Surface-water quality and flow Modeling Interest Group
by Phillip J. Zarriello1, Paul M. Barlow1, and Paul B. Duda2
1 U.S. Geological Survey, Northborough, MA
2 Aqua Terra Consultants, Dacatur, GA
For more information, please contact:
Phillip J. Zarriello
U.S. Geological Survey
10 Bearfoot Road
Northborough, MA 01532
Internet: pzarriel@usgs.gov
Phone: (508) 490-5010
FAX: (508) 490-5068
The STRMDEPL program, and instructions for its use with the GenScn interface to the HSPF model, may be downloaded from this site.
This version of the paper has all of the figures converted to thumbnails with links to the larger images. A version with all of the figures inline is also available; the download time may be longer, but the inline figures may be more convenient for viewing and printing.
Citation:
Zarriello, P.J., Barlow, P.M., and Duda, P.B., 2001, Simulating the effects
of ground-water withdrawals on streamflow in a precipitation-runoff model,
in Bridging the Gap: Meeting the World's Water and Environmental Resources
Challenges, Proceedings of the World Water and Environmental Resources
Congress, May 20-24, 2001, Orlando, Florida, 10 pages.
Abstract
Introduction
STRMDEPL-- streamflow depletion from pumped wells
Application of STRMDEPL in the HSPF watershed model
Water-supply Withdrawals In Excess of Streamflow
STRMDEPL extension in the GenScn interface
Conclusion
ReferencesPrecipitation-runoff models are used to assess the effects of water use and management alternatives on streamflow. Often, ground-water withdrawals are a major water-use component that affect streamflow, but the ability of surface-water models to simulate ground-water withdrawals is limited. As part of a Hydrologic Simulation Program-FORTRAN (HSPF) precipitation-runoff model developed to analyze the effect of ground-water and surface-water withdrawals on streamflow in the Ipswich River in northeastern Massachusetts, an analytical technique (STRMDEPL) was developed for calculating the effects of pumped wells on streamflow. STRMDEPL is a FORTRAN program based on two analytical solutions that solve equations for ground-water flow to a well completed in a semi-infinite, homogeneous, and isotropic aquifer in direct hydraulic connection to a fully penetrating stream. One analytical method calculates unimpeded flow at the stream-aquifer boundary and the other method calculates the resistance to flow caused by semipervious streambed and streambank material. The principle of superposition is used with these analytical equations to calculate time-varying streamflow depletions due to daily pumping.
The HSPF model can readily incorporate streamflow depletions caused by a well or surface-water withdrawal, or by multiple wells or surface-water withdrawals, or both, as a combined time-varying outflow demand from affected channel reaches. These demands are stored as a time series in the Watershed Data Management (WDM) file. This time-series data is read into the model as an external source used to specify flow from the first outflow gate in the reach where these withdrawals are located. Although the STRMDEPL program can be run independently of the HSPF model, an extension was developed to run this program within GenScn, a scenario generator and graphical user interface developed for use with the HSPF model. This extension requires that actual pumping rates for each well be stored in a unique WDM dataset identified by an attribute that associates each well with the model reach from which water is withdrawn. Other attributes identify the type and characteristics of the data. The interface allows users to easily add new pumping wells, delete exiting pumping wells, or change properties of the simulated aquifer or well. Development of this application enhanced the ability of the HSPF model to simulate complex water-use conditions in the Ipswich River Basin. The STRMDEPL program and the GenScn extension provide a valuable tool for water managers to evaluate the effects of pumped wells on streamflow and to test alternative water-use scenarios.
Ground-water withdrawals often are a major water-use component that affect streamflow. Ground-water flow models have been used to assess the interaction between pumped wells and streamflow, but these models generally do not treat the surface water and interflow (shallow ground-water flow that responds rapidly to precipitation) components in any detail. Also, ground-water flow models commonly do not include the area of the watershed that is not underlain by aquifer. Some effort has been made to couple ground-water flow models with surface-water flow models. Swain and Wexler (1996) linked the popular ground-water flow model MODFLOW (McDonald and Harbaugh, 1988) to the BRANCH (Schaffranek, 1987) river hydraulics flow model. Ramireddygari and others (2000) linked MODFLOW to the POTYLDR (Zovne and others, 1977) watershed model designed for simulating feedlot runoff. Sophocleous and Perkins (2000) linked MODFLOW to the SWAT (Arnold and others, 1998) watershed model designed for simulating agricultural runoff. Simulation of the stream-aquifer interaction by these methods requires a fully developed distributed ground-water flow model in addition to the development and linkage with a surface-water model.
