into or out of the model domain at each of these cells, 

and (3) head-dependent flow―a boundary head and “conductance” value are specified at each boundary cell so that 

computed flow into or out of the model varies with changes in 

head in the connected model cells. No matter which boundary 

type is selected, proximity of artificial boundaries to pumping wells is a potential problem in calculations of depletion. 

In figure 42, an artificial boundary along row 26 is distant 

from well A. Furthermore, well A is surrounded by surfacewater boundaries and the natural boundary of the edge of the 

aquifer. Placement of an artificial boundary in model row 26 is 

not likely to affect calculations of depletion by pumping well 

A. In contrast, well B is as close to the artificial boundary as 

it is to the surface-water boundary. A constant-head artificial 

boundary along row 26 likely will result in an underestimation of depletion by well B for any given time. In contrast, a 

specified-flow (including no-flow) artificial boundary at that 

location would result in an overestimation of the progression 
66 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

of depletion by well B. To calculate depletion for well B, the 

model should be extended enough distance downstream so 

that the drawdown from this well does not reach the artificial 

downstream boundary.

In some aquifers, groundwater divides that approximately 

underlie watershed boundaries define the extent of a subunit 

of the aquifer beneath the watershed. If interest is in modeling 

groundwater processes in the particular watershed, a common 

practice is to represent the bounding groundwater divides as 

no-flow boundaries. Under flow conditions that are steady, the 

groundwater divides are in fact no-flow boundaries because 

there is no movement of groundwater across the divides. A 

possible result of added pumping in the watershed, however, is 

that groundwater divides will be moved outward into adjacent 

watersheds. Divides that are represented as no-flow boundaries that are fixed in space may result in computed rates of 

streamflow depletion that occur faster than would be computed 

using a representation of divides that can move in response 

to pumping. If drawdown from pumping can propagate to 

groundwater divides, the best approach is to make the domain 

of the model large enough so that model boundaries are not 

on the groundwater divides adjacent to the pumping locations. 

In the example shown in figure 45, pumping locations A and 

B are both in watershed 1. Pumping location B is close to the 

stream segments in watershed 1, and drawdown from pumping 

at this location probably would not reach the boundaries of the 

watershed. In this case, a model that includes only the portion 

of the aquifer underlying watershed 1 may be a reasonable 

approach to simulating depletion from pumping at location B. 

In contrast, location A is closer to the watershed boundary than 

it is to stream segments in watershed 1. Pumping at location 

A likely would deplete surface water in stream segments in 

watersheds 1, 2, 3, and 4. Use of a model that includes only 

watershed 1 for this pumping location would force some of 

the drawdown, storage change, and depletion that should 

occur in adjacent watersheds to occur only in watershed 1. The 

result is an overestimation of depletion in watershed 1 and an 

underestimation of depletion in adjacent watersheds 2, 3, and 

4. To effectively simulate depletion from pumping at location 

A, the model must include the part of the aquifer underlying 

watersheds 1, 2, 3, and 4.

Response Functions and Capture Maps

Two important uses of analytical and numerical models are to generate streamflow-depletion response functions 

and capture maps (which are a type of response function). 

Response functions characterize the unique functional relation 

between pumping at a particular location in an aquifer and the 

resulting depletion in a nearby stream and provide hydrologists and water-resource managers with insight into how a 

particular stream or stream reach will respond to pumping 

at a particular well. Although response functions have been 

defined and used in different ways (and referred to by different names), all response functions have the common characteristic that they represent a change in streamflow that results 

from a change in pumping rate at a single well, independently 

of other pumping or recharge stresses that may be occurring 

simultaneously within the aquifer1. As demonstrated by the 

many examples provided in this report, the response function 

for a particular well and streamflow-location pair reflects the 

combined effects of several factors, including the distance of 

the well from the stream, the geometry of the aquifer system 

and stream network, the hydraulic properties of the aquifer and 

streambed materials, and the vertical depth of pumping from 

the aquifer. 

Theoretically, response functions could be determined 

by monitoring changes in streamflow that result from pumping at a particular well, but this approach is often not technically feasible because of difficulty in separating depletion 

changes from streamflow responses to other changes, such as 

those driven by climate. In practice, response functions are 

determined by using analytical or numerical models. Modelsimulated response functions are shown as either the rate or 

volume of streamflow depletion that occurs in response to 

pumping at a particular rate or, alternatively, as dimensionless 

fractions of the pumping rate or total volume of withdrawal 

at a well, as described in Box B. Reporting response functions as dimensionless quantities is particularly useful when 

streamflow depletion responds linearly to pumping, because 

the dimensionless quantities are constants whose values are 

independent of the particular pumping rate used for their calculation. For example, if the dimensionless response function 

were 0.5 for a time and location of interest, the rate of streamflow depletion would be 0.5 Mgal/d for a pumping rate of 

