U.S. Department of the Interior

U.S. Geological Survey

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
Cover. Top: Gatehouse at Flints (Sandy) Pond in Lincoln, Massachusetts. Bottom: Water entering Holden Pond #1 from Kendall 

Reservoir, Holden, Massachusetts. (Both photographs taken by Andy Massey)
Refinement and Evaluation of the 

Massachusetts Firm-Yield Estimator Model 

Version 2.0

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

Prepared in cooperation with the 

Massachusetts Department of Environmental Protection

Scientific Investigations Report 2011–5125

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

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 http://pubs.usgs.gov/sir/2011/5125.)
iii

Acknowledgments

The authors thank Thomas Lamonte and Kari Winfield of the Massachusetts Department of 

Environmental Protection and Linda Hutchins of the Massachusetts Department of Conservation 

and Recreation for their technical reviews of this report.

The authors thank U.S. Geological Survey colleagues Marcus C. Waldron and Robert Dudley for 

their reviews and Lance Ostiguy for his help in the processing of bathymetric measurement data.
THIS PAGE INTENTIONALLY LEFT BLANK
v

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................2

Refinements to the Existing Firm-Yield Estimator Model ........................................................................2

Bathymetry and Stage-Storage Relations........................................................................................3

Surface-Water Inflows ........................................................................................................................7

Precipitation and Evaporation ............................................................................................................7

Groundwater Contributions...............................................................................................................13

Applications of the Firm-Yield Estimator Model .....................................................................................14

Application of the Firm-Yield Estimator Model to a Single-Reservoir System .........................14

Application of the Firm-Yield Estimator Model to a Multiple-Reservoir System......................14

Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs........................................................16

Sensitivity of Firm-Yield Estimates to Errors in Daily Streamflow...............................................16

Sensitivity of the Firm-Yield Model to Bathymetric-Map Accuracy...........................................20

Validation of Groundwater Parameters ..........................................................................................25

Effect of Drought Severity on Firm-Yield Estimates ...............................................................................26

Effect of Controlled Releases and Demand Management on Firm Yield............................................33

Controlled-Release Scenarios..........................................................................................................33

Summer Water-Demand Management...........................................................................................36

Reducing Reservoir Reliability Requirements................................................................................37

Tradeoffs Between Demand Management, Controlled Releases, and Reliability...................37

Summary and Conclusions.........................................................................................................................39

References Cited..........................................................................................................................................40

Appendix 1. Hypsographic Data ............................................................................................................43

Appendix 2. Bathymetric Maps..............................................................................................................45

Appendix 3. Reservoir-System Diagrams.............................................................................................47

Appendix 4. Monthly Percentile Streamflows.....................................................................................49
vi

Figures

1. Map showing locations of drainage areas for 71 drinking-water reservoirs in 

Massachusetts..............................................................................................................................4

2. Maps showing location of reservoirs and record length at A, precipitation stations 

and validations sites, and B, meteorological stations in Massachusetts and vicinity ...12

3. Diagrams showing water balances for a system of reservoirs in which A, water is 

transported by gravity and B, water is pumped from Reservoir 1 to Reservoir 2 ............17

4. Scatterplots showing A, mean percent difference and B, standard deviation of the 

percent difference of daily streamflows generated by the Sustainable Yield Estimator 

at 18 U.S. Geological Survey gaged sites in Massachusetts ..............................................19

5. Boxplot showing percent change in firm yield of selected reservoirs in 

Massachusetts after accounting for potential errors in daily streamflow in 500 

Monte Carlo simulations............................................................................................................21

6. Diagrams showing original and hypothetical 30-meter transect spacing for Upper 

Sackett Reservoir in Pittsfield, Massachusetts.....................................................................23

7. Graphs showing A–C, percent change in reservoir storage capacity and D–F, firm 

yield, resulting from transect spacings and patterns for three study reservoirs in 

Massachusetts............................................................................................................................24

8. Graph showing daily simulated and observed reservoir stage for Atkins Reservoir in 

Amherst, Massachusetts ..........................................................................................................26

9. Graph showing daily simulated and observed reservoir stage for Nagog Pond in 

Concord, Massachusetts ..........................................................................................................27

10. Boxplots showing A, percent below average streamflow and B, duration of droughts 

of the 1960s, 1980s, and 2002. C, Percent change in firm yield and D, reliability of firm 

yields when calculated with the droughts of the 1980s or 2002 .........................................32

11. Graph showing maximum monthly releases as a percentile of long-term monthly 

flows that is possible at various demand ratios for four reservoirs of increasing 

storage ratio ................................................................................................................................36

12. Boxplot showing percent changes of firm yield for Massachusetts reservoirs under 

various management scenarios...............................................................................................38

13. Graph showing tradeoff curves depicting the estimated yield in relation to controlled 

releases under various management scenarios for Upper Leahy Reservoir, in Lee, 

Massachusetts............................................................................................................................39
vii

Tables

1. Massachusetts drinking-water-supply systems and associated reservoirs included 

in this study....................................................................................................................................5

2. Reservoir basin characteristics and index streamgages in Massachusetts used in 

the Sustainable Yield Estimator..................................................................................................8

3. Nash-Sutcliffe Efficiency of daily precipitation at 33 gaged validation sites in 

Massachusetts............................................................................................................................13

4. Firm-yield estimates and 2000–2004 water usage for 38 reservoir systems in 

Massachusetts............................................................................................................................15

5. Distribution of firm yields resulting from 500 Monte Carlo simulations at selected 

reservoirs in Massachusetts ....................................................................................................20

6. Reservoir capacity and firm yield for selected reservoirs in Massachusetts 

calculated using various transect patterns and sampling-point densities.......................22

7. Firm yields and reliability of reservoirs in Massachusetts calculated using three 

major droughts in the historical record ..................................................................................28

8. Water usage and firm yields for reservoir systems in Massachusetts under various 

controlled-release, demand-management, and reliability scenarios................................34

Conversion Factors and Datum

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2

)

square mile (mi2

) 2.590 square kilometer (km2)

Volume

million gallons (Mgal) 3,785 cubic meter (m3

)

cubic foot (ft3

) 0.02832 cubic meter (m3)

Flow rate

foot per day (ft/d) 0.3048 meter per day (m/d)

cubic foot per second (ft3

/s) 0.02832 cubic meter per second (m3/s)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3

/s)

Transmissivity*

foot squared per day (ft2

/d) 0.09290 meter squared per day (m2/d)

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times 

foot of aquifer thickness [(ft3

/d)/ft2]ft. In this report, the mathematically reduced form, foot 

squared per day (ft2

/d), is used for convenience.
Refinement and Evaluation of the Massachusetts 

Firm-Yield Estimator Model Version 2.0

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

Abstract

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 dailystreamflow 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-demandreduction 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.

Introduction

The determination of available water for, and 

management of, public water supplies in Massachusetts 

drinking-water reservoirs has become increasingly complex as 

regulators try to provide adequate streamflows for ecological 

communities as well as increasing demands for drinking 

water. Controlled releases from reservoirs to satisfy ecological 

demands may impose further limits on the yield from a 

reservoir. A reservoir failure occurs when a reservoir is unable 

to provide sufficient water to meet demand. Reservoirs with 

high water demand relative to their firm yield are particularly 
2 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

at risk of failing during periods of drought. In order to 

ensure that reservoirs have sufficient water available even 

during extreme droughts, the Massachusetts Department of 

Environmental Protection (MassDEP) requires public water 

suppliers to estimate the firm yield of their reservoir systems.

The firm yield of a reservoir is defined as the maximum 

yield that can be delivered from a system without failure, 

even during a severe drought. To facilitate the calculation 

of a system’s firm yield, MassDEP developed the FirmYield Estimator (FYE) guidance document (Massachusetts 

Department of Environmental Protection, 1996) and model 

(Massachusetts Department of Environmental Protection, 

2000). The FYE model uses the water-balance equation to 

estimate reservoir storage over a period of time that includes 

the most extreme drought of record. The firm yield of a 

reservoir is calculated by solving the water-balance equation 

for each month of the simulation period with an initial yield of 

0 million gallons per day (Mgal/d). If the reservoir storage is 

does not fully deplete during the simulation, yield is increased, 

and the water-balance equation is solved again. Iteration 

continues with increasing yield until a reservoir failure occurs. 

The firm yield is the maximum yield that can be used in the 

water-balance equation without causing the reservoir to fail 

during the simulation period. Waldron and Archfield (2006) 

calculated firm yields for 25 single- and multiple-reservoir 

systems in Massachusetts and examined the sensitivity 

of the FYE model to various model inputs. Archfield and 

Carlson (2006) further refined the FYE model by developing 

a procedure to estimate groundwater flows into and out of 

reservoir storage. 

Growing demand for public water supply in 

Massachusetts may compete with ecosystem water needs, 

and there is increasing interest in ensuring that streams have 

adequate water to support aquatic communities. Reservoir 

impoundments can alter the natural streamflow patterns 

in reaches downstream of the dam. During periods when 

reservoir stage is lower than the spillway elevation, water 

cannot spill over the dam into the downstream reaches and 

can alter the characteristic pattern of high and low flows 

for that stream reach. These alterations to streamflow can 

be detrimental to downstream ecosystems and aquatic 

communities. Controlled releases from reservoir storage 

can be implemented to alleviate downstream ecosystem 

stress; however, these releases decrease reservoir storage. 

In some cases, meeting environmental streamflow needs 

during a severe drought may decrease reservoir yield enough 

that human needs cannot be met. Although the FYE model 

allows for user-specified monthly controlled releases, 

there have been no statewide applications of the model to 

examine the feasibility of implementing controlled releases in 

Massachusetts drinking-water reservoirs.

Water suppliers struggling to meet drinking-water 

demands or wishing to offset the effects of controlled flow 

releases may consider demand-management strategies such as 

outdoor summer water-use restrictions, or they may consider relaxing the no-fail reliability criterion of the reservoir, 

or a combination of these two strategies. Each strategy has 

advantages and disadvantages, and the appropriate solution 

may differ from one reservoir to another. Summer water-use 

restrictions limit non-essential water use during drought periods but may not conserve enough water to sustain use through 

long, multiyear droughts when winter and spring flows cannot 

replenish the reservoir. Relaxing the reliability requirement of 

a reservoir may provide a boost in yield, but reservoirs can run 

the risk of failure during very severe droughts. The MassDEP 

guidance document and original FYE model do not allow for 

user-specified reliability criteria or demand-management scenarios. For the current study, modifications to the FYE were 

developed to allow these options in order to assess the relative 

benefits of these operational strategies.

Purpose and Scope

The purpose of this report is to document the methods 

used to estimate firm yield for Massachusetts reservoirs and 

to examine the factors that affect the firm-yield estimates. The 

report describes several refinements to the existing firm-yield 

model, including simulation at a daily time step; refinement 

and validation of groundwater parameters; improved input 

data for streamflow, precipitation, and evaporation; and 

modification of the model to allow for demand-management 

scenarios and relaxed reliability criteria. Firm yields were 

calculated using the updated data and methodology for 25 

reservoir systems previously studied as well as 13 reservoir 

systems that were not examined in previous firm-yield studies. 

The sensitivity of the model to bathymetric-map accuracy, 

drought severity, and uncertainty in input data was examined. 

Finally, the tradeoffs between controlled releases and demandmanagement scenarios were examined.

Refinements to the Existing Firm-Yield 

Estimator Model

The Massachusetts Department of Environmental 

Protection (MassDEP) guidance document details a procedure 

for calculating the firm yield of a reservoir in Massachusetts. 

To facilitate this calculation, the Firm-Yield Estimator 

(FYE) model (Massachusetts Department of Environmental 

Protection, 1996) was developed on the basis of this 

methodology. The FYE model defines the firm yield as the 

maximum yield at which a water-supply reservoir or system 

of reservoirs can operate without failure during the drought of 

record. Waldron and Archfield (2006) examined the sensitivity 

of the FYE model to various inputs required by the model and 

evaluated the model’s overall procedure for estimating the firm 

yield for surface-water-dominated reservoirs in Massachusetts. 
Refinements to the Existing Firm-Yield Estimator Model 3

Archfield and Carlson (2006) expanded the methodology 

to include a set of equations used to estimate groundwater 

contributions to the reservoir water balance. 

Because of the difficulty in obtaining daily values for all 

of the water-balance components, previous firm-yield analyses 

in Massachusetts have been performed using a monthly time 

step. Fennessey (1995) showed that firm yields estimated at a 

monthly time step are higher than yields estimated from data 

at a daily time step. The MassDEP guidance document specifies a regression-based correction factor that is used to adjust 

the firm yield for errors introduced by using a monthly time 

step instead of a daily time step. However, the applicability 

and validation of the correction factor remains unverified for 

Massachusetts reservoirs. New advances in daily streamflow 

estimation, however, have made it feasible to run the FYE 

model at a daily time step. Running the model at a daily time 

step eliminates the need for a correction factor.

With a daily time step and units of volume, the reservoir 

water-balance equation is:

S Ar P E Aw Q Q Q Q Q Q S i i i i i st i y rr sp ow gw i i i i i i= − ( ) + − − − − ± +  −1 (1)

where

i = daily simulation time step;

Si = volume of water in usable storage for the 

current day, in million gallons;

Awi = reservoir drainage area, in square miles;

Qsti = streamflow per unit drainage area, in miles1;

Ari = area of the reservoir surface, in square 

miles1;

Pi = precipitation, in miles1;

Ei = evaporation from the reservoir surface, in 

miles1;

Qgwi = groundwater contributions or losses for the 

current day, in million gallons;

αi = peak-usage factor, dimensionless;

Qy = yield for the current day, in million gallons;

Qrri = controlled release, in million gallons;

Qspi = uncontrolled spill, in million gallons; and

Qowi = withdrawal from the reservoir by other 

users, in million gallons.

The firm yield is calculated by successively solving the 

water-balance equation over the period of record, starting at 

a full pool volume and increasing the yield at each repetition. 

The firm yield is the maximum yield volume that can be used 

without causing the reservoir volume to decrease to zero. For 

this study, firm yields were determined for 71 reservoirs—45 

previously studied reservoirs and 26 new reservoirs—belonging to 38 reservoir systems (fig. 1; table 1). For the purposes of 

this study, a reservoir system refers to one or more reservoirs 

1

 Precipitation, streamflow, and evaporation are in units of length and, when 

multiplied by Ari, become volumes (in cubic miles) that are converted to million gallons.

that are hydrologically connected. Firm yields for previously 

studied reservoir systems were re-estimated using the revised 

FYE-model methods and data. These revised firm yields 

supersede estimates of firm yield from Waldron and Archfield 

(2006) and Archfield and Carlson (2006). Previous estimates 

of firm yields are no longer considered valid.

Reservoir-specific characteristics that affect model estimates of firm yield include the stage-storage relation, storage 

capacity, streamflows, direct precipitation, and evaporation 

from the reservoir surface. For reservoirs that are connected 

to an aquifer, the aquifer transmissivity and surficial geology 

underlying the reservoir also affect groundwater flows to and 

from the reservoir. 

Bathymetry and Stage-Storage Relations

Bathymetric surveys were completed for 26 reservoirs 

that were not previously studied. Surveys were completed 

during the spring months of 2008 and 2009 when reservoirs 

were full or nearly full. Reservoir depths were determined 

with a narrow-beam echo sounder along transects across 

each reservoir. The location of each depth measurement was 

determined with a global positioning system (GPS). Reservoirspillway elevations and intake elevations were provided by 

the public water supplier. In order to convert water depths 

to bottom elevations, the water depths were first adjusted to 

account for the reservoir stage on the day of the survey by 

adding the distance between the water surface and the spillway 

to each measurement. The reservoir bottom elevation was then 

calculated as the difference between the spillway elevation and 

the corrected depth measurements.

The GPS data were differentially corrected and imported 

into a geographic information system (GIS). Reservoir 

outlines were digitized from 1:5,000 digital orthoimagery 

(Office of Geographic and Environmental Information, 2005). 

Smoothed reservoir contours were generated from bottom 

elevations using a spatially interpolated grid in ArcINFO. 

