In cooperation with the State of Michigan Department of Environmental Quality, 

and the State of Michigan Department of Natural Resources 

STRMDEPL08—An Extended Version of STRMDEPL 

with Additional Analytical Solutions to Calculate 

Streamflow Depletion by Nearby Pumping Wells 

U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2008–1166

STRMDEPL08—An Extended Version of 

STRMDEPL with Additional Analytical 

Solutions to Calculate Streamflow 

Depletion by Nearby Pumping Wells 

By Howard W. Reeves 

In cooperation with the State of Michigan Department of Environmental Quality, 

and the State of Michigan Department of Natural Resources 

Open-File Report 2008–1166

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

For product and ordering information:

World Wide Web: http://www.usgs.gov/pubprod

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U.S. Government.

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

reproduce any copyrighted materials contained within this report.

Suggested citation: 

Reeves, H.W., 2008,STRMDEPL08—An extended version of STRMDEPL with additional analytical solutions to calculate streamflow depletion by nearby pumping wells: U.S. Geological Survey Open-File Report 2008–1166, 22 p. 
iii

Preface

This report describes a computer program that implements four analytical solutions to estimate 

streamflow depletion by a nearby pumping well. The program is named STRMDEPL08 and is an 

extension of the program STRMDEPL written by Barlow (2000). The major extension to STRMDEPL is the addition of the two analytical solutions presented by Hunt (1999, 2003). Technical 

review of this report by Paul Barlow and Randy Bayless, and editorial review and assistance by 

Bonnie Stich Fink and Dorothy Tepper strengthened the presentation and is gratefully acknowledged. 

The program may be obtained using the Internet at http://water.usgs.gov/software/ground_

water.html/. The performance of the program has been tested in a variety of cases. Additional 

use of the program, however, may reveal errors that were not detected in the testing. Users are 

requested to send notification of any errors found in this report or in the computer program to:

Office of Ground Water

U.S. Geological Survey

411 National Center

Reston, VA 20192

(703) 648-5001

HWR – May 2008
iv

Figures 

1. Diagram showing alternate conceptual models for streamflow depletion by a 

pumping well: (A) fully penetrating stream with no streambed resistance, (B) fully 

penetrating stream with streambed resistance, (C) partially penetrating stream 

with streambed resistance, and (D) partially penetrating stream in an aquitard 

with pumping from underlying leaky aquifer............................................................................2

2–6. Graphs showing: 

2. Results from three streamflow-depletion solutions for the special case in 

which the solutions should yield identical results .........................................................6

3. Hunt (1999) solution (equation 5) shown for a range of streambedconductance values with values of no streambed resistance shown as 

reference...............................................................................................................................7

4. Hunt (2003) solution for pumping from a leaky aquifer underlying a stream 

in an aquitard with varying hydraulic properties and Hunt (1999) solution 

showed as reference ..........................................................................................................9

5. Comparison of fully penetrating stream (Hantush, 1965) and partially 

penetrating stream (Hunt, 1999) solutions for case where solutions should 

yield identical results ........................................................................................................10

6. Response to time-varying pumping comparing three pumping scenarios: 

3 months of pumping at 1 cubic foot per second with 12 hours of pumping 

followed by 12 hours of no pumping (half-day pumping); 3 months of 

pumping at 1 cubic foot per second with 3 1⁄2 days of pumping followed by 

3 1⁄2 days of no pumping (half-week pumping); and 3 months of continuous 

pumping at 0.5 cubic feet per second (half-rate pumping).........................................11

Contents

Preface ...........................................................................................................................................................iii

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

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

Analytical Solutions.......................................................................................................................................1

Modifications to STRMDEPL........................................................................................................................5

Verification of Model Results.......................................................................................................................5

Constant Pumping—First Set of Test Cases.....................................................................................5

Time-Varying Pumping Rates—Second Set of Test Cases............................................................8

Summary of Modified Code........................................................................................................................12

References Cited..........................................................................................................................................12

Appendix 1. Input Instructions and Example Files..............................................................................14

Example Input File...............................................................................................................................16

Example Output File............................................................................................................................18

Example Plot File.................................................................................................................................21
v

Conversion Factors and Symbols 

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

Flow rate

cubic foot per second (ft3

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

gallon per minute (gal/min) 0.000063 cubic meter per second (m3

/s)

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Transmissivity*

foot squared per day (ft2

/d) 0.09290 meter squared per day (m2/d)

*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.

List of Symbols

Roman characters

( ) ( )2 1 '/''



 = − tBK

a ,

( ) 2 '/''



S

tBK b = , in the function G(,t) in the Hunt (2003) solution,

B' is the thickness of the aquitard (length), 

B" is the distance from the bottom of the stream to the top of the leaky aquifer 

(length),

b' is the thickness of the streambed (length),

b is the stream width (length), 

d is the distance from the well to the stream (length),

i is the number of time intervals (dimensionless), 

K is the hydraulic conductivity of the aquifer (length per time),

K' is the hydraulic conductivity of the streambed (length per time), 

K" is the hydraulic conductivity of the aquitard (length per time),

k is the time interval number (dimensionless),

L is the streambed leakance (length), 

Qs is the rate of streamflow depletion (cubic length per time),

Qw is the pumping rate (cubic length per time),

Qs(ti) is the streamflow depletion at time interval i (cubic length per time),
vi

Q0(t0) is the initial pumping rate of the well prior to changes in the pumping rate, 

which yields the depletion at time equal to t

0

 (cubic length per time),

	 ∆Qk(tk) is the change in pumping rate during the interval k (cubic length per time),

R(t0) is the ratio of streamflow depletion to the initial pumping rate of the well prior 

to changes in the pumping rate given by either equation 1 or 2 at time equal 

to t

0

 (dimensionless),

R(ti) is the ratio of streamflow depletion to pumping rate given by either equation 1 

or 2 at time interval i (dimensionless),

S is the storativity or specific yield of the aquifer (dimensionless),

T is the transmissivity of the aquifer (square length per time), 

t is the time,

t

i is the length of time from the beginning of the pumping analysis to the time of 

interest, and

t

0 is the length of time prior to the analysis at the initial pumping rate.

Greek characters

	  is the variable of integration (dimensionless),

	 λ is the streambed conductance term (length per time), and 

	 σ	 is the specific yield of the aquitard (dimensionless).

Functions

















n

2n

 

is the Binomial Coefficient (dimensionless), 

erfc() is the complementary error function (dimensionless), 

exp() is the exponential function (dimensionless), 

F(,t) is a function in the Hunt (2003) solution (dimensionless),

G(,t) is a function in the Hunt (2003) solution (dimensionless),

Io() is the Modified Bessel function of zero order (dimensionless), and

P() is an Incomplete Gamma function (dimensionless). 
Abstract

STRMDEPL, a one-dimensional model using two analytical solutions to calculate streamflow depletion by a nearby 

pumping well, was extended to account for two additional 

analytical solutions. The extended program is named STRMDEPL08. The original program incorporated solutions for 

a stream that fully penetrates the aquifer with and without 

streambed resistance to ground-water flow. The modified program includes solutions for a partially penetrating stream with 

streambed resistance and for a stream in an aquitard subjected 

to pumping from an underlying leaky aquifer. The code also 

was modified to allow the user to input pumping variations at 

other than 1-day intervals. The modified code is shown to correctly evaluate the analytical solutions and to provide correct 

results for half-day time intervals.