1.0 Mgal/d, and 2.0 Mgal/d for a pumping rate of 4.0 Mgal/d. 

As described previously, a stream-aquifer system is linear if 

(1) the transmissivity of the aquifer does not change as the 

pumping rates of the wells change and (2) the rate of flow at 

1

Some examples of the application of response functions to stream-aquifer 

systems include those described by Maddock (1974), Morel-Seytoux and 

Daly (1975), Morel-Seytoux (1975), Illangasekare and Morel-Seytoux (1982), 

Danskin and Gorelick (1985), Maddock and Lacher (1991), Reichard (1995), 

Male and Mueller (1992), Mueller and Male (1993), Fredericks and others 

(1998), Barlow and others (2003), Cosgrove and Johnson (2004, 2005), and 

Ahlfeld and Hoque (2008). Although this report focuses on streamflow-depletion response functions, it should be noted that response functions also can 

be generated for other types of variables that describe the state of a groundwater system, such as groundwater-level declines, groundwater velocities, 

and aquifer-storage changes (see, for example, Maddock and Lacher, 1991; 

Gorelick and others, 1993; Ahlfeld and Mulligan, 2000; and Ahlfeld and others, 2005 and 2011). 
84°30'15”

84°40'15”

45°06’

44°54'

1

2 3

4

5

A

B

0

0

10 20 MILES

10 20 KILOMETERS

1

A

1

EXPLANATION

Approximate location of surface-water 

 and groundwater divides

Stream segments

Watershed designation

Hypothetical well location

MICHIGAN

Study

area

Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 67

Figure 45. Five adjacent watersheds in north-central Michigan overlying a groundwater system. Pumping locations A and B are both 

within watershed 1, but construction of a model to compute depletion for a well at location A will require inclusion of some adjacent 

watersheds in the model domain (modified from Reeves and others, 2009).

the stream-aquifer boundary is a linear function of the groundwater level near the stream.

Response functions that characterize total depletion of 

all streams (and sometimes other features) within a basin 

are referred to here as “global response functions.” Conversely, response functions that characterize depletion in a 

particular stream or segment of a stream are referred to as 

“local response functions.” Furthermore, “transient response 

functions” characterize depletion through time until some 

maximum time interval and “steady-state response functions” 

characterize ultimate depletion without regard to the time 

required to reach that state. Some key points relating to these 

types of response functions are as follows:

1. Transient response functions for each pumping location 

are defined by a number of values through time.

2. Global transient response functions expressed as a 

fraction of pumping rate will start at zero at the onset of 

pumping and will trend toward a maximum value of 1.0, 

as shown by the curve in figure B–1B in Box B.
68 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

3. Local transient response functions may trend toward a 

value less than 1.0 if the pumping causes depletion in 

locations in addition to the stream or segment of interest.

4. Steady-state response functions are a single value for each 

pumping location. 

5. Global steady-state response functions are equal to 1.0, 

assuming that streams are the ultimate source of pumped 

water. 

6. The sum of local steady-state response functions for 

all stream segments affected by a pumped well is equal 

to 1.0.

Concepts relating to global and local, transient and 

steady-state response functions are further illustrated by the 

two maps in figure 46. Dimensionless response-function 

values are shown in figure 46A for three wells in the watershed 

after 10 years of pumping. The stream location for which the 

response coefficients were determined is the outflow point 

from the basin. For this hypothetical aquifer, the responsefunction value for well A is largest because the well is closer 

to the stream network than the other two wells; the value for 

well C is smallest because it is furthest from the stream network. Figure 46B illustrates steady-state local response-function values for one of the tributaries to the main stem (stream 

segment 1). In this example, the system has reached steadystate conditions, and streamflow depletion is the only source 

of water to the wells. Each response-function value shown in 

figure 46B represents the change in streamflow at the point 

just upstream from the confluence of the tributary with the 

main stem in response to pumping at each of the three wells. 

The response-function value is largest for well A because it is 

adjacent to the tributary, whereas the response-function value 

for well B is lowest because it captures most of its discharge 

from the main stem (stream segments 3 and 5) and very little 

discharge from the tributary denoted as stream segment 1. 

An alternative approach to calculating response functions for only a few locations is to show maps of the spatial 

distribution of values of response functions for large regions 

of an aquifer. Response-function maps are particularly useful 

for illustrating the effects of pumping location on streamflow 

depletion within a large set of possible pumping locations 

within an aquifer (Leake and others, 2010). One approach has 

been to show values of the global transient response function 

for a particular pumping time, such as 10 years (for examples, 

see Leake, Pool, and Leenhouts, 2008; and Leake and Pool, 

2010). Such maps, referred to as “capture maps,” provide 

water-resource managers with a visual tool that can be used 

to determine the effects of pumping at specific locations on 

total streamflow depletion. Using values from local transient 

or steady-state response functions, capture maps also can be 

created to illustrate effects of pumping location on specific 

streams or stream segments (Cosgrove and Johnson, 2005; 

Leake and others, 2010). The goal of any of these types 

of capture maps is to help convey an understanding of the 

effects of well placement on depletion in areas of interest 

and to provide a possible tool for use in siting new wells or 

recharge facilities. 

The procedure for making response-function or capture 

maps requires use of a well-constructed groundwater model. 

The model must include streams and other appropriate features 

as head-dependent boundaries, and any boundaries that do not 

represent actual physical features must be at distances such 

that they do not affect calculated depletion. For details on 

constructing these maps, see Leake and others (2010).