A triangulated irregular network (TIN) model was generated using GPS position, bottom elevation, and the digitized 

reservoir shoreline. Reservoir volumes and surface areas 

were computed using the TIN surface model at 2-foot (ft) 

intervals. This method calculates the volume at each grid cell 

of the bottom-elevation map, making it more accurate than 

estimating volume from surface contours alone. Stage-storage 

relations developed from the bathymetric data were used to 

estimate reservoir surface area and reservoir stage based on 

reservoir-storage volumes at each daily time step during the 

simulation. Interpolation was used to estimate these quantities 

at volumes that fall between contour intervals. Stage-storage 

relations and bottom-elevation maps for reservoirs that were 

not previously studied by Waldron and Archfield (2006) are 

included in appendixes 1 and 2.
4 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0 10 16

4

39

67

9

15

33

68

2

17

13

35

48

11

21

66

6

57

58

41

46

14

54

22

5

44

70

1

55

71

7

65

27

61

69 3

8

12

18

20

19

28

24

25

26

23

29

34

32

31

30

38

36

35

40

45

50

47

52

51

53

49

56

42

43

64

63 62

60

59

70° 71° 72°

70° 71° 72° 73°

73°

42° 42°41° 41°

0 30 45 60 15 MILES

0 40 60 80 20 KILOMETERS

EXPLANATION

Drainage area of reservoirTown boundary

10 Reservoir identifier. Reservoir names 

are shown in table 1

Base map from USGS and MassGIS digital coverages, State Plane Coordinate System, NAD 83

Figure 1. Locations of drainage areas for 71 drinking-water reservoirs in Massachusetts.
Refinements to the Existing Firm-Yield Estimator Model 5

Table 1. Massachusetts drinking-water-supply systems and associated reservoirs included in this study.—Continued

[ID, identifier; SUASCO, Sudbury, Assabet, Concord; DPW, Department of Public Works]

Water supplier Reservoir name Reservoir ID Drainage basin

Amherst Water Department Atkins Reservoir 18 Connecticut

Hill Reservoir 21 Connecticut

Hawley Reservoir 19 Connecticut

Amethyst Brook Intake 20 Connecticut

Ashburnham/Winchendon Joint Water Board Upper Naukeag Lake 54 Millers

Concord Water Department Nagog Pond 55 SUASCO

Danvers Water Department Emerson Brook Pond 58 Ipswich

Middleton Pond 60 Ipswich

Swan Pond 59 Ipswich

Fall River Water Department North Watuppa Reservoir 67 Narragansett Bay

Copicut Reservoir 68 Buzzards Bay

Fitchburg Water Department Bickford Pond 41 Chicopee

Mare Meadow Reservoir 40 Chicopee

Meetinghouse Reservoir 44 Nashua

Wachusett Lake 45 Nashua

Scott Reservoir 42 Nashua

Fitchburg Reservoir 43 Nashua

Lovell Reservoir 46 Nashua

Greenfield Water Department Green River 10 Deerfield

Leyden Glen Reservoir 9 Deerfield

Hingham/Hull (Aquarian Water Company) Accord Pond 65 Boston Harbor

Hinsdale Water Department Belmont Reservoir 8 Housatonic

Lee Water Department Schoolhouse Reservoir 2 Housatonic

Upper (Leahey) Reservoir 1 Housatonic

Leicester (Cherry Valley and Rochdale Water) Henshaw Pond 29 French

Leominster DPW–Water Division Distributing Reservoir 51 Nashua

Morse Reservoir 50 Nashua

Haynes Reservoir 49 Nashua

Simonds Pond 52 Nashua

Goodfellow Pond 53 Nashua

Notown Reservoir 48 Nashua

Fall Brook Reservoir 47 Nashua

Lincoln Water Department Flints Pond (Sandy Pond) 69 Charles

Marlborough DPW–Water and Sewer Division Millham Reservoir 57 SUASCO

Williams Lake 56 SUASCO

Milford Water Company Echo Lake 70 Charles
6 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 1. Massachusetts drinking-water-supply systems and associated reservoirs included in this study.—Continued

[ID, identifier; SUASCO, Sudbury, Assabet, Concord; DPW, Department of Public Works]

Water supplier Reservoir name Reservoir ID Drainage basin

North Brookfield Water Department Doane Pond 28 Chicopee

Horse Pond 27 Chicopee

Pittsfield Water Department Ashley Lake/Lower Ashley Intake 3 Housatonic

Farnham Reservoir 7 Housatonic

Sandwash Reservoir 6 Housatonic

Upper Sackett Reservoir 5 Housatonic

Cleveland Reservoir 4 Housatonic

Scituate Water Department Tack Factory Pond 66 South Coastal

Southbridge Water Department Hatchet Pond 23 Quinebaug

Hatchet Brook Reservoir #3 24 Quinebaug

Hatchet Brook Reservoir #4 25 Quinebaug

Hatchet Brook Reservoir #5 26 Quinebaug

Cohasse Brook Reservoir 22 Quinebaug

Springfield Water Department Borden Brook Reservoir 15 Westfield

Cobble Mountain Reservoir 16 Westfield

South Deerfield Water Supply District Roaring Brook Reservoir 11 Connecticut

Whately Reservoir 12 Connecticut

Wakefield Water Department Crystal Lake 61 North Coastal

Westborough Water Department Sandra Pond 71 SUASCO

Westfield Water Department Granville Reservoir 13 Westfield

Montgomery Reservoir 14 Westfield

West Springfield Water Department Bearhole Reservoir 17 Westfield

Winchester Water Department Middle Reservoir 63 Mystic

North Reservoir 62 Mystic

South Reservoir 64 Mystic

Worcester Water Department Holden Reservoir #1 35 Blackstone

Holden Reservoir #2 36 Blackstone

Kettle Brook Reservoir #1 30 Blackstone

Kettle Brook Reservoir #2 36 Blackstone

Kettle Brook Reservoir #3 32 Blackstone

Kettle Brook Reservoir #4 33 Blackstone

Lynde Brook Reservoir 34 Blackstone

Kendall Reservoir 37 Nashua

Pine Hill Reservoir 38 Nashua

Quinapoxet Reservoir 39 Nashua
Refinements to the Existing Firm-Yield Estimator Model 7

Surface-Water Inflows

Surface-water inflow volumes are generally orders 

of magnitude larger than the volumes of climatic waterbalance components or groundwater contributions, making 

them one of the most important inputs in the determination 

of the firm yield. A recently developed method makes it 

possible to estimate daily streamflows for most locations 

in Massachusetts. The Sustainable Yield Estimator (SYE) 

(Archfield, 2010) application was used to estimate daily 

streamflow for all the reservoirs in this study. The SYE uses 

a regression-based method to develop a daily-flow-duration 

curve for an ungaged stream for the period of October 1, 

1960 to September 30, 2004. The flow-duration curve is then 

transformed into a daily time series by equating the quantiles 

of the ungaged flow-duration curve to a flow-duration curve 

of a gaged index stream during the same time period. This 

method is similar to the method of streamflow estimation used 

in previous Massachusetts firm-yield studies (Waldron and 

Archfield, 2006) and the MassDEP FYE guidance document; 

however, the SYE tool employs new regression techniques 

and more robust index-streamflow-selection methods. For 

single-reservoir systems, basin characteristics used in the 

SYE regression equations were calculated for the entire 

reservoir watershed, excluding the reservoir area (table 2). For 

reservoirs in series along a stream, the areas of all upstream 

reservoir watersheds were excluded from the calculation of 

downstream reservoir basin characteristics. 

Precipitation and Evaporation

Records of daily precipitation and temperature were 

obtained from 226 National Climatic Data Center (NCDC) 

climate stations in and around Massachusetts (fig. 2). There 

were 157 stations with daily precipitation records ranging 

from 1 to 44 years during the simulation period. Stations had 

varying amounts of missing data throughout the record, and 

no station had a complete daily record for the entire 44 years. 

In order to obtain a complete daily precipitation record at each 

reservoir, inverse-squared distance weighted interpolation of 

gaged precipitation stations was used. Although this method 

can result in an underestimation of precipitation variability, 

this method has been shown to perform as well or better than 

using data from the nearest precipitation station to estimate 

daily precipitation (Kruizinga and Yperlaan, 1978). For 

each day of the simulation period, inverse-squared distance 

interpolation was performed using the three nearest gaged 

stations within 15 miles (mi) that had recorded precipitation 

data for that day. Because each meteorological station had 

records of differing lengths, the set of stations used in the daily 

interpolation of precipitation may have varied from day to day 

for a given FYE reservoir site.

The interpolated daily precipitation was cross-validated 

using observed data from 31 long-term precipitation gages. 

Gages with over 40 years of data were chosen for validation, 

as well as two gages in the western part of Massachusetts 

where gages with 40-year records were not available. For 

each validation gage, inverse-squared distance weighted 

interpolation of the surrounding gages was used to produce 

a time series of daily precipitation for the gaged location. 

The estimated daily precipitation at each gaged station was 

then compared to the observed data, and the Nash Sutcliffe 

Efficiency (NSE) was calculated (Nash and Sutcliffe, 1970). 

The NSE is a commonly used indicator to assess the fit of a 

hydrologic model. An NSE value of 1 indicates a perfect fit 

between observed and modeled values. An NSE of 0 means 

that the modeled data has the same amount of error as just 

using the mean of the observed data. A negative NSE indicates 

that the mean of the observed data provides a better estimate 

than the modeled data. The NSE for the 31 validation gages 

ranged from -0.16 to 0.87 with a median of 0.68 (table 3). 

Only one site, located at the Worcester Regional Airport, had a 

NSE of less than zero. This site is located in a sparsely gaged 

area. Only one other gage falls within 5 mi of the Worcester 

site, and that gage has data from only October 1960 to 

November 1962. The second nearest gage to the Worcester site 

is 9.8 mi away. An analysis of the interpolated time series for 

the Worcester site shows that NSE calculated from October 

1960 to November 1962 is 0.58, whereas the NSE for the 

remaining period is -0.23, indicating that interpolation results 

may be more unreliable when gaged sites are farther than 5 mi 

away. Other validation sites that performed poorly are located 

in areas of the State that are not densely gaged, indicating that 

estimated daily precipitation may be less accurate for reservoirs in sparsely gaged areas of Massachusetts.

Daily precipitation time series were validated using 

observed precipitation at two reservoirs. Daily precipitation 

measurements were available for Atkins Reservoir for 

March 1, 1994 to September 30, 2004, and for Echo Lake for 

October 1, 1960 to September 30, 1967. The interpolated precipitation time series showed good agreement with observed 

precipitation for both Atkins Reservoir and Echo Lake, with 

NSEs of 0.94 and 0.75, respectively (table 3).

Evaporation from lakes depends on meteorological 

factors as well as physical characteristics of the lake, 

but is generally equivalent to estimates of potential 

evapotranspiration. Daily evaporation from each reservoir 

was estimated using Hargreaves’ equation for potential 

evapotranspiration (Hargreaves and Samni, 1982). This 

is a temperature-based method requiring daily average 

temperatures and daily temperature ranges. Daily minimum 

and maximum temperatures were interpolated from the NCDC 

gaged climate stations. There were 94 climate stations with 

daily minimum and maximum temperature records for periods 

ranging from 1 to 44 years during the simulation period. 

Temperatures were interpolated using inverse-squared distance 

for each reservoir in the same manner as for precipitation. 
8 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 2. Reservoir basin characteristics and index streamgages in Massachusetts used in the Sustainable Yield Estimator.—Continued

[mi2, square miles; ft, feet; in, inches; °C, degrees Celsius; SYE, Sustainable Yield Estimator; DPW, Department of Public Works; X- and Y-coordinates in 

Water supplier Reservoir name

Drainage area, 

excluding 

surface area

(mi2)

Mean 

basin 

elevation

(ft)

Average 

annual precipitation

(in)

Percentage 

of basin 

that is open 

water

Amherst Water Department Atkins Reservoir 1.72 735.28 48.18 0.18 

Hill Reservoir 4.05 1,052.11 49.01 0.00 

Hawley Reservoir 1.50 877.33 48.58 0.07 

Amethyst Brook Intake 0.63 641.52 48.17 0.00 

Ashburnham/Winchendon Joint Water Board Upper Naukeag Lake 1.37 1,197.61 49.15 0.25 

Concord Water Department Nagog Pond 0.77 255.53 46.46 0.75 

Danvers Water Department Emerson Brook Pond 3.26 118.93 46.56 2.88 

Middleton Pond 1.32 118.73 46.81 14.21 

Swan Pond 1.19 127.79 46.63 1.94 

Fall River Water Department North Watuppa Reservoir 8.47 167.87 48.95 1.87 

Copicut Reservoir 5.66 193.97 49.14 0.02 

Fitchburg Water Department Bickford Pond 3.03 1,226.32 49.90 0.11 

Mare Meadow Reservoir 2.64 1,165.12 48.81 0.05 

Meetinghouse Reservoir 1.32 1,124.74 48.79 0.00 

Wachusett Lake 1.32 1,155.20 50.08 13.64 

Scott Reservoir 0.73 1,006.59 48.81 0.07 

Fitchburg Reservoir 1.90 1,161.41 49.36 0.16 

Lovell Reservoir 3.20 1,012.32 48.99 0.17 

Greenfield Water Department Green River 52.06 1,239.88 51.06 0.55 

Leyden Glen Reservoir 5.16 950.26 49.52 0.10 

Hingham/Hull (Aquarian Water Company) Accord Pond 0.79 161.96 46.75 0.62 

Hinsdale Water Department Belmont Reservoir 0.37 1,899.15 49.92 4.57 

Lee Water Department Schoolhouse Reservoir 2.94 1,889.41 53.39 1.60 

Upper (Leahey) Reservoir 0.63 1,808.39 51.21 0.00 

Leicester (Cherry Valley and Rochdale Water) Henshaw Pond 0.88 865.80 48.92 6.20 

Leominster DPW–Water Division Distributing Reservoir 1.14 810.73 49.56 0.00 

Morse Reservoir 0.28 802.11 49.65 0.00 

Haynes Reservoir 0.34 889.48 50.09 0.00 

Simonds Pond 0.18 806.71 49.11 0.00 

Goodfellow Pond 0.41 776.33 48.99 0.20 

Notown Reservoir 3.96 853.66 49.43 0.00 

Fall Brook Reservoir 1.21 814.81 49.98 0.18 

Lincoln Water Department Flints Pond (Sandy Pond) 0.55 267.40 46.99 0.01 

Marlborough DPW–Water and Sewer Division Millham Reservoir 3.40 367.12 47.95 0.23 

Williams Lake 0.26 459.58 47.90 7.02 
Refinements to the Existing Firm-Yield Estimator Model 9

Massachusetts State Plane meters; Elevation determined from the U.S. Geological Survey 30-meter National Elevation Dataset]

X-coordinate 

of the 

basin 

outlet

Y-coordinate 

of the 

basin 

outlet

Average 

maximum 

monthly 

temperature 

(°C)

Percentage of 

basin 

that is 

wetland

Percentage 

of basin that 

is underlain 

by sand and 

gravel

X-coordinate 

of the 

basin 

centroid

Y-coordinate 

of the 

basin 

centroid

SYE 

selected 

index-gage 

station 

number

SYE selected index-gage station name

118777

122433

122301

121496

164340

205467

238199

239406

237151

231755

238117

164479

164177

166748

168481

173121

171935

173661

108115

108452

250453

64426

60722

58665

167375

176425

176232

175076

175060

174545

173915

176961

215274

190750

194093

908834

903927

903193

903761

934333

917705

928219

927213

926546

825696

827911

914888

916252

920465

918229

929106

932770

929522

933534

935080

880610

910317

900541

898849

886553

919701

918736

918327

921964

921838

921424

916339

908829

899448

898424

13.81

13.29

13.49

14.03

13.04

15.06

14.97

14.98

14.95

14.97

14.96

12.79

12.98

13.18

12.93

13.57

13.16

13.50

12.60

13.16

14.97

11.44

11.37

11.61

13.54

13.97

14.26

13.78

13.98

13.97

13.85

14.12

15.04

14.76

14.62

1.48

7.74

1.68

1.18

5.92

2.03

21.55

16.30

21.33

10.01

15.38

7.04

10.05

6.83

2.93

0.93

3.16

3.25

1.56

2.01

9.09

2.07

9.91

1.42

10.39

1.80

0.00

2.76

0.91

5.28

7.39

5.14

10.62

9.40

1.36

8.83

14.17

8.63

30.51

0.00

7.67

2.17

5.23

1.81

22.23

12.46

0.00

0.20

0.00

31.48

0.00

0.87

0.43

3.46

0.00

41.52

0.00

0.00

0.00

2.31

11.01

11.80

2.11

0.00

30.40

5.25

0.00

5.41

12.95

0.00

120426

124269

123102

122101

165210

204811

236141

238221

235723

233089

237949

166284

164906

165767

168711

172300

171006

172349

102185

108237

250131

63828

62276

59529

167098

175631

176215

174682

174887

174160

173605

176023

215247

192695

194406

909179

905494

902723

903622

934113

918242

929547

926859

928121

829278

830452

914773

917830

920066

916854

929338

933726

931483

947478

938076

880232

910493

898907

899287

887692

919403

918123

918051

921729

922081

920156

916544

909592

899418

898748

01174565

01174900

01174901

01174902

01161500

01097300

01100700

01100701

01100702

01106000

01106001

01095220

01095221

01095222

01095223

01096000

01096001

01096002

01170100

01170101

01105600

01174566

01174567

01174568

01175670

01095224

01095225

01095226

01095227

01095228

01095229

01095230

01097301

01095231

01097302

West Branch Swift River near Shutesbury, Mass.

Cadwell Creek near Belchertown, Mass.

Cadwell Creek near Belchertown, Mass.

Cadwell Creek near Belchertown, Mass.

Tarbell Brook near Winchendon, Mass.

Nashoba Brook near Acton, Mass.

East Meadow River near Haverhill, Mass.

East Meadow River near Haverhill, Mass.

East Meadow River near Haverhill, Mass.

Adamsville Brook at Adamsville, R.I.

Adamsville Brook at Adamsville, R.I.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Squannacook River near West Groton, Mass.

Squannacook River near West Groton, Mass.

Squannacook River near West Groton, Mass.

Green River near Colrain, Mass.

Green River near Colrain, Mass.

Old Swamp River near South Weymouth, Mass.

West Branch Swift River near Shutesbury, Mass.

West Branch Swift River near Shutesbury, Mass.

West Branch Swift River near Shutesbury, Mass.

Sevenmile River near Spencer, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Nashoba Brook near Acton, Mass.

Stillwater River near Sterling, Mass.