Introduction

This report documents modifications to the STRMDEPL 

(STReaMflow DEPLetion by wells) computer code (Barlow, 

2000) to incorporate two additional streamflow-depletion analytical solutions. The original program evaluated the solutions 

for a stream that fully penetrates the aquifer with and without 

streambed resistance to ground-water flow. The additional 

solutions extend the code to simulate streamflow depletion 

from a partially penetrating stream with streambed resistance 

(Hunt, 1999) and from a stream in an aquitard subjected to 

pumping from an underlying leaky aquifer (Hunt, 2003). 

These two additional analytical solutions may be more appropriate for cases where a pumping well is potentially interacting 

with a small stream that does not fully penetrate the aquifer. 

The differences between the original solutions and the two 

solutions by Hunt (1999, 2003) implemented in the modified 

code are summarized by schematics of the conceptual models (fig. 1 and Hunt, 1999). The modified program is termed 

STRMDEPL08. Test cases illustrating the performance of the 

modified program and documentation of the input and output 

files are presented in this report. The desire to modify STRMDEPL to include the Hunt (1999, 2003) solutions was identified in a cooperative research project between the U.S. Geological Survey (USGS) and the Michigan Departments of 

Natural Resources and Environmental Quality. The work was 

completed during 2007 and prepared for publication in 2008.

Analytical Solutions

The STRMDEPL computer code (Barlow, 2000) implements two analytical solutions for streamflow depletion by 

a well and uses superposition to allow for varying pumping 

rates. The first solution is for a system with a stream that fully 

penetrates the aquifer with no streambed resistance between 

the stream and the aquifer (fig. 1A) and may be expressed as 

(Glover and Balmer, 1954; Jenkins, 1968) 

Q Q d S

Tt s w =

æ

è

ç

ç

ç

çç

ö

ø

÷

÷

÷

÷

÷ erfc ,

2

4 (1)

where

Qs is the rate of streamflow depletion (cubic 

length per time),

Qw is the pumping rate (cubic length per time),

erfc() is the complementary error function 

(dimensionless), 

d is the distance from the well to the stream 

(length),

S is the storativity or specific yield of the 

aquifer (dimensionless),

T is the transmissivity of the aquifer (square 

length per time), and

t is the time.

STRMDEPL08—An Extended Version of STRMDEPL with 

Additional Analytical Solutions to Calculate Streamflow 

Depletion by Nearby Pumping Wells 

By Howard W. Reeves 
2 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

d

b’ d 

Qw

d 

Qw

(D)

B’ B’’

d

b 

(C) 

Qw

(A) (B) 

Qw

Figure 1. Alternate conceptual models for streamflow depletion by a pumping well: (A) fully penetrating stream with 

no streambed resistance, (B) fully penetrating stream with streambed resistance, (C) partially penetrating stream with 

streambed resistance, and (D) partially penetrating stream in an aquitard with pumping from underlying leaky aquifer. 

[d is the distance from the well to the stream, Qw is the pumping rate from the well, b’ is the thickness of the streambed, 

B’ is the distance from the land surface to the top of the leaky aquifer, B’’ is the distance from the bottom of the stream to 

the top of the leaky aquifer, and b is the width of the stream.] 
Analytical Solutions 3

The major assumptions used to derive equation 1 are 

•	 horizontal flow dominates any potential vertical 

flow so that the Dupuit assumption is valid; 

•	 the aquifer is homogeneous, isotropic, and has 

constant saturated thickness; 

•	 the aquifer is either confined or changes in 

hydraulic head in the aquifer are small compared 

to the saturated thickness, allowing the equation 

describing ground-water flow to be linearized; 

•	 the stream is straight, infinitely long, and fully 

penetrates the aquifer; 

•	 the pumping does not change the stage of the 

stream; 

•	 the hydraulic conductivity of the streambed is 

similar or greater than the aquifer and does not 

offer resistance to ground-water flow; 

•	 there is no streambank storage; 

•	 the pumping rate is constant; and 

•	 the aquifer extends to infinity away from the 

stream. 

Examination of equation 1 reveals that streamflow depletion depends on aquifer properties, the distance from the well 

to the stream, and time. Initially after pumping, streamflow 

depletion is small and the source of water to the well is from 

storage in the aquifer. At long times, determined by aquifer properties and the distance from the well to the stream, 

streamflow depletion approaches the pumping rate.

The second solution is for a system with a stream that 

fully penetrates the aquifer with streambed resistance between 

the stream and the aquifer (fig. 1B) and may be expressed as 

(Hantush, 1965) 

1 1 D 3

4T S W 













¬

®

­

­

­

­

­ ERFC





 

¢

¡

¡

¡

4T

3,

D

,

4

 











¬

®

­

­

­

­ EXP ERFC 

T

3,

D 3

4T 



















¬

®

­

­

­

­

­

 ̄

±

°

°

°

 (2)

where

L is the streambed leakance (length), and

exp() is the exponential function (dimensionless).

The streambed leakance is defined as 

L Kb

K = '' , (3)

where

K is the hydraulic conductivity of the aquifer 

(length per time),

K’ is the hydraulic conductivity of the streambed 

(length per time), and

b’ is the thickness of the streambed (length).

The assumptions used to derive equation 1 are used for 

this equation. In this case, the streambed also offers additional 

resistance to flow as described by equation 3. If streambed 

leakance approaches zero, then equation 2 collapses to the 

equation describing streamflow depletion with no streambed 

resistance, equation 1 (see Hantush, 1965; Hunt, 1999). The 

behavior with time for this equation is similar to that for equation 1. The streambed resistance slows the response of the 

system, but ultimately, at long times, the streamflow depletion 

approaches the pumping rate. 

Equations 1 and 2 were programmed in the STRMDEPL 

computer code. The code also implemented superposition to 

allow for changing pumping rates, which may be expressed as 

(Barlow, 2000) 

Q t Q t R t Q t R t s i k k

i

k i k ( ) = + ()() å ( ) ( ) = 0 0 0 - + 1

D 1 , (4)

where

Qs(ti) is the streamflow depletion at time interval 

i (cubic length per time),

Q0(t0) is the initial pumping rate of the well prior to 

changes in the pumping rate, which yields 

the depletion at time equal to t

0

 (cubic 

length per time),

∆Qk(tk) is the change in pumping rate during the 

interval k (cubic length per time),

R(t0) is the ratio of streamflow depletion to the 

initial pumping rate of the well prior to 

changes in the pumping rate given by 

either equation 1 or 2 at time equal to 

t

0

 (dimensionless),

R(ti) is the ratio of streamflow depletion to 

pumping rate given by either equation 1 

or 2 at time interval i (dimensionless),

t

i is the length of time from the beginning of the 

pumping analysis to the time of interest,

t

0 is the length of time prior to the analysis at the 

initial pumping rate,

i is the number of time intervals 

(dimensionless), and

k is the time interval number (dimensionless).