The ability to simulate the time-delayed response of ground-water withdrawals on streamflow is critical in precipitation-runoff models used to assess the effects of water-use and management alternatives on streamflow. Reasonable simulations of the effects of ground-water withdrawals on streamflow can be obtained under appropriate conditions using simple analytical methods. A HSPF precipitation-runoff model (Bicknell and others, 1997) developed to analyze the effect of ground-water and surface-water withdrawals on streamflow in the Ipswich River in northeastern Massachusetts (Zarriello and Ries, 2000) incorporated an analytical technique (STRMDEPL) for calculating the effects of pumped wells on streamflow depletion. This paper describes the STRMDEPL program, its use in the HSPF precipitation-runoff model, and a graphic interface developed for running STRMDEPL with HSPF.
STRMDEPL is a FORTRAN program developed by Barlow (2000) to calculate time-varying streamflow depletion caused by a pumped well. The program is based on two analytical solutions to the ground-water flow equation; (1) the unimpeded connection between the stream and aquifer (Jenkins, 1968), and (2); the resistance to flow at the boundary between the stream and aquifer caused by semipervious streambed and streambank material (Hantush, 1965). Superposition is used to calculate the influence of time-varying daily pumping rates on streamflow depletion. The theoretical description of STRMDEPL is reproduced here from Barlow (2000).
Jenkins (1968) presented the most widely applied analytical solution for determining time-varying rates of streamflow depletion by wells. For application of this solution, several simplifying assumptions concerning the aquifer and adjoining stream must be made. These assumptions, which are described in Theis (1941), Glover and Balmer (1954), and Jenkins (1968), are:
The analytical solution presented in Jenkins (1968) is
and
Qs is the rate of streamflow depletion
(cubic length per time);
Qw is the pumping rate of the well
(cubic length per time);
d is the perpendicular 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 time.
Inspection of equation 1 indicates that at small time, the argument
of the complementary error function (U) becomes large, and the
function itself approaches zero. This indicates that immediately after
withdrawal begins, the source of water to the well is aquifer storage, and
there is little or no streamflow depletion. As time increases, the rate of
streamflow depletion contributing water to the well increases and ultimately
approaches the rate of withdrawal of the well as steady-state conditions
are achieved and contributions from aquifer storage approach zero (that
is, Qs 
Qw as t 
).
Streamflow depletion consists of two components. The first is captured ground-water discharge, which is ground water that would have discharged to the stream and contributed to the total amount of streamflow had the well not been pumping. The second component is induced infiltration, which is streamflow that is drawn out of the stream and into the aquifer. The analytical solutions presented here do not differentiate between these two components of streamflow depletion; they simply provide a total depletion that consists of both captured ground-water discharge and induced infiltration.
Three of the variables in equation 1 that affect streamflow depletion are often combined into a single varable that characterizes a particular stream-aquifer-well system. This variable has been referred to as the streamflow depletion factor (sdf)
The ratio of transmissivity to storativity is defined as the hydraulic diffusivity of the aquifer (T/S). When a well is close to a stream (that is, a small d), or when the diffusivity of the aquifer is very large, streamflow depletion will begin soon after withdrawal begins. Conversely, if a well is far from a stream, or the diffusivity of the aquifer is very small (such as water-table aquifers in which the storativity is assumed equal to the specific yield of the aquifer), there may be a substantial time lag between the onset of pumping and the beginning of streamflow depletion.
The amount of streamflow depletion that results from pumping can be reduced by resistance to flow through streambed and streambank materials at the stream-aquifer boundary. In such cases, the streambed and streambank materials are referred to as being semipervious. Hantush (1965) derived an analytical solution for streamflow depletion by wells that accounts for the presence of semipervious materials at the stream-aquifer boundary for the same aquifer, stream, and well conditions used to derive equation 1. His solution is
(2)
where
K is hydraulic conductivity of the aquifer (length
per time);
K' is hydraulic conductivity of the streambank
(length per time); and
b' is thickness of the streambank (length).
As the value of the streambank leakance term increases (that is, resistance to flow at the stream- aquifer boundary increases), streamflow depletion responds more slowly to pumping, and streamflow depletion rates are smaller than those that would occur in the absence of semipervious streambank materials.