Nashoba Brook near Acton, Mass.
10 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 2. Reservoir basin characteristics and index streamgages in Massachusetts used in the Sustainable Yield Estimator.—Continued

[mi2, square miles; ft, feet; in, inches; °C, degrees Celsius; SYE, Sustainable Yield Estimator; DPW, Department of Public Works; X- and Y-coordinates in 

Water supplier Reservoir name

Drainage area, 

excluding 

surface area

(mi2)

Mean 

basin 

elevation

(ft)

Average 

annual precipitation

(in)

Percentage 

of basin 

that is open 

water

Milford Water Company Echo Lake 1.26 434.41 48.04 0.00 

North Brookfield Water Department Doane Pond 0.75 971.14 48.56 1.45 

Horse Pond 0.79 1,008.25 48.58 0.25 

Pittsfield Water Department Ashley Lake/Lower Ashley Intake 2.43 1,876.28 51.47 0.01 

Farnham Reservoir 2.93 1,871.90 52.10 3.30 

Sandwash Reservoir 1.67 1,956.55 53.44 0.83 

Upper Sackett Reservoir 0.86 1,793.27 50.80 0.00 

Cleveland Reservoir 13.74 1,900.26 52.30 0.05 

Scituate Water Department Main Reservoir 3.50 91.99 49.42 0.85 

Southbridge Water Department Hatchet Pond 0.18 909.38 51.55 4.88 

Hatchet Brook Reservoir #3 0.58 769.80 51.10 0.00 

Hatchet Brook Reservoir #4 0.54 767.57 51.41 0.04 

Hatchet Brook Reservoir #5 0.88 876.36 51.60 0.31 

Cohasse Brook Reservoir 1.76 783.94 51.61 0.00 

Springfield Water Department Borden Brook Reservoir 7.64 156.94 53.83 0.95 

Cobble Mountain Reservoir 35.88 179.39 54.74 1.03 

South Deerfield Water Supply District Roaring Brook Reservoir 3.97 847.42 49.32 0.00 

Whately Reservoir 1.22 690.84 47.68 0.29 

Wakefield Water Department Crystal Lake 0.74 144.64 47.83 0.00 

Westborough Water Department Sandra Pond 1.10 512.74 48.13 0.67 

Westfield Water Department Granville Reservoir 5.14 169.87 51.79 0.01 

Montgomery Reservoir 2.47 169.42 51.64 0.92 

West Springfield Water Department Bearhole Reservoir 5.51 156.94 47.83 9.65 

Winchester Water Department Middle Reservoir 0.22 188.78 47.89 0.00 

North Reservoir 0.53 181.41 47.91 0.63 

South Reservoir 0.35 196.31 47.85 0.00 

Worcester Water Department Holden Reservoir #1 4.31 988.16 49.10 0.26 

Holden Reservoir #2 0.66 870.25 48.89 10.78 

Kettle Brook Reservoir #1 1.05 997.81 49.09 0.19 

Kettle Brook Reservoir #2 0.46 1,056.53 49.21 9.47 

Kettle Brook Reservoir #3 0.68 1,102.12 49.32 0.00 

Kettle Brook Reservoir #4 1.65 1,155.72 49.32 0.03 

Lynde Brook Reservoir 2.99 955.96 48.90 0.90 

Kendall Reservoir 1.42 962.25 49.11 0.00 

Pine Hill Reservoir 6.20 1,051.33 48.91 1.65 

Quinapoxet Reservoir 19.23 978.06 49.24 1.16 
Refinements to the Existing Firm-Yield Estimator Model 11

Massachusetts State Plane meters; Elevation determined from the U.S. Geological Survey 30-meter National Elevation Dataset]

X-coordinate 

of the 

basin 

outlet

Y-coordinate 

of the 

basin 

outlet

Average 

maximum 

monthly 

temperature 

(°C)

Percentage of 

basin 

that is 

wetland

Percentage 

of basin that 

is underlain 

by sand and 

gravel

X-coordinate 

of the 

basin 

centroid

Y-coordinate 

of the 

basin 

centroid

SYE 

selected 

index-gage 

station 

number

SYE selected index-gage station name

199336

152832

152716

61112

59624

62375

62981

67217

261649

151250

152645

152344

151867

154253

81048

84932

104207

105145

235056

191280

87851

91646

102251

231596

231403

231434

169341

169817

167666

167001

166337

165489

169080

167957

166626

168780

882420

892890

893521

907556

905955

903170

908976

914454

882089

864151

867506

866907

866016

866456

876485

875556

913954

913574

916292

888045

871847

883065

875730

911210

912841

910191

895131

894051

889650

891321

892458

893916

888876

899596

900134

904242

14.89

13.37

13.26

11.49

11.40

11.26

11.67

11.40

14.90

13.60

13.96

13.87

13.67

13.92

12.78

12.90

13.57

13.91

14.88

14.59

13.65

13.30

15.08

14.84

14.85

14.86

13.32

13.70

13.21

13.08

13.00

12.92

13.39

13.43

13.09

13.33

7.43

6.03

9.44

7.71

12.11

17.66

5.35

11.65

19.31

0.13

1.11

3.18

4.57

4.32

6.82

5.31

3.48

1.40

4.44

5.81

0.93

8.82

5.77

2.84

2.99

2.13

3.82

1.15

5.77

2.72

8.00

10.67

8.28

2.22

8.44

9.26

0.00

0.00

0.00

0.00

0.00

0.00

0.00

2.15

8.34

0.00

1.60

1.17

1.42

0.00

1.94

2.00

3.30

0.00

14.16

21.87

4.68

6.54

26.76

0.00

8.29

0.00

5.85

6.58

0.00

0.00

0.00

0.00

0.00

5.65

0.00

9.04

198632

152294

152338

63253

60066

63447

63448

67782

259381

150964

152153

152234

151592

152957

79241

79243

102484

104560

234734

190928

86724

91509

103356

231654

231998

231549

168502

169470

166741

166530

166039

166060

168367

167553

164905

166454

883339

892837

894330

904598

905596

902808

907981

913389

882706

863976

867618

866210

864861

863965

875630

881286

914911

914117

915498

886932

872716

885160

879967

911686

912548

910787

896269

894531

890617

891878

893177

894897

890969

898601

899773

907298

01111500

01175671

01175672

01174569

01174570

01174571

01174572

01331400

01105731

01126600

01126601

01126602

01126603

01126604

01187300

01187400

01169900

01169901

01097303

01111501

01187401

01174573

01171800

01097304

01097305

01097306

01175673

01175674

01175675

01175676

01175677

01175678

01175679

01095232

01095233

01095234

Branch River at Forestdale, R.I.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

West Branch Swift River near Shutesbury, Mass.

West Branch Swift River near Shutesbury, Mass.

West Branch Swift River near Shutesbury, Mass.

West Branch Swift River near Shutesbury, Mass.

Dry Brook near Adams, Mass.

Indian Head River at Hanover, Mass.

Blackwell Brook near Brooklyn, Conn.

Blackwell Brook near Brooklyn, Conn.

Blackwell Brook near Brooklyn, Conn.

Blackwell Brook near Brooklyn, Conn.

Blackwell Brook near Brooklyn, Conn.

Hubbard River near West Hartland, Conn.

Valley Brook near West Hartland, Conn.

South River near Conway, Mass.

South River near Conway, Mass.

Nashoba Brook near Acton, Mass.

Branch River at Forestdale, R.I.

Valley Brook near West Hartland, Conn.

West Branch Swift River near Shutesbury, Mass.

Bassett Brook near North Hampton, Mass.

Nashoba Brook near Acton, Mass.

Nashoba Brook near Acton, Mass.

Nashoba Brook near Acton, Mass.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

Sevenmile River near Spencer, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.

Stillwater River near Sterling, Mass.
12 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Figure 2. Location of reservoirs and record length at A, precipitation stations and validations sites, and B, meteorological 

stations in Massachusetts and vicinity.

0 20 40 60 80 KILOMETERS

0 15 30 45 60 MILES

EXPLANATION

Precipitation record length, in years

1 to 15

Greater than 15 to 30

Greater than 30 to 44

Precipitation validation site

Town boundary

Reservoir drainage area

70°

70°

71°

71°

72°

72°

73°

73°

43° 43°

42° 42°

41° 41°

0 20 40 60 80 KILOMETERS

0 15 30 45 60 MILES

EXPLANATION

Temperature record length, in years

1 through 15

16 through 30

31 through 44

Town boundary

Reservoir drainage area

70°

70°

71°

71°

72°

72°

73°

43° 73° 43°

42° 42°

41° 41°

A

B

Worcester Regional Airport
Refinements to the Existing Firm-Yield Estimator Model 13

Table 3. Nash-Sutcliffe Efficiency of daily precipitation at 

33 gaged validation sites in Massachusetts.

[NCDC COOP ID, National Climatic Data Center Cooperative Station 

identifier; --, no data]

Precipitation-gage location NCDC COOP 

ID

Nash-Sutcliffe 

Efficiency

Amherst 190120 0.67

Ashburnham 190190 0.52

Barre Falls Dam 190408 0.81

Bedford 190535 0.53

Belchertown 190562 0.86

Birch Hill Dam 190666 0.84

East Milton/Blue Hill 190736 0.49

Logan Airport, Boston 190770 0.66

Brockton 190860 0.51

Buffumville Lake, Charlton 190998 0.77

Franklin 192997 0.84

Hardwick 193401 0.84

Haverhill 193505 0.60

Heath 193549 0.73

Hingham 193624 0.70

Holyoke 193702 0.57

Knightville Dam, Huntington 193985 0.75

Lanesboro 194075 0.65

Lawrence 194105 0.36

Middleboro 194711 0.70

Middleton 194744 0.79

Newburyport 195285 0.42

Plymouth/Kingston 196486 0.69

Reading 196783 0.68

Rochester 196938 0.67

Southbridge 197627 0.87

Taunton 198367 0.37

Tully Lake, Royalston 198573 0.83

West Medway 199316 0.81

West Otis 199371 0.65

Worcester Regional Airport 199923 -0.16

Atkins Reservoir, Amherst -- 0.94

Echo Lake, Concord -- 0.75

Groundwater Contributions

Where a reservoir is in contact with an aquifer, groundwater may flow into or out of the reservoir depending on 

aquifer water table and reservoir stage. When reservoir stage 

falls because water is being used to meet demand, the decrease 

in stage will cause water from the aquifer to flow into the 

reservoir until the reservoir stage and aquifer water table 

regain equilibrium. In contrast, when reservoir stage rises, 

water from the reservoir may flow into the aquifer. During an 

extended drawdown period, groundwater inflows can potentially provide enough additional water to the reservoir storage 

to maintain a yield that would otherwise lead to failure.

Rorabaugh (1964) developed an analytical solution to the 

groundwater-flow equation for the case of one-dimensional 

flow in a finite-width aquifer bounded by a stream. Archfield 

and Carlson (2006) adapted these equations to estimate the 

groundwater contribution to reservoir storage due to timevarying changes in reservoir stage and applied the equations 

in the FYE model. When reservoir stage changes from one 

time step to the next, groundwater contributions are estimated 

as a flow rate per unit length (Archfield and Carlson, 2006, 

equations 3, 4, and 5). The flow rate is then multiplied by a 

scaling factor, L, which is the estimated length of reservoir 

shoreline in contact with the aquifer, in order to determine 

the total volume of groundwater flow per day. In the analysis 

by Archfield and Carlson (2006), L was parameterized as a 

constant, calculated as the perimeter in contact with sand and 

gravel for a reservoir at full pool. In reality, a reservoir may be 

in contact with an aquifer along any part of its bottom surface 

area, not just the perimeter, and the area that is in contact with 

the aquifer will decrease as the reservoir storage volume is 

depleted. Reservoirs at very low storage levels have a much 

smaller surface area that could be interacting with the aquifer 

and thus, the scaling parameter should vary with this 

surface area. 

Parameterizing L as a constant results in overestimation of groundwater contributions during extreme reservoir 

drawdown periods when reservoir storage is low. Archfield 

and Carlson (2006) found that the overestimation of groundwater flows at low reservoir-storage levels led to numerical instabilities in the groundwater-flow equations, making 

groundwater-flow estimates for some reservoirs impossible. In 

order to better characterize groundwater contributions for this 

study, the scaling parameter L was allowed to vary on the basis 

of the reservoir stage. At full pool, L was defined in the same 

manner as in Archfield and Carlson (2006), as the length of the 

perimeter that intersected sand and gravel deposits. This was 

determined in a GIS by intersecting the full-pool contour line 

with a digital data layer of sand and gravel deposits (Office of 

Geographic and Environmental Information, 2004). In order 

to estimate the value of L when the reservoir stage was lower 

than full pool, the surface area of the reservoir at each contour 

interval was overlaid on the digital data layer of sand and 

gravel deposits. The value of L at each contour was estimated 

by decreasing the value of L at full pool in proportion to the 

decrease in the area which intersected sand and gravel at that 

contour level. 
14 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Applications of the Firm-Yield 

Estimator Model

Firm yields were determined for 38 reservoir systems in 

Massachusetts. Of these, 23 were single-reservoir systems, 

and 15 were multiple-reservoir systems. Reservoirs whose 

firm yield had been previously determined were re-evaluated 

using updated methods and data. Previous firm-yield studies 

in Massachusetts (Waldron and Archfield, 2006; and Archfield 

and Carlson, 2006) used a monthly time step, which can cause 

an overestimation of the firm yield (Fennessey, 1995). The 

inclusion of daily streamflows and meteorological data as well 

as a refined method for estimating groundwater flows in this 

study resulted in firm-yield estimates that differ from those 

found in Waldron and Archfield (2006). 

Firm-yield estimates for both single- and multiplereservoir systems are shown in table 4. Water-use data from 

Annual Statistical Reports provided by MassDEP for the years 

2000 to 2004 indicate that 32 out of the 38 reservoir systems 

are currently operating below their firm yield or marginally at 

their firm yield. Because year-to-year usage in a system can 

vary, systems in which average usage was within 10 percent of 

the firm yield may be operating within the firm yield in some 

years but above the firm yield in other years. These reservoirs 

were listed as marginally operating within the firm yield.

Application of the Firm-Yield Estimator Model to 

a Single-Reservoir System

Single-reservoir systems consist of one reservoir that 

does not receive water from any other reservoir. Inflows 

to a single-reservoir system consist of streamflow into the 

reservoir from the surrounding watershed, precipitation 

that falls directly on the reservoir surface, and groundwater 

inflows. Outflows from a single-reservoir system are 

evapotranspiration, groundwater outflows, water withdrawals 

for public water supply or other uses, and releases from the 

reservoir for downstream flow requirements. Firm yields 

for a single-reservoir system are computed by successively 

solving the water-balance equation for the reservoir over the 

44-year simulation period, increasing the yield each time by a 

minimum of 0.001 million gallons (Mgal). The highest yield 

that can be used without the reservoir failing for one day is the 

firm yield. 

Echo Lake in Hopkinton, Massachusetts, currently 

augments the amount of available water in the reservoir by a 

diversion from the Charles River (not shown in fig. 1) approximately 2.5 mi below the Echo Lake Dam, at the crossing of 

Dilla Street in Milford, Mass. Water from the river at this point 

can be pumped back into the reservoir. The maximum pumping rate for the diversion is 3 million gallons per day (Mgal/d), 

and pumping primarily occurs during March through May 

(Metcalf and Eddy, 1997). In order to simulate this unique 

situation, streamflow for the length of the Charles River from 

the diversion point up to the Echo Lake Dam was estimated 

using SYE. The FYE model was modified for this reservoir 

only, such that a maximum of 3 Mgal/d of streamflow from 

the Charles River and from Echo Lake spillage during the 

previous simulated time step was added back into Echo Lake 

storage at the end of each simulation time step during the 

months of March through May. Including the Charles River 

diversion in the simulation of Echo Lake increased the firm 

yield by 35 percent, from 0.83 Mgal/d without the diversion to 

1.12 Mgal/d including the diversion. A previously estimated 

firm yield for this lake, calculated using a reservoir capacity of 

384 Mgal obtained from historical documents and without the 

Charles River skimming, is 0.56 Mgal/d (Metcalf and Eddy, 

1997). The current study used a reservoir capacity of 

461.6 Mgal based on volume estimates from current 

bathymetric measurements of the reservoir.

Main Reservoir in Scituate is simulated as a singlereservoir system, although water is actually transported from 

Main Reservoir to Old Oaken Bucket Pond by way of First 

Herring Brook (not shown in fig. 1) before being pumped to 

the water-treatment facility. Because of excessive aquaticplant growth, bathymetric measurements could not be made 

in Old Oaken Bucket Pond. Because the stage-storage relation 

could not be determined for this reservoir, the firm yield could 

not be estimated. On the basis of the relative sizes of these two 

reservoirs, most of the available water for this system comes 

from Main Reservoir. Because storage in Old Oaken Bucket 

Pond was not considered for this analysis, the firm yield for 

this system represents a conservative estimate. 

Application of the Firm-Yield Estimator Model to 

a Multiple-Reservoir System

Of the 71 reservoirs included in this study, 48 are in 

reservoir systems in which multiple reservoirs are hydrologically connected. Reservoirs may be configured in a variety 

of ways and can transfer water either through uncontrolled 

spills from an upstream reservoir that is at full pool into a 

river or open channel that transports water by gravity into a 

downstream reservoir, or by pumping water from one reservoir to another. Reservoir-configuration diagrams for newly 

surveyed reservoirs in this study are included in appendix 3. 

Configurations for previously studied reservoir systems are 

included in Archfield and Waldron (2006). Because individual 

reservoirs in a system have different storage capacities, they 

will not necessarily deplete and refill at the same rates. The 

optimal firm yield for a multiple-reservoir system depends 

on the time-varying withdrawal operations of each individual 

reservoir in the system. Estimating the optimal firm yield for 

a multiple-reservoir system requires complex optimization 

methods which are beyond the scope of this study. However, 

an approximation of a multiple-reservoir-system firm yield can 

be made by assuming that all reservoirs are operating at their 

individual maximum yield.
Applications of the Firm-Yield Estimator Model 15

Table 4. Firm-yield estimates and 2000–2004 water usage for 38 reservoir systems in Massachusetts.

[Actual average annual usage refers to the period 2000–2004. Reservoirs with usage that was within 10 percent of the firm yield are considered marginally 

meeting their firm yield; Mgal/d, million gallons per day; DPW, Department of Public Works]

Water supplier Reservoir system

Firm yield, 

no releases

(Mgal/d)

Actual average 

annual usage

(Mgal/d)

Operating at less 

than firm yield?