Example capture maps showing global transient response 

functions for the Upper San Pedro Basin (Leake, Pool, and 

Leenhouts, 2008) are shown in figure 47. The mapped area 

is the extent of the lower basin-fill aquifer, represented as 

layer 4 of the groundwater model by Pool and Dickinson 

(2007). Global response in this case is mostly from changes 

to streamflow in the San Pedro and Babocomari Rivers, but 

also includes minor components of reductions in groundwater 

evapotranspiration and in springflow (that is, groundwater 

discharge to springs). For the times shown, 10 years (fig. 47A) 

and 50 years (fig. 47B), pumping in the area shaded in the 

darkest blue indicates that depletion would be between 0 and 

10 percent (a fraction from 0 to 0.1) of the pumping rate for 

that time. Similarly, depletion from pumping in the darkest 

red area on each map indicates depletion would be between 

90 and 100 percent (a fraction from 0.9 to 1.0) of the pumping 

rate for that time. As would be expected, the general pattern is 

that depletion from pumping nearer the rivers is greater than 

from pumping at more distant locations for either time shown; 

however, amounts of depletion vary along the streams. Leake, 

Pool, and Leenhouts (2008) attribute the complexities in the 

patterns shown to spatial variations in aquifer geometry and 

aquifer properties. A low-permeability clay layer that exists 

between some pumping locations and connected streams may 
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 69

1 1

1

2 2

3 3

4 4

5 5

A

0.7

A

A

0.9

C

0.2

C

0.3

0.5

B

0.1

B

A B EXPLANATION

Stream segment(s) from which 

 depletion is calculated

Well, with identifier and fraction

 of pumping rate that is 

 streamflow depletion

Stream-segment number

Figure 46. A, Diagram of transient response functions for the outflow point of the basin after 10 years of pumping. B, Diagram of 

steady-state response functions for a tributary stream to the main stem (modified from Leake and others, 2010).

contribute to complexity in the patterns shown. Comparison 

of the 10-year and 50-year capture maps indicates the progression of depletion through time, with substantially more areas 

of yellow, orange, and red colors in the 50-year map than in 

the 10-year map. Because these maps show global response, 

maps for increased pumping time would be more red, and 

if pumping time was such that a new steady-state condition 

would be reached for any pumping location, the map would be 

solid red. 

Other examples of maps to understand depletion as a 

function of pumping location include mapping of streamdepletion factors by Jenkins and Taylor (1974) and Burns 

(1983). COHYST Technical Committee (2004), Peterson and 

others (2008), and Stanton and others (2010) used numerical 

models to map lines of equal depletion as a fraction of volume 

pumped at specific times for locations in Nebraska. Some 

authors have used response-function maps to group wells 

(or regions of an aquifer) having similar effects on specific 

stream reaches into aquifer response zones. Examples of this 

approach are provided for the Eastern Snake River Plain aquifer in Idaho by Hubbell and others (1997) and Cosgrove and 

Johnson (2004 and 2005).

In addition to mapping responses for a specific time, it is 

also possible to construct maps showing the time it would take 

to reach a particular depletion level of interest. For example, 

depletion-dominated supply of pumped water (fig. 9) occurs 

when depletion exceeds half of the pumping rate. Figure 48 

shows the time it would take to reach depletion-dominated 

supply of pumping from the lower basin-fill aquifer in the 

Upper San Pedro Valley. For most areas adjacent to the Babocomari and San Pedro Rivers, depletion-dominated supply is 

reached within 20 years of pumping, but in the southern extent 

of the aquifer and in places along the east and west margins of 

the aquifer, depletion-dominated supply would not be reached 

within 100 years (fig. 48).
70 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Major roads

Less 0

More

Total capture,

as a fraction

of pumping rate

EXPLANATION

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

A. 10 years

0 10 KILOMETERS

0 5

5

10 MILES

3450000 3450000

3400000 3400000

550000

600000

Base from U.S. Geological Survey digital data, 1:100,000,1982

Universal Transverse Mercator projection, Zone 12, NAD83

Mule

Mountains

Huachuca Mountains

ARIZONA

SONORA

Babocomari River

San

Pedro

River

Fort Huachuca

Tombstone

Charleston

Palominas

Bisbee

Sierra

Vista

Perennial and ephemeral streams

Figure 47. Computed capture of streamflow, riparian evapotranspiration, and springflow that would result for withdrawal of water 

at a constant rate for, A, 10 years and, B, 50 years from the lower basin-fill aquifer in the upper San Pedro Basin, Arizona. The color at 

any location represents the fraction of the withdrawal rate by a well at that location that can be accounted for as changes in outflow 

from and (or) inflow to the aquifer for model boundaries representing streams, riparian vegetation, and springs (from Leake, Pool, and 