The amount of streamflow depletion that occurs in response to pumping will be reduced if the stream does not penetrate the full thicknesss of the aquifer. The effect of partial penetration is accounted for in equations 1 and 2 by replacing the actual distance from the well to the stream (d) by an effective distance from the pumped well to the streambank (x0). Guidelines for determining x0 are provided by Hantush (1965) and by Spalding and Khaleel (1991). Spalding and Khaleel show that the effective distance of the well from the stream is a function of the actual distance from the well to the stream and the extent of penetration of the stream into the aquifer. Recently, Hunt (1999) developed an analytical solution that directly accounts for partial penetration of a stream.
One of the assumptions made in the development of equations 1 and 2 is that the pumping rate of the well is steady during any period of pumping. The equations can be used in conjunction with the method of superposition to calculate streamflow depletion in response to time-varying pumping rates at the well. The use of superposition is appropriate here because the underlying ground-water flow equation on which each solution is based is linear.
In the superposition approach, incremental changes in streamflow depletion in response to time-varying pumping rates are accounted for by summing the depletions that occur in response to each pumping rate. A superposition equation (Stallman, 1962; Moench, 1971; Butt and McElwee, 1985) can be written for total streamflow depletion as
(3)
where
Qs(ti) is the rate of streamflow
depletion at time step i (cubic length per time);
Q0(t0) is the initial pumping rate
of the well during t0 (cubic length per time);
Qk(tk) is the change in pumping rate
of the well during interval k (cubic length per time);
F(t0),F(ti-k+1) are the values
of either erfc(U) or 
(depending on whether equation 1 or equation 2 is selected) at times t0 and ti-k+1, respectively
(dimensionless);
ti is the length of time from the beginning
of pumping to the time of interest;
tk is the time corresponding to time step k;
to is the length of time of the initial pumping
rate prior to the start of the analysis;
i is the number of time steps (dimensionless); and
k is the time step number (dimensionless).
Equation 3 assumes a constant time-step size of one time unit, such as 1 day. Streamflow depletions are calculated for each time of interest (ti), and each time of interest is equal to the product of the constant time-step size (for example, 1 day) by the number of time steps.
STRMDEPL was developed for use in a HSPF watershed model developed to determine the effects of ground-water withdrawals on streamflow in the Ipswich River Basin in northeastern Massachusetts. Streamflow depletions were calculated individually with STRMDEPL for all pumped municipal wells and other large-capacity wells for the calibration period October 1989 through September 1993. Streamflow depletions caused by the pumping of wells along a reach were combined with any surface-water withdrawals in that reach to obtain a single time-series of the total water withdrawal for the reach. The total withdrawal for each reach is read into the HSPF model from the appropriate WDM (Flynn and others, 1995) data set by the EXT SOURCE block (external source) of the UCI (User Control Input) file. These withdrawals are time-dependent volume demands passed to the first outflow gate in a RCHRES (a stream or reservoir segment). Accordingly, these withdrawals must be satisfied before any water can exit from the next outflow gate, which, in most cases, is the water routed to the downstream reach. In reaches with no withdrawals, water is routed downstream through a single outflow gate.
Streamflow depletion caused by ground-water withdrawals is substantially less variable than actual pumping rates of wells because of the damping effect of diffusivity of the aquifer and the distance of the well from the stream. Figure 1 shows the daily pumping of a supply well in the Ipswich River Basin, the smoothed 15-day moving average pump rate, and the calculated streamflow depletion caused by ground-water pumping at the well. Also note the lag between the 15-day moving average pumping rate (smoothed curve) and the streamflow depletion. The extent of the lag will depend on aquifer properties and the distance of the well from the stream.
Figure 1. Actual and 15-day moving average daily pumping rate from
a well in the Ipswich River Basin, Mass., and the calculated streamflow
depletion resulting from the pumped well.
During long periods of dry weather, ground-water withdrawals can exceed streamflow in a river reach; that is, withdrawals exceed captured ground-water discharge and induced infiltration. When this happens, water is removed from ground-water storage and the water table continues to fall while pumping occurs. This transient condition typically occurs only during long dry periods in the Ipswich River Basin; nevertheless, this condition required special consideration in the HSPF model to preserve the mass balance of water.