Amherst Water Department Atkins Reservoir 1.16 0.83 Yes

Ashburnham/Winchendon Upper Naukeag Lake 1.72 1.06 Yes

Concord Water Department Nagog Pond 0.86 0.09 Yes

Fall River Water Department North Watuppa system 18.20 12.89 Yes

Fitchburg Water Department Lovell Reservoir system 2.77 0.18 Yes

Fitchburg Water Department Meetinghouse system 5.61 2.71 Yes

Fitchburg Water Department Wachusett Lake 1.08 0.35 Yes

Greenfield Water Department Leyden Glen Reservoir 0.69 0.57 Yes

Hingham/Hull (Aquarian Water Company) Accord Pond 0.66 0.59 Yes

Lee Water Department Schoolhouse Reservoir 0.84 0.51 Yes

Leicester (Cherry Valley and Rochdale Water) Henshaw Pond 0.35 0.26 Yes

Lincoln Water Department Flints Pond 0.59 0.38 Yes

Marlborough DPW–Water and Sewer Division Millham system 1.83 1.40 Yes

North Brookfield Water Department Doane Pond system 0.71 0.42 Yes

Pittsfield Water Department Ashley Lake 1.37 0.21 Yes

Pittsfield Water Department Cleveland Reservoir 9.18 7.96 Yes

Pittsfield Water Department Farnham Reservoir system 2.51 2.23 Yes

Pittsfield Water Department Upper Sackett Reservoir 0.50 0.08 Yes

South Deerfield Water Supply District Whately system 1.07 0.68 Yes

Southbridge Water Department Hatchet Brook system 2.78 1.69 Yes

Springfield Water Department Cobble Mountain system 42.70 36.57 Yes

Wakefield Water Department Crystal Lake 0.40 0.28 Yes

West Springfield Water Department Bearhole Reservoir 1.40 0.73 Yes

Westborough Water Department Sandra Pond 0.80 0.67 Yes

Westfield Water Department Granville Reservoir 3.03 2.47 Yes

Westfield Water Department Montgomery Reservoir 1.13 0.00 Yes

Amherst Water Department Centennial system 0.87 0.83 Marginally

Lee Water Department Upper (Leahey) Reservoir 0.59 0.54 Marginally

Leominster DPW–Water Division Fall Brook Reservoir 0.84 0.88 Marginally

Leominster DPW–Water Division Simonds Pond system 2.26 2.32 Marginally

Scituate Water Department Main Reservoir 0.63 0.61 Marginally

Winchester Water Department South Reservoir system 1.01 1.10 Marginally

Danvers Water Department Middleton Pond system 2.79 3.09 No

Greenfield Water Department Green River 0.42 0.52 No

Hinsdale Water Department Belmont Reservoir 0.12 0.15 No

Leominster DPW–Water Division Distributing Reservoir system 0.58 0.87 No

Milford Water Company Echo Lake 11.12 1.40 No

Worcester Water Department Holden Pond system 17.15 23.87 No

1

 Firm yield for Echo Lake includes water from the Charles River diversion.
16 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

The algorithm for calculating the firm yield of a multiple-reservoir system depends on its configuration and the 

method of water transport between reservoirs (fig. 3). For 

two reservoirs connected by either a river or open channel, 

water released from the upstream reservoir in order to meet 

demand, as well as any uncontrolled spills and controlled 

releases from the reservoir, is transported to the downstream 

reservoir. For two reservoirs that transport water through 

pumping, only the volume of water that is pumped from the 

first reservoir is added as a water input to the second reservoir, 

and uncontrolled spills and controlled releases are lost from 

the system. The firm-yield model first estimates the firm yield 

of the uppermost reservoir, which does not receive water from 

any other reservoirs, in the same manner as a single-reservoir 

system. The spillage volume, Qspi and the yield volume, 

Qyi are calculated for each simulation day and saved by the 

model. After the simulation for the first reservoir is finished, 

the model begins the simulation for the second reservoir and 

includes the inputs from the previous reservoir in the water 

balance. If the reservoirs are connected by pumping, the 

daily-yield volume from the previous reservoir is added as an 

additional inflow into the water-balance equation of the second 

reservoir. For reservoirs connected by gravity, the daily-yield 

volume, Qyi, and the daily uncontrolled spill volume, Qspi, are 

added as additional inflows into the water balance of the second reservoir. The maximum pump capacity may be set by the 

user. If the usage exceeds the pump capacity on a given day, 

only the maximum pump-capacity volume is transferred to the 

second reservoir, and the excess water remains in storage in 

the first reservoir. For systems with more than two reservoirs, 

firm yields of reservoirs that contribute water to any other 

reservoir are estimated before the receiving reservoir. The 

system firm yield is the firm yield calculated at the terminal 

reservoir after accounting for inflows from other reservoirs in 

the system. 

The FYE is most appropriate for estimating yields of 

relatively simple multiple-reservoir configurations and reservoir operations. Because the model calculates the yield of each 

reservoir in the system sequentially, reservoir configurations 

in which water is routed through a reservoir more than once 

cannot be handled by the FYE. Only one reservoir system 

in the study had a configuration that could not be adequately 

modeled by the FYE. The Worcester system consists of 10 

individual reservoirs with Holden Reservoir #1 as the terminal 

reservoir. Water is pumped into Holden Reservoir #1 from 

Lynde Brook Reservoir and gravity-fed by Kendall Reservoir. Water from Holden Reservoir #1 may be pumped either 

directly to the filtration plant or into Holden Reservoir #2 for 

storage, then back into Holden Reservoir #1. Because Holden 

Reservoir #1 both receives water from and releases water to 

Holden Reservoir #2, it cannot be modeled by the sequential 

algorithm used in the FYE. In order to estimate the firm yield 

for this system, Holden Reservoirs #1 and #2 were modeled 

as one reservoir with the combined reservoir characteristics 

of both individual reservoirs. Because of the operational 

complexities of this system, the firm yield estimated by the 

FYE may be less certain than in simpler reservoir systems.

Firm-Yield Estimate Uncertainty and 

Sensitivity to Model Inputs

Uncertainty in firm yields determined using the FYE 

comes from many sources, including uncertainty in input 

data—such as daily streamflow, evaporation, precipitation, and 

stage-storage relations—and uncertainty associated with the 

estimation of groundwater-flow contributions. For reservoir 

systems that are operating at or near their estimated firm yield, 

the uncertainty associated with the firm-yield estimates could 

result in reservoirs exceeding their true firm yield. If the firmyield estimate is higher than the true value of the firm yield, 

reservoirs risk failing if they are operating near their firmyield estimate.

An analytical method to examine the effects of the combined uncertainty from all of the input data errors has not been 

determined for the FYE; however, the sensitivity of the model 

to individual sources of uncertainty can be examined. Daily 

streamflow volumes are generally many times greater than 

groundwater contributions and direct precipitation or evaporation from the reservoir surface. Therefore, relative uncertainties in the daily streamflow time series have the potential to 

contribute the greatest amount of uncertainty in the water 

balance equation and the resulting firm-yield estimate. The 

storage capacity of the reservoir is also important in estimating 

the firm yield. Reservoir volume and stage/storage relations 

are calculated from bathymetric-survey data. There is little 

guidance available regarding the number of bathymetric-data 

points needed to accurately assess reservoir capacity and 

the manner in which errors in this calculation might affect 

the firm-yield estimates. A final source of uncertainty in the 

firm-yield estimates comes from the equations used to estimate groundwater contributions to the water balance. These 

equations have not been extensively tested for use in reservoir 

simulation models, and parameter estimates for these equations are uncertain. 

Sensitivity of Firm-Yield Estimates to Errors in 

Daily Streamflow

In order to investigate the potential sensitivity of the FYE 

to input streamflow errors, a series of Monte Carlo simulations 

were performed in which the daily-streamflow inputs were 

perturbed by a random-error term during the calculation of the 

firm yield for a particular reservoir. The range of firm-yield 

estimates obtained after many simulations is representative 

of the amount of uncertainty that can be expected in the firm 

yield due to errors in the input streamflow time series. 
Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs 17

A

B

Gravity Pumped

S1,i 1,i 1,i EP 1,i Aw1Qst α y rr sp QQ Q Q Q S gw 1,(i–1) 1,i 1 1,i 1,i 1,i 1,i Ar 1,i ow

S 2,i EP Aw2Qst α y rr sp QQ Q Q Q S gw 2,(i–1) 2,i 2,i Qsp1,i 2,i Ar2,i 2,i 2,i 2 2,i ow α y rr QQ 1 1,i 2,i 2,i 1,i

S1,i 1,i 1,i EP 1,i Aw1Qst α y rr sp QQ Q Q Q S gw 1,(i–1) 1,i 1 1,i 1,i 1,i 1,i Ar 1,i ow

S 2,i EP Aw2Qst α y rr sp QQ Q Q Q S gw 2,(i–1) 2,i 2,i

Qspi

2,i Ar2,i 2,i 2,i 2 2,i ow α

Q

Qy

rr

1 1,i

i

2,i 2,i

Qy

Qowi

Si

i

Ari

Pi

Ei

Qsti

αi

 = uncontrolled spill, in million gallons 

= withdrawal from the reservoir by other users,

 in million gallons

 = volume of water in usable storage for the current 

 day, in million gallons 

= area of the reservoir surface, in square miles

= precipitation, in miles

 = evaporation from the reservoir surface, in miles 

= reservoir drainage area, in square miles 

= streamflow per unit drainage area, in miles

 = peak-usage factor, dimensionless 

Reservoir water balance for a gravity connected system

Reservoir water balance for a pumped system

= yield for the current day, in million gallons i

Qgwi = groundwater contributions or losses for 

 the current day, in million gallons

= controlled release, in million gallons

= daily simulation time step

Awi

EXPLANATION

Reservoir 1

Reservoir 1

Reservoir 2

Reservoir 2

Subscripts 1 and 2 identify the reservoirs

Figure 3. Water balances for a system of reservoirs in which A, water is transported by gravity and B, water is pumped from 

Reservoir 1 to Reservoir 2.
18 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

In order for the result of a Monte Carlo sensitivity analysis to be meaningful, the errors added to the streamflow in the 

simulations must accurately characterize the uncertainty in the 

input data. Uncertainty associated with SYE streamflow estimates is an area of ongoing research and is beyond the scope 

of this project (Archfield and others, 2010). However, as a first 

attempt at characterizing the uncertainty associated with FYE 

streamflow inputs, the structure of the randomly generated 

Monte Carlo error terms was based on the relative errors from 

a SYE cross-validation dataset. SYE-generated daily streamflows were computed for 18 U.S. Geological Survey (USGS) 

gaged sites and compared to the observed streamflow values 

(Archfield and others, 2010). The percent difference between 

the SYE predicted daily flows and the observed flows from 

these 18 sites was calculated for each day as 

PD = (Qest – Qobs)/Qest , (2)

where

PD is the percent difference between the SYE 

predicted streamflow and observed 

streamflow,

Qobs is the observed streamflow, and

Qest is the estimated streamflow.

For each of the gages, the exceedence probability of each of 

the daily flows also was calculated. For each exceedence probability, the mean percent difference between observed and estimated flows across all 18 gaged sites was calculated as well as 

the standard deviation of the percent differences.

Figure 4 shows that for streamflows with exceedence 

probabilities up to about 0.6, the mean percent difference 

between observed and predicted is near zero, and the standard 

deviation of the percent differences is fairly constant, indicating that flows in this range are relatively unbiased but contain 

some amount of random error. For low streamflows with 

higher exceedence probabilities, the mean percent difference 

between observed and predicted deviates from zero, and the 

mean standard deviation of the differences increases, indicating a potential bias and greater uncertainty in the low daily 

streamflows. Since low flows generally occur during drought 

periods, underprediction of streamflows during these times 

could lead to underprediction of the firm-yield estimate.

In order to construct a random-error term for inclusion in 

the Monte Carlo simulations, the percent difference between 

observed and predicted daily streamflows was assumed to 

be normally distributed. The mean and standard deviation of 

the sample distribution for the percent difference between 

observed and predicted flows were estimated from figure 4. 

For simulated flows with exceedence probabilities less than 

0.6, the error term was generated from a Gaussian distribution with a mean of zero and a standard deviation of 0.3. 

In order to capture the greater uncertainty in the low flows, 

simulated streamflows with exceedence probabilities greater 

than 0.95 were generated from a Gaussian distribution with 

a mean of -0.75 and a standard deviation of 1. Streamflows 

with exceedence probabilities of 0.6 to 0.95 were generated 

from a Gaussian distribution with a mean of -0.25 and a 

standard deviation of 0.5. Although the percent differences 

between observed and predicted streamflows are large at 

higher exceedence probabilities, the percent difference represents a very small volume of water, because flows at the 

0.95 exceedence probability and above are generally very low 

for the stream gages in the cross-validation dataset. Random 

percent errors generated for each day of the simulation were 

applied to the daily streamflows as 

Q*= Qest – (Erri * Qest) (3)

where

Q* is the daily streamflow modified by random 

error term,

Qest is the daily-streamflow volume estimated by 

the SYE, and

Erri is the randomly generated error term.

Monte Carlo simulations with 500 repetitions were 

run for 22 reservoirs in the study, and the distribution of the 

resulting firm yields for each reservoir is shown in table 5. 

Firm yields generated by the Monte Carlo simulations in the 

selected reservoir were somewhat higher than the original 

firm-yield estimates. This is due to the underprediction bias 

in the lowest streamflows. When this bias is corrected in the 

Monte Carlo simulations, firm yields increase. The mean firm 

yield generated by the Monte Carlo simulations ranged from 

0.6 to 10.6 percent higher than original firm-yield estimates 

across all 22 reservoirs, indicating that firm yields computed 

by the model are potentially underestimated by this amount 

and therefore represent a conservative estimate of the firm 

yield (table 5).

The mean percent change in firm yield was used to 

compare the sensitivity behaviors of different reservoirs. Mean 

percent change in firm yield was calculated as the percent 

difference between the initial firm-yield estimate and the mean 

firm-yield estimate generated by the Monte Carlo simulation. 

The mean percent changes in firm yields were highest in reservoirs with low storage ratios, defined as the reservoir capacity 

divided by the mean annual streamflow. This indicates that 

these low-storage reservoirs are more sensitive to errors in the 

streamflow input data than reservoirs with high storage ratios 

(fig. 5). 

It is important to note that because the sample distribution used to generate the random errors in the Monte 

Carlo simulations was based on the average behavior at 18 

gaged sites, it may not accurately characterize the errors in 

streamflow input data at all FYE reservoirs. The errors in the 

streamflows for any particular reservoir may have more or less 

bias or variability than the average relative errors at the gaged 

sites and, therefore, would have a different range of firm-yield 

estimates. In addition, this method does not account for autocorrelation of the daily relative errors in streamflows. Further 

study regarding uncertainty in the SYE tool is needed for a 

more precise sensitivity analysis of the effects of streamflow 

input data on the firm yield.
Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs 19

Overprediction of daily flows

Underprediction of daily flows

-3.00

-2.50

-2.00

-1.50

0.00

0.50

1.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.00

1.00

2.00

3.00

4.00

5.00

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Standard deviation of relative errors

B

Exceedence probability of simulated streamflows

Exceedence probability of simulated streamflows

Mean percent difference between observed

and simulated streamflows -0.50

-1.00

A

Figure 4. A, Mean percent difference and B, standard deviation of the percent difference of daily streamflows generated by the 

Sustainable Yield Estimator at 18 U.S. Geological Survey gaged sites in Massachusetts.
20 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 5. Distribution of firm yields resulting from 500 Monte Carlo simulations at selected reservoirs in Massachusetts.

[Mgal/d, million gallons per day]

Reservoir name

Firm-yield 

estimate

(Mgal/d)

Mean firm-yield 

estimate from Monte 

Carlo simulations

(Mgal/d)

Standard deviation 

of Monte Carlo firmyield estimates

Highest Monte Carlo 

firm-yield estimate

(Mgal/d)

Lowest Monte Carlo 

firm-yield estimate

(Mgal/d)

Ashley Lake 1.37 1.42 0.02 1.47 1.36

Atkins Reservoir 1.16 1.28 0.02 1.33 1.23

Belmont Reservoir 0.12 0.12 0.00 0.13 0.12

Bickford Reservoir 1.91 1.96 0.02 2.01 1.91

Cleveland Reservoir 9.18 9.56 0.10 9.86 9.24

Cohasse Reservoir 1.16 1.19 0.02 1.24 1.13

Copicut Reservoir 7.30 7.41 0.05 7.56 7.25

Emerson Brook Reservoir 1.22 1.27 0.02 1.32 1.23

Fall Brook Reservoir 0.84 0.86 0.01 0.89 0.82

Farnham Reservoir 1.62 1.69 0.02 1.74 1.63

Fitchburg Reservoir 1.22 1.24 0.01 1.27 1.20

Flints Pond 0.59 0.59 0.00 0.61 0.58

Granville Reservoir 3.03 3.32 0.13 3.59 3.07

Hatchet Pond 0.21 0.21 0.00 0.22 0.21

Henshaw Pond 0.35 0.37 0.01 0.38 0.35

Horse Pond 0.50 0.51 0.01 0.53 0.49

Leyden Glen Reservoir 0.69 0.75 0.01 0.79 0.71

Quinapoxet Reservoir 4.21 4.46 0.03 4.57 4.38

Sandwash Reservoir 0.89 0.93 0.01 0.97 0.89

Schoolhouse Reservoir 0.84 0.91 0.01 0.94 0.88

Upper Sackett Reservoir 0.50 0.51 0.01 0.53 0.48

Wachusett Lake 1.08 1.10 0.02 1.15 1.06

Sensitivity of the Firm-Yield Model to 

Bathymetric-Map Accuracy

Water-depth measurements of a reservoir are necessary to 

determine the maximum storage capacity of the reservoir and 

the relation between reservoir stage and storage. Reservoirdepth measurements are interpolated using a GIS to create a 

continuous bathymetric map from which lake volume can be 

determined. Because the firm yield of a reservoir is dependent 

upon the storage capacity, it is important that the number of 

water-depth measurements collected is adequate to characterize this input variable to the FYE model. 

Bathymetric measurements are generally made along 

parallel or gridded straight-line transects of the lake. The 

spacing of transect intervals is important because the density of water-depth measurements affects the accuracy of the 

computer-generated bathymetric maps and computed storage 

capacity. Although it is beneficial to have as many measurement points as possible, very high density transect intervals 

may be prohibitively time consuming and expensive to obtain, 

especially for large reservoirs. However, if the spacing of 

measurement transects is too wide and point density too low, 

important physiographical features may be missed, causing 

errors in the resulting bathymetric-contour maps and storage calculations. Wilson and Richards (2006) show that lake 

capacity computed from bathymetric surveys decreases as 

transect-interval spacing increases. Storage capacity calculated 

from 400- and 800-ft transect intervals differed by 15.6 and 

36.8 percent, respectively, from storage capacity calculated 

using 50-ft transect intervals. 