Leenhouts, 2008).
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 71

0Less

More

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Major roads

EXPLANATION

0 10 KILOMETERS

0 5

5

10 MILES

3450000 3450000

3400000 3400000

550000

600000

Base from U.S. Geological Survey digital data, 1:100,000,1982

Universal Transverse Mercator projection, Zone 12, NAD83

Mule

Mountains

Huachuca Mountains

ARIZONA

SONORA 

Babocomari River

San

Pedro

River

Perennial and ephemeral streams

Fort Huachuca

Tombstone

Charleston

Palominas Bisbee

Sierra

Vista

Total capture,

as a fraction

of pumping rate

B. 50 years

Figure 47. Continued.
0 10 KILOMETERS

0 5

5

10 MILES

3450000 3450000

3400000 3400000

550000

600000

Base from U.S. Geological Survey digital data, 1:100,000,1982

Universal Transverse Mercator projection, Zone 12, NAD83

ARIZONA

SONORA

Mountains

Mule

Huachuca Mountains

Babocomari River

San

Pedro

River

Fort Huachuca

Tombstone

Charleston

Bisbee Major roads

0

EXPLANATION

10

20

30

40

50

60

70

80

90

100

Pumping time to

reach depletiondominated supply,

in years

Palominas

Sierra

Vista

Perennial and ephemeral streams

Figure 48. Computed time to reach a depletion-dominated supply of pumped water for the lower basin-fill aquifer in the Upper San 

Pedro Basin, Arizona, when streamflow depletion exceeds half of the pumping rate.

72 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow
Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 73

Management of Streamflow Depletion 

Managing the effects of streamflow depletion by wells 

is one of the most common and often one of the most challenging aspects of conjunctively managing groundwater and 

surface-water systems. The effect of a groundwater withdrawal 

on the timing, rates (or volumes), and locations of streamflow 

depletions is substantially different from those caused by a 

surface-water withdrawal, which has an immediate effect on 

the rate of streamflow at the point of withdrawal. As demonstrated throughout this report, there can be a significant delay 

between when a well begins to pump and when the impacts of 

that pumping are realized in nearby streams. These delays can 

range from days to decades, and in some cases the full impact 

of pumping may not be realized within a period of time that is 

meaningful for practical management of a water-supply system. Moreover, unless the pumping site is located very close 

to the stream, streamflow will not recover immediately after 

pumping stops because of the residual pumping effects on 

streamflow depletion. As a result, in many hydrogeologic settings management of pumping rates in response to short-term 

fluctuations in streamflow conditions such as might be desired 

during periods of low streamflow or drought is unlikely to 

have an immediate impact on streamflow (Jenkins, 1968a; 

Bredehoeft, 2011a). 

Other factors, such as determining the locations of 

streamflow depletions, also complicate management strategies. Streamflow reductions caused by pumping occur both 

upstream and downstream from the point of withdrawal, and 

may be distributed among more than one stream; the exact 

locations of these reductions may not be easily defined without 

extensive field investigations or modeling studies. Also, many 

aquifers are tapped by large numbers of wells, and it may not 

be possible to accurately determine the history of groundwater pumping at each well. It is the sum total of streamflow 

effects caused by pumping from many wells that need to be 

managed. A related issue is that an individual well may not 

produce depletion that is measurable. This is particularly true 

for large rivers. Finally, aquifers are hidden from view, and 

even extensive field programs may not be able to define the 

hydrogeology of a groundwater system in sufficient detail to 

accurately define the timing of streamflow depletion from an 

individual well. 

In spite of these challenges, water-resource managers 

often want to understand how pumping rates and pumping 

schedules might be managed to control the effects of pumping 

on streamflow depletion. Doing so requires both a long-term 

perspective (Bredehoeft, 2011a) and an understanding of how 

streamflow responds to pumping at each well individually 

and at all wells simultaneously. Several examples of the types 

of analyses that can be done to determine long-term impacts 

have been illustrated in this report, such as the generation 

of response functions and capture maps by use of numerical 

models. Simulations of specific time-varying and cyclic pumping schedules at individual wells also are useful to determine 

how aquifer properties and well distance may affect the timing 

and variability of streamflow depletion, such as demonstrated 

for three irrigation wells pumping at various distances from a 

stream (fig. 21). 

An example of some of the issues involved in managing 

streamflow depletion is illustrated for a typical water-resource 

management problem, which is to determine pumping schedules that meet water-supply demands while simultaneously 

meeting minimum streamflow requirements at specific stream 

locations and for specific periods of time. For this example, 

an evaluation is made of a single, hypothetical stream that is 

in hydraulic connection with an aquifer that is pumped from 

June through August to supply water for irrigation. In the 

absence of pumping, the annual pattern of streamflow for the 

hypothetical system ranges from a maximum of 55.0 ft3

/s in 

early spring (March 31) to a minimum of 40.5 ft3/s in early 

fall (September 30) (fig. 49). Water managers have determined 

that a minimum streamflow requirement of 35 ft3/s is to be 

maintained throughout the year to meet instream flow needs. 

Irrigators want to pump 6 Mgal/d (9.3 ft3/s) from the aquifer 

from two possible well sites to meet their irrigation requirements. The management problem is to determine whether 

or not pumping rates can be determined for the two wells to 

simultaneously meet the irrigation demands and instreamflow requirements.

Because of the simplicity of the physical system, the 

Glover analytical model is used to determine streamflow 

depletion caused by different combinations of pumping rates 

at each well (fig. 49). The first well (A) is located 300 ft from 

the stream and the second well (B), 1,000 ft from the stream. 

