U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5227

Prepared in cooperation with the

Massachusetts Department of Environmental Protection

The Massachusetts Sustainable-Yield Estimator:

A decision-support tool to assess water availability at 

ungaged stream locations in Massachusetts

0 50 MILES

0 50 KILOMETERS

Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005

Massachusetts State Plane projection, North American Datum 1983 

BOSTON

RHODE

ISLAND

NEW

YORK VERMONT NEW

HAMPSHIRE

MAINE

MASSACHUSETTS

CONNECTICUT

A T L A N T I C

O C E A N

QUAB

PAWE

EBEM

PEND

WOOH SALR

TENM LITT

HOPC BLAC BURL

MOUN TAUN

WADI

SALC

NIPM

BRAN

BLAB

VALL HUBB

DORC

IHEA

OLDS

GRGB WBWE

SEVE SYKE

BASS

MILL CADW

SOUT HOPM NASH

DRYB

MOSS NORT SQUA

PRIE

NBHO GREC TARB

GREW EMEA

CONT STON

SBPI

COLD BEAR SAXT

OYST

SOU1

WARN

WBWA

(01154000) (01155000)

(011085800)

(01154000)

(01086000)

(01089000)

(01073000)

(01100700)

(01097300)

(01091000)

(01093800)

(01096000)

(01161500)

(01105730)

(01174000)

(01175670)

(01176000)

(01193500)

(01105600)

(01170100)

(01107000)

(01162500)

(01121000)

(01331400)

(01332000)

(01333000)

(01169000)

(01169900)

(01171500)

(01089000)

(01174900)

(01181000)

(01180000)

(01188000)

(01198000)

(01198500)

(01199050)

(01200000)

(01187300)

(01187400)

(01194500)

(01120000)

(01108000)

(01111300)

(01111500)

(01165500)

(01126600)

(01123000)

(01118300)

(01118500)

(01109000)

(01082000)

(01118000)

90

495

495

90

STIL

PONA

PEEP

BRRI

INDI

STCT

WBSW

BBNH

(01174565)

(01095220)

(01115098)

(01115187)

(01117460)

(01195100)

(01184100)

(010965852)

42°

43°

72° 70°

(01109200)

WBPA

ADAM

(01106000)

PAWR

(01117500)

WOOA

(01117800)

NOOS

(01115630)

EXPLANATION

State boundary

Interstate highway

U.S. Geological Survey

streamflow-gaging stations 

Streamflow-gaging station

HOPM

(01174000)

Station code—

U.S. Geological Survey

station number in parenthesis

Estimated Pearson r correlation

coefficient with the logarithm of daily

streamflows at the U.S. Geological

Survey streamflow-gaging station

01174900, Cadwell Creek near 

Belchertown, MA (CADW)

0.75 – 0.80

0.80 – 0.85

0.85 – 0.90

0.90 – 0.95

0.95 – 1.0

0.70 – 0.75

25

25

Prepared in cooperation with the

Massachusetts Department of Environmental Protection

Scientific Investigations Report 2009–5227

U.S. Department of the Interior

U.S. Geological Survey

The Massachusetts Sustainable-Yield 

Estimator: A decision-support tool 

to assess water availability at ungaged 

stream locations in Massachusetts

By Stacey A. Archfield, Richard M. Vogel, Peter A. Steeves, Sara L. Brandt, 

Peter K. Weiskel, and Stephen P. Garabedian
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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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:

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 decision-support 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.

ISBN 978 1 4113 2664 4
iii

Contents

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

Introduction.....................................................................................................................................................2

Safe versus Sustainable Yield ............................................................................................................2

Existing Tools to Estimate Streamflow and Assess Water Availability in Massachusetts.......2

Purpose and Scope ..............................................................................................................................5

Estimation of Unregulated, Daily Mean Streamflow................................................................................5

Estimation of a Continuous Flow-Duration Curve at Ungaged Sites............................................5

Streamgages, Flow-Duration-Curve Statistics, and Basin Characteristics ......................5

Regression against Basin Characteristics .............................................................................7

Regression against Streamflow Quantiles ..............................................................................9

Estimation of Streamflow Time Series by use of a Reference Streamgage ...............................9

Reference Streamgages...........................................................................................................11

Selection of a Reference Streamgage...................................................................................11

Comparison of Observed and Estimated Streamflows.................................................................13

Uncertainty of Estimated Streamflows ...........................................................................................18

Streamflow Adjusted for Groundwater and Surface-Water Withdrawals and Discharges...........22

Reported Groundwater and Surface-Water Withdrawals and Discharges .............................22

Disaggregation of Withdrawal and Discharge Volumes..............................................................24

Use of the STRMDEPL Program .......................................................................................................25

Estimation of Streamflow when Groundwater and Surface-Water Divides are 

not Coincident.................................................................................................................................27

Calculation of Sustainable Yields Using the Massachusetts Sustainable-Yield Estimator 

(MA SYE) Tool..................................................................................................................................27

Limitations.....................................................................................................................................................29

Summary........................................................................................................................................................30

Acknowledgments.......................................................................................................................................31

References Cited..........................................................................................................................................31

Appendix 1. Statewide maps of selected basin characteristics used to estimate 

unregulated, daily streamflows ................................................................................. on CD-ROM
iv

Figures

1. Diagram showing translation of a flow-duration curve to a time series of estimated 

streamflow using the QPPQ method, showing (A) the observed time series, (B) flowduration curve, (C) exceedence probability, and (D) estimated time series for the 

Massachusetts Sustainable-Yield Estimator tool ...................................................................4

2–4. Map showing—

2. Locations of contributing basins to 47 stream reaches monitored by U.S. 

Geological Survey streamgages with greater than 20 years of observed, daily 

mean streamflow data including streamflow during the drought of the 1960s, in 

Connecticut, Massachusetts, New Hampshire, New York, Vermont, and Rhode 

Island, generally considered to be the southern New England study area...............6

3. Locations of contributing basins to 66 stream reaches monitored by U.S. 

Geological Survey streamgages, used as reference sites to estimate 

unregulated, mean streamflow with the Massachusetts Sustainable-YieldEstimator tool, southern New England study area.......................................................12

4. Estimated Pearson r correlations with the logarithm of daily streamflows 

at the U.S. Geological Survey streamgages (A) 01174900, Cadwell Creek 

near Belchertown, MA (CADW), and (B) 01095220, Stillwater River 

near Sterling, MA (STIL)...................................................................................................14

5–6. Boxplots showing—

5. Distribution of basin characteristics used in six regression equations to 

estimate unregulated, daily mean streamflow at selected streamflow quantiles 

and range of characteristics used to validate the estimated mean, daily 

streamflows computed by the Massachusetts Sustainable-Yield Estimator 

(MA SYE) tool......................................................................................................................16

6. Distribution of goodness-of-fit statistics, (A) Nash-Sutcliffe efficiency values 

and (B) percent root-mean-square error, computed from observed and estimate 

mean, daily streamflow values at 18 U.S. Geological Survey streamgages............16

7–9. Graphs showing—

7. Observed and estimated (A-B) annual, (C-D) monthly, and (E-F) daily mean 

streamflows for U.S. Geological Survey streamgages 01187300, Hubbard River 

near West Harland, CT (HUBB) and 01188000, Burlington Brook near Burlington, 

CT (BURL), southern New England study area, 1960–2004. .......................................17

8. Observed and estimated streamflow quantiles by exceedence probability 

for U.S. Geological Survey streamgages (A, C, and D) 01187300, Hubbard 

River near West Harland, CT (HUBB) and (B) 01188000, Burlington Brook near 

Burlington, CT (BURL), southern New England study area ........................................18

9. Observed and estimated streamflows for U.S. Geological Survey streamgages 

(A-B) 01187300, Hubbard River near West Harland, CT (HUBB) and (C-D) 

01188000, Burlington Brook near Burlington, CT (BURL) showing the best 

(A-B) and worst (C-D) agreement between unregulated observed and 

estimated mean, daily streamflow, in linear space and log space, southern 

New England study area, 1960–62 ..................................................................................19

10. Boxplots showing distribution of observed streamflow and streamflow estimated 

by the Massachusetts StreamStats and Massachusetts Sustainable-Yield-Estimator 

tool for eight exceedence probabilities at 29 U.S. Geological Survey streamgages 

in Massachusetts .......................................................................................................................20
v

Tables

1. Summary of 66 U.S. Geological Survey streamgages, number of streamflow 

observations, and the periods of observed, daily mean streamflow record, 

New England study area ...........................................................................................................34

2. Streamflow quantiles corresponding to 17 exceedence probabilities estimated 

from the observed period of record at 47 U.S. Geological Survey streamgages, 

New England study area ...........................................................................................................38

3. Basin, climate, and land-use characteristics at five U.S. Geological Survey 

streamgages, tested for use in the Massachusetts Sustainable-Yield Estimator tool .....8

4. Number of streamgages, regression method, explanatory variables, estimated 

regression coefficients, and regression diagnostics for streamflows at six 

exceedence probabilities used to estimate the daily, period-of-record flow-duration 

curve with the Massachusetts Sustainable-Yield-Estimator tool ........................................9

5. Number of streamgages, regression method, explanatory variables, estimated 

regression parameters, and regression diagnostics for streamflows at 11 

exceedence probabilities used to estimate the daily period-of-record flow-duration 

curve for the Massachusetts Sustainable-Yield-Estimator tool.........................................10

6. Description of MOVE.3 (Vogel and Stedinger, 1985) record extension for four 

U.S. Geological Survey reference streamgages in the New England study area...........11

7. Water-use type, number of sites, reporting units and statistics, and time and spatial 

resolution of water withdrawal and discharge sites in the statewide water-use 

database used with the Massachusetts Sustainable-Yield-Estimator tool to adjust 

daily, unregulated streamflow at ungaged sites in Massachusetts ..................................24

8. Source of water withdrawals, towns, and years of monthly data used to determine 

characteristic demand curves for public water supply groundwater and surface–

water withdrawals in Massachusetts.....................................................................................26

11. Graph showing Nash-Sutcliffe efficiency values obtained from the cross-validation 

experiments in relation to values obtained from regression equations to estimate 

uncertainty in the daily unregulated streamflows estimated by the Massachusetts 

Sustainable-Yield-Estimator tool..............................................................................................21

12. Map showng locations of groundwater and surface-water withdrawals and 

discharges in Massachusetts used by the Massachusetts Sustainable-YieldEstimator tool to adjust the unregulated, daily mean streamflow......................................23

13. Boxplots showing distribution of the monthly fraction of the total annual withdrawal 

volumes for (A) groundwater and (B) surface-water public-water-supply 

withdrawals in Massachusetts ................................................................................................25

14. Graph showing streamflow depletion estimated by the STRMDEPL program for 

a range of diffusivity values and distances between a hypothetical withdrawal 

location and stream....................................................................................................................27

15. Map showing locations in Massachusetts near the mouths of major streams 

for which unregulated and regulated streamflows were simulated using a 

groundwater-flow model because groundwater and surface-water divides are 

not coincident..............................................................................................................................28
vi

Conversion Factors

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

square foot (ft2) 0.09290 square meter (m2)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 0.003785 cubic meter (m3) 

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

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

cubic foot per second per square

mile [(ft3/s)/mi2]

 0.01093 cubic meter per second per square

kilometer [(m3/s)/km2]

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

gallon per day (gal/d) 0.003785 cubic meter per day (m3/d)

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

Specific capacity

gallon per minute per foot 

[(gal/min)/ft)]

 0.2070 liter per second per meter [(L/s)/m]

Hydraulic conductivity

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

Transmissivity*

foot squared per day (ft2/d) 0.09290 meter squared per day (m2/d) 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

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.
vii

Abbreviations

EPA Environmental Protection Agency

ESRI Environmental Systems Research Institute, Inc.