The effect of water-depth measurement density on reservoir capacity and firm-yield estimation was examined using 

three reservoirs which represent typical reservoir sizes and 

shapes in Massachusetts. Upper Sackett Reservoir, located in 

Pittsfield, Mass., is the smallest of the three reservoirs, with an 

area of 19 acres and a gently sloping “U”-shaped lake-bottom 

topography. Cohasse Reservoir in Southbridge, Mass., is a 

long, narrow valley impoundment with a surface area of 
Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs 21

xx

x

x

x

x

x

x

x

x

xx

x

x

x

x

xxx

x x

x

x

x

x

x

xx

x

x x

x

x

x

x

x

x

o

x

x

x

x

x

x

x

x

x

xx

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

x

x

x

xxx

x

x

x

x

xx

x

x

x

x

x

x

x

x

x

x

-5

0

5

10

15

20

Percent change in firm yield

Leyden Glen Reservoir

Schoolhouse Reservoir

Farnham Reservoir

Quinapoxet Reservoir

Belmont Reservoir

Henshaw Pond

Cleveland Reservoir

Emerson Brook Reservoir

Granville Reservoir

Sandwash Reservoir

Atkins Reservoir

Upper Sackett Reservoir

Ashley Lake

Cohasse Reservoir

Wachusett Lake

Fall Brook Reservoir

Bickford Reservoir

Horse Pond

Fitchburg Reservoir

Copicut Reservoir

Hatchet Pond

Flints Pond

Increasing storage ratio

75th percentile

Outlier

Outlier

50th percentile

(median)

25th percentile

Interquartile

range

x

x

EXPLANATION

Figure 5. Percent change in firm yield of selected reservoirs in Massachusetts after accounting for potential errors in daily streamflow 

in 500 Monte Carlo simulations.

56 acres and a steeply sloping “V”-shaped lake bottom. South 

Reservoir in Winchester, Mass., is the largest of the three 

reservoirs with an area of 72 acres and a relatively flat lake 

bottom. The area-to-perimeter ratios of Cohasse Reservoir, 

South Reservoir, and Upper Sackett Reservoir were 154.9, 

183.0, and 202.6, respectively. Lake depths ranged from 45 

to 53 ft, and surveys from all three reservoirs included high 

water-depth measurement densities. Original transect spacing for these three lakes ranged from 15 to 50 meters (m) and 

always included at least one complete shoreline-perimeter 

transect (table 6).

Survey measurements were interpolated using the 

TOPOGRID command in ARC/INFO (Environmental 

Systems Research Institute, Inc., 1994) to create bathymetric 

surfaces for each reservoir. Reservoir storage capacity was 

computed using the Volume tool in the 3D Analyst toolbox 

(Environmental Systems Research Institute, Inc., 1994). For 

the purposes of this uncertainty analysis, this bathymetric 

surface was assumed to be the true lake bottom from which 

water depths at points along hypothetical transects of 

varying spacings and patterns using a GIS were measured. 

Hypothetical transect lines were applied in three patterns: 

parallel lines across the width of the lake, perpendicular 

gridded lines across the width and length of the lake, and 

gridded lines with an additional perimeter transect (fig. 6). 

Each transect pattern was applied using five different transect 

spacings: 15, 30, 60, 90, and 120 m, respectively. Points 

were placed every 5 m along each transect and overlaid on 

top of the reference bathymetric surface from which the depth 

was obtained. Water depths along the hypothetical transects 

were used to create a new bathymetric surface using the same 

method as for the original transect measurements, in addition 

to calculating reservoir storage capacity and stage-storage 

relations. The reservoir capacity and stage-storage data were 

entered into the FYE, and the firm yield was calculated for 

each transect pattern. The storage volume and firm yield 

estimated from the different transect patterns were then 
22 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0 Table 6. Reservoir capacity and firm yield for selected reservoirs in Massachusetts calculated using various transect patterns and sampling-point densities. [m, meters; pts/acre, points per acre; Mgal, million gallons; Mgal/d, million gallons per day; --, no data] Transect pattern Transect width (m) Cohasse Reservoir Upper Sackett Reservoir South Reservoir Bathymetric sampling point density (pts/acre) Usable storage capacity (Mgal) Firm yield (Mgal/d) Bathymetric sampling point density (pts/acre) Usable storage capacity (Mgal) Firm yield (Mgal/d) Bathymetric sampling point density (pts/acre) Usable storage capacity (Mgal) Firm yield (Mgal/d) Actual survey measurements -- 71.33 369.99 1.16 127.19 162.73 0.51 58.05 411.29 0.44 Parallel transects only 15 21.98 366.22 1.15 25.49 159.68 0.51 25.30 395.60 0.43 30 11.07 359.95 1.14 12.64 157.70 0.50 12.67 377.58 0.42 60 5.65 346.51 1.12 6.32 149.46 0.49 6.42 334.24 0.39 90 3.77 325.45 1.09 4.23 134.65 0.46 4.44 288.37 0.35 120 2.88 290.51 1.04 3.19 119.26 0.44 2.86 199.71 0.27 Gridded transects 15 94.25 369.68 1.16 50.58 160.37 0.51 50.41 400.40 0.43 30 24.10 364.98 1.15 24.99 159.68 0.51 25.34 391.69 0.43 60 12.38 358.61 1.14 12.64 155.80 0.50 12.77 357.40 0.40 90 7.96 346.89 1.13 8.36 147.76 0.49 8.55 332.53 0.39 120 6.48 336.95 1.11 6.77 140.85 0.47 6.30 295.97 0.36 Gridded transects with added perimeter transect 15 107.43 369.23 1.16 62.67 160.93 0.51 63.80 402.62 0.44 30 37.28 364.78 1.15 37.09 160.63 0.51 38.73 398.39 0.43 60 25.56 358.55 1.14 24.74 159.46 0.51 26.16 383.19 0.42 90 21.14 352.32 1.13 20.46 156.91 0.50 21.95 375.06 0.42 120 19.65 345.16 1.12 18.87 152.58 0.49 19.70 364.54 0.41
Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs 23

Original bathymetricsurvey transect paths

Hypothetical 30-meter 

parallel transects

Hypothetical 30-meter 

gridded transects

Hypothetical 30-meter

gridded transects with 

added perimeter transect

Figure 6. Original and hypothetical 

30-meter transect spacing for Upper 

Sackett Reservoir in Pittsfield, 

Massachusetts.

compared to the volume and firm yield estimated from original 

transect measurements (table 6).

Errors in estimated reservoir volume and firm yield were 

smallest for Cohasse Reservoir, which is long and narrow, and 

were largest in South Reservoir, which has a sprawling, flatbottomed lake form, indicating that reservoir shape may play 

a role in bathymetric accuracy. In general, parallel transects 

spaced farther than 15 m apart did a poor job of characterizing the bathymetry. Gridded transects performed better: in 

Cohasse and Upper Sackett Reservoirs, gridded transects 

spaced 60-m apart or less produced results with minimal (less 

than 5 percent) error rates in volume and firm yield. Gridded 

transects spaced 30 m or less apart in South Reservoir also 

produced minimal error rates. Adding a perimeter transect to 

gridded transects did not result in an appreciable improvement in volume or firm-yield accuracy in Cohasse Reservoir; 

however, in Upper Sackett and South Reservoirs, which have 

rounder reservoir shapes and lower perimeter-to-area ratios, 

the addition of a perimeter transect improved the volume 

and firm-yield estimates by roughly 50 percent. The percent 

changes in reservoir storage capacity and firm yield for 

selected reservoirs are shown in figure 7.

For each hypothetical transect-pattern scenario, the average spatial density of measurement points was calculated as 

the number of measurement points divided by the reservoir 

surface area. Measurement densities fewer than 10 measurements per acre resulted in unreliable bathymetric maps with 

volume errors between 6 and 51 percent and yield-estimate 

errors between 3 and 40 percent. Errors in volume and firmyield estimates were less than 5 percent when point densities 

were above more than 20 points per acre.

It is important to note that errors in bathymetric maps and 

calculations can also arise as a result of the methods employed 

during GIS processing. The type of interpolation method 

used, grid-cell size, and degree of smoothing can all affect 

the resulting bathymetric-map calculations and resulting firm 

yield. Bathymetry calculations may be more or less sensitive 

to the density of depth measurements when analyzed using 

different GIS techniques than those used here.
24 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

-60

-45

-30

-15

0

0 20 40 60 80 100 120 140

Percent change in storage capacity

C Cohasse Reservoir

Transect width, in meters

B South Reservoir 

Percent change in storage capacity

Transect width, in meters

-15

0

-45

-30

-60

0 20 40 60 80 100 120 140

D Upper Sackett Reservoir

Percent change in firm yield

Transect width, in meters

-45

-35

-25

-15

-5

0 20 40 60 80 100 120 140

E South Reservoir

Percent change in firm yield

-45

-35

-25

-15

-5

0 20 40 60 80 100 120 140

Transect width, in meters

-60

-45

-30

-15

0

0 20 40 60 80 100 120 140

A Upper Sackett Reservoir

Percent change in storage capacity

F Cohasse Reservoir

Percent change in firm yield

-45

-35

-25

-15

-5

0 20 40 60 80 100 120 140

Transect width, in meters

EXPLANATION

Gridded transects with added perimeter transect

Gridded transects

Parallel transects

Transect width, in meters

Figure 7. A–C, Percent change in reservoir storage capacity and D–F, firm yield, resulting from transect spacings and 

patterns for three study reservoirs in Massachusetts.
Firm-Yield Estimate Uncertainty and Sensitivity to Model Inputs 25

Validation of Groundwater Parameters

Reservoir-aquifer geometry in the FYE is parameterized 

by (1) the length of shoreline in contact with sand and gravel, 

(2) the distance from the reservoir shoreline to the aquifer 

boundary, and (3) the transmissivity of the aquifer (Archfield 

and Carlson, 2006). The first two of these parameters are 

estimated by intersecting reservoir-shoreline locations with 

maps of sand and gravel deposits (Office of Geographic and 

Environmental Information, 2004). The calculated perimeter 

length is highly sensitive to the spatial scale of the lakeboundary map layer, and little guidance is available regarding 

proper map scale for estimating this parameter. Transmissivity 

values are based on published USGS hydrologic atlases, which 

lack numerical and geographical precision and are unavailable 

for some areas of Massachusetts.

Archfield and Carlson (2006) show that the FYE model is 

most sensitive to the transmissivity of the aquifer and length of 

shoreline in contact with sand and gravel. Groundwater flows 

into and out of the reservoir are highest during periods when 

reservoir stage is changing, so inaccuracies in these calculations due to parameter estimation will be most pronounced 

during periods of extreme reservoir storage changes. In the 

case where either of these two groundwater parameters is 

overestimated, the FYE will overestimate groundwater flows 

entering the reservoir during drought periods. This would 

cause the simulated reservoir stages to be too high and could 

lead to an overestimation of firm yield.

An attempt was made to use observational data to calibrate estimates of groundwater parameters. The FYE model 

was modified to accept observed water-use withdrawal rates 

in place of the yield in the water-balance equation and also 

to output daily reservoir stage. Simulated reservoir stage was 

then compared to observed reservoir stage. If other modelinput time series such as streamflow, precipitation, and wateruse withdrawal volumes, are known with certainty, groundwater parameters can be calibrated by minimizing discrepancies 

between observed and simulated reservoir stage. The requisite 

observational data for a rigorous validation of groundwater 

parameters were not available for any of the reservoirs in the 

study; however a limited amount of observational data was 

available from water suppliers for Nagog Pond in Acton, 

Mass., and Atkins Reservoir in Amherst, Mass.

Observational data for Atkins Reservoir include daily precipitation, daily withdrawal volumes, and daily reservoir stage 

for March 1994 to September 2004. The FYE was run for this 

time period using observational precipitation and water-use 

rates. The simulation period includes several reservoir critical periods in which the reservoir stage decreases from full 

pool to a local minimum, then fully refills. The most severe 

drawdown period occurred on October 12, 2002, when the 

reservoir dropped to roughly 44 percent of its total capacity. 

Comparison of observed and simulated reservoir stages shows 

that reservoir stage was overestimated during these severe 

critical periods (fig. 8). Other deviations in the shape of the 

simulated stage when compared to the observed stage, such 

as the delayed reservoir recovery in several of the drawdown 

periods, are most likely caused by errors in daily streamflow, 

precipitation, or evaporation input time series. The consistent 

bias in estimating the peak drawdown stage, however, may be 

caused by inaccuracies in groundwater parameters.

Because the firm yield is determined from the lowest reservoir stage during a severe drawdown period, it is important 

that the model can accurately predict the magnitude of a drawdown. Errors in simulated reservoir stage at nearly full-pool 

volumes or in the timing of the simulated drawdown period or 

recovery period are less important in estimating the firm-yield 

value. Transmissivity and parameter L were adjusted in order 

to minimize bias in the simulation during the major drawdown 

periods. Agreement between observed and simulated reservoir stages during the major drawdown periods improved by 

decreasing transmissivity and parameter L by 30 to 50 percent 

of their original values (fig. 8). However, errors in the shape 

of the simulated daily reservoir stage remain due to errors 

in the streamflow, precipitation, and evaporation time series. 

Because of errors in the other input data series, the values for 

transmissivity and parameter L could not be calibrated with 

a high degree of precision, but the results of the simulations 

indicate that initial estimates of transmissivity and perimeter 

length in contact with the aquifer may have been too high. 

Despite a lack of precision in these variables, the inclusion of 

groundwater contributions did improve the agreement between 

observed and simulated reservoir stages compared to a simulation using only streamflow and climate inputs to the system.

Atkins Reservoir is almost fully surrounded by sand and 

gravel deposits; however, surficial-geology maps show that 

only a small portion of the area of Nagog Pond intersects with 

sand and gravel deposits. In addition, estimated transmissivity 

values for this area are low, indicating a relatively limited 

groundwater influence in this reservoir. Available data 

for Nagog Pond include once-monthly reservoir stage 

observations and total monthly water-use withdrawal volumes 

for the period of February 1975 to September 1984. Monthly 

withdrawal data were disaggregated into daily withdrawals 

by dividing the monthly total by the number of days in each 

month. These daily values were used in place of the yield 

term in the modified FYE model, and simulated stages were 

compared to observed reservoir stages. Drawdown periods 

are less severe in the observed record for Nagog Pond than 

for Atkins Reservoir. The lowest reservoir stage occurred in 

November 1980, when reservoir storage was at 62 percent of 

maximum capacity.

Comparison of the simulated reservoir stage with the 

observed reservoir stage shows a slight underestimation of 

reservoir stage during drawdown periods (fig. 9). There is 

also an overall negative bias in the last half of the simulation, 

from about 1980 to 1984. A consistent deviation of modeled 

reservoir stage from measured stage, such as that seen here, 

is most likely caused by errors in the streamflow, precipitation, or evaporation input data and not errors in groundwater 

parameters. Nagog Pond has fewer nearby climate stations 

than other reservoirs in the study, making the meteorological 
26 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

420

425

430

435

440

445

450

Reservoir stage relative to local datum, in feet

2/25/1994 7/10/1995 11/21/1996 4/5/1998 8/18/1999

Date

12/30/2000 5/14/2002 9/26/2003

Observed stage

Uncalibrated simulation

Simulation with calibrated groundwater parameters

Lowest intake stage

EXPLANATION

Figure 8. Daily simulated and observed reservoir stage for Atkins Reservoir in Amherst, Massachusetts.

input data more uncertain for this reservoir. Increasing the 

groundwater parameters for transmissivity and L by as much 

as 300 percent resulted in only minor effects on the simulated 

stage of this reservoir (fig. 9); parameter adjustments greater 

than this are unrealistic based on geologic maps of the area. In 

this case, it is most likely that errors in the prediction of daily 

reservoir stage during droughts are due to errors in other input 

data, and a calibration of the groundwater parameters for this 

reservoir cannot be determined.

Groundwater is an important component of the water 

balance for many reservoirs in Massachusetts. The ability to 

accurately estimate groundwater flows in and out of these 

reservoirs is necessary for an accurate firm-yield estimate. 

Archfield and Carlson (2006) show that changes in the 

groundwater parameters L and T of 80 percent can lead to 

10- to 40-percent changes in the firm yield.. Further study is 

needed in order to validate these parameters, improve methods 

for their estimation, and improve the numerical methods 

with which they are incorporated in the model. In particular, 

accurate time series for observed streamflow and precipitation 

are needed so that comparisons of observed and simulated 

reservoir stages are not confounded by errors in the estimation 

of these inputs.

Effect of Drought Severity on FirmYield Estimates

A system’s firm yield depends largely on the severity 

of the drought used in its estimation. The FYE calculates 

firm yield by increasing reservoir yield in the water-balance 

equation throughout the simulation period, until the reservoir 

fails. A firm yield calculated using a very severe or extended 

drought will be lower than a yield calculated using a milder, 

shorter drought. For most reservoirs in Massachusetts, the 

multiple-year drought of the mid-1960s was the most severe 

drought on record; however, other severe droughts occurred 
Effect of Drought Severity on Firm-Yield Estimates 27

210

215

220

225

June 74 Feb. 75 Oct. 75 June 76 Feb. 77 Oct. 77 May 78 Jan. 79 Sept. 79 May 80 Jan. 81 Sept. 81 May 82 Jan. 83 Sept. 83 Apr. 84 Dec. 84

Observed stage

Uncalibrated simulation

Simulation with transmissivity and parameter L 

increased by 300 percent

EXPLANATION

Month/Year

Reservoir stage relative to local datum, in feet

Lowest intake stage at 183 feet

Figure 9. Daily simulated and observed reservoir stage for Nagog Pond in Concord, Massachusetts.

during the 1980s and in 2002. Differences in the firm yields 

determined from the droughts in the historical record and the 

behavior of reservoirs under different drought conditions have 

not been evaluated in Massachusetts.

Drought periods can be defined in terms of either a 

prolonged period of below-average precipitation (meteorological drought) or streamflow (hydrologic drought). Hydrologicdrought periods may differ slightly from meteorologicaldrought periods because of evaporation and groundwater 

storage. Because the firm yield is more sensitive to streamflow 

than to direct precipitation, hydrologic drought is considered 

in this analysis.