The use of superposition is appropriate because the 

underlying ground-water-flow equations used to derive the 

equations are linear for confined aquifers and nearly linear for 

unconfined aquifers meeting the assumptions required by the 

solutions. As discussed by Barlow (2000), the initial pumping rate prior to changes in the system is used to establish 

the starting conditions for the analysis. In some systems, the 

stream may have already been subjected to pumping and the 

analysis is focused on how the system changes as this initial 

rate is changed.
4 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

The solution for a partially penetrating stream with 

streambed resistance (fig. 1C) may be written as (Hunt, 1999) 

1 1 S W  ERFC

 

¢

¡

¡

¡

D 3

4T













¬

®

­

­

­

­

­





T

34

D

4

 











¬

®

­

­

­

­ EXP ER 

M M FC  M 

 

T

34

D 3

4T















¬

®

­

­

­

­

­

 ̄

±

°

°

°



 (5)

where

λ	 is the streambed conductance term (length 

per time).

The major difference in the assumptions used to derive 

this equation compared to equations 1 and 2 is that the stream 

is assumed to be very narrow and only extend a small distance 

into the aquifer, allowing it to be mathematically modeled as 

a straight line crossing an infinite aquifer. The aquifer now 

is infinite in the horizontal direction, and drawdown may 

occur in the aquifer on the side of the stream opposite from 

the pumping well (Hunt, 1999). In this model, streamflow 

depletion is described by a simple Darcy expression describing the flux between the stream and the aquifer (Hunt, 1999). 

The aquifer is assumed to remain in hydraulic contact with the 

stream, which means that the pumping well does not cause the 

hydraulic head in the aquifer to be lower than the streambed 

(see comment by Rushton, 1999; and analysis by Peterson 

and Zhang (2000), Osman and Bruen (2002), and Bruen and 

Osman (2004) for cases where the hydraulic head in the aquifer does decrease below the streambed). 

Note the similarity in form between the partially penetrating stream solution (equation 5) and the fully penetrating 

stream solution (equation 2). As discussed by Hunt (1999), 

the solutions given by equations 2 and 5 are identical if the 

streambed conductance is set to 

l = 2

T

L . (6)

The analytical solution for a stream in an aquitard with 

pumping from an underlying leaky aquifer (fig. 1D) may be 

written as (Hunt, 2003) 

 

1 1 D 3

4T

T

34

D

4 S W 













¬

®

­

­

­

­

­

 











¬

®

­

­

­

­ ERFC EXP

 

  

M M  

¢

¡

¡

¡

  	   	 M M B B B

 





 

T

34

D 3

4T

 & T ' T D













¬

®

­

­

­

­

­

  ̈

 ̄

±

°

°

°

ERFC  (7)

In this equation, F(,t) and G(,t) are functions that may be 

calculated as (Hunt, 2003) 

 

& T 3D

4T

4T

3D   B 	 EXPB  









¬

®

­

­

­

­



   Q

T

3D

D

4

T

EXP

B M M B M

 

 

 34















¬

®

­

­

­

­  ­­

T

34

D 3

4T















¬

®

­

­

­

­

­ ERFC  BM

 B (8)

 

B A

A B

N

N















¬

®

­

­

­

­













¬

®

­

­  ­

­

­ 	 
  















¬

®

­

­

­

­

­ 

 ̄

±

°

°

°

° 

d

0 N A B AB

A B

N

N

 





 

' T E )O AB A B   	  	 B   	 
 

  



 

¢

¡

¡

¡

¡

 

 (9)

where 

a

K B t = ( ) ( ) - ''/ '

s 1 a2

, (10)

b

K B t

S = ( ) ''/ ' a2

, (11)

	  is the variable of integration (dimensionless),

Io() is the Modified Bessel function of zero order 

(dimensionless),

2n

n

æ

è

ç

ç

ç

çç

ö

ø

÷

÷

÷

÷

÷ is the Binomial Coefficient (dimensionless), 

P() is an Incomplete Gamma function 

(dimensionless),

K" is the hydraulic conductivity of the aquitard 

(length per time),

B' is the thickness of the aquitard (length), and

σ is the specific yield of the aquitard 

(dimensionless).

In this report, the streambed conductance, , is given by,

l = K b

B

''

'' , (12)

where 

b is the stream width (length), and

B" is the distance from the bottom of the stream 

to the top of the leaky aquifer (length).
Verification of Model Results 5

The assumptions used to derive this solution are similar to those used for the other solutions. The drawdowns in 

both the aquitard and leaky aquifer are assumed to be small 

compared to the saturated thicknesses such that the Dupuit 

assumption holds for each aquifer. The aquifers are infinite, 

homogeneous, and have constant thickness. Flow between 

the aquitard and the leaky aquifer is described by Darcy’s 

Law; pumping is constant. The stream is infinitely long, 

and, although stream width is used to estimate the streambed 

conductance (equation 12), the stream width is assumed to 

approach zero in the solution such that the stream may be 

modeled as a line that crosses the infinite aquifer. An alternate 

statement of this last assumption is that the well is far enough 

away from the stream such that the stream may be modeled as 

a line (Hunt, 2003).

Note that this solution is a modification of the partially 

penetrating stream solution (equation 5) so that modification 

to the code entails the evaluation of the integral containing the 

F(,t) and G(,t) functions. Methods to evaluate the functions

F(,t) and G(,t) are discussed by Hunt (2003). Also note that 

the program was written to allow input of a value for streambed conductance, , while allowing the hydraulic conductivity 

of the aquitard, K", to be set to zero despite the definition of 

streambed conductance given by equation 11 (see appendix 1). 

The ability to set K" to zero is helpful for testing the code 

because the solution collapses to the Hunt (1999) solution 

under that condition.

Modifications to STRMDEPL

The modifications to STRMDEPL include (1) changes to 

the number of input variables to accommodate the Hunt (1999, 

2003) solutions, (2) the addition of a flag to indicate to the 

program which solution should be evaluated, (3) modifications 

to read in and use a constant time increment other than one 

day, and (4) incorporation (into the code) of the equations to 

evaluate the two additional solutions. Appendix 1 details the 

input file required to use the program. Subroutines to evaluate 

the Modified Bessel and Incomplete Gamma functions were 

based on the approximations given in Abramowitz and Stegun 

(1965). The integral of the functions F(,t) and G(,t) with 

respect to  was estimated using numerical integration with 

seven Gauss points (Gauss points and weights from Abramowitz and Stegun, 1965). 

Verification of Model Results

The performance of STRMDEPL08 was tested using 

several test cases. The first set of test cases demonstrate 

performance of the code under constant pumping and illustrate 

the behavior of both the Hunt (1999) solution, equation 5, and 

the Hunt (2003) solution, equation 7. The second set of test 

cases shows the performance of the code under time-varying 

pumping. The use of time intervals other than 1-day in input 

and output time series also is illustrated in the second set of 

tests. 

Constant Pumping—First Set of Test Cases

The first set of test cases examines the performance of the 

model under constant pumping. The solution for the partially 

penetrating stream with streambed resistance (equation 5) is 

identical to the solution for the fully penetrating stream with 

streambed resistance (equation 2) if the streambed-resistance 

term and the streambed-leakance term are adjusted as shown 

in equation 6. Additionally, the solution for pumping from 

a leaky aquifer (equation 7) reduces to that for a partially 

penetrating stream with streambed resistance (equation 5) if 

the hydraulic conductivity of the aquitard, K", is set to zero. 

