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Scientific Investigations Report 2011–5125

Prepared in cooperation with the
Massachusetts Department of Environmental Protection

Refinement and Evaluation of the Massachusetts
Firm-Yield Estimator Model Version 2.0

By Sara B. Levin, Stacey A. Archfield, and Andrew J. Massey

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The firm yield is the maximum average daily withdrawal that can be extracted from a reservoir without risk of failure during an extended drought period. Previously developed procedures for determining the firm yield of a reservoir were refined and applied to 38 reservoir systems in Massachusetts, including 25 single- and multiple-reservoir systems that were examined during previous studies and 13 additional reservoir systems. Changes to the firm-yield model include refinements to the simulation methods and input data, as well as the addition of several scenario-testing capabilities. The simulation procedure was adapted to run at a daily time step over a 44-year simulation period, and daily streamflow and meteorological data were compiled for all the reservoirs for input to the model.

Another change to the model-simulation methods is the adjustment of the scaling factor used in estimating groundwater contributions to the reservoir. The scaling factor is used to convert the daily groundwater-flow rate into a volume by multiplying the rate by the length of reservoir shoreline that is hydrologically connected to the aquifer. Previous firm-yield analyses used a constant scaling factor that was estimated from the reservoir surface area at full pool. The use of a constant scaling factor caused groundwater flows during periods when the reservoir stage was very low to be overestimated. The constant groundwater scaling factor used in previous analyses was replaced with a variable scaling factor that is based on daily reservoir stage. This change reduced instability in the groundwater-flow algorithms and produced more realistic groundwater-flow contributions during periods of low storage.

Uncertainty in the firm-yield model arises from many sources, including errors in input data. The sensitivity of the model to uncertainty in streamflow input data and uncertainty in the stage-storage relation was examined. A series of Monte Carlo simulations were performed on 22 reservoirs to assess the sensitivity of firm-yield estimates to errors in daily-streamflow input data. Results of the Monte Carlo simulations indicate that underestimation in the lowest stream inflows can cause firm yields to be underestimated by an average of 1 to 10 percent. Errors in the stage-storage relation can arise when the point density of bathymetric survey measurements is too low. Existing bathymetric surfaces were resampled using hypothetical transects of varying patterns and point densities in order to quantify the uncertainty in stage-storage relations. Reservoir-volume calculations and resulting firm yields were accurate to within 5 percent when point densities were greater than 20 points per acre of reservoir surface.

Methods for incorporating summer water-demand-reduction scenarios into the firm-yield model were developed as well as the ability to relax the no-fail reliability criterion. Although the original firm-yield model allowed monthly reservoir releases to be specified, there have been no previous studies examining the feasibility of controlled releases for downstream flows from Massachusetts reservoirs. Two controlled-release scenarios were tested—with and without a summer water-demand-reduction scenario—for a scenario with a no-fail criterion and a scenario that allows for a 1-percent failure rate over the entire simulation period. Based on these scenarios, about one-third of the reservoir systems were able to support the flow-release scenarios at their 2000–2004 usage rates. Reservoirs with higher storage ratios (reservoir storage capacity to mean annual streamflow) and lower demand ratios (mean annual water demand to annual firm yield) were capable of higher downstream release rates. For the purposes of this research, all reservoir systems were assumed to have structures which enable controlled releases, although this assumption may not be true for many of the reservoirs studied.

Revised October 25, 2011

First posted September 8, 2011

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For additional information contact:
Director, Massachusetts-Rhode Island Water Science Center, 10 Bearfoot Road, Northborough, MA 01532

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Suggested citation:

Levin, S.B., Archfield, S.A., and Massey, A.J., 2011, Refinement and evaluation of the Massachusetts firm-yield estimator model version 2.0: U.S. Geological Survey Scientific Investigations Report 2011–5125, 49 p., plus CD–ROM. (Also available at




Purpose and Scope

Refinements to the Existing Firm-Yield Estimator Model

Bathymetry and Stage-Storage Relations

Surface-Water Inflows

Precipitation and Evaporation

Groundwater Contributions

Applications of the Firm-Yield Estimator Model

Application of the Firm-Yield Estimator Model to a Single-Reservoir System

Application of the Firm-Yield Estimator Model to a Multiple-Reservoir System

Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs

Sensitivity of Firm-Yield Estimates to Errors in Daily Streamflow

Sensitivity of the Firm-Yield Model to Bathymetric-Map Accuracy

Validation of Groundwater Parameters

Effect of Drought Severity on Firm-Yield Estimates

Effect of Controlled Releases and Demand Management on Firm Yield

Controlled-Release Scenarios

Summer Water-Demand Management

Reducing Reservoir Reliability Requirements

Tradeoffs Between Demand Management, Controlled Releases, and Reliability

Summary and Conclusions

References Cited

Appendix 1. Hypsographic Data

Appendix 2. Bathymetric Maps

Appendix 3. Reservoir-System Diagrams

Appendix 4. Monthly Percentile Streamflows

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