Neither the HSPF model nor the STRMDEPL program account for changes in ground-water storage that result from withdrawals in excess of streamflow, but with the 'Special Actions' feature of the HSPF model (Jobes and others, 1998) the mass balance of water could be preserved when withdrawals exceeded streamflow. The special action developed as part of this study accounts for a running deficit between the actual withdrawals and the withdrawals satisfied by streamflow in the simulation. The special action then replenishes this deficit when streamflow exceeds demands, thereby maintaining the hydrologic mass balance of the system over the simulation period. In effect, replenishing the deficit by the SA is analogous to recharging the lost ground-water storage. A detailed description of how the special action operates is given in Zarriello and Ries (2000).
GenScn (Kittle and others, 1998) is a graphical user interface developed to aid in the GENeration and analysis of watershed simulation SceNarios. GenScn is especially useful with the HSPF model. An extension to GenScn was developed to run STRMDEPL and update the appropriate WDM files for the simulation of alternative ground-water withdrawals. The STRMDEPL extension requires the actual well pumping rate to reside as a WDM data set along with appropriate target data sets for the computed streamflow depletions and the combined withdrawals for a reach. Attribute information is assigned to these data sets for the extension to identify the wells, streamflow depletions computed for the well, and to combine the appropriate streamflow depletions and surface-water withdrawals for a reach. The required attribute information includes:
IDLOCN--Identifies the reach associated with the well.
IDCONS--Identifies the constituent, and is populated with one of the following
values:
PUMP--is the time-series of the actual well pump rate
DEPL--is the times-series of the computed streamflow depletion
TOTDEPL--is the times-series of the total withdrawals from a
reach
STAID--is a unique identifier for each well.
IDSCEN--is the scenario name, in this case set to OBSERVED.
The STRMDEPL extension is loaded into an existing GenScn project as an external program through the 'Analysis-New' menu option. The STRMDEPL program itself is independent of GenScn, so it can be enhanced or modified if needed. Once the extension has been loaded, the STRMDEPL extension may be selected from the Analysis menu as shown in figure 2. The OBSERVED scenario must also be selected in the Scenario window (middle) to find the data sets in the WDM file for the actual pumping rates. Figure 2 also shows the general configuration of the GenScn interface documented in Kittle and others (1998).
(larger image)
Figure 2. Accessing the STRMDEPL extension within the GenScn
interface.
Selection of STRMDEPL queries the WDM file for all data sets that have been identified as PUMP in the attribute IDCONS and brings up the table shown in figure 3. Each pumped well is identified by the unique well identification number (STAID attribute) and reach where the well is located (IDLOCN attribute). The user can add new wells to a reach or edit the STRMDEPL variables of existing wells (unshaded area in figure 3). If a well has an existing streamflow depletion input file (named xxxyyy.sdi, where xxx corresponds to the STAID and yyy corresponds to IDLOCN; in a 'strmdepl' subdirectory under the working directory where GenScn is running), the information required to run the STRMDEPL program is filled in automatically from this file. If the stream depletion for a well is simulated (bottom center left button, fig. 3), an output file generated by the STRMDEPL program created with the same name prefix and a xxxyyy.sdo suffix. The formats of the input and output files are documented by Barlow (2000).
(larger image)
Figure 3. STRMDEPL extension window within the GenScn graphic-user
interface.
Input information required to run STRMDEPL extension includes the perpendicular distance of the well from the stream, diffusivity, and a flag indicating whether the streambank is semipervious. If the streambank is semipervious (true) then a value for streambank leakance is required. An optional preexisting pump rate and the number of days prior to the analysis can be specified to set an initial equilibrium condition. The bottom left key 'Edit Multipliers' (fig. 3) allows the user to specify monthly factors for adjusting the pumping rate.
If stream depletions are simulated, the user is prompted to overwrite existing streamflow depletion time-series data. If these time-series are updated, the user is prompted to update the combined withdrawals for reaches. If a well is not used in a given simulation, but was previously simulated, the last streamflow depletion computed for the well is used in the HSPF simulation. After STRMDEPL is run for a given scenario, the HSPF simulation is run with the new withdrawal rates.
The STRMDEPL program extends the ability of watershed models to simulate the time-delay effects of ground-water withdrawals on streamflow, under appropriate conditions, by means of a simple analytical technique. This technique requires only a few input variables, and thus is easy to apply. The STRMDEPL extension in GenScn allows users to simulate pumping conditions quickly and easily in the HSPF model. This will enhance water-resource managers' ability to assess and understand the interrelated effects of surface-water and ground-water withdrawals on streamflow, and to develop sound management practices to protect these resources.
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