Setting the hydraulic conductivity of the aquitard to zero effectively makes the underlying leaky aquifer a strictly confined 

aquifer. The first test of the modified code demonstrated that 

the Hunt (1999) solution generated results identical to the 

original code using the Hantush (1965) option if  is set to 

2T/L (equation 6). The Hunt (2003) option was then tested 

by using the same suite of input data values and setting K" 

to zero. For this test, T = 1,000 ft2

/d, L = 100 ft,  = 20 ft/d, 

d = 500 ft, S = 0.1, and Qw = 0.557 ft3/s (250 gal/min). The 

results from the modified code for 100 days of pumping are 

identical for the three solution options (fig. 2). These results 

demonstrate that the modified code is evaluating the equations 

correctly.

To illustrate the behavior of the solution for varying 

values of the streambed-conductance value, , a plot similar 

to that presented by Hunt (1999) was generated using the 

modified code (fig. 3). In this figure, the ratio of streamflow 

depletion to pumping rate is shown plotted against a dimensionless group, 4Tt/Sd2

, which is dimensionless time. Six 

curves are shown for varying values of d/T. Results for the no 

streambed-resistance (Jenkins, 1968) solution also are shown 

to confirm that the Hunt (1999) solution approaches the solution for no streambed resistance as  gets large. Dimensionless 

groups allow this figure to be used to show the behavior of 

the solution for the potential range of S,T,d, and  combinations. As shown in the figure, as the streambed conductance 

decreases, for a given aquifer and distance between the well 

and the stream, the response of the stream to the pumping is 

delayed. In the extreme case of streambed conductance equal 

to zero, the streamflow depletion becomes zero (equation 5) 

and the drawdown solution becomes the Theis solution for a 

well in an infinite confined aquifer (Hunt, 1999). Streamflow 

depletion increases as the streambed conductance is increased 

or the distance between the well and the stream is decreased. 

In all cases of non-zero streambed conductance, the solution 

will eventually reach a constant value in which the streamflow 

depletion is equal to the pumping rate. This steady-state condition is required because the only source of water to the well 

in the system other than storage in the aquifer is streamflow 

capture.
6 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

Figure 2. Results from three streamflow-depletion solutions for the special case in which the solutions should yield identical results. 

0.60.50.4

0

0.20.1

0 10 20 30 40 50 60 70 80 90 100

TIME AFTER PUMPING BEGINS, IN DAYS

PUMPING RATEHANTUSH, 1965HUNT, 1999HUNT, 2003

PUMPING RATE OR STREAMFLOW DEPLETION, 

 IN CUBIC FEET PER SECOND 0.3
Verification of Model Results 7 Figure 3. Hunt (1999) solution (equation 5) shown for a range of streambed-conductance values with values of no streambed resistance shown as reference. [

T is the transmissivity, t is time, 

S is storativity or specific yield, 

d is the distance from the well to the stream, 

 is the streambed conductance, 

Qw is the pumping rate, and 

Qs is the streamflow depletion.] 

0

0.80.60.40.2

1

0.1 1 10 100 1000

0.01

0.03

0.1

0.3

1.0

d/T = 50,000

+ = NO-STREAMBED RESISTANCE SOLUTION

   

DIMENSIONLESS TIME (4Tt/(Sd2)) 

) w /Qs DIMENSIONLESS STREAMFLOW DEPLETION (Q
8 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

The nature of the solution for pumping from a leaky 

aquifer (equation 6) is illustrated by generating a plot similar 

to that presented by Hunt (2003) using the modified code 

(fig. 4). The correct behavior of the code is observed by 

(1) visual comparison to the plot from Hunt (2003) and (2) the 

comparison of the partially penetrating stream solution (Hunt, 

1999) to the leaky-aquifer solution (Hunt, 2003) for the case 

where the streambed conductance, , is given a finite value, 

but the hydraulic conductivity of the aquitard, K", is set to zero 

(fig. 4). For this special case, the aquitard does not provide 

water to the pumping well but the stream does. Under these 

conditions, the system acts as a confined aquifer and the 

leaky-aquifer solution (Hunt, 2003) collapses to the partially 

penetrating stream solution (Hunt, 1999). 

As the hydraulic conductivity of the aquitard is increased, 

it can provide water from storage to the pumped leaky aquifer, 

and the solution takes on a leaky-aquifer or delayed-yield 

behavior. The delayed-yield behavior is characterized by a 

double inflection of the curve and longer time required to 

reach specific values of streamflow depletion (fig. 4). The 

nature of the solution is that after pumping begins, there is 

some initial drawdown in the leaky aquifer and streamflow 

depletion begins. Depending on the aquifer and aquitard properties, however, the rate of streamflow depletion may level off 

because the hydraulic head in the aquitard responds to changes 

in head in the underlying leaky aquifer and water is released 

from storage in the aquitard. After some time, the head in the 

aquitard approaches the head in the underlying leaky aquifer 

and the rate of water release from the aquitard declines. As 

the aquitard releases less water, the rate of streamflow depletion increases until, at steady state, the streamflow depletion 

becomes equal to the pumping rate. Water released from 

storage of the aquitard only delays the attainment of steadystate streamflow depletion because, in this model, the aquitard cannot be a long-term source of water. If the hydraulic 

conductivity of the aquitard is great enough, the system will 

respond like an unconfined aquifer with the specific yield 

of the aquitard, and the double-inflection behavior noted at 

intermediate values of aquitard hydraulic conductivity will be 

difficult to observe. This behavior is illustrated in the series of 

curves shown in figure 4; as the (K"/B')d2

/T ratio increases, the 

aquitard supplies more water and delays streamflow depletion. 

Time-Varying Pumping Rates—Second Set of 

Test Cases

The second set of test cases demonstrates the performance of the model under time-varying pumping rates. The 

time-varying pumping-rate test was expected to perform without any problems because the constant pumping-rate solutions 

for the modified code matched the results from the original 

code for the test cases and visually matched published results 

from Hunt (1999) and Hunt (2003). The only modification to 

the superposition algorithm programmed in STRMDEPL was 

that the time increment was changed from a fixed value of 

1 day to an optional variable input by the user. The program 

still requires an input time series of pumping rates at a fixed 

increment, but the increment can be different than 1 day. The 

length of the increment in days also is read by the program. 

Note that because this is an analytical solution, the time increment used is only to allow variation in the pumping rate; the 

solution is accurate for any time interval evaluated. The output 

series produced by the code is identical to the input series.

The first test uses the same parameters as the first constant-rate pumping test: T = 1,000 ft2

/d, L = 100 ft,  = 20 ft/d, 

d = 500 ft, S = 0.1, and Qw = 0.557 ft3/s (250 gal/min). The 

pumping begins after 31 days and continues for 28 days. The 

fully penetrating stream solution (Hantush, 1965) and the 

partially penetrating stream solution (Hunt, 1999) were evaluated using the modified code. Two input time intervals were 

tested: a half-day interval and a 1-day interval. The parameters 

were set so that the fully penetrating solution and the partially 

penetrating solution should yield identical results. The results 

demonstrate that the modified code evaluates the Hunt (1999) 

solution correctly, and that the modifications to allow different time intervals in the solution were implemented correctly 

(fig. 5).