MassDEP Massachusetts Department of Environmental Protection

MassGIS Massachusetts Geographic Information System

MA SYE Massachusetts Sustainable-Yield Estimator

NPDES National Pollutant Discharge Elimination System

FDC Flow-duration curve

GIS Geographic-information system

IHA Indicators of Hydrologic Alteration

NAHAT National Hydrologic Assessment Tool

N-S E Nash-Sutcliffe efficiency

NPDES National Pollutant Discharge Elimination System

PDF Probability density function

STRMDEPL STReaMflow DEPLetion by wells

WMA Water Management Act
(This page intentionally left blank)
The Massachusetts Sustainable-Yield Estimator: 

A decision-support tool to assess water availability 

at ungaged stream locations in Massachusetts

By Stacey A. Archfield, Richard M. Vogel, Peter A. Steeves, Sara L. Brandt, Peter W. Weiskel, 

and Stephen P. Garabedian

Abstract

Federal, State and local water-resource managers require 

a variety of data and modeling tools to better understand water 

resources. The U.S. Geological Survey, in cooperation with 

the Massachusetts Department of Environmental Protection, 

has developed a statewide, interactive decision-support tool 

to meet this need. The decision-support tool, referred to as 

the Massachusetts Sustainable-Yield Estimator (MA SYE) 

provides screening-level estimates of the sustainable yield 

of a basin, defined as the difference between the unregulated 

streamflow and some user-specified quantity of water that 

must remain in the stream to support such functions as recreational activities or aquatic habitat. The MA SYE tool was 

designed, in part, because the quantity of surface water available in a basin is a time-varying quantity subject to competing 

demands for water.

To compute sustainable yield, the MA SYE tool estimates 

a daily time series of unregulated, daily mean streamflow for 

a 44-year period of record spanning October 1, 1960, through 

September 30, 2004. Selected streamflow quantiles from an 

unregulated, daily flow-duration curve are estimated by solving six regression equations that are a function of physical and 

climate basin characteristics at an ungaged site on a stream of 

interest. Streamflow is then interpolated between the estimated 

quantiles to obtain a continuous daily flow-duration curve. 

A time series of unregulated daily streamflow subsequently 

is created by transferring the timing of the daily streamflow 

at a reference streamgage to the ungaged site by equating 

exceedence probabilities of contemporaneous flow at the two 

locations. One of 66 reference streamgages is selected by kriging, a geostatistical method, which is used to map the spatial 

relation among correlations between the time series of the logarithm of daily streamflows at each reference streamgage and 

the ungaged site. Estimated unregulated, daily mean streamflows show good agreement with observed unregulated, daily 

mean streamflow at 18 streamgages located across southern 

New England. Nash-Sutcliffe efficiency goodness-of-fit values 

are between 0.69 and 0.98, and percent root-mean-square-error 

values are between 19 and 283 percent.

The MA SYE tool provides an estimate of streamflow 

adjusted for current (2000–04) water withdrawals and discharges using a spatially referenced database of permitted 

groundwater and surface-water withdrawal and discharge 

volumes. For a user-selected basin, the database is queried to 

obtain the locations of water withdrawal or discharge volumes 

within the basin. Groundwater and surface-water withdrawals 

and discharges are subtracted and added, respectively, from 

the unregulated, daily streamflow at an ungaged site to obtain 

a streamflow time series that includes the effects of these withdrawals and discharges. Users also have the option of applying an analytical solution to the time-varying, groundwater 

withdrawal and discharge volumes that take into account the 

effects of the aquifer properties on the timing and magnitude 

of streamflow alteration.

For the MA SYE tool, it is assumed that groundwater and 

surface-water divides are coincident. For areas of southeastern 

Massachusetts and Cape Cod where this assumption is known 

to be violated, groundwater-flow models are used to estimate 

average monthly streamflows at fixed locations. The MA SYE 

tool can be applied only to basins with ranges of physical and 

climate basin characteristics that are within the range under 

which the regression equations were developed. For example, 

the MA SYE tool is valid for basins whose drainage areas are 

between approximately 4 and 294 square miles. There are 

several limitations to the quality and quantity of the spatially 

referenced database of groundwater and surface-water withdrawals and discharges. The adjusted streamflow values do 

not account for the effects on streamflow of climate change, 

septic-system discharge, impervious area, non-public watersupply withdrawals less than 100,000 gallons per day, and 

impounded surface-water bodies.
2 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Introduction

The amount of surface water available for withdrawal in 

a basin is dependent upon several variables including, but not 

limited to, the total amount of water available (the unregulated 

streamflow at the outlet of the basin), the amount of water 

being withdrawn or discharged at a moment in time from 

the basin, the effects of those withdrawals or discharges on 

streamflow, the period of analysis, and the amount of water 

that may be needed to sustain aquatic habitat or support recreational uses. Surface-water availability also is dependent upon 

the effects of land cover (urbanization) and dams (both passive 

and actively managed dams) on streamflow, and the effects of 

climate change.

Safe versus Sustainable Yield

The term “safe yield” has historically been used to 

describe the amount of water available from a groundwater 

or surface-water source. Typically, the concept of safe yield 

implies that a single value represents the water available for 

withdrawal in a basin given some singular constraint, such 

as an engineering limitation or climate condition. In Massachusetts, legislation requires the Massachusetts Department of Environmental Protection (MassDEP) to regulate 

the permitting of water withdrawals greater than a 100,000 

gallon-per-day threshold volume relative to the safe yield of a 

basin (Massachusetts Water Management Act, M.G.L. c. 21G). 

The exact regulatory definition of safe yield (from 310 CMR 

36.00: The Water Management Act Regulations) is 

...the maximum dependable withdrawals that can be 

made continuously from a water source, including 

ground or surface water, during a period of years 

in which the probable driest period or period of 

greatest water deficiency is likely to occur; provided 

however, that such dependability is relative and is a 

function of storage and drought probability.

This definition is consistent with the historical interpretation of safe yield as a single value determined from a sole constraint on water availability; in the Massachusetts definition, 

that constraint is a period of severe drought. In recent years, 

attention has been given to other constraints that may affect 

the water availability in a basin, such as the preservation of 

the aquatic resources of the basin. Historically, this constraint 

has been a minimum-flow target that is constant over time. 

Poff and others (1997) state that the ecological-flow needs of 

a basin should reproduce the “natural-flow regime,” meaning that ecological-flow needs should reflect the magnitude, 

frequency, duration, timing, and rate of change that occurs 

naturally in streamflow. A single minimum-flow target would 

not be adequate to meet those needs; therefore, the sustainable 

yield of the basin, if constrained by ecological-flow needs, will 

not be a constant value.

To address the limitations of the safe-yield definition, 

recent literature has proposed that water availability is better 

expressed as a “sustainable yield” rather than a safe yield 

(Sophocleous, 2000; Alley and Leake, 2004; and Maimone, 

2004). Sustainable yield is a measure of water availability that 

simultaneously considers the spatial and temporal availability 

of water (Maimone, 2004), as well as the complex interplay 

between the time varying and competing demands for water, 

such as human and ecological water needs (Alley and Leake, 

2004). The concept of sustainable yield signifies the complexity and interdependence of some variables that affect water 

availability. To understand and quantify the sustainable yield 

of a basin, water managers and planners require flexible tools 

that address as many of these variables as possible and at the 

appropriate time scales.

Existing Tools to Estimate Streamflow and 

Assess Water Availability in Massachusetts

The calculation of sustainable yield and water availability in a basin require an estimate of unregulated, or baseline, streamflow conditions at the time scales appropriate to 

understanding the competing needs for water in a basin. For 

example, assessment tools used to understand ecological-flow 

needs typically require baseline streamflow values at the daily 

time scale (Black and others, 2005; The Nature Conservancy, 

2005; Hendrickson and others, 2006). A variety of modeling 

tools have been used to estimate water availability in ungaged 

basins in Massachusetts; however, not all tools provide data on 

streamflow at the daily scale. These tools range from regression models that estimate annual or low-flow conditions at 

regional scales using a small set of explanatory characteristics 

of an ungaged basin (for example, Vogel and others, 1999 and 

Reis and Friesz, 2000) to calibrated, physically based models 

tailored to the conditions of individual Massachusetts Planning 

Basins (DeSimone and others, 2002; DeSimone, 2004; Zarriello and Ries, 2000; Barbaro and Zarriello, 2006; Barbaro, 

2007).

In Massachusetts, quantile-based regression models were 

used to estimate selected unregulated low-flow streamflow 

statistics by relating the physical and climate characteristics 

of gaged basins to 13 low-flow streamflow statistics (Reis and 

Friesz, 2000). Reis and Friez (2000) related the median August 

streamflow value; the 7-day, 2-year and the 7-day, 10-year 

streamflow values; and streamflow quantiles at the 50-, 60-, 

70-, 75-, 80-, 85-, 90-, 95-, 98-, and 99-percent exceedence 

probabilities (that is, the streamflow values exceeded 50, 60, 

70, 75, 80, 85, 90, 95, 98, and 99 percent of the time, respectively) to the drainage area, mean basin slope, area of terrain 

underlain by stratified drift per unit of total stream length, 

and the location of the basin. These quantile-based regression 

equations are currently used in the Massachusetts StreamStats application (U.S. Geological Survey, 2009) to estimate 

unregulated low-flow streamflow statistics at ungaged sites.
Introduction 3

Fennessey (1994) and Fennessey and Vogel (1990) used 

a parameter-based regression model to estimate daily streamflow quantiles at ungaged locations in the northeastern and 

mid-Atlantic United States, including Massachusetts. The 

parameter-based regression model, in which it is assumed 

that daily streamflow values can be represented by a particular continuous probability density function (PDF), provides 

a simple equation for approximating the structure of daily 

streamflow. The parameters of the PDF are regressed against 

readily measured physical and climate characteristics of gaged 

basins to estimate daily streamflow quantiles at an ungaged 

site. Fennessey (1994) found that the parameters of the generalized Pareto distribution were related to the drainage area, 

average annual precipitation, average annual snowfall, runoffcurve number (Soil Conservation Service, 1986), mean channel slope, and mean elevation of the basin (Fennessey, 1994). 

Whereas the Reis and Friesz (2000) regression equations estimate streamflow quantiles only at the 50-, 60-, 70-, 75-, 80-, 

85-, 90-, 95-, 98-, and 99-percent exceedence probabilities, the 

parameter-based regression model can provide an estimate of 

a streamflow quantile at any exceedence probability, including 

the high-flow quantiles, which were not estimated by Ries and 

Friesz (2000).

In contrast to statistically based regression models that 

require only a few parameters to estimate streamflow, physically based basin models can be used to estimate streamflows 

at the monthly, daily, or sub-daily time scales. Basin models 

simulate specific hydrologic processes such as runoff generation, evapotranspiration, groundwater and surface-water 

interactions, and hydrologic responses to pumping and discharge stresses. In some cases, model uncertainty is explicitly 

considered (Walter and Leblanc, 2008). Such models are 

appropriate for detailed evaluation of the hydrologic effects of 

human stresses on streamflows, lake levels, and groundwater 

levels. Nonetheless, due to the substantial training, expertise, 

and time required to calibrate and use these physically based 

models, implementation of these models for a statewide, 

screening-level assessment of water availability is both cost 

and time prohibitive.