Hydrologic droughts can be characterized in terms of 

their duration and intensity. The 3-month moving streamflow 

average was calculated from the daily streamflow record 

and compared to the average seasonal streamflow from the 

entire long-term streamflow record. Seasonal flow periods 

were defined as: spring (March through May), summer (June 

through August), autumn (September through November), 

and winter (December through February). The drought 

duration was defined as the number of consecutive months for 

which the 3-month moving average is less than the average 

seasonal flow. Drought intensity was calculated as the percent 

difference between the magnitude of the 3-month moving 

average streamflow and the average seasonal streamflow 

over the duration of the drought, expressed as a percentage of 

average streamflow. 

Using the daily streamflow record generated from the 

SYE, hydrologic droughts were characterized for reservoirs 

in Massachusetts. Analysis of droughts focused on the 

droughts in the 1960s, 1980s, and 2002, as these were the 

three most severe droughts for most Massachusetts reservoirs. 

The drought of the 1960s is notable for its extended length. 

Durations for this drought ranged from 20 to 69 months, with 

a median of 38 months (table 7, fig. 10). Average 3-month 

streamflows during this drought were 48 to 74 percent below 

average over the duration of the 1960s drought. Droughts in 

the 1980s and 2002 were shorter in duration but in some cases 
28 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 7. Firm yields and reliability of reservoirs in Massachusetts calculated using three major droughts in the historical record.—Continued

[Dates are in months and years from 1964 to 2002; Mgal/d, million gallons per day]

1960s drought 1980s drought 

Storage 

ratio

Drought 

length

(months)

Drought 

intensity

(percent below average 

streamflow)

Firm 

yield

(Mgal/d)

Date of 

maximum 

storage 

depletion

Drought 

length

(months)

Drought 

intensity

(percent below average 

streamflow)

Firm 

yield

(Mgal/d)

Date of 

maximum 

storage 

depletion

Reliability

(percent)

Accord Pond 0.60 20 47.9 0.67 Sep-66 22 54.8 0.66 Sep-81 100.0 

Amythest Brook Intake 0.01 36 68.2 0.06 Nov-64 5 58.6 0.10 Sep-83 98.7 

Ashley Lake 0.37 36 68.1 1.37 Feb-66 24 35.8 1.91 Feb-81 98.4 

Atkins Reservoir 0.31 36 66.9 1.16 Oct-66 20 39.2 1.69 Oct-81 96.4 

Bearhole Reservoir 0.04 47 58.8 1.40 Nov-64 8 72.8 1.84 Feb-81 98.4 

Belmont Reservoir 0.17 36 73.6 0.12 Feb-66 23 39.1 0.16 Feb-81 98.7 

Bickford Reservoir 0.59 36 66.2 1.91 Jan-66 17 41.6 2.73 Jan-81 98.4 

Borden Brook Reservoir 0.70 37 57.8 6.34 Nov-66 11 39.0 8.88 Nov-81 96.6 

Cleveland Reservoir 0.26 64 53.6 9.18 Feb-65 8 80.2 9.39 Feb-81 99.9 

Cohasse Reservoir 0.40 69 57.2 1.16 Feb-66 12 37.4 1.73 Nov-85 97.0 

Crystal Lake 0.49 47 65.5 0.40 Nov-66 11 59.3 0.68 Sep-85 97.2 

Distributing Reservoir 0.01 36 67.2 0.15 Nov-64 5 54.8 0.23 Sep-83 98.1 

Doane Pond 0.11 47 69.5 0.21 Feb-66 8 61.0 0.34 Nov-80 95.7 

Echo Lake 0.79 38 66.7 0.83 Jan-67 11 46.4 1.33 Nov-85 97.3 

Emerson Brook 0.26 38 62.3 1.22 Feb-66 15 59.1 1.59 Nov-85 98.5 

Fall Brook Reservoir 0.57 36 68.2 0.84 Feb-66 17 43.0 1.31 Oct-81 97.1 

Fitchburg Reservoir 0.70 48 69.3 1.22 Mar-67 15 61.7 1.97 Jan-86 96.7 

Goodfellow Pond 0.04 36 67.4 0.07 Nov-64 17 41.9 0.10 Nov-80 99.2 

Granville Reservoir 0.26 38 57.9 3.03 Feb-66 12 61.9 4.21 Feb-81 98.2 

Hatchet Brook Reservoir #3 0.31 69 59.5 0.32 Feb-66 11 36.5 0.49 Feb-85 97.1 

Hatchet Brook Reservoir #4 0.87 69 58.8 0.51 Dec-66 12 39.1 0.81 Nov-86 95.2 

Hatchet Brook Reservoir #5 0.37 69 58.2 0.57 Feb-66 12 38.9 0.86 Nov-85 97.1 

Hatchet Pond 1.55 69 63.2 0.21 Jan-67 14 33.5 0.35 Feb-89 94.1 

Hawley Reservoir 0.01 36 67.1 0.17 Nov-64 21 40.2 0.31 Sep-80 98.4 

Haynes Reservoir 0.69 36 70.6 0.26 Oct-66 23 29.8 0.44 Mar-89 96.6 

Henshaw Pond 0.21 47 68.3 0.35 Feb-66 8 59.6 0.57 Feb-81 95.9 

Hill Reservoir 0.01 36 64.9 0.65 Dec-64 18 42.5 0.97 Feb-81 98.4 

Holden Reservoir #1 0.37 47 64.1 2.58 Nov-66 16 38.4 4.20 Nov-88 95.5 

Holden Reservoir #2 0.70 47 68.9 0.47 Mar-67 16 44.2 0.78 Mar-89 96.2 

Horse Pond 0.62 47 69.0 0.50 Jan-67 16 43.4 0.87 Mar-89 95.7 

Kendall Reservoir 0.91 36 64.9 1.49 Nov-66 23 25.3 2.16 Nov-88 95.9 

Kettle Brook Reservoir #1 0.03 47 68.4 0.12 Nov-64 12 48.2 0.22 Nov-84 96.6 

Kettle Brook Reservoir #2 0.50 47 71.0 0.27 Jan-67 16 46.3 0.47 Mar-89 95.9 

Kettle Brook Reservoir #3 0.42 47 69.6 0.38 Jan-67 16 44.3 0.65 Jan-89 96.0 

Kettle Brook Reservoir #4 0.56 47 67.2 1.08 Jan-67 16 41.3 1.83 Jan-89 96.0 

Leyden Glen Reservoir 0.02 58 57.1 0.69 Feb-65 14 11.7 0.71 Feb-81 99.9 

Lovell Reservoir 0.23 47 71.7 1.16 Feb-66 15 61.3 1.80 Nov-85 98.0 

Lynde Brook Reservoir 0.35 47 66.6 1.51 Feb-66 8 58.4 2.59 Feb-81 95.9 

Main Reservoir 0.09 35 64.2 0.63 Dec-65 23 59.1 0.77 Oct-80 99.4 
Effect of Drought Severity on Firm-Yield Estimates 29

1980s drought 2002 drought

Number 

of failure 

events

Average 

failure 

duration 

(days)

Average 

yield deficit 

during 

failure 

(Mgal/d)

Drought 

length 

(months)

Drought 

intensity 

(percent below average 

streamflow)

Firm yield 

(Mgal/d)

Date of 

maximum 

storage 

depletion

Reliability 

(percent)

Number 

of failure 

events

Average 

failure 

duration 

(days)

Average 

yield deficit 

during 

failure 

(Mgal/d)

0

17

13

20

19

8

13

16

2

15

16

14

30

11

7

13

9

13

11

18

29

16

23

22

19

32

22

18

10

23

19

21

10

12

9

1

7

16

5

0

12

20

29

14

27

20

34

6

32

28

22

23

40

35

36

58

10

26

26

26

29

41

12

29

21

12

40

61

30

35

26

65

54

72

3

47

42

18.4

0.0

0.6

35.2

36.5

14.4

3.3

69.3

246.3

30.3

52.3

17.6

2.8

4.9

58.8

40.1

40.9

95.7

0.8

78.4

11.2

23.2

23.7

14.9

1.8

9.2

7.9

5.2

125.4

42.5

22.5

71.2

4.2

26.4

29.7

114.2

2.6

64.2

85.3

7.4

13

22

23

22

17

25

20

12

10

10

10

20

20

20

12

20

22

20

12

10

10

10

10

22

20

20

22

20

20

20

20

20

20

20

20

10

12

20

4

49.8

55.3

54.7

54.9

54.2

55.7

49.2

47.0

34.8

40.5

58.3

49.5

56.7

54.6

57.5

50.5

53.7

50.3

47.1

56.9

41.9

41.5

59.6

54.6

52.9

55.3

52.2

51.4

56.1

56.1

48.5

55.5

58.1

56.7

54.4

40.8

60.3

53.8

57.6

0.75

0.10

1.81

1.49

1.81

0.16

2.49

8.70

12.87

1.45

0.65

0.21

0.27

1.17

1.72

1.13

1.94

0.10

4.53

0.40

0.71

0.72

0.31

0.28

0.38

0.49

0.91

3.48

0.69

0.74

1.86

0.15

0.39

0.53

1.54

1.19

1.82

2.14

1.06

Oct-02

Jan-02

Feb-03

Nov-02

Oct-02

Mar-02

Nov-02

Nov-02

Jan-02

Dec-02

Nov-02

Oct-02

Jan-02

Nov-02

Feb-02

Nov-02

Dec-02

Oct-02

Nov-02

Mar-02

Dec-02

Dec-02

Feb-03

Feb-02

Nov-02

Feb-02

Feb-02

Nov-02

Dec-02

Nov-02

Nov-02

Dec-01

Dec-02

Dec-02

Dec-02

Feb-02

Mar-02

Dec-02

Oct-02

99.2

98.8

99.0

98.0

98.6

98.7

98.9

97.0

94.3

99.0

97.6

98.7

98.9

98.2

97.7

98.3

97.0

99.2

97.7

99.1

97.0

99.0

96.4

98.8

98.1

98.2

98.8

97.9

97.4

97.5

98.6

99.3

97.8

97.9

97.8

98.5

97.8

97.9

95.4

14

13

4

11

14

7

10

15

51

4

12

12

7

9

12

13

5

13

13

4

21

4

11

16

14

11

17

7

6

16

9

7

3

3

3

20

8

6

33

10

15

39

29

16

30

17

33

18

41

32

17

26

32

31

21

96

10

28

35

23

41

52

12

22

27

12

49

70

25

25

17

119

114

1,173

12

44

56

22.2

9.2

0.8

74.8

32.7

16.5

3.7

49.0

228.9

155.2

56.3

19.6

1.9

4.1

37.2

37.7

19.3

160.3

0.8

95.7

12.0

17.3

28.2

17.3

1.6

5.9

9.2

4.5

131.3

43.6

16.1

41.0

1.8

39.9

51.0

152.4

16.0

61.1

95.9

18.6
30 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 7. Firm yields and reliability of reservoirs in Massachusetts calculated using three major droughts in the historical record.—Continued

[Dates are in months and years from 1964 to 2002; Mgal/d, million gallons per day]

1960s drought 1980s drought 

Storage 

ratio

Drought 

length

(months)

Drought 

intensity

(percent below average 

streamflow)

Firm 

yield

(Mgal/d)

Date of 

maximum 

storage 

depletion

Drought 

length

(months)

Drought 

intensity

(percent below average 

streamflow)

Firm 

yield

(Mgal/d)

Date of 

maximum 

storage 

depletion

Reliability

(percent)

Mare Meadow Reservoir 1.36 36 67.4 2.68 Dec-66 23 26.9 3.70 Mar-89 97.1 

Meetinghouse Reservoir 0.97 36 68.3 1.12 Dec-66 23 28.2 1.78 Mar-89 95.6 

Middle Reservoir 1.15 47 70.0 0.15 Jan-67 14 39.2 0.28 Aug-89 96.4 

Millham Reservoir 0.20 36 61.8 1.79 Nov-65 16 44.3 2.47 Feb-81 97.7 

Montgomery Reservoir 0.18 38 59.6 1.13 Feb-66 8 69.2 1.35 Feb-81 99.0 

Morse Reservoir 0.29 36 70.1 0.17 Feb-66 11 26.1 0.28 Feb-81 96.4 

North Reservoir 0.98 47 66.9 0.39 Jan-67 14 36.4 0.65 Sep-89 96.4 

Notown Reservoir 0.37 36 64.9 2.13 Feb-66 17 40.3 3.11 Feb-81 97.9 

Pine Hill Reservoir 1.00 36 64.4 5.52 Nov-66 23 24.7 7.86 Mar-89 95.9 

Quinapoxet Reservoir 0.13 36 60.2 4.21 Nov-64 16 42.2 4.88 Nov-80 99.8 

Roaring Brook Dam 0.09 59 57.8 0.98 Dec-64 8 78.6 1.23 Nov-80 99.4 

Sandra Pond 0.28 38 63.9 0.80 Dec-66 15 36.4 1.21 Nov-81 95.7 

Sandwash Reservoir 0.28 36 69.6 0.89 Feb-66 24 36.8 1.31 Feb-81 97.6 

Schoolhouse Reservoir 0.08 36 68.7 0.84 Dec-64 22 36.8 1.11 Feb-81 99.4 

Scott Reservoir 0.47 48 70.8 0.40 Feb-66 15 63.5 0.61 Nov-85 97.5 

Simonds Pond 0.17 36 72.4 0.07 Feb-65 11 28.9 0.08 Feb-81 99.0 

Swan Pond 0.38 38 64.1 0.44 Nov-65 15 61.1 0.53 Nov-85 99.7 

Upper (Leahey) Reservoir 0.97 36 72.3 0.59 Dec-66 23 36.0 0.88 Mar-89 97.1 

Upper Naukeag Lake 1.43 46 73.1 1.72 Mar-67 9 21.1 2.71 Mar-89 91.7 

Upper Sackett Reservoir 0.35 36 71.4 0.50 Sep-65 14 59.5 0.72 Sep-85 97.7 

Wachusett Lake 0.55 36 66.3 1.08 Oct-66 23 27.2 1.69 Mar-89 96.6 

Whately Reservoir 0.02 59 60.5 0.09 Nov-63 8 81.6 0.10 Oct-80 99.6 
Effect of Drought Severity on Firm-Yield Estimates 31

1980s drought 2002 drought

Number 

of failure 

events

Average 

failure 

duration 

(days)

Average 

yield deficit 

during 

failure 

(Mgal/d)

Drought 

length 

(months)

Drought 

intensity 

(percent below average 

streamflow)

Firm yield 

(Mgal/d)

Date of 

maximum 

storage 

depletion

Reliability 

(percent)

Number 

of failure 

events

Average 

failure 

duration 

(days)

Average 

yield deficit 

during 

failure 

(Mgal/d)

19

31

9

17

6

24

18

13

21

3

10

12

13

10

4

9

5

11

89

11

24

5

24

22.7

64.6

21.4

26.8

23.8

32.6

26.1

31.4

13.3

10.5

57.8

29.2

9.5

102.0

17.4

9.2

42.1

14.9

34.1

22.9

13.0

127.6

39.7

15.7

32.3

23.3

4.6

19.3

61.6

226.3

94.8

8.7

56.4

26.9

6.0

51.4

0.9

20.3

38.7

33.9

22.4

35.3

0.9

20

20

10

10

10

20

12

20

20

19

10

20

23

23

12

20

12

25

12

24

20

10

50.3

51.1

62.4

54.8

44.9

52.4

30.3

47.4

47.3

45.8

56.9

53.3

56.1

54.9

61.9

54.6

59.1

53.9

51.2

54.0

48.9

59.4

3.21

1.52

0.27

2.43

1.49

0.24

0.62

2.95

6.91

5.04

1.39

1.04

1.19

1.12

0.63

0.09

0.51

0.78

2.40

0.63

1.44

0.15

Dec-02

Nov-02

Dec-02

Nov-02

Feb-02

Nov-02

Dec-02

Nov-02

Nov-02

Nov-01

Dec-01

Dec-02

Nov-02

Feb-02

Dec-02

Feb-02

Nov-01

Dec-02

Feb-03

Oct-02

Nov-02

Nov-01

99.0

98.3

97.1

98.0

98.4

98.0

97.2

98.4

98.5

99.6

98.3

97.6

98.6

99.3

97.3

98.4

99.8

98.4

97.0

98.7

98.2

97.6

8

15

5

14

8

14

11

10

8

4

18

4

6

11

5

9

2

8

37

8

18

22

21

17.7

93.4

22.9

32.5

22.5

40.3

25.8

29.4

16.3

15.3

95.8

36.3

10.3

87.8

29.4

16.0

32.5

13.2

26.0

16.2

17.6

88.4

26.9

22.2

34.8

34.7

3.7

23.1

57.8

172.7

116.1

15.9

75.3

30.4

6.4

45.6

2.0

35.9

24.4

27.4

14.8

19.6

2.3
32 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

x

x

x

x

x

x

x

x

75th percentile

Outlier

Outlier

50th percentile

(median)

25th percentile

Interquartile

range

EXPLANATION

1960s 1980s 2002

0

10

20

30

40

50

60

70

Drought duration in months

B x

x

1980 2002

0

20

40

60

80

100

Percent change in firm yield

C

x

x

x

x

10

30

50

70

90

Percent below average streamflow

1980 2002

90

92

94

96

98

100

102

Reliability, in percent

1960 1980 2002

A

D

Figure 10. A, Percent below average streamflow and B, duration of droughts of the 1960s, 1980s, and 2002. C, Percent change in 

firm yield and D, reliability of firm yields when calculated with the droughts of the 1980s or 2002.

more intense during the drought period. Drought durations for 

both the 1980s and 2002 droughts ranged from 4 to 25 months. 

Reservoirs underwent a wide range of drought intensities in 

the 1980s with average streamflows 12 to 82 percent below 

normal levels. Some reservoirs underwent two separate 

droughts in the 1980s, one at the beginning of the decade and 

one at the end. For the purposes of this study, the most severe 

of the two 1980s droughts was used. Streamflows were -30 to 

62 percent below average levels during the 2002 drought.