Three of the many possible combinations of pumping rates 

at the two wells to meet the irrigation demand are shown in 

figure 49. When the well closest to the stream is pumped at 

the full 6 Mgal/d, the minimum streamflow requirement is 

not met for a short period of time at the end of each pumping cycle (late August into early September). However, when 

the pumping rate at this well is reduced to 3 Mgal/d and the 

remaining 3 Mgal/d of the demand is supplied by pumping at 

the well furthest from the stream, the maximum rate of depletion is reduced and the minimum streamflow requirement is 

met. The maximum rate of depletion is further reduced as the 

proportion of pumping from well B increases, with the smallest effect occurring for the case in which all of the withdrawal 

is from well B. The results shown for this simple streamaquifer system reflect differences in the underlying streamflow 

response functions for each well, which in this case result 

from differences in the distance of each well from the stream.

This simple example demonstrates how pumping rates 

might be managed to control the timing of streamflow depletion by taking advantage of the variability in streamflow 

responses to pumping at different wells. For a water-supply 

system with just a few wells and a single stream location of 

interest, alternative pumping rates can be tested relatively easily to determine if pumping schedules can be found that simultaneously meet water-supply demands and minimum instreamflow requirements. A trial-and-error testing approach such as 

this becomes impractical however for a typical hydrogeologic 
74 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Minimum streamflow requirement

30

35

40

45

50

55

60

0 1 2 3

Time, in years

No pumping at either well

Pumping period

Well A pumps at 6 Mgal/d

Each well pumps at 3 Mgal/d

Well B pumps at 6 Mgal/d

Streamflow, in cubic feet per second

EXPLANATION

Figure 49. Streamflow for a hypothetical stream-aquifer system for different pumping conditions. Hydraulic diffusivity of aquifer is 

10,000 feet squared per day. Wells are located 300 feet (well A) and 1,000 feet (well B) from the stream. [Rates of streamflow depletion 

were calculated by using a computer program described in Reeves (2008), which includes the Glover analytical model. The calculated 

depletion rates were then subtracted from the streamflow hydrograph without pumping (top curve on the figure) to determine the 

resulting decreased rates of streamflow. Mgal/d, million gallons per day]

setting in which there are multiple pumping wells and multiple streams for which minimum streamflow requirements 

have been established. For complex settings such as these, a 

technique called simulation-optimization modeling might be 

used. In this approach, a numerical simulation model (or, less 

often, an analytical model) is combined with a mathematical 

optimization technique to identify pumping schedules that best 

meet management objectives and constraints. The simulation 

model accounts for the physical behavior of the stream-aquifer 

system, whereas the optimization model accounts for the 

management aspects of the problem. Examples of the use of 

simulation-optimization modeling for management of streamflow depletion by wells include those described by Young 

and Bredehoeft (1972), Maddock (1974), Morel-Seytoux 

and Daly (1975), Morel-Seytoux (1975), Illangasekare and 

Morel-Seytoux (1982), Bredehoeft and Young (1983), Peralta 

and others (1988), Matsukawa and others (1992), Male and 

Mueller (1992), Mueller and Male (1993), Basagaoglu and 

Marino (1999), Barlow and others (2003), Ahlfeld and Hoque 

(2008), and Stanton and others (2010). The technique is 

described in detail by Gorelick and others (1993) and Ahlfeld and Mulligan (2000) and has been implemented for use 

with some of the widely available groundwater models (for 

example, the Groundwater-Management Process developed 

for MODFLOW by Ahlfeld and others, 2005).

An example of the use of simulation-optimization 

modeling to determine long-term average pumping schedules 

that meet groundwater-development goals and minimum 

streamflow requirements is provided by the results of a 

study for the Big River Basin of Rhode Island by Granato 

and Barlow (2005). Minimum streamflow requirements that 

are protective of aquatic habitats are often not well defined, 

and, as a result, water-resource and environmental agencies 

commonly evaluate the effects of alternative streamflow 

standards on groundwater-development options before 

implementing a particular regulatory standard. This was the 

case for the Big River Basin when, at the time of the study, 

State water-resource and environmental-management agencies 

were considering more than a dozen alternative minimum 

streamflow standards for implementation. 

A numerical model developed to simulate groundwater 

flow and groundwater/surface-water interactions within the 

basin was linked with an optimization model that represented 

management goals and constraints. The management object 

was to determine the maximum amount of groundwater that 

could be pumped from more than a dozen wells in the basin. 

The maximum rate of withdrawal was limited, however, by 

constraints placed on the minimum amount of streamflow 

required at four streamflow locations. Each of the proposed 

minimum streamflow standards was defined in terms of the 

minimum streamflow required at each streamflow site per 

square mile of drainage area to each site. For example, for a 

defined standard of 0.5 cubic foot per second per square mile 

[(ft3

/s)/mi2], the minimum flow required at a stream location 

having a 30 mi2 drainage area would be 15 ft3/s.

The combined simulation-optimization model was run 

several times to determine a range of optimal withdrawal rates 

for alternative definitions of the minimum streamflow standard 

at the four stream sites. Not surprisingly, the results of the 

simulation-optimization model indicated that as the minimum 
streamflow standard was increased, the total amount of pumping within the basin that would be possible decreased (fig. 50). 

Graphs such as the one shown in figure 50 are often referred to 

as trade-off curves, because they illustrate the trade-offs that 

decision makers must consider between minimum streamflow 

standards and maximum rates of groundwater development. 