Mid-range in complexity between regression-based 

models and physically based models is the QPPQ method, 

introduced and named by Fennessey (1994) and also published 

by Hughes and Smakhtin (1996), Smakhtin (1999), Smakhtin 

and Masse (2000), and Mohamoud (2008). Fennessey (1994) 

paired the parameter-regression model with the use of a 

reference streamgage to estimate an unregulated, daily mean 

streamflow time series at an ungaged site. In this approach, 

daily streamflow quantiles at the ungaged site are estimated 

using the parameter-based regression model, which results in 

a continuous daily flow-duration curve (FDC) (the relation 

between exceedence probability and streamflow for each day 

of observed streamflow) at the ungaged site. The FDC is translated into a time series by use of a reference streamgage. As 

explained in Waldron and Archfield (2006), the observed time 

series of streamflow at the reference streamgage (Q) (fig. 1A) 

is used to construct an FDC (fig. 1B), which represents the 

probability of exceedence (P) for each unique streamflow 

value in the record. The assumption is then made that the 

probability of exceeding a flow at the reference streamgage 

is equivalent to the probability of exceeding a flow at the 

ungaged site (P) (fig. 1C). Lastly, by equating the exceedence 

probabilities at the ungaged site and reference streamgage, the 

dates of streamflow associated with each exceedence probability at the reference streamgage are transferred to the ungaged 

site to assemble a time series of streamflow at the ungaged site 

(Q) (fig. 1D).

The parameter-regression method coupled with the QPPQ 

method developed by Fennessey (1994) has been previously 

applied in the estimation of inflows to drinking-water reservoirs in Massachusetts (Waldron and Archfield, 2006). However, the parameter-regression equations in Fennessey (1994) 

cannot be used to estimate the FDC in an interactive, GISbased application because the calculation of the runoff-curve 

number is not able to be automated. Archfield (2009) demonstrated several issues with the assumption that the generalized 

Pareto PDF can represent the structure of daily streamflow. 

Also, the selection criteria for the reference streamgage were 

not addressed in Fennessey (1994) or Waldron and Archfield 

(2006).

To provide estimates of the unregulated, daily mean 

streamflow and, ultimately, a tool to estimate screening-level 

values of sustainable yield for a basin in Massachusetts, the 

U.S. Geological Survey, in cooperation with the Massachusetts 

Department of Environmental Protection, has developed a 

statewide, interactive decision-support tool termed the Massachusetts Sustainable-Yield-Estimator (MA SYE) tool. In addition to estimating screening-level values of sustainable yield 

for a basin, users of the MA SYE can compare the sustainable 

yield values to estimates of daily streamflow adjusted for current (2000–04) permitted water withdrawals and discharges in 

the basin of interest. 

The MA SYE tool is a hindcasting tool that estimates 

unregulated, daily mean streamflow over a 44-year period 

from October 1, 1960, through September 30, 2004. Unregulated, daily mean streamflows are estimated using a quantilebased regression method similar to the equations in Ries and 

Friesz (2000) coupled with the QPPQ method (Fennessey, 

1994; Hughes and Smakhtin, 1996; Smakhtin, 1999; Smakhtin 

and Masse, 2000; Mohamoud, 2008).

Supporting technical details on the development of the 

methods used by the MA SYE tool are provided in Archfield 

(2009). For the tool to compute sustainable yield, users provide flow targets specifying the quantity of water to remain in 

the stream to meet ecological flow, recreational flow, or some 

other need. Water withdrawals and discharges are used in the 

MA SYE tool to adjust unregulated daily mean streamflow. In 

this study, flows at streamgages in southern New England were 

related to readily available physical and climate basin characteristics to develop quantile-based regression models, and a 

criterion was developed to select the reference streamgage.
4 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

TIME

Flow-duration curve

estimated by the

parameter-based

regression method 

at the ungaged site.

D

EXCEEDENCE PROBABILITY

GAGED STREAMFLOWS UNGAGED STREAMFLOWS

Flow-duration curve 

at the reference 

streamgage.

A B

C

Streamflow

quantile for

gaged site

Estimated

streamflow

quantile for

ungaged site

Figure 1. Translation of a flow-duration curve to a time series of estimated streamflow using the QPPQ method, showing (A) the 

observed time series, (B) flow-duration curve, (C) exceedence probability, and (D) estimated time series for the Massachusetts 

Sustainable-Yield Estimator tool. (Adapted from Fennessey, 1994, and Waldron and Archfield, 2006).
Estimation of Unregulated, Daily Mean Streamflow 5

Purpose and Scope

This report represents the release and documentation of 

the MA SYE tool, which is used to determine streamflow at 

ungaged sites in Massachusetts. The data and methods used to 

develop the tool are documented, as well as the functionality 

and limitations.

Estimation of Unregulated, Daily Mean 

Streamflow

Unregulated, daily mean streamflow values are estimated for a period of 16,071 days (44 years from October 1, 

1960, through September 30, 2004) using the MA SYE tool. 

Unregulated, daily mean streamflow values are used in the MA 

SYE tool to provide the baseline streamflow conditions from 

which user-specified flow targets are subtracted to determine 

sustainable-yield values for the basin. The MA SYE tool is 

used to estimate unregulated, daily streamflow with a twostep process that expands on the works of Fennessey (1994), 

Hughes and Smakhtin (1996), Smakhtin (1999), Smakhtin and 

Masse (2000), Ries and Friesz (2000), and Mohamoud (2008). 

First, the MA SYE tool is used to estimate a continuous daily 

FDC, which is based on 16,071 streamflow quantiles (one 

value for each day in the study period). The estimated streamflows are then transformed to a time series of daily streamflow 

using the QPPQ method (fig. 1) (Fennessey, 1994; Hughes and 

Smakhtin, 1996; Smakhtin, 1999; Smakhtin and Masse, 2000; 

Mohamoud, 2008).

Estimation of a Continuous Flow-Duration Curve 

at Ungaged Sites

Quantile-based regression is used to estimate streamflow 

quantiles for six exceedence probabilities. An additional 11 

streamflow quantiles are estimated by solving a regression 

equation that uses another estimated streamflow quantile as 

the explanatory variable. The remaining 16,054 streamflow 

quantiles are determined by log-linear interpolation to obtain a 

continuous daily FDC with 16,071 streamflow quantiles.

Although Reis and Friesz (2000) also used quantile-based 

regression equations, new quantile-based regression equations 

were developed because of the availability of recent highresolution data sets, as well as additional streamflow data, all 

published since 2000. Furthermore, Reis and Friesz (2000) 

developed regression equations only for low-flow streamflow 

quantiles. The parameter-based regression equations used by 

Fennessey (1994) were not considered for use in estimating 

the FDC because of the challenges in determining an appropriate PDF to represent daily streamflow (Archfield, 2009).

Streamgages, Flow-Duration-Curve Statistics, 

and Basin Characteristics 

Armstrong and others (2008) identified 85 USGS 

streamgages that monitor the least-regulated streams/stream 

reaches in southern New England. A subset of 47 streamgages 

and contributing basins were used to estimate the FDC at 

an ungaged site (fig. 2). The 47 streamgages were selected 

because the observed streamflow record contained greater 

than 20 years of values, including records from the drought 

of the 1960s (table 1, at end of report). This drought encompassed Massachusetts and is generally considered the drought 

of record. Armstrong and others (2008) provide a detailed 

description of the geologic, hydrologic, and climatic conditions in the study area, as well as information on water 

use, land cover, and the presence of dams within the study 

basins. Daily, continuous streamflow observations at the 47 

streamgages were recorded for 20 to 86 years. Additional 

information on the locations, streamgage names and numbers, 

and periods of record can be found in Armstrong and others 

(2008).

To develop the quantile-based regression equations, the 

dependent variable, the streamflow quantiles, and the independent variables, which are the physical and climate basin 

characteristics, were quantified for each of the 47 streamgages. 

To compute the streamflow quantiles, the observed daily 

streamflows were ranked and an exceedence probability was 

computed for each corresponding ranked streamflow using 

the Weibull plotting position (Stedinger and others, 1993). 

Streamflow quantiles were estimated at the following: the 

0.01, 0.05, 0.10, 0.15, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 

0.85, 0.9, 0.95, and 0.99 exceedence probabilities (table 2, at 

end of report). The 15 streamflow quantiles include 8 quantiles 

also estimated by Ries and Friesz (2000) and 7 quantiles that 

represent high flows, which correspond to streamflows at low 

exceedence probabilities. Streamflow quantiles at the 0.00062 

and 0.999938 exceedence probabilities also were estimated 

from the observed streamflow data (table 2, at end of report). 

The 0.00062 and 0.999938 exceedence probabilities are those 

for the largest and smallest streamflow quantiles calculated 

using the Weibull plotting position for a record containing 

16,071 streamflow observations. The streamflow values are 

estimated with the MA SYE tool to provide upper and lower 

bounds on the estimated daily streamflows. The streamflows at 

the 0.00062 and 0.999938 exceedence probabilities were estimated for only 26 streamgages because a streamflow record of 

at least 16,071 daily observations is required to estimate these 

quantiles. Streamflow quantiles at each of the 17 exceedence 

probabilities were estimated from their observed streamflow 

records using the non-parametric quantile estimators presented 

in equations 2a and 2b of Vogel and Fennessey (1994).
6 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts Figure 2. Locations of contributing basins to 47 stream reaches monitored by U.S. Geological Survey streamgages with greater than 20 years of observed, daily mean streamflow data including streamflow during the drought of the 1960s, in Connecticut, Massachusetts, New Hampshire, New York, Vermont, and Rhode Island, generally considered to be the southern New England study area. BOSTON RHODE ISLAND NEW

YORK

VERMONT

NEWHAMPSHIRE

MAINE

MASS

ACHUSETTS

CONNECTICUT

A T L A N T I C

O C E A N

EXPLANATION

Streamgages 

U.S. Geological Surveystreamgage used byArmstrong and others (2008)to classify streamflow in Massachusetts

HOPM

(01174000)

Four-letter station code withU.S. Geological Survey streamgagenumber in parenthesis

Contributing basin to a streammonitored by a U.S. Geological Surveystreamgage

U.S. Geological Surveystreamgage not used byArmstrong and others (2008)

OYST* (01073000) U.S. Geological Survey streamgage used for validation

70° 72°

43°42°

0 50 MILES

0 50 KILOMETERS

Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005,Massachusetts State Plane projection, North American Datum 1983 

25

25

QUAB*

PAWE*

EBEM

PAWR*

PEND*

WOOH SALR*

ADAM

WOOA LITT*

TENM HOPC

BURL*

MOUN*

TAUN

WADI* SALC

NIPM

BRAN*

BLAB VALL

HUBB*

GRGB WBWE*

SEVE

SYKE

MILL* CADW

HOPM NASH

MOSS SQUA* NORT* PRIE* NBHO TARB

GREW*

STON

CONT

SBPI

BEAR COLD SAXT

OYST*

SOU1 WARN

WBWA

(01154000) (01155000)

(011085800)

(01154000)

(01086000) (01089000)

(01073000)

(01097300)

(01091000)

(01093800)

(01096000) (01161500)

(01174000)

(01175670)

(01176000)

(01193500)

(01162500)

(01121000)

(01332000)

(01333000)

(01169000)

(01171500) (01174900)

(01181000)

(01180000)

(01188000)

(01198000)

(01198500)

(01199050)

(01200000)

(01187300)

(01187400)

(01194500)

(01120000)

(01106000)

(01108000)

(01111300)

(01111500)

(01165500)

(01117500)

(01123000)

(01118300)

(01118500)

(01109000)

(01082000)

(01118000)

(01117800)
Estimation of Unregulated, Daily Mean Streamflow 7

This study tested 22 physical and climate basin characteristics (table 3) for use as explanatory (independent) variables. 