The sensitivity of reservoir firm yield to drought severity 

was examined by calculating the firm yield using three different drought periods: 1960s, 1980s and 2001–2002 droughts. 

In order to calculate the firm yield using a drought from the 

1980s or 2002, the FYE model was modified to consider only 

failures during the drought in question when calculating the 

firm yield. Reservoir failures that occurred either before or 

after the drought being studied were ignored by the model, and 

the firm yield was incremented until a failure occurred during 

the drought in question. This method produces results identical to the results of a simulation performed with a truncated 

historical record, as long as the reservoir returns to full pool 

before the drought period of interest. Reservoirs that did not 

return to full pool from one drought to the next were removed 

from the analysis. All reservoirs were run as single-reservoir 

systems for the purpose of this analysis.

For most reservoirs, the drought of the 1960s was the 

most severe and resulted in the lowest firm-yield estimate. 

Accord Pond in Hingham, Mass., was the only exception. 

For this reservoir, the firm yield estimated for a drought in 

1981 was slightly lower than the yield estimated for the 1960s 

drought. Overall, firm yields exceeded those during the 1960s 

drought by an average of 49 percent for the drought in the 

1980s and 41 percent for the drought of 2001–2002. Individual reservoirs responded differently to these two droughts. 

Approximately three quarters of the reservoirs underwent 

more severe conditions during the 2001–2002 drought than in 
Effect of Controlled Releases and Demand Management on Firm Yield 33

the drought of the 1980s, leading to lower firm-yield estimates 

for the 2001–2002 drought than for the 1980s drought. 

Reservoirs operating at a firm yield computed for a less 

severe drought run the risk of failure should a more severe 

drought occur. The risk of failure for a particular reservoir can 

be characterized by the reservoir’s reliability, resilience, and 

vulnerability. For each day of the simulated record, the reservoir state was classified as being either a failure or not. Reliability is the percentage of days in which the reservoir did not 

fail throughout the entire simulation. The reliability reflects the 

overall failure rate for the entire simulation period. For a given 

reliability, failures may occur in several long-duration events 

or many short-duration events. A failure event is the period of 

consecutive days a reservoir is in a failing state. The resilience 

of a reservoir and is defined as the average of the durations 

of all the failure events during the simulation. Reservoirs that 

recover quickly after a failure are more resilient and will have 

a shorter average failure duration. The magnitude of a failure 

is characterized by the yield deficit, which is the difference 

between the daily water demand and the daily amount that the 

reservoir is able to supply during a failure event. 

In order to investigate the risk and magnitude of potential failures due to operating at a firm yield calculated for 

a drought other than the 1960s drought, the water-balance 

equation was solved using the estimated firm yields for the 

1980s and 2002 droughts for each reservoir and allowing the 

reservoir to fail during other time periods in the simulation. 

These simulations were used to calculate reservoir reliability, 

average failure duration, and average yield deficit. Average 

reliabilities of reservoirs operating at the 1980s and 2002 firm 

yields were 97 and 98 percent, respectively (fig. 10). Average 

failure durations across reservoirs ranged from several days to 

several months. This information is useful for gaging the 

risk of failure should a drought more severe than any on 

record occur. 

Effect of Controlled Releases and 

Demand Management on Firm Yield

Reservoirs that are managed solely to maintain storage 

and meet human water demand can affect downstream areas 

by depleting the amount of water available for ecological communities and disrupting natural streamflow patterns. When a 

river is impounded to create a drinking-water reservoir, water 

that would have flowed downstream is allocated to fill the 

reservoir or used to supply drinking water. During periods in 

which the reservoir is at full storage, any inflows that exceed 

water demand and natural reservoir outflows will spill to the 

downstream reach. During periods in which the reservoir 

water surface is below the spillway, downstream reaches will 

not receive any water. 

Several recent studies have highlighted the effects of 

impoundments on Massachusetts streams and fish communities (Weiskel and others, 2010; Armstrong and others, 

2010), and more consideration is being given to the environmental needs in the river reach downstream from a reservoir impoundment. One approach to mitigate the effects 

of impoundments on downstream reaches is to implement 

controlled releases from the reservoir into the stream either by 

manipulating spillway boards or through a release valve. Such 

releases would necessarily decrease the firm yield of a reservoir because they would increase the daily reservoir outflows, 

causing less water to be available for withdrawals. For reservoirs operating near their firm yield, meeting environmental 

flow requirements during a drought period could jeopardize 

the ability of the reservoir to meet drinking-water demands.

The effects of imposing instream-flow requirements may 

potentially be offset by implementing several management 

strategies. Water demand in Massachusetts typically peaks 

during summer months when water availability is the lowest. 

Reservoir storage may become depleted during these periods, 

leaving little or no water available for environmental flow 

releases. Demand-management scenarios such as nonessential summer water-use restrictions may help to lower water 

demand during these periods, allowing more water to be available for environmental flows. Another potential management 

strategy is to relax the definition of firm yield to allow reservoir operation at less than 100 percent reliability. Although 

this may put the reservoir at risk of occasional failure during 

severe droughts, this strategy may be feasible in towns that 

have emergency water sources or that can import water from 

other systems. Understanding the effects of management 

scenarios and controlled releases on firm yield is necessary 

for water-supply managers and regulators to evaluate the risks 

and tradeoffs between allocations of water for human versus 

environmental needs.

Controlled-Release Scenarios

The FYE can account for user-specified monthly release 

rates for downstream environmental flows. The choice of 

an appropriate controlled-release scenario for any particular 

reservoir in Massachusetts is an area of ongoing research. For 

illustrative purposes in this report, two hypothetical reservoir release scenarios were developed to test the effects of 

controlled releases on reservoir firm yield. For each month, 

a flow-duration curve was developed from the 44-year daily 

streamflow record. Monthly controlled releases for the two 

scenarios were set at the 10th- and 25th-percentile monthly 

flow volumes (appendix 4). For multiple-reservoir systems, 

reservoir releases were implemented at each reservoir in the 

system based on the respective streamflows estimated for 

each individual reservoir. Firm yields were calculated for 

each of the two controlled-release scenarios and compared 

with reported usage data from 2000 to 2004 (table 8). For the 

purposes of this study, all reservoirs were considered capable 

of releasing water downstream. This may not be possible in all 

systems because reservoirs may not have a release structure 

installed for this purpose.
34 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Table 8. Water usage and firm yields for reservoir systems in Massachusetts under various controlled-release, demand-management, 

[Mgal/d, million gallons per day; %, percent; DPW, Department of Public Works]

Scenarios with no controlled releases 

Water supplier Reservoir system

Average 

annual 

usage 

2000–2004

(Mgal/d)

Firm yield 

with no-fail 

criteria and 

no demand 

management

(Mgal/d)

Firm yield 

with no-fail 

criteria and 

demand 

management

(Mgal/d)

Firm yield 

with 1% failure criteria, 

no demand 

management

(Mgal/d)

Firm yield 

with 1% failure criteria 

and demand 

management

(Mgal/d)

Amherst Water Department Amethyst Brook Intake system 0.83 0.87 0.93 1.19 1.36 

Amherst Water Department Atkins Reservoir 0.83 1.16 1.23 1.25 1.40 

Ashburnham/Winchendon Upper Naukeag Lake 1.06 1.72 1.81 1.88 1.98 

Concord Water Department Nagog Pond 0.09 0.86 1.02 0.96 1.27 

Danvers Water Department Middleton Pond system 3.09 2.79 3.06 3.14 3.40 

Fall River Water Department North Watuppa system 12.89 18.20 19.05 20.01 20.69 

Fitchburg Water Department Lovell Reservoir system 0.18 2.77 2.89 3.20 3.43 

Fitchburg Water Department Meetinghouse system 2.71 5.61 6.33 6.30 6.63 

Fitchburg Water Department Wachusett Lake 0.35 1.08 1.18 1.24 1.36 

Greenfield Water Department Green River 0.52 0.42 0.42 1.49 1.49 

Greenfield Water Department Leyden Glen Reservoir 0.57 0.69 0.69 1.12 1.17 

Hingham/Hull (Aquarian Water Company) Accord Pond 0.59 0.66 0.77 0.75 0.87 

Hinsdale Water Department Belmont Reservoir 0.15 0.12 0.13 0.15 0.16 

Lee Water Department Schoolhouse Reservoir 0.51 0.84 0.89 1.14 1.23 

Lee Water Department Upper (Leahey) Reservoir 0.54 0.59 0.64 0.67 0.73 

Leicester (Cherry Valley and Rochdale Water) Henshaw Pond 0.26 0.35 0.36 0.43 0.46 

Leominster DPW–Water Division Distributing Reservoir system 0.87 0.58 0.66 0.66 0.78 

Leominster DPW–Water Division Fall Brook Reservoir 0.88 0.84 0.90 0.98 1.10 

Leominster DPW–Water Division Simonds Pond system 2.32 2.26 2.43 2.77 2.99 

Lincoln Water Department Flints Pond 0.38 0.59 0.64 0.68 0.73 

Marlborough DPW–Water and Sewer Division Millham system 1.40 1.83 1.99 2.15 2.32 

Milford Water Company Echo Lake 1.40 1.12 1.20 1.42 1.42 

North Brookfield Water Department Doane Pond system 0.42 0.71 0.74 0.80 0.86 

Pittsfield Water Department Ashley Lake 0.21 1.37 1.41 1.82 1.90 

Pittsfield Water Department Cleveland Reservoir 7.96 9.18 9.47 10.53 11.17 

Pittsfield Water Department Farnham system 2.23 2.51 2.66 2.98 3.21 

Pittsfield Water Department Upper Sackett Reservoir 0.08 0.50 0.55 0.58 0.64 

Scituate Water Department Main Reservoir 0.61 0.63 0.70 0.81 0.94 

South Deerfield Water Supply District Whately system 0.68 1.07 1.11 1.09 1.26 

Southbridge Water Department Hatchet Brook system 1.69 2.78 2.87 3.28 3.57 

Springfield Water Department Cobble Mountain system 36.57 42.70 45.14 45.42 48.83 

Wakefield Water Department Crystal Lake 0.28 0.40 0.44 0.47 0.51 

West Springfield Water Department Bearhole Reservoir 0.73 1.40 1.53 1.72 1.99 

Westborough Water Department Sandra Pond 0.67 0.80 0.86 0.89 0.95 

Westfield Water Department Granville Reservoir 2.47 3.03 3.18 3.66 3.95 

Westfield Water Department Montgomery Reservoir 0.00 1.13 1.17 1.35 1.43 

Winchester Water Department South Reservoir system 1.10 1.01 1.07 1.11 1.20 

Worcester Water Department Holden Pond system 23.87 17.15 17.64 18.87 20.38 
Effect of Controlled Releases and Demand Management on Firm Yield 35

and reliability scenarios.

Scenarios with 10th-percentile monthly flow releases Scenarios with 25th-percentile monthly flow releases

Firm yield 

with no-fail 

criteria and 

no demand 

management

(Mgal/d)

Firm yield 

with no-fail 

criteria and 

demand 

management

(Mgal/d)

Firm yield 

with 1% failure criteria, 

no demand 

management

(Mgal/d)

Firm yield 

with 1% failure criteria 

and demand 

management

(Mgal/d)

Firm yield 

with no-fail 

criteria and 

no demand 

management

(Mgal/d)

Firm yield 

with no-fail 

criteria and 

demand 

management

(Mgal/d)

Firm yield 

with 1% failure criteria, 

no demand 

management

(Mgal/d)

Firm yield 

with 1% failure criteria 

and demand 

management

(Mgal/d)

0.34

0.81

1.44

0.71

2.01

13.39

2.12

4.32

0.77

0.00

0.21

0.50

0.06

0.43

0.47

0.19

0.37

0.61

1.60

0.45

1.06

0.90

0.55

0.89

5.99

1.92

0.34

0.13

0.80

2.31

33.01

0.24

0.78

0.55

1.79

0.60

0.82

11.34

0.46

0.86

1.52

0.84

2.18

14.01

2.21

4.79

0.85

0.00

0.21

0.57

0.06

0.45

0.52

0.19

0.44

0.65

1.72

0.49

1.14

0.96

0.57

0.92

6.30

2.03

0.37

0.13

0.89

2.38

34.80

0.27

0.87

0.59

1.87

0.63

0.86

11.74

0.71

0.90

1.58

0.79

2.21

14.78

2.49

4.83

0.91

0.00

0.45

0.59

0.08

0.62

0.56

0.24

0.47

0.71

1.64

0.52

1.25

1.05

0.63

1.25

7.22

2.20

0.39

0.51

0.83

2.76

35.54

0.29

0.94

0.62

2.35

0.80

0.91

12.37

1.01

0.99

1.66

1.02

2.39

15.27

2.66

5.21

1.00

0.00

0.48

0.67

0.08

0.66

0.60

0.27

0.55

0.81

1.92

0.56

1.35

1.16

0.68

1.35

7.74

2.38

0.44

0.61

1.04

2.97

37.97

0.32

1.05

0.66

2.55

0.89

0.98

13.61

0.56

0.60

1.22

0.62

1.41

10.80

1.64

3.54

0.61

0.00

0.00

0.40

0.02

0.17

0.41

0.08

0.27

0.46

1.21

0.36

0.60

0.72

0.45

0.61

4.15

1.60

0.24

0.00

0.41

2.00

27.36

0.14

0.00

0.37

0.91

0.24

0.70

3.57

0.79

0.63

1.29

0.73

1.53

11.30

1.71

3.89

0.67

0.00

0.00

0.45

0.02

0.17

0.45

0.12

0.29

0.49

1.31

0.39

0.64

0.77

0.47

0.63

4.35

1.69

0.26

0.00

0.50

2.05

28.74

0.16

0.00

0.40

0.96

0.24

0.74

9.20

0.63

0.68

1.35

0.68

1.57

11.93

2.03

4.02

0.73

0.00

0.00

0.47

0.04

0.25

0.49

0.15

0.36

0.55

1.25

0.42

0.79

0.85

0.52

0.90

5.34

1.87

0.28

0.12

0.45

2.33

29.55

0.17

0.21

0.42

1.48

0.43

0.75

9.82

0.86

0.75

1.42

0.85

1.70

12.37

2.17

4.35

0.79

0.00

0.00

0.53

0.04

0.27

0.53

0.17

0.40

0.62

1.53

0.45

0.85

0.94

0.56

0.98

5.75

2.03

0.32

0.14

0.55

2.46

31.21

0.19

0.25

0.46

1.59

0.49

0.82

10.66
36 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

Controlled releases for the two scenarios lowered firm 

yields by an average of 35 percent for the 10th-percentile 

flow-release scenario and 55 percent for the 25th-percentile 

flow-release scenario. Of the 38 systems studied, 16 were able 

to meet or marginally meet their current (2000 to 2005) usage 

requirements while releasing monthly 10th-percentile flows, 

and 11 were able to meet or marginally meet their current 

usage while releasing 25th-percentile flows. Because yearto-year usage in a system can vary, systems in which average 

usage was within 10 percent of the firm yield of a particular 

scenario may be operating within the firm yield in some years 

but above the firm yield in other years. These reservoirs are 

listed as marginally operating within the firm yield (table 8).

Summer Water-Demand Management

Outdoor summer water-use restrictions are often implemented by water-resources managers as a way to conserve 

water during drought periods. Water usage peaks during 

summer months due to outdoor water use, such as irrigation, 

residential-lawn watering, or filling of swimming pools. Outdoor summer water-use restrictions decrease the summer water 

demand and often go into effect when a reservoir falls below a 

certain level. Demand-reduction scenarios can be implemented 

in several stages as the reservoir falls to successively lower 

levels. The firm-yield-model code was altered to allow the 

user to specify a summer water-use-restriction scenario. This 

type of demand-management scenario can be specified by the 

user as a percentage by which to decrease demand during summer months (June–September) when the reservoir falls below 

a user-specified percentage of its total capacity. If reservoir 

storage falls below the percentage of total capacity specified in 

the demand-management scenario on any simulation day, and 

the simulation is in a summer month, the yield, Qy

,for that day 

is decreased by the percentage specified by the user. Simulation then continues as usual. When a multiple-reservoir system 

is simulated, the demand-management scenario is applied to 

all reservoirs in the system.

The amount of summer water-demand reductions that 

can be achieved by summer outdoor water restrictions is 

highly variable and depends on many factors such as climate, 

land use, and population density. Further study is needed 

to determine appropriate demand-reduction strategies for 

Massachusetts reservoirs. For illustrative purposes in this 

report, the effect of implementing one hypothetical demandmanagement scenario was examined for the reservoir systems 

in this study. The demand-management scenario specified 

0

0 0.1 0.2 0.3 0.4 0.5

Henshaw Reservoir

Upper Naukeag Lake 

EXPLANATION

Leyden Glen Reservoir

Storage ratio

Wachusett Lake

Demand ratio 

S/Q = 0.21

S/Q = 0.02

S/Q = 0.55

S/Q = 1.43

0.2

0.4

0.6

0.8

1.0

1.2

S/Q

Maximum monthly release, in percentile of monthly flow

Figure 11. Maximum monthly 

releases as a percentile of longterm monthly flows that is possible 

at various demand ratios for four 

reservoirs of increasing storage ratio.
Effect of Controlled Releases and Demand Management on Firm Yield 37

a 15-percent demand reduction when the reservoir fell to 

60 percent of its maximum capacity, a 25-percent demand 

reduction when the reservoir fell to 40 percent of its maximum 

capacity, and a 35-percent demand reduction when the 

reservoir fell to 20 percent of its total capacity. Reducing 

summer demand in this way increased firm yields by an 

average of 7 percent. By implementing this demand-reduction 

scenario, two of the six systems that are currently operating 

above the estimated firm yield were able to marginally 

meet demand requirements. In addition, this demand 

scenario enabled one additional reservoir system to support 

25th-percentile flow releases and four additional systems to 

support 10th-percentile flow releases (table 8).