The behavior of time-varying pumping on streamflow 

depletion is shown in the second test using the modified code 

and the partially penetrating stream solution (equation 5). 

For this case, T = 2,000 ft2/d,  = 10 ft/d, d = 250 ft, and 

S = 0.05. The pumping begins after 244 days and continues 

for 91 days and then is followed by another 91-day pumping 

cycle that begins after 274 days. This time series was used to 

represent summer irrigation pumping and a time series that 

begins on October 1 of a calendar year. The aquifer conditions 

and distance to the stream were selected to be representative 

of conditions encountered in the field and to yield different 

streamflow-depletion estimates depending on the pumping 

scenario used. Three pumping scenarios were tested. In the 

first scenario, the well is pumped at 1 ft3

/s for 12 hours followed by 12 hours with no pumping for the 91-day pumping 

cycles (half-day pumping in fig. 6). In the second scenario, 

the pumping rate is set to 1 ft3/s for 3-1⁄2 days followed by no 

pumping for 3-1⁄2 days for the 91-day pumping cycles (halfweek pumping in fig. 6). In the third scenario, the pumping 

rate is equal to 0.5 ft3/s for 24 hours of continuous pumping 

for the 91-day pumping cycles (half-rate pumping in fig. 6). 
Verification of Model Results 9 Figure 4. Hunt (2003) solution for pumping from a leaky aquifer underlying a stream in an aquitard with varying hydraulic properties and Hunt (1999) solution showed as reference. [

T is the transmissivity, t is time, 

S is storativity of the leaky aquifer, 

σ is the specific yield of the aquitard, K” is the hydraulic 

conductivity of the aquitard, B’ is the thickness of the aquitard, 

d is the distance from the well to the stream, 

 is the streambed conductance, 

Qw is the 

pumping rate, and 

Qs is the streamflow depletion.] 

0

0.90.80.70.60.50.40.30.20.1

1

0.1 1 10 100 1000 10000

0.01

0.1

1.0

d/T = 0.3S/

 = 0.1

10

+ = PARTIALLY PENETRATING STREAM SOLUTION

 (HUN

T, 1999) 

DIMENSIONLESS TIME (4Tt/(Sd2)) 

) w /Qs DIMENSIONLESS STREAMFLOW DEPLETION (Q (K''/B')d2/T = 0
10 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

Figure 5. Comparison of fully penetrating stream (Hantush, 1965) and partially penetrating stream (Hunt, 1999) solutions for case where solutions should yield identical results. [Pumping begins after 31 days and lasts for 28 days. The results shown are for two time intervals: half-day and 1 day.] 

0.30.2

I

C

 HANTUSH, HALF-DAY

 HUNT, HALF-DAY

 HANTUSH, ONE DAY

 HUNT, ONE DAY

0

0.05

0.1

0 20 40 60 80 100 120

TIME, IN DAYS

 STREAMFLOW DEPLETION, IN CUBIC FEET PER SECOND 0.25 0.15
Verification of Model Results 11 Figure 6. Response to time-varying pumping comparing three pumping scenarios: 3 months of pumping at 1 cubic foot per second with 12 hours of pumping followed by 12 hours of no pumping (half-day pumping); 3 months of pumping at 1 cubic foot per second with 3 1⁄2 days of pumping followed by 3 1⁄2 days of no pumping (half-week pumping); and 3 months of continuous pumping at 0.5 cubic feet per second (half-rate pumping). 

0.60.50.4

0 3

HALF-DAY PUMPINGHALF-WEEK PUMPINGHALF-RATE PUMPING

0

0

0.20.1

.3

200 300 400 500 600 700 800

TIME, IN DAYS

STREAMFLOW DEPLETION, IN CUBIC FEET PER SECOND
12 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

The total volume of water pumped for the three scenarios 

is the same. The important feature of these solutions is that 

although the total volume of pumping is the same for the three 

scenarios, the maximum streamflow depletion differs between 

the scenarios. In this case, the 3-1⁄2 day pumping at 1 ft3/s followed by 3-1⁄2 days of no pumping impacts the stream more 

in terms of the calculated maximum streamflow depletion 

compared to either 12 hours of pumping followed by 12 hours 

of no pumping or continuous pumping at 0.5 ft3/s. In this case, 

the 12-hour cycle at 1 ft3/s is nearly identical to continuous 

pumping at 0.5 ft3/s. The behavior results from the close proximity of the well to the stream, the high aquifer dispersivity 

because of the high value for transmissivity, and the low value 

for storativity. This test illustrates the findings by Wallace 

and others (1990) that if maximum streamflow depletion in 

response to cyclic pumping is of interest, then, in some cases, 

actual pumping schedules must be used because continuous 

pumping at the average value for the cyclic schedule may 

under-estimate the streamflow depletion.

Summary of Modified Code

The computer program evaluating the analytical solutions 

for streamflow depletion by a pumping well by Barlow (2000) 

was modified to include two additional analytical solutions 

as part of a cooperative research project with the Michigan 

Departments of Natural Resources and Environmental Quality. 

The original program, STRMDEPL, evaluates the solution 

for streamflow depletion for a fully penetrating stream with 

no streambed resistance (Glover and Balmer, 1954; Jenkins, 

1968) and the solution for streamflow depletion for a fully 

penetrating stream with streambed resistance (Hantush, 1965). 

The modified code, STRMDEPL08, also evaluates solutions 

for streamflow depletion from a partially penetrating stream 

with streambed resistance (Hunt, 1999) and from a stream in 

an aquitard subjected to pumping from an underlying leaky 

aquifer (Hunt, 2003). These two additional analytical solutions 

may be more appropriate for cases where a pumping well is 

potentially interacting with a small stream that does not fully 

penetrate the aquifer. The required input file for the modified 

code and example output files produced by the code are shown 

in appendix 1. The code itself is provided on the website listed 

in the Preface of this report. This code was tested and satisfactorily evaluated four analytical solutions for streamflow depletion by a pumping well. The nature of the solutions for varying 

parameter values was discussed. 

References Cited

Abramowitz, Milton, and Stegun, I.A., 1965, Handbook of 

mathematical functions with formulas, graphs, and mathematical tables: New York, Dover Publications, Inc., 1045 p.

Barlow, P.M., 2000, Documentation of computer program 

STRMDEPL—A program to calculate streamflow depletion 

by wells using analytical solutions, in Zarriello, P.J., and 

Ries, K.G., III, A precipitation-runoff model for analysis 

of the effects of water withdrawals on streamflow, Ipswich River Basin, Massachusetts: U.S. Geological Survey 

Water-Resources Investigations Report 00–4029, p. 77–89. 

Bruen, M.P., and Osman, Y.Z., 2004, Sensitivity of 

stream-aquifer seepage to spatial variability of the saturated 

hydraulic conductivity of the aquifer: Journal of Hydrology, 

v. 293, no. 1–4, p. 289–302.

Glover, R.E., and Balmer, G.G., 1954, River depletion resulting from pumping a well near a river: Transactions, American Geophysical Union, v. 35, no. 3, p. 468–470.

Hantush, M.S., 1965, Wells near streams with semipervious beds: Journal of Geophysical Research, v. 70, no. 12, 

p. 2829–2838.