For example, point A on the graph corresponds to a minimum 

streamflow standard of 0.5 (ft3/s)/mi2 at each of the four stream 

sites. For this proposed standard, an average annual pumping 

rate of 12 Mgal/d from the basin would be possible. Although 

the overall results of the study could be anticipated without a 

model—that is, that groundwater development would decrease 

as the streamflow standard was increased—the specific rates of 

pumping at each of the wells, and therefore from the basin as 

a whole, could not. The shape of the curve in figure 50 reflects 

the unique hydrogeologic and hydrologic conditions within the 

basin and the distribution of the pumping wells relative to the 

locations of the streamflow constraint sites.

Both of the examples described in this section and 

illustrated in figures 49 and 50 were related to managing 

groundwater withdrawals to meet specified rates of minimum 

streamflow. However, a number of studies have demonstrated 

the utility of artificial-recharge strategies at injection wells 

or artificial-recharge basins to increase streamflow or to 

offset the effects of withdrawals, such as was illustrated in 

figure 26. Additional examples of the use of artificial recharge 

to augment streamflow are provided in the studies by Burns 

(1984), Bredehoeft and Kendy (2008), and Barber and 

others (2009). 

Minimum streamflow requirement, in cubic feet per 

second per square mile

Average annual pumping rate from all wells, in

million gallons per day

A

0.2 0.3 0.4 0.5 0.6 0.7 0.8

0

17

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Increasing restriction on streamflow depletion

Figure 50. Example application of simulation-optimization 

modeling to determine trade-offs between minimum streamflow 

requirements and maximum groundwater pumping rates, Big River 

Basin, Rhode Island (modified from Granato and Barlow, 2005). 

Lateral-move irrigation 

system used on turf farms, 

Pawcatuck River Basin, Rhode 

Island. Concerns about the 

effects of groundwater and 

surface-water withdrawals 

on aquatic habitat in the basin 

prompted local, State, and 

Federal agencies to explore 

water-management strategies 

that minimize the effects of 

withdrawals on aquatic habitat 

(Breault and others, 2009). 

Photograph by Robert F. Breault, U.S. Geological Survey

Approaches for Monitoring, Understanding, and Managing Streamflow Depletion by Wells 75
76 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

Conclusions

Understanding and managing streamflow depletion is 

a major challenge in regulation and management of groundwater use in coupled groundwater/surface-water systems. 

Scientific research in conjunction with practical applications 

of this research to real-world field settings over the past seven 

decades have made important contributions to the understanding of the processes and factors that affect the timing, locations, and rates of streamflow depletion, and for evaluating 

alternative approaches for managing depletion. The following 

primary conclusions can be drawn from this research and the 

many field applications:

Sources of water to a well: The sources of water to a 

well are reductions in aquifer storage, increases in the rates 

of recharge (inflow) to an aquifer, and decreases in the rates 

of discharge (outflow) from an aquifer. The latter two components are referred to as capture. In many groundwater 

systems, the primary components of capture are groundwater 

that would otherwise have discharged to a connected stream 

or river in the absence of pumping (referred to as captured 

groundwater discharge) and streamflow drawn into an aquifer 

because of the pumping (induced infiltration of streamflow).

Components of streamflow depletion: Both captured 

groundwater discharge and induced infiltration of streamflow 

result in reductions in the total rate of streamflow. Streamflow depletion, therefore, is the sum of captured groundwater 

discharge and induced infiltration. Captured groundwater 

discharge is often the primary component of streamflow depletion, but if pumping rates are relatively large or the locations 

of withdrawal relatively close to a stream, then induced infiltration may become an important component of streamflow 

depletion. 

Time response of streamflow depletion: Reductions in 

aquifer storage are the primary source of water to a well during the early stages of pumping. The contribution of water 

from storage decreases and the contribution from streamflow 

depletion increases with time as the hydraulic stress caused by 

pumping expands outward away from the well and reaches one 

or more areas of the aquifer from which water can be captured. 

At some point in time, streamflow depletion will be the dominant source of water to the well (that is, more than 50 percent 

of the discharge from the well) and after an extended period 

of time may become the only source of water to the well. The 

time at which streamflow depletion is the only source of water 

to a well is referred to as the time to full capture.

Factors that affect streamflow depletion: Many factors 

affect the timing of the response of streamflow depletion to 

pumping at a particular well. These include the geologic structure, dimensions, and hydraulic properties of the groundwater 

system; the locations and hydrologic conditions along the 

boundaries of the groundwater system, including the streams 

and streambed hydraulic properties; the horizontal and vertical 

distances of wells from the streams; and pumping schedules at 

the wells. In a system with predominantly horizontal groundwater flow, well distance and the hydraulic diffusivity of the 

aquifer are two of the most important factors. Streamflow 

depletion will occur more rapidly for a well pumping relatively close to a stream from an aquifer having a relatively 

high value of hydraulic diffusivity and less rapidly for a well 

pumping far from a stream from an aquifer having a relatively 

low value of hydraulic diffusivity. In settings in which vertical 

groundwater-flow components are important, distributions of 

vertical and horizontal hydraulic conductivity, specific storage, specific yield, and aquifer thickness, in addition to well 

distance from the stream, are the key properties that control 

the timing of depletion. Aquifer extent is also an important 

variable. The time to full capture for wells pumping from narrow river-valley aquifers that are bounded at their margins by 

relatively impermeable materials can be short (days to years), 

whereas the time to full capture for wells pumping from 

regionally extensive aquifer systems can be quite long (years 

to centuries). 