Armstrong and others (2008) provide the basin characteristics for 44 of the 47 streamgages, as well as details about 

the source and resolution of the characteristics. Physical and 

climate basin characteristics for the three streamgages not 

reported in Armstrong and others (2008) are given in table 3. 

Location variables also were tested as explanatory variables 

because they are considered substitutes for spatially varying 

characteristics that could not be readily obtained.

Regression against Basin Characteristics 

Streamflow values at the 0.000062, 0.01, 0.05, 0.2, 0.4, 

and 0.8 exceedence probabilities (table 2) were regressed 

against the 22 basin characteristics listed in table 3. Regression 

equations were developed using weighted least-squares and 

ordinary least-squares regression (table 4). When weighted 

least-squares regression was used, regression weights were 

applied to the dependent variables and were computed as a 

function of the number of days of observed streamflow on 

which the estimated streamflow statistic was based. Two sets 

of regression equations were initially developed; one set of 

equations resulted from the use of the ordinary least-squares 

method and one set of equations resulted from the use of the 

weighted least-squares regression method. The final regression 

equations developed for streamflow quantiles at the 0.2, 0.4, 

and 0.8 exceedence probabilities used the ordinary leastsquares regression equations because substantial reduction 

in prediction errors were observed over the weighted leastsquares regression equations at these streamflow quantiles. 

Furthermore, streamflow quantiles used as the dependent variables in the regression equations were estimated using at least 

20 years (7,300 days) of daily observations, making it unlikely 

that the record length affected the estimates of these quantiles.

Natural-log transformations of the dependent variables 

(streamflow quantiles at selected exceedence probabilities) 

and explanatory variables (physical and climate basin characteristics) were conducted to effectively linearize the relations 

between the variables. Because the regression equations were 

developed in logarithmic space, the form of the regression 

equation is

Y = expb0X1

b1

X2

b2

...Xn

bn

expBCF , (1)

where

Y is the dependent variable (the streamflow 

quantiles),

Xn is the independent variables (either a basin 

characteristic or another estimated 

streamflow quantile),

	 bn is the regression estimated coefficient for 

explanatory variable Xn,

	 b0 is the regression-estimated constant term, 

exp is the base of the natural logarithm and, 

BCF is the bias correlation factor.

Bias correction factors were estimated using the Smearing Estimator (Duan, 1983) to remove bias in the regression 

estimates of the streamflow quantiles. Zero values in the 

regression variables were present in less than 2 percent of the 

basin characteristics. A streamgage with a zero value for a 

particular characteristic was not used to test the significance of 

that basin characteristic. Streamflow quantile values were all 

greater than zero.

The statistical software package Minitab was used to 

develop the regression equations. Stepwise regression was 

used to narrow the 22 basin characteristics to a smaller pool 

of potentially significant basin characteristics. All regression 

coefficients in the regression equations were significantly different from zero at the 0.05 significance level (table 4). Residuals (observed minus regression-estimated streamflow values) 

(plotted in log space) were generally homoscedastic and 

effectively normally distributed with greater than 75-percent 

confidence. Sites that greatly affected the fit of the regression 

models were removed from the final equations. These were 

sites such that their inclusion substantially reduced model fit. 

Variables in the final equations had variance-inflation factors 

of less than 2.5, meaning the correlations between the independent variables are minimal. Regression-coefficient values 

and other diagnostics are shown in table 4.

Daily streamflows are complex, and physical and climate 

processes affect portions of the FDC differently; different 

variables are related to different streamflow quantiles. For 

example, the percent of terrain underlain by sand and gravel 

deposits can affect low streamflow values; however, high 

streamflow values are not related to this variable (table 4). 

Percent of basin that is open water is used to estimate 

streamflow for the 40-percent exceedence probability and is 

negatively correlated with streamflow (table 4). Percent of 

basin that is wetlands is used to estimate streamflow for the 

1-percent exceedence probability and is negatively correlated 

with streamflow (table 4). Average annual precipitation is 

used to estimate streamflow for the 1-, 5-, 20-, and 40-percent 

exceedence probabilities and is positively correlated with 

streamflow (table 4). Average maximum monthly temperature 

is used to estimate streamflow for the 80-percent exceedence 

probability and is negatively correlated with streamflow 

(table 4). Percent of basin of underlain by sand and gravel 

deposits was found to have a significant effect on the regression equation used to estimate streamflow at the 40- and 

80-percent exceedence probabilities and is positively correlated with streamflow (table 4). Statewide maps of these 

characteristics are presented in appendix 1.
8 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Table 3. Basin, climate, and land-use characteristics at five U.S. Geological Survey streamgages, tested for use in the 

Massachusetts Sustainable-Yield Estimator tool.

[These streamgages are not listed in table 3 of Armstrong and others (2008). Sources of the characteristics can be found in Armstrong and others (2008). 

Elevation characteristics are determined from the U.S. Geological Survey 30-meter National Elevation Dataset.]

Streamgage number 01086000 01107000 01109200 01180000 01188000

Streamgage name Warner River 

at Davisville, 

NH

Dorchester Brook 

near Brockton, 

MA

West Branch 

Palmer River near 

Rehoboth, MA

Sykes Brook 

at Knightville, 

MA

Burlington Brook 

near Burlington, 

CT

Streamgage code WARN DORC WBPA SYKE BURL

Basin, climate, and land-use characteristics and values

Drainage area, in square miles 145.99 4.84 4.59 1.69 4.1

Mean basin elevation, in feet 938.42 192.23 143.65 1,099.28 923.19

Maximum basin elevation, in feet 2,689.4 279.37 253.26 1,319.29 1,170.39

Minimum basin elevation, in feet 391.55 114.93 101.97 645.37 759.55

Percent of basin with elevation above 500 

feet

92.13 0 0 100 100

Elevation at the outlet of the station, in feet 403.33 126.97 108.1 645.37 778.02

Slope, in percent rise 12.7 2.53 1.75 13.96 5.82

Percent of basin that is underlain by sand 

and gravel deposits

4.23 22.45 65.79 0 33.03

X-coordinate at the station, in Massachusetts State Plane meters181124.86 235931.22 220378.27 86990.6 78034.81

Y-coordinate at the station, in Massachusetts State Plane meters1000085.97 867990.31 847719.56 894290.31 838067.81

X-coordinate at the center of the basin, in 

Massachusetts State Plane meters

166775.22 234694.48 219306.68 86033.68 76027.35

Y-coordinate at the center of the basin, in 

Massachusetts State Plane meters

1005190.34 871472.62 849452.99 896583.21 837132.47

Average annual precipitation, in inches 47.07 48.46 48.8 51.58 53.37

Average maximum temperature, in degrees 

Fahrenheit

13.05 15.25 15.19 13.34 13.86

Average minimum temperature, in degrees 

Fahrenheit

1.36 4.32 4.67 0.98 1.93

Percent of basin that is underlain by sand 

and gravel deposits

4.61 14.38 17.73 9.72 1.08

Percent of basin that is open water 1.99 0.21 0.37 1.07 0.05

Percent of basin that is forested 83.88 35.27 74.99 85.44 65.92

Percent of basin that is underlain by hydrologic soils group A10.2 11.96 24.42 0 14.56

Percent of basin that is underlain by hydrologic soils group B6.17 8.32 7.98 1.81 20.55

Percent of basin that is underlain by hydrologic soils group C77.6 61.98 36.61 89.97 37.28

Percent of basin that is underlain by hydrologic soils group D3.79 15.36 30.61 7.05 26.34
Estimation of Unregulated, Daily Mean Streamflow 9

Table 4. Number of streamgages, regression method, explanatory variables, estimated regression coefficients, and regression 

diagnostics for streamflows at six exceedence probabilities used to estimate the daily, period-of-record flow-duration curve with the 

Massachusetts Sustainable-Yield-Estimator tool.

[**, characteristic not included in regression equation; †, Bias correction factor computed from Duan (1983), WLS, weighted-least squares; OLS, ordinaryleast squares]

Exceedance probability 0.000 0.01 0.05 0.2 0.4 0.8

General regression information

Number of streamgages used to develop regression equation 26 46 46 45 45 46

Regression method WLS WLS WLS OLS OLS OLS

Standard deviation of model error, reported on log space 0.058 0.018 0.012 0.075 0.102 0.261

Coefficient of determination, asjusted for the number of predictor 

variables, R-squared (adj)

90.7 98.9 99.5 99.6 99.3 96.5

Characteristics in the regression equation and coefficient value

Constant term 1.786 -33.705 -24.866 5.066 20.203 49.726

Drainage area 0.820 0.938 0.978 0.994 1.031 1.048

Mean basin elevation 0.451   **  ** **

Average annual precipitation ** 2.539 2.129 0.949 0.750 **

Percent of basin that is open water   **  ** -0.028 **

Percent of basin that is wetlands ** -0.091   **  **

Percent of basin that is underlain by sand and gravel deposits   **  ** 0.036 0.151

Average maximum monthly temperature   **  ** ** -2.367

X-location of the basin outlet   **  0.085 0.108 **

Y-location of the basin outlet   1.345 **  ** **

Y-location of the basin centroid ** 1.942 ** -0.641 -1.769 -3.297

Bias correlation factor† 1.030 1.010 1.002 1.003 1.004 1.031

Regression against Streamflow Quantiles

Originally, 11 additional streamflow quantiles were 

regressed against physical and climate basin characteristics; however, because the regression equations were 

developed independently for streamflow quantiles at each 

of the exceedence probabilities, there was no constraint to 

ensure that estimated streamflows decreased with increasing exceedence probability. Thus the inherent structure of the 

data that ensures streamflow quantiles decrease with increasing exceedence probability is not preserved—a physical 

impossibility. To enforce physical consistency, 11 streamflow 

quantiles were recursively regressed against another estimated 

streamflow quantile. The process was done by first regressing one of the six streamflow quantiles estimated using basin 

characteristics against another quantile. This established an 

equation relating one quantile to another. The equations were 

then used to recursively estimate streamflow quantiles at 11 

additional exceedence probabilities. For example, the streamflow quantile at the 80-percent exceedence probability is 

obtained by solving a quantile-based regression equation that 

is a function of basin characteristics. However, the streamflow 

quantile at the 85-percent exceedence probability is obtained 

using the relation between the streamflow quantiles at the 80- 

and 85-percent exceedence probabilities. Only the estimated 

streamflow at the 80-percent exceedence probability is needed 

to estimate the streamflow at the 85-percent exceedence probability. Subsequent streamflow quantiles are estimated from 

the relation between one quantile and another (table 5). After 

streamflow quantiles at the 17 exceedence probabilities are 

solved, streamflow is log-linearly interpolated between these 

quantiles to obtain a continuous, daily FDC.