Hunt, Bruce, 1999, Unsteady stream depletion from ground 

water pumping: Ground Water, v. 37, no. 1, p. 98–102.

Hunt, Bruce, 2003, Unsteady stream depletion when pumping 

from semiconfined aquifer: Journal of Hydrologic Engineering, v. 8, no. 1, p. 12–19.

Jenkins, C.T., 1968, Computation of rate and volume of stream 

depletion by wells: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. D1, 17 p.

Osman, Y.Z., and Bruen, M.P., 2002, Modelling stream-aquifer seepage in an alluvial aquifer—an improved loosing-stream package for MODFLOW: Journal of Hydrology, 

v. 264, no. 1–4, p. 69-86.

Peterson, D.M., and Zhang, H, 2000, Simulation of stream 

losses affected by the vadose zone, in Bentley, L.R., Sykes, 

J.F., Brebbia, C.A., Gray, W.G., and Pinder, G.F., eds., 

Computational Methods in Water Resources—

Volume 2—Computational methods, surface water systems and hydrology, Proceedings of the XIII International 

Conference on Computational Methods in Water Resources, 

Calgary, Alberta, Canada, June 2000: Rotterdam, 

A.A. Balkema, p. 1131–1138.

Rushton, Ken, 1999, Discussion of “Unsteady stream depletion from ground water pumping” by B. Hunt, 

January–February 1999 issue, v. 37, no. 1, p. 98–102: 

Ground Water, v. 37, no. 6, p. 805.

Wallace, R.B., Darama, Yakup, and Annable, M.D., 1990, 

Stream depletion by cyclic pumping of wells: Water 

Resources Research, v. 26, no. 6, p. 1263–1270. 
Appendix 
14 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

Appendix 1. Input Instructions and Example Files 

One input file is required to run STRMDEPL08. The 

name of the file is prompted from the code. It also may be 

supplied at the command line. The program may be run 

from the command line:

> STRMDEPL08.exe

Enter name of file containing input data:

example.dat

Enter name of file for program results:

example.out

Enter name of plot file (return for no plot file):

example.plt

File names have been read.

>

Alternatively, 

> STRMDEPL08.exe example.dat example.out 

example.plt

>

Bold font indicates user input. The format for the input file 

was taken from the original STRMDEPL program (Barlow, 

2000), and existing data files should be able to be used with 

only minor changes. The input is read in free format. Each 

input line may be up to 140 characters in length and the 

input variables may be separated by blanks or commas. 

Line 1: Title

Line 2: Well identifier

Line 3: XWELL, DIFFUS, ISOLN, SLEAK, STOR, 

SIGMA, BPP, BP, RKPRME, STRWTH, DELT

Line 4: INTIME, QWINIT

Line 5: NPD

Lines 6 – NPD: CDATE(I), QWELL(I)

The inputs are:

Title: Title of the simulation that may be up to 

100 characters in length. The title is printed 

on the output file. Leave blank if no title is 

desired.

Well identifier: Identifying string for the pumping well that 

may be up to 20 characters in length. The 

identifying string is printed on the output file. 

Leave blank if no well identifier is desired.

XWELL: Distance from well to stream, feet.

DIFFUS: If ISOLN (see next input variable) 

<=1: diffusivity of aquifer, square feet per 

second, and if ISOLN > 1, transmissivity of 

aquifer, square feet per second.

ISOLN: Flag to specify choice of analytical solution 

used:

0 = fully penetrating with no streambed 

resistance, equation 1 (Jenkins, 1968),

1 = fully penetrating stream with streambed 

resistance, equation 2 (Hantush, 1965),

2 = partially penetrating stream with streambed resistance, equation 5 (Hunt, 1999), and

3 = stream in an aquitard with pumping 

from an underlying leaky aquifer, equation 7 

(Hunt, 2003).

SLEAK: If ISOLN = 1, streambed leakance, feet, 

if ISOLN = 2, streambed conductance, feet 

per second, 

if ISOLN = 3, default streambed conductance 

if RKPRIME=0, feet per second. This value 

is not used if ISOLN=0 and should be entered 

as 0.

STOR: If ISOLN > 1, storativity or specific yield, 

dimensionless. This value is not used if 

ISOLN ≤ 1 and should be entered as 0.

SIGMA: If ISOLN = 3, specific yield of aquitard containing stream, dimensionless. This value is 

not used if ISOLN ≤ 2 and should be entered 

as 0.

BPP: If ISOLN = 3, distance from streambed to top 

of the leaky aquifer, feet. This value is not 

used if ISOLN ≤ 2 and should be entered as 

0.

BP: If ISOLN = 3, thickness of aquitard containing stream, feet. This value is not used if 

ISOLN ≤ 2 and should be entered as 0.

RKPRIME: If ISOLN = 3, hydraulic conductivity of aquitard, feet per second. This value is not used 

if ISOLN ≤ 2 and should be entered as 0. If 

RKPRIME is set to 0.0 and 

ISOLN = 3, then the value of SLEAK is used 

for the streambed conductance in the solution. If RKPRIME is not zero, then equation 

(12) is used to calculate streambed conductance. λ = (RKPRIME)(STRWTH)/(BPP).
Appendix 1 15

STRWTH: If ISOLN = 3, stream width, feet. This 

value is not used if ISOLN ≤ 2 and should 

be entered as 0.

DELT: Time interval size, days. If 0.0 is read, the 

time interval is set to 1 day. Because this 

is an analytical solution, the time interval 

should match the interval of pumping rate 

changes. Solution accuracy does not depend 

on the interval used. The time interval must 

be uniform for the input pumping record. 

The maximum time interval is 28 days. 

The date string would have to be converted 

to Julian days for longer time intervals.

INTIME: Number of pumping days prior to start of 

the analysis.

QWINIT: Pumping rate prior to start of analysis in 

cubic feet per second. As discussed by 

Barlow (2000), the variables INTIME 

and QWINIT allow the user to establish 

an initial streamflow depletion before the 

analysis period. Streamflow depletion 

calculated for the time intervals and pumping 

rates specified below are added to the 

initial streamflow depletion. The values for 

INTIME and QWINIT should be adjusted to 

reflect the conditions of the system before the 

analysis period.

NPD: Number of time intervals for the analysis. 

This may be set to 1 for a single evaluation of 

the solution using the value entered for DELT 

as the time for the evaluation.

CDATE(I): Date for time interval (I) in YYYYMM

DDHH format (10 character string). 

QWELL(I): Pumping rate for time interval (I), cubic feet 

per second.