Effects of confining layers on depletion: Various geologic 

features that act as conduits or barriers to groundwater flow 

can affect the timing of streamflow depletion from groundwater pumping and also can affect which streams are affected 

by the pumping. Horizontal or nearly horizontal beds of clay, 

silt, or other geologic materials that are of substantially lower 

hydraulic conductivity than adjacent aquifer material may be 

laterally discontinuous or form laterally extensive confining 

units that separate adjacent aquifers. Even though confining 

layers can slow down the progression of depletion in comparison to equivalent aquifer systems without confining layers, it 

is not reasonable to expect that pumping beneath an extensive 

confining layer will entirely eliminate depletion. For some 

well locations, discontinuous confining beds of clay may actually increase the depletion process relative to a condition in 

which the beds are absent.

Aquifer recharge and streamflow depletion: The longterm average or transient rates of recharge to an aquifer 

(or the predevelopment rates and directions of flow within 

an aquifer) will not affect the total amount of depletion that 

results from pumping a well, because the sources of capture 

to a well result from changes in the predevelopment recharge 

and discharge rates to or from an aquifer and not the absolute 

rates of recharge or discharge themselves. Because the natural 

rate of recharge does not affect the quantity of streamflow that 

can be captured by a well, it cannot be assumed that the total 

amount of groundwater development from an aquifer system 

is ‘‘safe’’ or ‘‘sustainable’’ at rates up to the long-term average 

recharge rate. The amount of depletion that can be captured is 

dependent on the total amount of water in the stream and the 

amount of reduced streamflow that a community or regulatory authority is willing to accept. However, recharge rates 

do affect the relative contributions of captured groundwater 

discharge and induced infiltration to total streamflow depletion: relatively high rates of recharge (or predevelopment 

flow rates through the aquifer) will result in relatively high 

rates of captured groundwater discharge, whereas relatively 

low rates of recharge will result in relatively high rates of 

induced infiltration. 
Conclusions 77

Distribution of streamflow depletion along stream 

reaches: Groundwater pumping causes streamflow depletion 

in streams and stream reaches that are both upgradient and 

downgradient from the location of withdrawal; the effect of 

pumping is not confined to those reaches that are immediately 

adjacent to the well. Some stream reaches will be affected 

more than others, depending on the distance of the pumped 

well from each reach and the three-dimensional distribution 

and hydraulic properties of the sediments that compose the 

groundwater system and adjoining streambeds. Cumulative 

streamflow depletion increases in the downstream direction 

of a basin, and the total amount of depletion in the direction 

of the outflow point (or points) from the basin will, over time, 

tend toward the total pumping rate of the well or wells that 

pump from the basin.

Disconnected and dry stream reaches: Two important 

assumptions that have been made throughout the report are 

that the stream and underlying aquifer remain hydraulically 

connected by a continuous saturated zone and that the stream 

does not become dry. In extreme cases of large-scale groundwater development and limited streamflow, groundwater 

levels can be drawn down below the bottom of the streambed 

and the stream may eventually lose all of its water to the 

aquifer. Under such conditions, there will not be enough water 

available from streamflow depletion to offset the pumping by 

a well or wells in the aquifer. 

Streamflow depletion after pumping stops: Streamflow 

depletion continues after pumping stops because it takes time 

for groundwater levels to recover from the previous pumping stress and for the depleted aquifer defined by the cone of 

depression to be refilled with water. The time of maximum 

streamflow depletion often may occur after pumping has 

stopped. Eventually, the aquifer and stream may return to 

their pre-pumping conditions, but the time required for full 

recovery may be quite long and exceed the total time that the 

well was pumped. Over the time interval from when pumping 

starts until the system fully recovers to its prepumping levels, 

the volume of streamflow depletion will equal the volume of 

water pumped.

Variable- and cyclic-pumping effects: Pumping schedules 

at wells fluctuate in response to water-supply demands that 

change on daily, seasonal, and longer-term intervals. Intermittent- and cyclic-pumping schedules result in variable or 

cyclic patterns of streamflow depletion, but the overall effect 

of an aquifer is to damp the variability and amplitude (range) 

of pumping rates such that the resulting rates of streamflow 

depletion are less variable and smaller in amplitude than the 

pumping stress itself. The damping effect is enhanced as the 

distance of the pumped well increases from a stream or the 

diffusivity of the aquifer decreases, and at some distance the 

effects of an intermittent- or cyclic-pumping pattern become 

indistinguishable from a constant pumping pattern at a cycle 

(or long-term)-average pumping rate.

Basinwide analyses: Many groundwater basins have 

hundreds or thousands of pumped wells. Individually, these 

wells may have little effect on streamflow depletion, but small 

effects of many wells within a basin can combine to produce 

substantial effects on streamflow and aquatic habitats. Moreover, basinwide groundwater development typically occurs 

over a period of several decades, and the resulting cumulative 

effects on streamflow depletion may not be fully realized for 

years. As a result of the large number of wells and complex 

history of development, it is often necessary to take a basinwide perspective to assess the effects of groundwater withdrawals on streamflow depletion. 