Estimation of Streamflow Time Series by use of 

a Reference Streamgage

The MA SYE tool transforms the daily mean FDC at an 

ungaged site to a time series of daily mean streamflow using 

the QPPQ method (Fennessey, 1994; Hughes and Smakhtin, 

1996; Smakhtin, 1999; Smakhtin and Masse, 2000; Mohamoud, 2008). The QPPQ method uses a reference streamgage to 

assign a date to each streamflow quantile along the estimated 

FDC by relating the exceedence probabilities at the ungaged 

site to the reference streamgage (fig. 1).
10 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts Table 5. Number of streamgages, regression method, explanatory variables, estimated regression parameters, and regression diagnostics for streamflows at 11 exceedence probabilities used to estimate the daily period-of-record flow-duration curve for the Massachusetts Sustainable-Yield-Estimator tool. [†, Bias correction factor computed from Duan (1983), WLS, weighted-least squares; QX, streamflow value at the X divided by 100 exceedence probability] Exceedance probability Number of streamgages used to develop regression equation Regression method Standard deviation of model error, reported on log space Coefficient of determination, asjusted for the number of predictor variables, R-squared (adjusted) Value of constant term in the regression equation Value of regression coefficient estimated for the explanatory variable Explanatory variable Bias correlation factor† 0.1 47 WLS 0.006 99.9 0.228 0.993 Streamflows at the Q15 estimated from the observed values 1.003 0.15 47 WLS 0.006 99.9 0.229 0.988 Observed streamflows at the Q20 1.003 0.3 47 WLS 0.006 99.9 0.345 0.986 Observed streamflows at the Q40 1.004 0.5 46 WLS 0.004 99.9 -0.335 1.011 Observed streamflows at the Q40 0.100 0.6 47 WLS 0.006 99.9 -0.367 1.01 Observed streamflows at the Q50 0.999 0.7 46 WLS 0.010 99.8 -0.463 1.02 Observed streamflows at the Q60 0.998 0.85 45 WLS 0.007 99.9 -0.346 1.03 Observed streamflows at the Q80 0.999 0.9 46 WLS 0.010 99.8 -0.386 1.04 Observed streamflows at the Q85 1.002 0.95 46 WLS 0.015 99.6 -0.492 1.06 Observed streamflows at the Q90 1.002 0.99 46 WLS 0.022 99.1 -0.665 1.05 Observed streamflows at the Q95 1.024 0.100 25 WLS 0.120 90.3 -1.525 1.204 Observed streamflows at the Q99 1.026
Estimation of Unregulated, Daily Mean Streamflow 11

Reference Streamgages

The MA SYE tool selects a reference streamgage from 

1 of 66 reference streamgages across southern New England 

(table 1; fig. 3). The reference streamgages include the 61 

streamgages used by Armstrong and others (2008) to hydrologically classify Massachusetts streams and 5 additional 

streamgages that are also considered unregulated by Armstrong and others (2008), which enhanced the number of reference streamgages.

The QPPQ method requires that the reference streamgage 

and ungaged site have daily streamflow records for the time 

period of interest. Therefore, all reference streamgages in 

the MA SYE also must have records of 16,071 daily streamflows spanning October 1, 1960 through September 30, 2004. 

Therefore, the records for 50 of the 66 reference streamgages 

were extended using the MOVE.3 technique (Vogel and 

Stedinger, 1985) to ensure all reference streamgages had a 

period of streamflow record from October 1, 1960, through 

September 20, 2004. It is important to note that the streamflow values at the reference streamgage are not used in the 

QPPQ method; only the date and exceedence probabilities at 

the reference streamgage are used. Record extension for these 

streamgages followed the approach detailed in Armstrong and 

others (2008). Information on the record extension for 46 of 

the 50 reference streamgages is located in Armstrong and others (2008); record-extension information for the additional 4 

reference streamgages is listed in table 6 of this report.

Selection of a Reference Streamgage

For the QPPQ method, it is assumed that the date of a 

particular streamflow being exceeded at the ungaged site is 

the same as at the reference streamgage. For example, if the 

streamflow on October 1, 1974, is exceeded 95 percent of the 

time at the reference streamgage, the streamflow exceeded 

95 percent of the time at the ungaged site also occurred on 

October 1, 1974. By extension to other streamflow quantiles, 

for the QPPQ method it is assumed that the high-flow, midrange flow, and low-flow events occur on the same day at both 

the reference streamgage and the ungaged site. Therefore, the 

ideal reference streamgage would be the one with the most 

streamflows correlated to those at the ungaged site. The MA 

SYE tool quantifies the correlation between the timing of 

the streamflows at 66 reference streamgages and those at the 

ungaged site by use of the Pearson r correlation coefficient 

(Helsel and Hirsch, 1992). The assumption of equivalent 

exceedence probabilities occurring on the same day is more 

likely to hold for two sites that have a value of Pearson r correlation coefficient close to one, which means the high-flow, 

mid-range flow, and low-flow events occur on exactly the 

same day at both the reference streamgage and the ungaged 

site. 

Although the Pearson r correlation coefficient value is 

easily computed for two gaged sites, the Pearson r correlation coefficient value cannot be directly measured for streamflows at a gaged and ungaged site. For this reason, the MA 

Table 6. Description of MOVE.3 (Vogel and Stedinger, 1985) record extension for four U.S. Geological Survey reference streamgages 

in the New England study area.

[These four reference streamgages were not used in Armstrong and others (2008). MOVE.3, Maintenance of Varience Extension, type-3]

Streamgage 

number Streamgage name Streamgage(s) used for MOVE.3 record extension

Correlation 

coefficient

Period of 

extension

01086000 Warner River near Davisville, NH Soucook River near Concord, NH (01089000) 0.95 1979–1987

Soucook River at Pembroke Road near Concord, NH (01089100)0.97 1988–2001

Squannacook River near West Groton, MA 

(01096000)

0.92 1987–1988

01180000 Sykes Brook at Knightville, MA West Branch Westfield River 01181000) 0.97 1975–2004

01107000 Dorchester Brook near Brockton, MA Wading River near Norton, MA (01109000) 0.93 1960–1962, 

1974–2004

01109200 West Branch Palmer River near Rehoboth, MA Pendleton Hill Brook near Clarks Falls, CT 

(01118300)

0.90 1960–1962, 

1974–2004
12 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts Figure 3. Locations of contributing basins to 66 stream reaches monitored by U.S. Geological Survey streamgages, used as reference sites to estimate unregulated, mean streamflow with the Massachusetts Sustainable-Yield-Estimator tool, southern New England study area. EXPLANATION Streamgages U.S. Geological Survey streamgage used by Armstrong and others (2008) to classify streamflow in Massachusetts HOPM (01174000) Four-letter station code with U.S. Geological Survey streamgage number in parenthesis Contributing basin to a stream monitored by a U.S. Geological Survey streamgage U.S. Geological Survey streamgage not used by Armstrong and others (2008) BOSTON RHODE ISLAND VERMONT NEW HAMPSHIRE MAINE MASS

ACHUSETTS

CONNECTICUT

NEW

YORK

A T L A N T I C

O C E A N

70° 72°

43°42°

Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005,Massachusetts State Plane projection, North American Datum 1983 0 50 MILES

0 50 KILOMETERS 25

25

QUAB

INDI

PAWE

EBEM

PAWR

PEND

BRRI

WOOH SALR

ADAM

WOOA NOOS LITT

TENM HOPC

BLAC BURL

PONA MOUN

PEEP

WBPA

TAUN

WADI SALC

STCT

NIPM BRAN

BLAB VALL

HUBB

DORC

IHEA

OLDS GRGB WBWE SEVE

SYKE

BASS

MILL CADW STIL

WBSW

HOPM NASH

SOUT DRYB

MOSS SQUA NORT PRIE

GREC NBHO TARB

GREW BBNH EMEA

STON

CONT

SBPI

BEAR COLD SAXT

OYST

SOU1

WARN

WB

WA

(01154000) (01155000)

(011085800)

(01154000)

(01086000) (01089000)

(01073000)

(01100700)

(01097300)

(010965852)

(01091000)

(01093800)

(01096000) (01161500)

(01095220)

(01105730)

(01174000)

(01175670)

(01176000)

(01193500)

(01184100)

(01105600)

(01170100)

(01107000)

(01162500)

(01121000)

(01331400)

(01332000)

(01333000)

(01169000)

(01169900)

(01174565)

(01171500)

(01089000)

(01174900)

(01181000)

(01180000)

(01188000)

(01198000)

(01198500)

(01199050)

(01200000)

(01187300)

(01187400)

(01194500)

(01195100)

(01120000)

(01106000)

(01108000)

(01111300) (01111500)

(01165500)

(01117500)

(01126600)

(01123000)

(01118300)

(01118500)

(01115098)

(01115187)

(01109000)

(01109200)

(01082000)

(01118000)

(01117800)

(01117460)

(01115630)
Estimation of Unregulated, Daily Mean Streamflow 13

SYE estimates the correlation between the natural log of the 

streamflows at the ungaged site and each potential reference 

streamgage to select the reference streamgage for which logarithms of the daily streamflow are estimated to have the highest correlation with the logarithms of the daily streamflows at 

the ungaged site.

Time-series correlations between the ungaged site and 

each reference streamgage were obtained through kriging (Isaaks and Srivastava, 1989), a geostatistical method. 

For a given reference streamgage, the Pearson r correlation 

coefficient value was computed from the logarithms of the 

observed, concurrent daily streamflows at the given reference 

streamgage and each of the other reference streamgages used 

by the MA SYE tool. A spherical variogram model (Isaaks 

and Srivastava, 1989) was then developed for each reference 

streamgage to quantify the relation between the distances 

between each pair of reference streamgages and the differences in the Pearson r correlation coefficient values between 

each pair of reference streamgages. Each variogram model 

quantifies the Pearson r correlation-coefficient value for 

any ungaged site in relation to a reference streamgage. The 

reference streamgage with the highest Pearson r correlation 

coefficient value in relation to the ungaged site is selected for 

use with the QPPQ method. The MA SYE tool requires only 

the Massachusetts State-Plane coordinates of the ungaged site 

in order to select the reference streamgage. The variogram 

models can be used to create prediction maps of the Pearson r

correlation coefficient value for each reference streamgage, 

which show the correlation between a reference streamgage 

and any ungaged site in Massachusetts (fig. 4). For the CADW 

01174900 streamgage (fig. 4A), the areas with the higher 

estimated correlations form an ellipsoid with the major axis 

trending in the southwest-northeast direction; however, for the 

STIL 01095220 streamgage (fig. 4B), correlations appear to 

decrease radially with distance. Archfield (2009) provides a 

detailed explanation and validation of the variogram models.

Comparison of Observed and Estimated 

Streamflows

A time series of unregulated, daily mean streamflow at an 

ungaged site is assembled in the following steps: (1) solve the 

regression equations, (2) interpolate between the regressionestimated streamflow quantiles to obtain a daily FDC at the 

ungaged site, (3) select the reference streamgage, and (4) 

apply the QPPQ method. To evaluate the MA SYE tool for 

use in estimating daily, unregulated streamflows at an ungaged 

site, a validation procedure was used at 18 streamgages 

because observed streamflow for the period-of-record of interest (October 1, 1960, to September 30, 2004) was available 

for these streamgages (fig. 2 and table 1). For each of the 18 

streamgages, the FDC regression equations were re-developed 

independent of the streamgage, and the selection of the 

reference streamgage did not include the streamgage used in 

the kriging procedure. In effect, this validation experiment 

evaluates the estimates of streamflow at a streamgage that 

was not used in the development of the MA SYE tool. The 18 

streamgages used in the cross-validation are representative of 

the distribution of basin characteristics at the 47 streamgages 

used to develop the continuous, daily FDC (fig. 5). 

Observed and estimated streamflows were then compared 

for goodness of fit at each of the removed streamgages, and 

a Nash-Sutcliffe (NS) efficiency value (Nash and Sutcliffe, 

1970) and percent root-mean-square-error (RMSE) values 

were computed for each of the 18 streamgages using the natural-log values of the observed and estimated daily streamflows. 