The amount of water available for downstream flow 

releases depends on the water demands of the reservoir and the 

storage ratio. The demand ratio is defined as the annual average water demand divided by the firm yield of the reservoir. 

For a given controlled-release rate, the maximum demand 

ratio possible for a reservoir may be calculated by dividing the 

firm yield calculated with controlled releases by the firm yield 

without releases. Reservoirs that are operating at or near their 

firm yield will have demand ratios close to 1. These reservoirs have less water available for downstream flow releases 

because most of the available water in storage is being allocated to human use. Reservoirs with low storage ratios are also 

less able to support high levels of controlled releases. Reservoirs with low storage in relation to their average daily streamflow are more susceptible to variability in daily streamflow 

and have proportionally less water available in storage during 

even minor periods of low flow. The maximum controlled 

releases (as percentiles of long-term monthly flows) that are 

possible at various demand ratios for selected reservoirs with 

increasing storage capacity are shown in figure 11. 

Reducing Reservoir Reliability Requirements

Reservoir reliability is set by the user by specifying the 

maximum number of days during the simulation when the 

reservoir is allowed to fail. Reliability is calculated as the 

percentage of days when the reservoir did not fail during the 

simulation. In order to run the FYE at a reliability of less 

than 100 percent, the model code was modified to allow the 

simulation to run through a failing state. When calculating 

the daily water balance, the model will first solve the waterbalance equation without allocating for yield. If reservoir 

storage at this point is sufficiently high to fully satisfy daily 

demand, then the usage term is subtracted, and simulation 

continues as normal. If the usable storage at this point is 

not sufficient to satisfy daily demand, then all the available 

water in storage is allocated to yield, bringing available 

storage to zero. The reservoir is considered to be failing in 

this situation because the amount of water supplied by the 

reservoir is less than the full demand volume. After the full 

44-year simulation is completed, the number of failure days is 

totaled. Yield is incrementally increased until the number of 

days of reservoir failures equals the amount specified by the 

user. The failures may occur in many short-duration events or 

a small number of long-duration events. The total number of 

failure events and the average duration of failure periods are 

reported for each reservoir simulation. In addition, the FYE 

also calculates and reports the average yield deficit. These 

failure statistics can help water managers gage the risks and 

potential costs of employing a strategy that includes relaxing 

the no-fail operating criterion of a reservoir. For multiplereservoir systems, the reliability set by the user is applied to 

all reservoirs in the system. 

In order to examine the effect of relaxing the no-fail 

criterion, simulations of the reservoir systems in this study 

were run using a 99-percent reliability criterion (fig. 12). This 

criterion allows for a total of 160 allowable failures during 

the 44-year simulation period. Relaxing the reliability criterion increased yields by an average of 25 percent. Under 

this scenario, estimated yields are sufficient to meet demand 

at all but three systems in the study. In addition, relaxing the 

reliability criterion enables two additional systems to support 

25th-percentile flow releases and nine additional systems to 

support 10th-percentile flow releases; these systems could not 

otherwise support releases under the no-fail scenario. 

Tradeoffs Between Demand Management, 

Controlled Releases, and Reliability

Implementing downstream release flows, implementing 

demand-management strategies, or operating the reservoir at 

a lower reliability all have risks and benefits associated with 

them. In determining the best possible strategy for any given 

reservoir system, a water manager may use any combination 

of these three strategies in order to maximize the reservoir 

yield at the lowest cost. Tradeoff curves can be constructed 

to examine the effect of different strategies on the firm yield. 

For a given reservoir, a family of tradeoff curves can be 

constructed showing the different combinations of controlled 

releases, reliability criteria, and demand-management strategies that can be used to achieve a target yield. Sample tradeoff 

curves for Upper Leahey Reservoir are shown in figure 13. 

On the basis of reported water usage for 2000–2004, Upper 

Leahey would be able to support only very minimal environmental flow releases without implementing some sort of 

demand-management strategy. In order to achieve controlled 

releases at the 10th percentile of monthly flows, a more severe 

outdoor summer water-use restriction scenario would need to 

be implemented than the one tested here.
38 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

x

xx

x

x

x

x

x

x

x

x

-100 x x

-50

0

50

100

Percent change in firm yield under various management scenarios

No required 

releases

Required releases set

at 10th percentile of 

monthly streamflow

Required releases set

at 25th percentile of 

monthly streamflow

x

100-percent reliability criteria, 

no demand management

100-percent reliability criteria, 

with summer demand 

management

99-percent reliability criteria, 

no demand management

99-percent reliability criteria, 

with summer demand 

management

75th percentile

Outlier

50th percentile

(median)

25th percentile

Interquartile

range

EXPLANATION

Figure 12. Percent changes of firm yield for Massachusetts reservoirs under various management scenarios.
Summary and Conclusions 39

0.2

0.4

0.6

0.8

0 5 10 20 25

Estimated firm yield, in million gallons per day

15

Percentile of monthly flows of controlled releases

Actual reported usage

100-percent reliability, no demand

management

100-percent reliability with demand

management

99-percent reliability, no demand 

management

99-percent reliability with demand

management

EXPLANATION

Figure 13. Tradeoff curves depicting the estimated yield in relation to controlled releases under various management 

scenarios for Upper Leahy Reservoir, in Lee, Massachusetts.

Summary and Conclusions

Procedures for determining the firm yield of a reservoir, which were previously developed, were further refined 

and implemented for 38 reservoir systems in Massachusetts, 

including 25 single- and multiple-reservoir systems that 

were examined in previous studies and 13 additional reservoir systems. Changes to the Firm-Yield Estimator (FYE) 

model include simulation of the 44-year historical record 

by daily time steps; the incorporation of daily input data for 

streamflow, precipitation, and evaporation; refinements to 

the groundwater simulation; and enhanced scenario-testing 

capabilities. This study documents the procedural refinements 

to the model, examines sources of uncertainty in the estimated 

firm yields, and demonstrates the use of the model to assess 

the feasibility of controlled releases under several example 

management scenarios. Because of these refinements, estimates of firm yield based on previous versions of the FYE are 

no longer considered valid.

Uncertainty in the FYE model comes from many sources, 

including errors in the input data for streamflow, precipitation, evaporation, and stage-storage relations. Reservoirs that 

overlie substantial sand and gravel deposits have additional 

uncertainty in firm-yield estimates because of uncertainty in 

estimating groundwater inflows and outflows to the reservoir. 

In addition, uncertainty in firm-yield estimates may arise from 

other factors, such as seepage or reservoir-operation details, 

that are not accounted for in the FYE. An analytical method 

to estimate overall uncertainty in the FYE model was not 

determined; however, the sensitivity of the model to errors in 

daily streamflow and stage-storage relations was examined. 

Because the lowest streamflows may be underestimated by 

the SYE, firm yields estimated by the FYE may be conservative. A Monte Carlo simulation showed that, on average, firm 

yields increased 1 to 10 percent after accounting for errors in 

daily streamflows. Errors in firm yields can also arise from 

errors in the stage-storage and volume calculations as a result 

of spatially imprecise bathymetric data. Experiments on three 
40 Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0

reservoirs showed that bathymetric data that are sampled too 

sparsely can result in an underestimation of reservoir volume 

and firm yield. Bathymetric surveys with measurement densities of less than 20 points per acre or transects spaced more 

than 30 to 60 meters apart resulted in underestimation of reservoir volume and firm-yield estimates by 5 percent or more.

Reservoirs in contact with sand and gravel may receive 

water flows from and may discharge to groundwater sources. 

In a previous study, equations were developed and implemented to estimate the magnitude of groundwater contributions to the reservoir water balance on the basis of changes 

in reservoir storage at each time step. The parameterization 

of these equations was refined in this study in order to allow 

the scaling factor to be adjusted on the basis of the changing 

reservoir stage. This eliminated instabilities in the groundwater-equation algorithm that arose during low-storage periods. 

Validation of the groundwater parameters at one reservoir 

indicated that parameter estimation from published maps is 

highly uncertain.

Firm yields estimated using the historical record are sensitive to the severity of droughts during the simulation periods. 

For this study, a 44-year historical record, which includes the 

most severe drought on record, was used for firm-yield estimation. Firm yields based on this drought may not be adequate 

to protect against failures should a more severe drought occur 

in the future. The sensitivity of firm yields to drought severity was examined by estimating firm yields based on three 

droughts during the simulation period. Firm yields based on 

droughts in the 1980s and 2002 exceeded those during the 

1960s drought by an average of 49 and 41 percent, respectively; however, operating reservoirs at these yields led to 

average failure rates of 2 to 3 percent when applied over the 

entire simulation period. 

Because of concern over water availability for ecological 

needs in Massachusetts streams, regulators may wish to 

examine the effects of regular releases from drinkingwater reservoirs to enhance instream flow downstream 

from impoundments. An analysis of two controlled-release 

scenarios showed that reservoirs with a large storage ratio 

(reservoir capacity divided by mean streamflow) and low 

demand ratio (average annual water demand as a percentage 

of the annual firm yield) were able to support the highest 

levels of flow releases without sacrificing yield for human 

use. Roughly half the reservoir systems studied were able to 

support minimal monthly flow releases equal to the monthly 

10th-percentile daily flow. Reservoirs can increase their daily 

yield by implementing summer water-use restrictions or by 

relaxing the no-fail criterion of the firm yield. One scenario 

involving hypothetical summer water-use restrictions and 

another involving a 1-percent failure criterion were tested. 

The scenario with summer water-use restrictions that was 

tested led to an average increase of 7 percent in the firm 

yield, which was generally not sufficient to enable controlled 

releases from a reservoir that was otherwise unable to support 

them. Relaxing the reservoir reliability to 99 percent led 

to an average increase of 25 percent in reservoir firm yield 

but also left the reservoir vulnerable to failures. Reservoir 

operators can weigh the relative risks and benefits of various 

management strategies using tradeoff curves and statistics for 

failure magnitude and duration.

References Cited

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.

Archfield, S.A., Vogel, R.M., Steeves, P.A., Brandt, 

S.L., Weiskel, P.K., and Garabedian, S.P., 2010, The 

Massachusetts Sustainable-Yield Estimator—A decisionsupport tool to assess water availability at ungaged stream 

locations in Massachusetts: U.S. Geological Survey 

Scientific Investigations Report 2009–5227, 41 p., plus 

CD–ROM.

Armstrong, D.S., Richards, T.A., and Brandt, S.L., 2010, 

Preliminary assessment of factors influencing riverine fish 

communities in Massachusetts: U.S. Geological Survey 

Open-File Report 2010–1139, 43 p.

Environmental Systems Research Institute, Inc. (ESRI), 

1994, ARC/INFO user guides, version7: Redlands, Calif., 

Environmental Systems Research Institute, Inc., 626 p.

Fennessey, N.M., 1995, The sensitivity of reservoir-yield 

estimates to model time step surface-moisture fluxes: 

Journal of Water Resources Planning and Management, 

v. 121, no. 4, July/August 1995, p. 310–317.

Hargreaves, G.H., and Samni, Z.A., 1982, Estimation of 

potential evapotranspiration: Journal of Irrigation and 

Drainage Division, Proceedings of the American Society of 

Civil Engineers, v. 108, p. 223–230.

Kruizinga, S., and Yperlaan, G.J., 1978, Spatial interpolation 

of daily totals of rainfall: Journal of Hydrology, v. 36, 

p. 65–73.

Massachusetts Department of Environmental Protection 1996, 

Estimating the firm yield of a surface water reservoir supply 

system in Massachusetts—A guidance document, version 

1.0: Prepared by N. Fennessey for the Massachusetts 

Department of Environmental Protection, Office of 

Watershed Management, variously paginated.

Massachusetts Department of Environmental Protection 2000, 

Firm yield estimator, version 1.0, software documentation: 

Prepared by Cambridge Environmental, Inc., for the 

Massachusetts Department of Environmental Protection, 

Office of Watershed Management, variously paged.
References Cited 41

Metcalf & Eddy, Inc., 1997, Water, aster plan and analysis 

of reservoir yield: Submitted to Milford Water Company, 

March 1997, variously paginated.

Nash, J.E., and Sutcliffe, J.V., 1970, River flow forecasting 

through conceptual models, part I—A discussion of 

principles: Journal of Hydrology, v. 10, no. 3, p. 282–290.

Office of Geographic and Environmental Information 

(Mass-GIS), 2004, Commonwealth of Massachusetts 

Executive Office of Environmental Affairs, 1:25,000-scale 

surficial geology digital data layer for sand and gravel 

deposits in Massachusetts, accessed January 15, 2009, at 

http://www.mass.gov/mgis/ftpsg.htm

Office of Geographic and Environmental Information 

(Mass-GIS), 2005, Commonwealth of Massachusetts 

Executive Office of Environmental Affairs, 1:5,000-scale 

Color Ortho Imagery of Massachusetts, accessed 

January 15, 2009, at http://www.mass.gov/mgis/ftpsg.htm

Rorabaugh, M.I., 1964, Estimating changes in bank storage 

and ground-water contribution to streamflow: International 

Association of Scientific Hydrology, Publication 63, 

p. 432–441.

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.

Weiskel, P.K., Brandt, S.L., DeSimone, L.A., Ostiguy, 

L.J., and Archfield, S.A., 2010, Indicators of streamflow 

alteration, habitat fragmentation, impervious cover, and 

water quality for Massachusetts stream basins: U.S. 

Geological Survey Scientific Investigations Report 2009–

5272, 70 p., plus CD–ROM.

Wilson, G.L., and Richards, J.M., 2006, Procedural 

documentation and accuracy assessment of bathymetric 

maps and area/capacity tables for small reservoirs: U.S. 

Geological Survey Scientific Investigations Report 2006–

5208, 24 p., plus oversize figures.
THIS PAGE INTENTIONALLY LEFT BLANK
Appendix 1

Appendix 1. Hypsographic Data

Tables of reservoir storage, surface area, stage, and length of reservoir perimeter in contact with 

sand and gravel for each reservoir included in this report that were not included in previous firmyield reports are located on the CD–ROM in the folder titled HypsographicData.

CD–ROM

[In pocket]

Contents

Amethyst Brook Intake Reservoir

Accord Pond

Atkins Reservoir

Borden Brook Reservoir

Cobble Mountain Reservoir

Copicut Reservoir

Crystal Lake

Echo Lake

Flints Pond

Hawley Reservoir

Hill Reservoir

Holden Reservoir #1

Holden Reservoir #2

Kendall Reservoir

Kettle Brook Reservoir #1

Kettle Brook Reservoir #2

Kettle Brook Reservoir #3

Kettle Brook Reservoir #4

Lynde Brook Reservoir

Main Reservoir

Nagog Reservoir

North Watuppa Reservoir

Quinapoxet Reservoir

Sandra Pond

Upper Naukeag Lake
THIS PAGE INTENTIONALLY LEFT BLANK
Appendix 2

Appendix 2. Bathymetric Maps

Bathymetric maps of all reservoirs included in this report that were not included in previous 

firm-yield reports are located on the CD–ROM in the folder titled BathymetricMaps.

CD–ROM

[In pocket]

Contents

Amherst Water Department

Aquarian Water Company, Hingham–Hull, Massachusetts

Ashburnham–Winchendon Joint Water Board

Concord Water Department

Fall River Water Division

Lincoln Water Department

Milford Water Company

Scituate Water Department

Springfield Water and Sewer Commission

Wakefield Water Department

Westborough Water Department

Worcester Water Department
THIS PAGE INTENTIONALLY LEFT BLANK
Appendix 3

Appendix 3. Reservoir-System Diagrams

Schematic diagrams of all reservoir systems included in this report that were not included in 

previous firm-yield reports are located on the CD–ROM in the folder titled SystemDiagrams.

CD–ROM

[In pocket]

Contents

Accord Pond Bottom Elevation, Volume, and Surface Area 

Hingham/Hull (Aquarian Water Company)

Amethyst Brook Intake

Amherst Water Department

Atkins Reservoir

Amherst Water Department

Borden Brook Reservoir

Springfield Water Department

Cobble Mountain Reservoir

Springfield Water Department

Copicut Reservoir

Fall River Water Department

Crystal Lake

Wakefield Water Department

Echo Lake

Milford Water Company

Flints Pond

Lincoln Water Department

Hawley Reservoir

Amherst Water Department

Hill Reservoir

Amherst Water Department

Holden Reservoir #1

Worcester Water Department

Holden Reservoir #2

Worcester Water Department

Kendall Reservoir

Worcester Water Department
Appendix 3

Kettle Brook Reservoir #1

Worcester Water Department

Kettle Brook Reservoir #2

Worcester Water Department

Kettle Brook Reservoir #3

Worcester Water Department

Kettle Brook Reservoir #4

Worcester Water Department

Lynde Brook Reservoir

Worcester Water Department

Main Reservoir

Scituate Water Department

Nagog Pond

Concord Water Department

North Watuppa Reservoir

Fall River Water Department

Pine Hill Reservoir

Worcester Water Department

Quinapoxet Reservoir

Worcester Water Department

Sandra Pond

Westborough Water Department

Upper Naukeag Lake

Ashburnham/Winchendon Joint Water Board
Appendix 4

Appendix 4. Monthly Percentile Streamflows

Tables of monthly 10th and 25th percentile reservoir inflows that were used for management 

scenarios in this report are located on the CD–ROM in the folder titled Monthly Flow Tables.

CD–ROM

[In pocket]

Tables

Monthly 10th Percentile of Streamflows Estimated Using the Sustainable Yield 

Estimator for Reservoirs in Massachusetts, 1960–2004

Monthly 25th Percentile of Streamflows Estimated Using the Sustainable Yield 

Estimator for Reservoirs in Massachusetts, 1960–2004
Prepared by the Pembroke Publishing Service Center.

For more information concerning this report, contact:

Director

U.S. Geological Survey

Massachusetts-Rhode Island Water Science Center

10 Bearfoot Road

Northborough, MA 01532

dc_ma@usgs.gov

or visit our Web site at:

http://ma.water.usgs.gov
Levin and others—Refinement and Evaluation of the Massachusetts Firm-Yield Estimator Model Version 2.0—Scientific Investigations Report 2011–5125

Printed on recycled paper