Publications—Scientific Investigations Report 2006–5044

Factors Affecting Firm Yield and the Estimation of Firm Yield for Selected Streamflow-Dominated Drinking-Water-Supply Reservoirs in Massachusetts

Prepared in cooperation with the Massachusetts Department of Environmental Protection

By Marcus C. Waldron and Stacey A. Archfield

U.S. Geological Survey Scientific Investigations Report 2006–5044

The body of the report is available in PDF Format (1,864 KB)

Appendix—Data, Records, and Input Files for Use in Estimating the Firm Yield of Massachusetts Drinking-Water-Supply Reservoirs


Factors affecting reservoir firm yield, as determined by application of the Massachusetts Department of Environmental Protection’s Firm Yield Estimator (FYE) model, were evaluated, modified, and tested on 46 streamflow-dominated reservoirs representing 15 Massachusetts drinking-water supplies. The model uses a mass-balance approach to determine the maximum average daily withdrawal rate that can be sustained during a period of record that includes the 1960s drought-of-record.

The FYE methodology to estimate streamflow to the reservoir at an ungaged site was tested by simulating streamflow at two streamflow-gaging stations in Massachusetts and comparing the simulated streamflow to the observed streamflow. In general, the FYE-simulated flows agreed well with observed flows. There were substantial deviations from the measured values for extreme high and low flows. A sensitivity analysis determined that the model’s streamflow estimates are most sensitive to input values for average annual precipitation, reservoir drainage area, and the soil-retention number-a term that describes the amount of precipitation retained by the soil in the basin.

The FYE model currently provides the option of using a 1,000-year synthetic record constructed by randomly sampling 2-year blocks of concurrent streamflow and precipitation records 500 times; however, the synthetic record has the potential to generate records of precipitation and streamflow that do not reflect the worst historical drought in Massachusetts. For reservoirs that do not have periods of drawdown greater than 2 years, the bootstrap does not offer any additional information about the firm yield of a reservoir than the historical record does. For some reservoirs, the use of a synthetic record to determine firm yield resulted in as much as a 30-percent difference between firm-yield values from one simulation to the next. Furthermore, the assumption that the synthetic traces of streamflow are statistically equivalent to the historical record is not valid.

For multiple-reservoir systems, the firm-yield estimate was dependent on the reservoir system’s configuration. The firm yield of a system is sensitive to how the water is transferred from one reservoir to another, the capacity of the connection between the reservoirs, and how seasonal variations in demand are represented in the FYE model.

Firm yields for 25 (14 single-reservoir systems and 11 multiple-reservoir systems) reservoir systems were determined by using the historical records of streamflow and precipitation. Current water-use data indicate that, on average, 20 of the 25 reservoir systems in the study were operating below their estimated firm yield; during months with peak demands, withdrawals exceeded the firm yield for 8 reservoir systems.




The Massachusetts Firm-Yield-Estimator Guidance Document and Model

Purpose and Scope

Factors Affecting Firm Yield

Criteria for Determining Model Applicability

Reservoir-Specific Properties

Bathymetry and Stage-Storage Relations

Required Releases

Peak-Usage Factors

Precipitation and Evaporation

Estimation of Surface-Water Inflows

QPPQ methods

Model Sensitivity to Flow-Duration-Curve Characteristics

Prediction of Flow-Duration Curves

Selection of Surface-Water Reference Stations

Application of the QPPQ Method to Determine Firm Yield

Limitations to the Application of the QPPQ Method

Precipitation and Streamflow Records

Comparison of Serial Correlation in the Historical and Synthetic Records

Comparison of Firm Yields Determined from the Historical and Synthetic Records

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 Multiple-Reservoir Systems

Reservoirs Connected by Gravity

Reservoirs Connected by Pumping

Estimation of the Firm Yield of a Reservoir System

Summary and Conclusions


References Cited

Description of Appendix

CD-ROM [in pocket]

Appendix. Data, Records, and Input Files for Use in Estimating the Firm Yield of Massachusetts Drinking-Water-Supply Reservoirs