NS values ranged from 0.98 to 0.69, with a median value of 

0.86 (fig. 6); percent RMSE values ranged from 19 to 284 

percent, with a median value of 55 percent (fig. 6). Observed 

and estimated annual, monthly, and daily mean streamflows 

for streamgages with the best and worst agreement over 

the full 44-year period show good agreement and relatively 

unbiased results (fig. 7). However, the highest and lowest daily 

mean streamflows appear to show a “hook” feature (fig. 7E 

and 7F). The hook feature is likely an artifact of the log-linear 

interpolation among the 17 regression-estimated streamflows. 

Observed and estimated FDCs, when examined at the highest 

and lowest streamflows, show that the assumption of a loglinear relation between streamflow quantiles at the highest and 

lowest streamflows may not be appropriate (fig. 8). Nevertheless, these flows represent only the 160 days of highest flow 

and the 160 days of lowest flow; the other 15,751 streamflows 

were estimated reasonably by the MA SYE tool.

A comparison of observed and estimated hydrographs 

for streamgages with the best (01187300, Hubbard River near 

West Harland, CT (HUBB)) and worst (01188000, Burlington Brook near Burlington, CT (BURL)) agreement over the 

period October 1, 1960, through September 30, 1962—the 

period of time at the start of the worst drought of record—

show good agreement in both real and log space (fig. 9A and 

9B). Differences between the observed and estimated daily 

mean streamflow shown for the 18 streamgages are likely to 

be typical of the differences one could expect when using the 

MA SYE tool because the range of basin characteristics for 

the 18 streamgages used in the cross-validation experiment 

are nearly identical to the range of these characteristics at the 

47 streamgages from which the regression equations were 

developed (fig. 5). 

Streamflow estimates at 29 streamgages used in the 

development of the MA SYE quantile-based regressions overlapped with those for the streamgages used by Ries and Friesz 

(2000) (table 1 identifies these 29 streamgages). The estimated 

streamflow quantiles from the MA SYE tool were compared 

with the observed streamflow quantiles and the Massachusetts 

StreamStats-estimated streamflow quantiles estimated at the 

0.50, 0.60, 0.70, 0.80, 0.85, 0.9, 0.95, and 0.99 exceedence 

probabilities by Ries and Friesz (2000) and used in the Massachusetts StreamStats equations. Before making the comparison at each streamgage, the streamgage was were removed 

from the MA SYE equations, and the regression coefficients 

were re-estimated. This ensured that the MA SYE-estimated 

streamflow quantile was not affected by the inclusion of this 
14 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

0 50 MILES0 50 KILOMETERS

Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005Massachusetts State Plane projection, North American Datum 1983 

BOSTON

RHODE

ISLAND

NEW

YORK VERMONT NEW

HAMPSHIRE

MAINE

MASS

ACHUSETTS

CONNECTICUT

A T L A N T I C

O C E A N

QUAB

PAWE

EBEM

PEND

WOOH SALR

LITT TENM

HOPC BL

AC BURL

MOUN TAUN

WADI

SALC

NIPM

BRAN

BLAB

VALL HUBB

DORC

IHEA

OLDS

GRGB WBWE

SEVE SYKE

MILL

BASS

CAD

HOPM

W

NASH SOUT

DRYB

MOSS SQUA NORT

PRIE GREC NBHO TARB

GREW EMEA

STON CONT

SBPI

BEAR COLD SAXT

OYST

SOU1

WARN

WB

WA

(01154000) (01155000)

(011085800)

(01154000)

(01086000)

(01089000)

(01073000)

(01100700)

(01097300)

(01091000)

(01093800)

(01096000)

(01161500)

(01105730)

(01174000)

(01175670)

(01176000)

(01193500)

(01105600)

(01170100)

(01107000)

(01162500)

(01121000)

(01331400)

(01332000)

(01333000)

(01169000)

(01169900)

(01171500)

(01089000)

(01174900)

(01181000)

(01180000)

(01188000)

(01198000)

(01198500)

(01199050)

(01200000)

(01187300)

(01187400)

(01194500)

(01120000)

(01108000)

(01111300)

(01111500)

(01165500)

(01126600)

(01123000)

(01118300)

(01118500)

(01109000)

(01082000)

(01118000)

90

495

495

90

STIL

PEEP

PONA

BRRI

INDI

STCT

WBSW

BBNH

(01174565)

(01095220)

(01115098)

(01115187)

(01117460)

(01195100)

(01184100)

(010965852)

43°42°

72° 70°

WBPA

(01109200)

ADAM

(01106000)

PAWR

(01117500)

WOOA

(01117800)

NOOS

(01115630)

EXPLANATION

State boundaryInterstate highway

U.S. Geological Surveystreamflow-gaging stations 

Streamflow-gaging station

HOPM

(01174000)

Station code

—

U.S. Geological Surveystation number in parenthesis

Estimated Pearson r correlationcoefficient with the logarithm of dailystreamflows at the U.S. GeologicalSurvey streamflow-gaging station01174900, Cadwell Creek near Belchertown, MA (CADW)

0.75 – 0.800.80 – 0.85

0.85 – 0.900.90 – 0.950.95 – 1.0

0.70 – 0.75

25

25

A

Figure 4. Estimated Pearson r correlations with the logarithm of daily streamflows at the U.S. Geological Survey streamgages (A) 01174900, Cadwell Creek nearBelchertown, MA (CADW), and (B) 01095220, Stillwater River near Sterling, MA (STIL).
Estimation of Unregulated, Daily Mean Streamflow 15 Figure 4. Estimated Pearson r correlations with the logarithm of daily streamflows at the U.S. Geological Survey streamgages (A) 01174900, Cadwell Creek near Belchertown, MA (CADW), and (B) 01095220, Stillwater River near Sterling, MA (STIL).—Continued

WBSW

STIL

STCT

PONA

INDI

BBNH

PEEP

BRRI

(01174565)

(01115187)

(01117460)

(01195100)

BOSTON

RHODEISLAND

NEW

YORK

VERMONT NEW

HAMPSHIRE

MAINE

MASS

ACHUSETTS

CONNECTICUT

A T L A N T I C

O C E A N

QUAB

EBEM PAWR PEND

WOOH

SALR

WOOA

LITT

TENM

BURL MOUN

TAUN

WADI

SALC

NIPM BRAN BLAB VALL

HUBB IHEA

OLDS

GRGB WBWE SEVE

MILL

CADW

NASH

SOUT

SQUA NORT PRIE GREC GREW

STON CONT

SAXT OYST

WARN WB

WA

(01154000)

(011085800) (01086000)

(01073000)

(01097300)

(01093800)

(01096000)

(01105730)

(01175670) (01176000)

(01193500)

(01105600)

(01170100) (01162500)

(01121000)

(01333000)

(01169000)

(01169900)

(01171500)

(01174900)

(01181000)

(01188000)

(01198000)

(01198500)

(01199050)

(01200000)

(01187300)

(01187400)

(01194500)

(01108000)

(01111300)

(01111500)

(01117500)

(01123000)

(01118300)

(01109000)

(01082000)

(01118000)

(01117800)

90

495

495

90 (01095220)

(010965852)

(01184100)

(01115098)

43°42°

72° 70°

Estimated Pearson r correlationcoefficient with the logarithm of dailystreamflows at the U.S. GeologicalSurvey streamflow-gaging station01095220, Stillwater River near Sterling, MA (STIL)

EXPLANATION

U.S. Geological Surveystreamflow-gaging stations 

Streamflow-gaging station

WBSW

(01174565)

Station code

—

U.S. Geological Surveystation number in parenthesis

0.75 – 0.800.80 – 0.85

0.85 – 0.900.90 – 0.950.95 – 1.0

0.70 – 0.75

0 50 MILES0 50 KILOMETERS

Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005Massachusetts State Plane projection, North American Datum 1983 

25

25

PAWE

(01118500)

B
16 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Figure 5. Distribution of basin characteristics used in six regression equations to estimate unregulated, daily mean streamflow at 

selected streamflow quantiles and range of characteristics used to validate the estimated mean, daily streamflows computed by the 

Massachusetts Sustainable-Yield Estimator (MA SYE) tool. 

Figure 6. Distribution of goodness-of-fit statistics, (A) Nash-Sutcliffe efficiency values and (B) percent root-mean-square error, 

computed from observed and estimate mean, daily streamflow values at 18 U.S. Geological Survey streamgages.

300

250

200

150

100

50

0

2,000

1,500

1,000

500

0

EXPLANATION

Median

25th percentile

75th percentile

Upper limit (75th percentile + 1.5 * 

(75th percentile - 25th percentile))

Lower limit (25th percentile + 1.5 * 

(75th percentile − 25th percentile))

(18) Sample size

MEAN BASIN ELEVATION,

IN FEET

DRAINAGE AREA,

IN SQUARE MILES

7

6

5

4

3

2

1

0

6

5

4

3

2

1

0

25

20

15

10

5

0

60

50

40

30

20

10

0

PERCENT OF BASIN THAT 

IS WETLANDS

PERCENT OF BASIN THAT IS

UNDERLAIN BY SAND

AND GRAVEL DEPOSITS

PERCENT OF BASIN THAT

 IS OPEN WATER

AVERAGE ANNUAL MINIMUM 

TEMPERATURE,

IN DEGREES FAHRENHEIT

(47)

(47)

(47)

(47)

(47)

(47)

(18)

(18) (18)

(18)

(18) (18)

Values above the upper limit 

or below the lower limit

1.0

0.8

0.6

0.4

0.2

0

NASH-SUTCLIFFE EFFICIENCY VALUE

A EXPLANATION

Median

25th percentile

75th percentile

Upper limit (75th percentile + 1.5 * 

(75th percentile - 25th percentile))

Lower limit (25th percentile + 1.5 * 

(75th percentile − 25th percentile))

PERCENT ROOT-MEAN-SQUARE ERROR

B

Values above the upper limit 

or below the lower limit

300

250

200

150

100

50

0
Estimation of Unregulated, Daily Mean Streamflow 17

Figure 7. Observed and estimated (A-B) annual, (C-D) monthly, and (E-F) daily mean streamflows for U.S. Geological 

Survey streamgages 01187300, Hubbard River near West Harland, CT (HUBB) and 01188000, Burlington Brook near 

Burlington, CT (BURL), southern New England study area, 1960–2004. 

OBSERVED STREAMFLOW,

IN CUBIC FEET PER SECOND

0.1

1

10

100

1,000

0.1 1 10 100 1,000

Nash-Sutcliffe efficiency value = 0.69

OBSERVED STREAMFLOW,

IN CUBIC FEET PER SECOND

ESTIMATED STREAMFLOW,

IN CUBIC FEET PER SECOND

Nash-Sutcliffe efficiency value = 0.98

0.1

1

10

100

1,000

10,000

0.1 1 10 100 1,000 10,000

ESTIMATED STREAMFLOW,

IN CUBIC FEET PER SECOND

ESTIMATED STREAMFLOW,

IN CUBIC FEET PER SECOND

01187300, Hubbard River near 

West Harland, CT (HUBB)

01188000, Burlington Brook near 

Burlington, CT (BURL) A B

C D

E F

1,000

10,000

100,000

1,000 10,000 100,000

100

1,000

10,000

100 1,000 10,000

1

10

100

1,000

10,000

1 10 100 1,000 10,000

1

10

100

1,000

10,000

1 10 100 1,000 10,000

ANNUAL ANNUAL

MONTHLY MONTHLY

MEAN DAILY MEAN DAILY
18 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

streamgage in the development of the equation. However, it 

was not possible to perform this operation on the equations 

developed by Ries and Friesz (2000); therefore, a rigorous 

comparison of the MA SYE and Massachusetts StreamStats 

could not be conducted. In all cases evaluated, however, the 

MA SYE-estimated streamflow quantiles were consistent with 

the observed streamflow quantiles and the streamflow quantiles estimated by the Massachusetts StreamStats equations 

(Ries and Friesz, 2000) (fig. 10). Furthermore, all MA SYEestimated streamflow values at each of the 29 streamgages fell 

within the 90-percent confidence intervals reported by Ries 

and Friesz (2000).