Streamflow depletion and water quality: Many of the 

problems associated with streamflow depletion do not require 

that the two components of depletion—captured groundwater 

discharge and induced infiltration—be differentiated, or individually quantified. This is the case, for example, for issues 

that are strictly related to questions of streamflow quantity, 

such as for water-rights administration or determination of 

minimum instream-flow requirements for aquatic habitats. For 

water-quality concerns, however, the relative contribution of 

captured groundwater discharge and induced infiltration has 

important implications to the resulting quality of the water 

in the stream, in the aquifer system, and pumped from wells. 

As a result, techniques of analysis that are needed to evaluate 

water-quality problems associated with streamflow depletion 

must be able to identify the specific components of depletion. 

For example, analytical solutions and superposition numerical models that can only identify changes in streamflow and 

not the absolute amount of streamflow will not be appropriate, 

whereas numerical models, particularly those that can track 

particles of water through a groundwater system or can simulate solute-transport processes may be.

Field methods for identifying and monitoring streamflow depletion: Two general approaches are used to monitor 

streamflow depletion: (1) short-term field tests lasting several 

hours to several months to determine local-scale effects of 

pumping from a specific well or well field on streams that are 

in relative close proximity to the location of withdrawal and 

(2) statistical analyses of hydrologic and climatic data collected over a period of many years to test correlations between 

long-term changes in streamflow conditions with basinwide 

development of groundwater resources. Direct measurement 

of streamflow depletion is made difficult by the limitations 

of streamflow-measurement techniques to accurately detect a 

pumping-induced change in streamflow, the ability to differentiate a pumping-induced change in streamflow from other 

stresses that cause streamflow fluctuations, and by the diffusive effects of a groundwater system that delay the arrival and 

reduce the peak effect of a particular pumping stress. 

Analytical-modeling methods to estimate streamflow 

depletion: Several analytical solutions to the groundwaterflow equation have been developed to estimate streamflow 

depletion by wells. These solutions are based on highly simplified representations of field conditions that are necessary 

to develop mathematical solutions to the groundwater-flow 

equation but that limit their applicability to real-world field 

conditions. Some of the important limitations of analytical 

solutions are that they cannot adequately represent aquifer 
78 Streamflow Depletion by Wells—Understanding and Managing the Effects of Groundwater Pumping on Streamflow

heterogeneity, the presence of multiple streams or complex stream geometry, or aquifers having complex, threedimensional geometries. Nevertheless, analytical solutions 

provide insight into several of the factors that affect streamflow depletion and are often used to make an initial estimate of 

the effect of a particular well on a nearby stream.

Numerical-modeling methods to estimate streamflow 

depletion: Numerical models are the most robust method for 

determining the rates, locations, and timing of streamflow 

depletion caused by pumping because they are capable of handling many of the common complexities of real groundwater 

systems. They are the only effective method for determining 

detailed, basinwide water budgets that account for the effects 

of complex pumping histories from large numbers of wells on 

all types of hydrologic features, including streams. Numerical 

models can be used to generate streamflow-depletion response 

functions and capture maps. Response functions characterize 

the unique functional relation between pumping at a particular location and the resulting depletion in a nearby stream or 

stream network, independently of other pumping or recharge 

stresses that may be occurring simultaneously within the aquifer. Capture maps, which are a type of response function, show 

the spatial distribution of response-function values for large 

regions of an aquifer, and provide a visual tool to illustrate the 

effects of pumping location on streamflow depletion within a 

large set of possible pumping locations within an aquifer.

Management of streamflow depletion: Managing streamflow depletion by wells is challenging because of the significant time delays that often occur between when pumping 

begins and when the effects of that pumping are realized in 

nearby streams. In many cases, it is not possible to reduce 

pumping rates during periods of low streamflow to substantially affect flow during the period of stress. Effective management of streamflow depletion requires both a long-term 

perspective and an understanding of how streamflow responds 

to pumping at each well individually and at all wells simultaneously. Numerical models are the most effective means 

to determine the effects of pumping on streamflow and to 

determine whether or not pumping schedules can be manipulated to meet minimum streamflow requirements. For conditions in which many wells pump from the same basin, the use 

of numerical models can be enhanced by their coupling with 

management models that identify the optimal pumping strategies to meet water-resource goals and constraints.

Depletion of other hydrologic features: Most aquifer systems are complex, with water moving from areas of recharge 

through geologic materials and discharging to streams, 

springs, rivers, and wetlands, and by plants that use groundwater. The introduction of groundwater pumping can affect all 

features connected to an aquifer. The emphasis of this report 

has been on the effects of pumping on connected streams, 

although most of the discussion that has been presented is 

equally applicable to other connected features. 

Acknowledgments

The authors thank William Alley, Marshall Gannett, 

Thomas Reilly, and Kay Hedrick-Naugle of the U.S. 

Geological Survey for their helpful technical and editorial 

comments on earlier drafts of this report and Christine 

Mendelsohn, U.S. Geological Survey, for preparation of the 

illustrations and layout of the final report. The authors also 

thank Michael Collier, Bob Herrmann, and U.S. Geological 

Survey personnel for allowing the use of their photographs in 

this report. 

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