1. Diagram showing possible sources and losses of water to a drinking-water reservoir

2. Graph showing changes in Bearhole Reservoir’s usable storage that resulted from withdrawing the yield that allowed for no more than one monthly reservoir failure during the historical period of record, West Springfield Water Department, West Springfield, Massachusetts

3-4. Maps showing:

3. Locations of drainage areas for 46 drinking-water reservoirs

4. Locations of climate stations whose records were used in the Massachusetts Firm-Yield Estimator model and the locations of drainage areas for 46 drinking-water reservoirs

5. Diagram showing description of the QPPQ method, which estimates daily streamflow at an ungaged location by equating the exceedence probability of a given flow at the gaged location with the exceedence probability at the ungaged location

6-7. Graphs showing:

6. Sensitivity of streamflow at the 10-, 50-, and 90-percent exceedence probabilities calculated by the QPPQ method to values of drainage-area characteristics for four drinking-water reservoirs: A, Granville Reservoir, Westfield Water Department; B, Belmont Reservoir, Hinsdale Water Department; C, Hatchet Pond, Southbridge Water Department; and D, Millham Reservoir, Marlborough DPW–Water and Sewer Division

7. Flow-duration curves for A, Sevenmile River near Spencer, Mass. (01175670); and B, Old Swamp River near South Weymouth, Mass. (01105600) measured and estimated by applying the QPPQ method to records from six streamflow-gaging stations in different hydrologic settings

8. Map showing locations of index streamflow-gaging stations that could be used to estimate streamflow by the QPPQ method and the locations of drainage areas for 46 drinking-water reservoirs

9-11. Graphs showing:

9. Comparison of estimated streamflows into Scott Reservoir from October 1949 through September 1951, Fitchburg Water Department

10. Relationship between the block length used to bootstrap a synthetic record of streamflow and the percentage of serial correlation in the observed streamflow that is preserved in the synthetic record

11. Comparison of firm yields determined from the historical record and 30 synthetic records constructed by bootstrapping 2-year blocks of the historical record for A, Bearhole Reservoir, West Springfield Water Department; B, Upper (Leahey) Reservoir, Lee Water Department; C, Fall Brook Reservoir,Leominster Department of Public Works–Water Division; and D, Cleveland Reservoir, Pittsfield Water Department

12. Water balances for a system of reservoirs in which A, water is released from reservoir 1 in an uncontrolled manner and is transported by gravity to reservoir 2; and B, water is pumped from reservoir 1 to reservoir 2


1. Massachusetts drinking-water-supply systems and associated reservoirs used to investigate factors affecting reservoir firm yield

2. Reservoir and drainage-basin characteristics for 70 Massachusetts drinking-water-supply reservoirs

3. Reservoir-specific properties for 46 drinking-water-supply reservoirs

4. Climate, soil, and basin characteristics for 46 drinking-water-supply reservoirs­­

5. Locations, drainage-basin characteristics, and climate data for streamflow-monitoring stations whose records were used to compare methods that estimate streamflow at an ungaged site

6. Identifiers, names, drainage areas, and records for 26 streamflow-monitoring stations that could be used to estimate surface-water flows to reservoirs

7. Streamflow-monitoring stations used as reference stations to estimate reservoir inflows, portions of streamflow records estimated for the stations, index stations used in the estimation, and correlation coefficients between log-transformed flow records for index and target stations

8. Firm-yield estimates determined by the historical record of streamflow and precipitation for 14 single-reservoir systems

9. Firm-yield estimates determined by the historical record of streamflow and precipitation for 31 reservoirs belonging to one of 11 multiple-reservoir systems

Suggested Citation:

Waldron, M.C., and Archfield, S.A., 2006, Factors affecting firm yield and the estimation of firm yield for selected streamflow-dominated drinking-water-supply reservoirs in Massachusetts: U.S. Geological Survey Scientific Investigations Report 2006-5044, 39 p.

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