Uncertainty of Estimated Streamflows

The uncertainty associated with estimated time series of 

unregulated, daily mean flow at an ungaged site involves three 

major components: (1) estimation of the FDC at the ungaged 

site, (2) choice of a reference streamgage based on maps 

of cross-correlations among flow records of existing gaged 

sites, and (3) transfer of daily streamflows from the reference 

streamgage to the ungaged site using the QPPQ method and its 

inherent assumptions. Each of these major components adds 

unique uncertainty to the estimated streamflows at the ungaged 

site, in addition to the measurement error associated with the 

observed streamflows used to develop the regression equations 

and the selection and use of the reference streamgage.

A rigorous uncertainty analysis would incorporate the 

uncertainty introduced by each of these sources of error in 

an integrated fashion that would result in prediction intervals 

that enclose the estimated unregulated, daily mean streamflows within a stated degree of confidence. If the MA SYE 

tool were based on a single modeling approach, such as the 

multivariate regression used in Ries and Friesz (2000), or a 

physically based model, one could employ standard methods 

Figure 8. Observed and estimated streamflow quantiles by exceedence probability for U.S. Geological Survey streamgages 

(A, C, and D) 01187300, Hubbard River near West Harland, CT (HUBB) and (B) 01188000, Burlington Brook near Burlington, CT 

(BURL), southern New England study area.

0.1

1

10

100

1,000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.1

1

10

100

1,000

10,000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Observed streamflow

Estimated streamflow

1

10,000 10

1,000

100

1

0.1

0 0.02 0.04 0.06 0.08 0.1 0.9 0.92 0.94 0.96 0.98

EXCEEDENCE PROBABILITY EXCEEDENCE PROBABILITY

STREAMFLOW, IN CUBIC FEET PER SECOND

STREAMFLOW, IN CUBIC FEET PER SECOND

EXPLANATION

EXCEEDENCE PROBABILITY EXCEEDENCE PROBABILITY STREAMFLOW, IN CUBIC FEET PER SECOND

STREAMFLOW, IN CUBIC

FEET PER SECOND

Regression-estimated

streamflow

C D

A Hubbard River near West Harland, CT (HUBB) B Burlington Brook near Burlington, CT (BURL)

01187300 01188000

01187300 01187300
Estimation of Unregulated, Daily Mean Streamflow 19 Figure 9. Observed and estimated streamflows for U.S. Geological Survey streamgages (A-B) 01187300, Hubbard River near West Harland, CT (HUBB) and (C-D) 01188000, Burlington Brook near Burlington, CT (BURL) showing the best (A-B) and worst (C-D) agreement between unregulated observed and estimated mean, daily streamflow, in linear space and log space, southern New England study area, 1960–62.

10/01/1960 12/30/1960 3/30/1961 6/28/1961 9/26/1961 12/25/1961 3/25/1962 6/23/1962 9/21/1962 10/1/1960 12/30/1960 3/30/1961 6/28/1961 9/26/1961 12/25/1961 3/25/1962 6/23/1962 9/21/1962

10/1/1960 12/30/1960 3/30/1961 6/28/1961 9/26/1961 12/25/1961 3/25/1962 6/23/1962 9/21/1962 10/1/1960 12/30/1960 3/30/1961 6/28/1961 9/26/1961 12/25/1961 3/25/1962 6/23/1962 9/21/1962

Nash-Sutcliffe efficiency value = 0.69 Nash-Sutcliffe efficiency value = 0.98Nash-Sutcliffe efficiency value = 0.69 Nash-Sutcliffe efficiency value = 0.98

A 01187300, Hubbard River near West Harland, CT (HUBB) C 01188000, Burlington Brook near Burlington, CT (BURL)

0

50

350300250200150100

0.1

1

10

100

1,000

STREAMFLOW, IN CUBIC FEET PER SECOND STREAMFLOW, IN CUBIC FEET PER SECOND

B

D

0

800600400200

1,4001,2001,000

0.1

1

10

100

1,000

10,000

STREAMFLOW, IN CUBIC FEET PER SECOND STREAMFLOW, IN CUBIC FEET PER SECOND Estimated streamflows Observed streamflows Estimated streamflows Observed streamflows Estimated streamflows Observed streamflows Estimated streamflows Observed streamflows

LINEAR SPACE LINEAR SPACE

LOG SPACE LOG SPACE
20 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Figure 10. Distribution of observed streamflow and streamflow estimated by the Massachusetts StreamStats and Massachusetts 

Sustainable-Yield-Estimator tool for eight exceedence probabilities at 29 U.S. Geological Survey streamgages in Massachusetts.

400

300

200

100

0

250

200

150

100

50

0

200

150

100

50

0

120

100

80

60

40

20

0

90

80

70

60

50

40

30

20

10

0

80

70

60

50

40

30

20

10

0

60

50

40

30

20

10

0

40

30

20

10

0

STREAMFLOW, IN CUBIC FEET PER SECOND

50-PERCENT EXCEEDENCE PROBABILITY 60-PERCENT EXCEEDENCE PROBABILITY

70-PERCENT EXCEEDENCE PROBABILITY 80-PERCENT EXCEEDENCE PROBABILITY

85-PERCENT EXCEEDENCE PROBABILITY 90-PERCENT EXCEEDENCE PROBABILITY

95-PERCENT EXCEEDENCE PROBABILITY 99-PERCENT EXCEEDENCE PROBABILITY

Massachusetts

StreamStats

Massachusetts

SustainableYield Estimator

Observed

streamflows

Massachusetts

StreamStats

Massachusetts

SustainableYield Estimator

Observed

streamflows

Values above the upper limit 

or below the lower limit

300 EXPLANATION

Median

25th percentile

75th percentile

Upper limit (75th percentile + 1.5 * 

(75th percentile - 25th percentile))

Lower limit (25th percentile + 1.5 * 

(75th percentile - 25th percentile))
Estimation of Unregulated, Daily Mean Streamflow 21

of uncertainty analysis for such model predictions. However, the estimated streamflows used in the MA SYE tool 

are derived from a variety of complex modeling steps so 

the standard methods of uncertainty analysis do not provide 

meaningful prediction intervals. Identifying the true uncertainty is unusually challenging given the interaction of the 

major MA SYE components. For example, employing the 

widely used method termed “generalized likelihood uncertainty estimation” (GLUE) (see Stedinger and others, 2008) 

does not suffice for this problem because GLUE applies only 

to physically based models, and there are many more sources 

of error in addition to the model parameter errors accounted 

for in a GLUE methodology. The actual uncertainty of the MA 

SYE-estimated streamflows is unknown and remains an area 

for future research.

To address the issue of uncertainty in this report, the 

conditions under which one can be expected to obtain the type 

of goodness-of-fit values reported (fig. 6) are documented. 

Because the goodness-of-fit values are based on rigorous 

cross-validation experiments, they represent the range of 

uncertainty that one can expect in future applications of the 

MA SYE tool at ungaged sites. For example, figure 6 demonstrates the use of cross-validation experiments, and shows that 

the use of the estimated time series of daily streamflows that 

resulted from the goodness-of-fit test generated NS efficiency 

values in the range of 0.69 to 0.98 with a median value of 

approximately 0.86. In other words, the range of uncertainty 

expected from future applications of the MA SYE at ungaged 

sites will vary across the spectrum of estimated daily streamflows as illustrated by the distribution NS efficiency values 

reported in figure 6 and time-series plots depicted in figure 9.

In a particular application of the MA SYE tool, the question will arise as to what would be the expected value of the 

NS efficiency value at an ungaged site. Multivariate ordinary 

least squares regression was employed to develop a predictive 

model for values of NS efficiency as a function of the information that would be available to the user of the MA SYE. 

The two key factors which drive our overall ability to transfer 

information from a reference streamgage to an ungaged site 

are the degree of correlation, r, between the natural logarithms 

of the daily streamflows at each site and the variability of the 

streamflows at the ungaged site. Here the variability of the 

daily streamflows is measured using the standard deviation of 

the natural logarithms of the daily streamflows denoted as sy. 

Note that for a lognormal variable x, its coefficient of variation 

depends only on sy where y=ln(x).

Because the efficiency values for reasonable models 

cannot exceed unity, logit, probit and complementary log-log 

models (see McCullagh and Nelder, 1983; and Agresti, 1990) 

were fit to the efficiency values, and all the models restricted 

predicted values of efficiency to be less than unity. Of the 

three candidate transformations, the probit model produced the 

most favorable results in terms of overall goodness-of-fit. A 

probit model was developed using multivariate ordinary least 

squares regression to fit the model

Φ-1(E) = b0 + b1 r + b2sy , (2)

where

Φ-1(E) is the inverse of a standard normal distribution 

evaluated at NS efficiency, E,

	 b0 is the regression-estimated constant term,

	 r	 is the correlation between the natural 

logarithms of the daily streamflows at each 

site,

	 b1 is the regression estimated coefficient for r,

	 sy is the standard deviation of the natural 

logarithms of the daily streamflows, and

	 b2 is the regression estimated coefficient for sy.

The resulting model, inverted to obtain an estimate of NS 

efficiency is

E = Φ[-14.388 + 14.033r + 1.9722sy] , (3)

where now Φ( ) is the cumulative distribution function for a 

standard normal random variable. The t-ratios of the model 

parameters b0 , b1, b2 are -3.08, 3.02 and 3.89, respectively, 

leading to p-values of 0.008, 0.009 and 0.001, respectively. 

The model has an adjusted R2 value equal to 48.4 with model 

residuals which are extremely well approximated by a normal 

distribution. A comparison of the values of NS efficiency 

estimated from the cross-validation experiments and those 

estimated using equation (3) is shown in figure 11.

The regression model shown in equation (3) documents 

how average values of goodness of fit vary with both r and 

0.5

0.6

0.7

0.8

0.9

1.0

0.5 0.6 0.7 0.8 0.9 1.0

NASH-SUTCLIFFE EFFICIENCY VALUE OBTAINED

FROM CROSS-VALIDATION EXPERIMENTS

NASH-SUTCLIFFE EFFICIENCY VALUE

OBTAINED FROM REGRESSION EQUATION

Figure 11. Nash-Sutcliffe efficiency values obtained from 

the cross-validation experiments in relation to values obtained 

from regression equations to estimate uncertainty in the daily 

unregulated streamflows estimated by the Massachusetts 

Sustainable-Yield-Estimator tool.
22 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

sy. In general, one expects the NS efficiency value to increase 

as the correlation between the reference streamgage and the 

ungaged site increases because that correlation reflects the 

overall similarity between the two sites. One also expects values of NS efficiency to increase for ungaged sites which have 

greater overall flow variability because the FDC regression 

equations have greater predictive capability in such cases. The 

greater predictive capability associated with the FDC regression equations relate to the recursive nature of the regressions. 

As sy increases, the quantiles of the FDC show greater correlation with each other, which results in recursive regressions 

with higher explanatory power. An open question remains 

as to what conditions would lead the QPPQ method to yield 

higher values of NS efficiency. Further research is needed to 

better understand these issues.

The t-ratios associated with r and sy reflect the fact that 

sy explains somewhat more of the overall variability in values 

of NS efficiency than r. The effect attributable to r could 

be caused largely by the choice of a reference streamgage, 

whereas the effects due to sy are due largely to the transfer 

of streamflow using the QPPQ method and the estimation of 

the FDC at the ungaged site using regression methods. Thus 

the regression in equation (3) seems to indicate that more 

accurate streamflow estimates will likely result from improvements in all three of the major steps associated with the SYE 

methodology.