Note that the solution is evaluated for each input CDATE(I), 

QWELL(I) pair. Output is produced for each of these evaluations. The time interval, DELT, is used in the computations 

and must match the interval implied by the CDATE entries.
16 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

2001010100 0.0000

2001010200 0.0000

2001010300 0.0000

2001010400 0.0000

2001010500 0.0000

2001010600 0.0000

2001010700 0.0000

2001010800 0.0000

2001010900 0.0000

2001011000 0.0000

2001011100 0.0000

2001011200 0.0000

2001011300 0.0000

2001011400 0.0000

2001011500 0.0000

2001011600 0.0000

2001011700 0.0000

2001011800 0.0000

2001011900 0.0000

2001012000 0.0000

2001012100 0.0000

2001012200 0.0000

2001012300 0.0000

2001012400 0.0000

2001012500 0.0000

2001012600 0.0000

2001012700 0.0000

2001012800 0.0000

2001012900 0.0000

2001013000 0.0000

2001013100 0.0000

2001020100 0.5570

2001020200 0.5570

2001020300 0.5570

2001020400 0.5570

2001020500 0.5570

2001020600 0.5570

2001020700 0.5570

2001020800 0.5570

2001020900 0.5570

2001021000 0.5570

2001021100 0.5570

2001021200 0.5570

2001021300 0.5570

2001021400 0.5570

2001021500 0.5570

2001021600 0.5570

2001021700 0.5570

2001021800 0.5570

2001021900 0.5570

2001022000 0.5570

2001022100 0.5570

2001022200 0.5570

2001022300 0.5570

2001022400 0.5570

2001022500 0.5570

2001022600 0.5570

2001022700 0.5570

2001022800 0.5570

2001030100 0.0000

2001030200 0.0000

2001030300 0.0000

2001030400 0.0000

2001030500 0.0000

2001030600 0.0000

2001030700 0.0000

2001030800 0.0000

2001030900 0.0000

2001031000 0.0000

2001031100 0.0000

2001031200 0.0000

2001031300 0.0000

2001031400 0.0000

2001031500 0.0000

Example Input File

Example Intermittent Pumping Problem with one-day time interval

WELL EXAMPLE 1

500, 0.0115740740740741, 2, 0.000231481481481481, 0.1, 0, 0, 0, 0, 0, 1

3650, 0.0

120 
Appendix 1 17

2001031600 0.0000

2001031700 0.0000

2001031800 0.0000

2001031900 0.0000

2001032000 0.0000

2001032100 0.0000

2001032200 0.0000

2001032300 0.0000

2001032400 0.0000

2001032500 0.0000

2001032600 0.0000

2001032700 0.0000

2001032800 0.0000

2001032900 0.0000

2001033000 0.0000

2001033100 0.0000

2001040100 0.0000

2001040200 0.0000

2001040300 0.0000

2001040400 0.0000

2001040500 0.0000

2001040600 0.0000

2001040700 0.0000

2001040800 0.0000

2001040900 0.0000

2001041000 0.0000

2001041100 0.0000

2001041200 0.0000

2001041300 0.0000

2001041400 0.0000

2001041500 0.0000

2001041600 0.0000

2001041700 0.0000

2001041800 0.0000

2001041900 0.0000

2001042000 0.0000

2001042100 0.0000

2001042200 0.0000

2001042300 0.0000

2001042400 0.0000

2001042500 0.0000

2001042600 0.0000

2001042700 0.0000

2001042800 0.0000

2001042900 0.0000

2001043000 0.0000
18 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

Example Output File

 *****************************************************

 * *

 * **** U.S. GEOLOGICAL SURVEY **** *

 * *

 * *** STRMDEPL08: PROGRAM OUTPUT *** *

 * *

 * ONE-DIMENSIONAL MODEL OF STREAMFLOW DEPLETION *

 * *

 * BY WELLS, BASED ON ANALYTICAL SOLUTIONS *

 * *

 * DEVELOPED BY JENKINS (1968) AND HANTUSH (1965) *

 * *

 * MODIFIED TO INCLUDE HUNT (1999, 2003) SOLUTIONS *

 * *

 * VERSION 1.0, FEBRUARY, 2008 *

 * *

 *****************************************************

Example Intermittent Pumping Problem with one-day time interval

SUMMARY OF INPUT DATA

---------------------

WELL IDENTIFIER: WELL EXAMPLE 1

WELL DISTANCE TO STREAM (XWELL): 0.500D+03 feet

TRANSMISSIVITY: 0.116D-01 square feet per second

STORATIVITY: 0.100D+00

STREAMBANK CODE (ISOLN): 2 (partially penetrating stream with 

 resistance, Hunt 1999)

STREAMBED CONDUCTANCE: 0.231D-03 feet per second

INITIAL TIME (INTIME): 3650 days

INITIAL PUMPING RATE (QWINIT): 0.000D+00 cubic feet per second

NUMBER OF PUMPING STEPS (NPD): 120

TIME STEP FOR PUMPING (DELT): 0.100D+01 days
Appendix 1 19

 DAY PUMPING STREAMFLOW

 RATE DEPLETION

 (cubic feet per second)

2001010100 0.0000 0.0000

2001010200 0.0000 0.0000

2001010300 0.0000 0.0000

2001010400 0.0000 0.0000

2001010500 0.0000 0.0000

2001010600 0.0000 0.0000

2001010700 0.0000 0.0000

2001010800 0.0000 0.0000

2001010900 0.0000 0.0000

2001011000 0.0000 0.0000

2001011100 0.0000 0.0000

2001011200 0.0000 0.0000

2001011300 0.0000 0.0000

2001011400 0.0000 0.0000

2001011500 0.0000 0.0000

2001011600 0.0000 0.0000

2001011700 0.0000 0.0000

2001011800 0.0000 0.0000

2001011900 0.0000 0.0000

2001012000 0.0000 0.0000

2001012100 0.0000 0.0000

2001012200 0.0000 0.0000

2001012300 0.0000 0.0000

2001012400 0.0000 0.0000

2001012500 0.0000 0.0000

2001012600 0.0000 0.0000

2001012700 0.0000 0.0000

2001012800 0.0000 0.0000

2001012900 0.0000 0.0000

2001013000 0.0000 0.0000

2001013100 0.0000 0.0000

2001020100 0.5570 0.0001

2001020200 0.5570 0.0028

2001020300 0.5570 0.0112

2001020400 0.5570 0.0235

2001020500 0.5570 0.0376

 DAY PUMPING STREAMFLOW

 RATE DEPLETION

 (cubic feet per second)

2001020600 0.5570 0.0522

2001020700 0.5570 0.0665

2001020800 0.5570 0.0802

2001020900 0.5570 0.0932

2001021000 0.5570 0.1055

2001021100 0.5570 0.1170

2001021200 0.5570 0.1278

2001021300 0.5570 0.1380

2001021400 0.5570 0.1475

2001021500 0.5570 0.1564

2001021600 0.5570 0.1649

2001021700 0.5570 0.1728

2001021800 0.5570 0.1804

2001021900 0.5570 0.1875

2001022000 0.5570 0.1942

2001022100 0.5570 0.2006

2001022200 0.5570 0.2067

2001022300 0.5570 0.2125

2001022400 0.5570 0.2180

2001022500 0.5570 0.2233

2001022600 0.5570 0.2283

2001022700 0.5570 0.2331

2001022800 0.5570 0.2378

2001030100 0.0000 0.2421

2001030200 0.0000 0.2437

2001030300 0.0000 0.2394

2001030400 0.0000 0.2309

2001030500 0.0000 0.2206

2001030600 0.0000 0.2097

2001030700 0.0000 0.1990

2001030800 0.0000 0.1886

2001030900 0.0000 0.1789

2001031000 0.0000 0.1698

2001031100 0.0000 0.1614

2001031200 0.0000 0.1535

2001031300 0.0000 0.1463

RESULTS

-------

STREAMFLOW DEPLETION AT BEGINNING OF ANALYSIS:

0.0000 cubic feet per second
20 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

 DAY PUMPING STREAMFLOW

 RATE DEPLETION

 (cubic feet per second)

2001031400 0.0000 0.1395

2001031500 0.0000 0.1333

2001031600 0.0000 0.1275

2001031700 0.0000 0.1221

2001031800 0.0000 0.1170

2001031900 0.0000 0.1123

2001032000 0.0000 0.1080

2001032100 0.0000 0.1038

2001032200 0.0000 0.1000

2001032300 0.0000 0.0964

2001032400 0.0000 0.0930

2001032500 0.0000 0.0897

2001032600 0.0000 0.0867

2001032700 0.0000 0.0839

2001032800 0.0000 0.0812

2001032900 0.0000 0.0786

2001033000 0.0000 0.0762

2001033100 0.0000 0.0739

2001040100 0.0000 0.0717

2001040200 0.0000 0.0696

2001040300 0.0000 0.0676

2001040400 0.0000 0.0657

2001040500 0.0000 0.0639

2001040600 0.0000 0.0622

 DAY PUMPING STREAMFLOW

 RATE DEPLETION

 (cubic feet per second)

2001040700 0.0000 0.0606

2001040800 0.0000 0.0590

2001040900 0.0000 0.0575

2001041000 0.0000 0.0560

2001041100 0.0000 0.0547

2001041200 0.0000 0.0533

2001041300 0.0000 0.0521

2001041400 0.0000 0.0508

2001041500 0.0000 0.0497

2001041600 0.0000 0.0485

2001041700 0.0000 0.0475

2001041800 0.0000 0.0464

2001041900 0.0000 0.0454

2001042000 0.0000 0.0444

2001042100 0.0000 0.0435

2001042200 0.0000 0.0426

2001042300 0.0000 0.0417

2001042400 0.0000 0.0409

2001042500 0.0000 0.0401

2001042600 0.0000 0.0393

2001042700 0.0000 0.0385

2001042800 0.0000 0.0378

2001042900 0.0000 0.0371

2001043000 0.0000 0.0364
Appendix 1 21

 DATE QWELL QS

 2001010100 0.0000 0.0000

 2001010200 0.0000 0.0000

 2001010300 0.0000 0.0000

 2001010400 0.0000 0.0000

 2001010500 0.0000 0.0000

 2001010600 0.0000 0.0000

 2001010700 0.0000 0.0000

 2001010800 0.0000 0.0000

 2001010900 0.0000 0.0000

 2001011000 0.0000 0.0000

 2001011100 0.0000 0.0000

 2001011200 0.0000 0.0000

 2001011300 0.0000 0.0000

 2001011400 0.0000 0.0000

 2001011500 0.0000 0.0000

 2001011600 0.0000 0.0000

 2001011700 0.0000 0.0000

 2001011800 0.0000 0.0000

 2001011900 0.0000 0.0000

 2001012000 0.0000 0.0000

 2001012100 0.0000 0.0000

 2001012200 0.0000 0.0000

 2001012300 0.0000 0.0000

 2001012400 0.0000 0.0000

 2001012500 0.0000 0.0000

 2001012600 0.0000 0.0000

 2001012700 0.0000 0.0000

 2001012800 0.0000 0.0000

 2001012900 0.0000 0.0000

 2001013000 0.0000 0.0000

 2001013100 0.0000 0.0000

 2001020100 0.5570 0.0001

 2001020200 0.5570 0.0028

 2001020300 0.5570 0.0112

 2001020400 0.5570 0.0235

 2001020500 0.5570 0.0376

 2001020600 0.5570 0.0522

 2001020700 0.5570 0.0665

 DATE QWELL QS

 2001020800 0.5570 0.0802

 2001020900 0.5570 0.0932

 2001021000 0.5570 0.1055

 2001021100 0.5570 0.1170

 2001021200 0.5570 0.1278

 2001021300 0.5570 0.1380

 2001021400 0.5570 0.1475

 2001021500 0.5570 0.1564

 2001021600 0.5570 0.1649

 2001021700 0.5570 0.1728

 2001021800 0.5570 0.1804

 2001021900 0.5570 0.1875

 2001022000 0.5570 0.1942

 2001022100 0.5570 0.2006

 2001022200 0.5570 0.2067

 2001022300 0.5570 0.2125

 2001022400 0.5570 0.2180

 2001022500 0.5570 0.2233

 2001022600 0.5570 0.2283

 2001022700 0.5570 0.2331

 2001022800 0.5570 0.2378

 2001030100 0.0000 0.2421

 2001030200 0.0000 0.2437

 2001030300 0.0000 0.2394

 2001030400 0.0000 0.2309

 2001030500 0.0000 0.2206

 2001030600 0.0000 0.2097

 2001030700 0.0000 0.1990

 2001030800 0.0000 0.1886

 2001030900 0.0000 0.1789

 2001031000 0.0000 0.1698

 2001031100 0.0000 0.1614

 2001031200 0.0000 0.1535

 2001031300 0.0000 0.1463

 2001031400 0.0000 0.1395

 2001031500 0.0000 0.1333

 2001031600 0.0000 0.1275

 2001031700 0.0000 0.1221

Example Plot File 
22 STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions

 DATE QWELL QS

 2001031800 0.0000 0.1170

 2001031900 0.0000 0.1123

 2001032000 0.0000 0.1080

 2001032100 0.0000 0.1038

 2001032200 0.0000 0.1000

 2001032300 0.0000 0.0964

 2001032400 0.0000 0.0930

 2001032500 0.0000 0.0897

 2001032600 0.0000 0.0867

 2001032700 0.0000 0.0839

 2001032800 0.0000 0.0812

 2001032900 0.0000 0.0786

 2001033000 0.0000 0.0762

 2001033100 0.0000 0.0739

 2001040100 0.0000 0.0717

 2001040200 0.0000 0.0696

 2001040300 0.0000 0.0676

 2001040400 0.0000 0.0657

 2001040500 0.0000 0.0639

 2001040600 0.0000 0.0622

 2001040700 0.0000 0.0606

 2001040800 0.0000 0.0590

 DATE QWELL QS

 2001040900 0.0000 0.0575

 2001041000 0.0000 0.0560

 2001041100 0.0000 0.0547

 2001041200 0.0000 0.0533

 2001041300 0.0000 0.0521

 2001041400 0.0000 0.0508

 2001041500 0.0000 0.0497

 2001041600 0.0000 0.0485

 2001041700 0.0000 0.0475

 2001041800 0.0000 0.0464

 2001041900 0.0000 0.0454

 2001042000 0.0000 0.0444

 2001042100 0.0000 0.0435

 2001042200 0.0000 0.0426

 2001042300 0.0000 0.0417

 2001042400 0.0000 0.0409

 2001042500 0.0000 0.0401

 2001042600 0.0000 0.0393

 2001042700 0.0000 0.0385

 2001042800 0.0000 0.0378

 2001042900 0.0000 0.0371

 2001043000 0.0000 0.0364

Howard W. Reeves—STRMDEPL08—An Extended Version of STRMDEPL with Additional Analytical Solutions—Open-File Report 2008–1166