

Publications—Scientific Investigations Report 20065045 
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)
Potential groundwater 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 groundwater 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 groundwaterflow equation for the case of onedimensional flow in a finitewidth aquifer bounded by a linear surfacewater feature such as a stream. These equations, which require only five input variables, were incorporated into an existing firmyieldestimator (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 surfacewaterbody shapes having a more realistic representation of a reservoir shoreline than a stream, a comparison of groundwaterflow rates simulated by the groundwater equations with flow rates simulated by a twodimensional, finitedifference groundwaterflow 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 reservoiraquifer systems were assumed to verify that the groundwaterflow 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 groundwaterflow equations to reservoirs in Massachusetts whose shorelines are in contact with a sand and gravel aquifer.
Abstract
Introduction
Purpose and Scope
The Existing FirmYieldEstimator Model for Reservoirs in Massachusetts
Determination of GroundWater Contributions to Reservoir Storage
NumericalModel Simulations of Idealized ReservoirAquifer Geometries
Analytical Simulations of Idealized ReservoirAquifer Geometries
Effect of Reservoir Shape on the Flow Rate between the Reservoir and Aquifer
Application of the GroundWaterFlow Equations to the FirmYieldEstimator Model
Modifications to the GroundWaterFlow Equations
NumericalModel Simulations of GroundWaterFlow Rates and Reservoir Water Levels
Modified FirmYieldEstimator Model Simulations of GroundWaterFlow Rates and Reservoir Water Levels
Comparison of Simulated GroundWaterFlow Rates and Reservoir Water Levels
Iterative Loop to Calculate the Change in Reservoir Stage
Effect of Uncertainty in the Input Variables to the GroundWaterFlow Equations
Sensitivity of Firm Yield to the Reservoir StageStorage Relation
Sensitivity of Firm Yield to Other Reservoir and Aquifer Input Variables
Potential Effect of GroundWater Contributions on Firm Yields for Reservoirs in Massachusetts
Summary
Acknowledgments
References Cited
1–3. Diagrams showing:
4.  Graphs showing differences between the numerically and analytically simulated groundwaterflow rates, and timing of the flows for selected reservoiraquifer geometries shown in figure 3. 
5.  Flow chart of the modified firmyieldestimator model. 
6.  Maps showing locations of four reservoiraquifer 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 reservoiraquifer systems patterned after the four reservoiraquifer 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 groundwater flow rates; and B, reservoir waterlevel elevations for four idealized reservoiraquifer systems during a 2year 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 firmyield simulations for four idealized reservoiraquifer systems. 
10.  Shape of the stagestorage relation for two drinkingwater reservoirs: A, Bearhole Reservoir; and B, Fitchburg Reservoir. 
11.  Sensitivity of firm yield to reservoir and aquifer characteristics for four idealized reservoiraquifer systems. 
12.  Map showing locations of nine reservoirs that have shorelines in contact with sand and gravel aquifers. 
Suggested Citation:
Archfield, S.A., and Carlson, C.S., 2006, Groundwater 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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