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Publications—Scientific Investigations Report 2006-5045

Prepared in cooperation with the Massachusetts Department of Environmental Protection

Ground-Water Contributions to Reservoir Storage and the Effect on Estimates of Firm Yield for Reservoirs in Massachusetts

By Stacey A. Archfield and Carl S. Carlson

U.S. Geological Survey Scientific Investigations Report 2006–5045

The body of the report is available in PDF Format ( 1,790 KB)


Abstract

Potential ground-water contributions to reservoir storage were determined for nine reservoirs in Massachusetts that had shorelines in contact with sand and gravel aquifers. The effect of ground water on firm yield was not only substantial, but furthermore, the firm yield of a reservoir in contact with a sand and gravel aquifer was always greater when the ground-water contribution was included in the water balance. Increases in firm yield ranged from 2 to 113 percent, with a median increase in firm yield of 10 percent. Additionally, the increase in firm yield in two reservoirs was greater than 85 percent.

This study identified a set of equations that are based on an analytical solution to the ground-water-flow equation for the case of one-dimensional flow in a finite-width aquifer bounded by a linear surface-water feature such as a stream. These equations, which require only five input variables, were incorporated into an existing firm-yield-estimator (FYE) model, and the potential effect of ground water on firm yield was evaluated. To apply the FYE model to a reservoir in Massachusetts, the model requires that the drainage area to the reservoir be clearly defined and that some surface water flows into the reservoir. For surface-water-body shapes having a more realistic representation of a reservoir shoreline than a stream, a comparison of ground-water-flow rates simulated by the ground-water equations with flow rates simulated by a two-dimensional, finite-difference ground-water-flow model indicate that the agreement between the simulated flow rates is within ±10 percent when the ratio of the distance from the reservoir shoreline to the aquifer boundary to the length of shoreline in contact with the aquifer is between values of 0.5 and 3.5.

Idealized reservoir-aquifer systems were assumed to verify that the ground-water-flow equations were implemented correctly into the existing FYE model; however, the modified FYE model has not been validated through a comparison of simulated and observed data. A comparison of simulated and observed reservoir water levels would further define limitations to the applicability of the ground-water-flow equations to reservoirs in Massachusetts whose shorelines are in contact with a sand and gravel aquifer.

TABLE OF CONTENTS

Abstract

Introduction

Purpose and Scope

The Existing Firm-Yield-Estimator Model for Reservoirs in Massachusetts

Determination of Ground-Water Contributions to Reservoir Storage

Numerical-Model Simulations of Idealized Reservoir-Aquifer Geometries

Analytical Simulations of Idealized Reservoir-Aquifer Geometries

Effect of Reservoir Shape on the Flow Rate between the Reservoir and Aquifer

Application of the Ground-Water-Flow Equations to the Firm-Yield-Estimator Model

Modifications to the Ground-Water-Flow Equations

Numerical-Model Simulations of Ground-Water-Flow Rates and Reservoir Water Levels

Modified Firm-Yield-Estimator Model Simulations of Ground-Water-Flow Rates and Reservoir Water Levels

Comparison of Simulated Ground-Water-Flow Rates and Reservoir Water Levels

Iterative Loop to Calculate the Change in Reservoir Stage

Effect of Uncertainty in the Input Variables to the Ground-Water-Flow Equations

Sensitivity of Firm Yield to the Reservoir Stage-Storage Relation

Sensitivity of Firm Yield to Other Reservoir and Aquifer Input Variables

Potential Effect of Ground-Water Contributions on Firm Yields for Reservoirs in Massachusetts

Summary

Acknowledgments

References Cited

Figures

1–3. Diagrams showing:

  1. Possible sources and losses of water for a hypothetical drinking-water reservoir.


  2. A, Reservoir water level at equilibrium with the water table in the surrounding aquifer; B, response of the water table to a decrease in the water level of the reservoir relative to the water table; or C, to an increase in the water level of the reservoir relative to the water table.


  3. A, Surface-water-body shapes; B, with underlying model grid (shown with surface-water-body shape 10) for reservoir-aquifer systems; and C, reservoir- stage fluctuations used to evaluate the effects of reservoir-aquifer geometry on the analytical solution to the ground-water flow equation derived by Rorabaugh (1964).


4. Graphs showing differences between the numerically and analytically simulated ground-water-flow rates, and timing of the flows for selected reservoir-aquifer geometries shown in figure 3.

5. Flow chart of the modified firm-yield-estimator model.

6. Maps showing locations of four reservoir-aquifer systems in Massachusetts: A, Fitchburg Reservoir; B, Morse Reservoir; C, Bearhole Reservoir; and D, Millham Reservoir.

7. Diagram of model grids used in the numerical simulations of four idealized reservoir-aquifer systems patterned after the four reservoir-aquifer systems shown in figure 6. Reservoir A is patterned after Fitchburg Reservoir (fig. 6A); Reservoir B is patterned after Morse Reservoir (fig. 6B); Reservoir C is patterned after Bearhole Reservoir (fig. 6C); Reservoir D is patterned after Millham Reservoir (fig. 6D).

8–11. Graphs showing:

8. A, Comparison of simulated average ground-water flow rates; and B, reservoir water-level elevations for four idealized reservoir-aquifer systems during a 2-year period of average climate and streamflow conditions (April 1975 through March 1977).

9. Sensitivity of firm yield to the closure criterion used in the iterative loop of the firm-yield simulations for four idealized reservoir-aquifer systems.

10. Shape of the stage-storage relation for two drinking-water reservoirs: A, Bearhole Reservoir; and B, Fitchburg Reservoir.

11. Sensitivity of firm yield to reservoir and aquifer characteristics for four idealized reservoir-aquifer systems.

12. Map showing locations of nine reservoirs that have shorelines in contact with sand and gravel aquifers.

Tables

  1. Reservoir and aquifer characteristics for four idealized reservoir-aquifer systems.


  2. Estimated reservoir and aquifer characteristics for nine reservoirs in Massachusetts whose reservoir shorelines are in contact with a sand and gravel aquifer.


  3. Potential effect of ground-water contributions to reservoir storage on firm yield for nine reservoirs in Massachusetts.

Suggested Citation:
Archfield, S.A., and Carlson, C.S., 2006, Ground-water contributions to reservoir storage and the effect on estimates of firm yield for reservoirs in Massachusetts: U.S. Geological Survey Scientific Investigations Report 2006–5045, 27 p.


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USGS Massachusetts–Rhode Island Water Science Center
10 Bearfoot Road
Northborough, MA 01532

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