Streamflow Adjusted for Groundwater 

and Surface-Water Withdrawals and 

Discharges

The MA SYE tool can modify estimates of unregulated, 

daily mean streamflow at an ungaged site on the basis of 

permitted groundwater and surface-water withdrawal and 

discharge locations contained within the basin of interest. For 

a user-selected basin, groundwater and surface-water withdrawals and discharges are subtracted and added, respectively, 

from the unregulated, daily streamflow to obtain a time series 

of daily streamflow at an ungaged site that has been adjusted 

by the reported 2000 through 2004 withdrawal and discharge 

volumes. Users also have the option to apply an analytical 

solution to time-varying groundwater withdrawals and discharges that incorporate the effects of the aquifer properties on 

the timing and magnitude of streamflow alteration.

Reported Groundwater and Surface-Water 

Withdrawals and Discharges

A statewide, spatially referenced database of groundwater 

and surface-water withdrawals and groundwater discharges 

from 2000 through 2004 was provided by the Massachusetts 

Geographic Information System (MassGIS) and MassDEP 

(Christian Jacques, Massachusetts Geographic Information System, written commun., 2007; Thomas Lamonte and 

Kari Winfield, Massachusetts Department of Environmental 

Protection, written commun., 2008). The U. S. Environmental 

Protection Agency (USEPA) provided the National Pollutant 

Discharge Elimination System (NPDES) surface-water discharge locations and volumes for 2000 through 2004, which 

are also included in the statewide database. 

The database of withdrawals and discharges contains 

6,581 locations of groundwater and surface-water withdrawals 

and discharges in Massachusetts (fig. 12 and table 7), covering four major categories: (1) groundwater and surface-water 

public-water-supply withdrawals, including community, noncommunity, and transient facilities using less than 100,000 

gallons per day; (2) groundwater and surface-water withdrawals greater than 100,000 gallons per day use as regulated by 

the Massachusetts Water Management Act (M.G.L. c. 21G), 

including public and non-public water suppliers (examples 

of the latter include golf courses and agricultural, commercial, and industrial facilities supplying water for non-human 

consumption); (3) groundwater pollutant discharges greater 

than 10,000 gallons per day as regulated by MassDEP (M.G.L. 

310 CMR 5), including discharges of sanitary sewer, industrial 

non-contact cooling waters, Laundromat and carwash waters, 

and water used in groundwater-treatment systems; and (4) 

NPDES surface-water discharges as regulated by the USEPA. 

Volumes of withdrawal and discharge are available for 

public-water-supply withdrawals, groundwater discharges, 

and NPDES surface-water discharges. Public- and non-public 

water-supply withdrawals greater than 100,000 gallons per 

day (withdrawals regulated by the WMA) are managed as a 

withdrawal system, and therefore, withdrawal volumes are 

reported as the sum of all sources within a withdrawal system, 

not by individual withdrawal source. Some withdrawal systems are comprised of only public-water-supply withdrawals, 

in which case, source volumes are also available; however, 

some withdrawal systems are a combination of public- and 

non-public-water-supply withdrawals (some withdrawal volumes are available by withdrawal source) and some are only 

non-public-water-supply withdrawals (no withdrawal volumes 

are available by withdrawal source). For withdrawal systems 

that contain both public- and non-public-water-supply withdrawal locations, the source-level withdrawals are subtracted 

from the total reported withdrawal volume for the system, and 

the remaining system withdrawal volumes are divided equally 

among the non-public-water-supply withdrawals to obtain 

source volumes for each withdrawal location in the system. 

For withdrawal systems that contain only non-public-watersupply withdrawal locations, the system withdrawal volumes 

are divided equally among the non-public-water-supply withdrawals to obtain source volumes for each withdrawal location 

in the system.
Streamflow Adjusted for Groundwater and Surface-Water Withdrawals and Discharges 23 Groundwater discharge greater than 15,000 gallons per day National Pollutant Discharge Elimination System (NPDES) surface-water discharge Public-water-supply withdrawal less than 100,000 gallons per day Public-water-supply withdrawal greater than 100,000 gallons per day Non-public water-supply withdrawal greater than 100,000 gallons per day Major basin boundary Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005 Massachusetts State Plane projection, North American Datum 1983 EXPLANATION Water-use locations Town boundary 42°

43°

72° 70°

0 50 KILOMETERS 250 50 MILES 25

Figure 12. Locations of groundwater and surface-water withdrawals and discharges in Massachusetts used by the Massachusetts Sustainable-Yield-Estimator tool to adjust the unregulated, daily mean streamflow.
24 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Disaggregation of Withdrawal and Discharge 

Volumes

The MA SYE tool adjusts the unregulated, daily mean 

streamflow using the permitted groundwater and surface-water 

withdrawals in the statewide database; however, the resolution and quality of the reported data are not uniform (table 7), 

and daily withdrawal and discharge volumes are not reported. 

Therefore, withdrawal and discharge volumes must first be 

disaggregated to daily values before the unregulated, daily 

mean streamflow can be adjusted. In the MA SYE tool, data 

reported in the spatially referenced database can be overridden 

and replaced by more detailed information or by hypothetical 

withdrawal and discharge volumes.

Groundwater and surface-water discharge volumes are 

recorded monthly in the statewide database. To obtain daily 

discharge values, the monthly volumes are divided by the 

number of days in each respective month, which results in 

constant daily discharge values over each month. 

Groundwater and surface-water withdrawals are reported 

annually in the statewide database. Annual volumes are 

disaggregated to monthly values using one of three monthly 

withdrawal patterns. For non-public-water-supply withdrawals, volumes are disaggregated from annual to monthly values 

using a constant monthly withdrawal pattern. Daily volumes 

are computed by dividing the monthly volumes by the number 

of days in each respective month. For public-water-supply 

withdrawals, separate monthly withdrawal patterns are used 

Table 7. Water-use type, number of sites, reporting units and statistics, and time and spatial resolution of water withdrawal and 

discharge sites in the statewide water-use database used with the Massachusetts Sustainable-Yield-Estimator tool to adjust daily, 

unregulated streamflow at ungaged sites in Massachusetts.

[*, volumes are reported for either the source of the water or as a sum of volumes from aggregated withdrawal sources]

Water-use type

Number 

of sites in 

statewide 

database

Reporting units Reported statistic

Time 

resolution 

of reported 

data

Resolution of reported data*

Public-water-supply withdrawal 

less than 100,000 gallons per 

day

2,361 Million gallons 

per year

Annual total Annual data Withdrawal volumes reported for 

water source

Public-water-supply withdrawal 

greater than 100,000 gallons 

per day

1,420 Million gallons 

per year

Annual total Annual data Withdrawal volumes reported for 

water source

Non-public water-supply 

withdrawal greater than 

100,000 gallons per day

715 Million gallons 

per day

Daily volume Annual data Withdrawal volumes reported 

as sum of volumes from 

aggregated withdrawal sources

Non-public water-supply 

withdrawal greater than 

100,000 gallons per day used 

for cranberry production

1,028 Area cultivated, 

in square 

miles

Acres Annual data Withdrawal volumes reported 

as sum of volumes from 

aggregated withdrawal sources

Ground-water discharge greater 

than 10,000 gallons per day

204 Gallons per day Maximum daily 

discharge

Monthly data Withdrawal volumes reported for 

water source

National Pollutant Discharge 

Elimination System (NPDES) 

surface-water discharge

854 Million gallons 

per day or 

gallons per 

day 

Annual average, 

30-day average, 

monthly average, 

daily average, 

rolling average, 

weekly average

Monthly data Withdrawal volumes reported for 

water source
Streamflow Adjusted for Groundwater and Surface-Water Withdrawals and Discharges 25

0.25

0.20

0.15

0.10

0.05

0

January

February

March

April

May

June

July

August

September

October

NovemberDecember

FRACTION OF ANNUAL WITHDRAWALS

0.25

0.20

0.15

0.10

0.05

0

A Groundwater withdrawals

B Surface-water withdrawals

EXPLANATION

Mean

Median

25th percentile

75th percentile

Values above the upper limit 

or below the lower limit

Upper limit (75th percentile + 1.5 * 

(75th percentile − 25th percentile))

Lower limit (25th percentile + 1.5 * 

(75th percentile − 25th percentile))

Median line

Mean line

Figure 13. Distribution of the monthly fraction of the total annual withdrawal volumes for (A) groundwater and (B) surface-water 

public-water-supply withdrawals in Massachusetts.

for groundwater and surface-water withdrawals. These patterns were computed using a sample of towns across Massachusetts that had source-level electronically available monthly 

volumes (table 8). Selected towns had either all groundwater 

(25 towns) or all surface-water ( 6 towns) withdrawal volumes 

for the periods shown in table 8. Monthly volumes for a town 

were divided by the total annual withdrawal volume to obtain 

the fraction of annual water withdrawal from the groundwater or surface-water sources in each month. For towns with 

groundwater withdrawals, average monthly fractions vary 

between the summer and winter months (fig. 13A). For towns 

with surface-water withdrawals, average monthly fractions do 

not vary substantially, even in the summer months (fig. 13B). 

The demand curves used in the MA SYE tool are the median 

values of the monthly demand fractions in each month (fig. 

13). After disaggregating withdrawal volumes to monthly 

volumes using one of the three characteristic demand patterns, the MA SYE computes daily water-use values from 

the monthly values by dividing the monthly volumes by the 

number of days in each respective month.

Use of the STRMDEPL Program

Several assumptions are made about the withdrawal and 

discharge volumes when using the MA SYE tool, including 

a steady-state condition between a groundwater withdrawal 

or discharge and streamflow. For the steady-state condition, 
26 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

it is assumed that there are no time-lag effects of groundwater 

withdrawals or discharges on streamflow. For some groundwater withdrawal and discharge locations, this may be a reasonable assumption; however, for other groundwater withdrawal 

and discharge locations this assumption may not hold. 

To account for time-lag effects, users have the option 

of applying the program STMDEPL (Barlow, 2000) to 

account for the effects of the aquifer on streamflow depletion or augmentation. The STMDEPL program requires three 

parameters: (1) the transmissivity of the aquifer, T, in units 

of square length per time, (2) the storativity of the aquifer, 

S, a dimensionless quantity, and (3) the distance between the 

withdrawal or discharge location and the nearest surface-water 

body within the same basin, in length units. As input to the 

STRMDEPL program, the transmissivity (T) and storativity 

(S) are combined and entered as a single parameter, known as 

diffusivity (S/T).

For the purposes of the MA SYE, it was not practical 

to assign diffusivity values to each of the 4,250 groundwater 

withdrawal and discharge locations because of the time and 

effort involved, and because, for many locations, the diffusivity value is unknown. Furthermore, time-lag effects are likely 

to be negligible for groundwater withdrawals and discharges 

located in close proximity to a surface-water body; therefore, 

populating diffusivity values for these locations would not 

be useful. To understand the relation between proximity and 

time-lag effects on streamflow, a simple sensitivity experiment using STRMDEPL was performed. STRMDEPL was 

used to simulate the streamflow depletion for a broad range 

of diffusivities and distances between a hypothetical groundwater-withdrawal location and the nearest surface-water body 

(fig. 14). For distances less than 250 feet, streamflow depletion 

is about equal to the withdrawal rate from the well, and the 

time-lag effects of the withdrawal on streamflow are negligible 

(fig. 14).

Diffusivity values are not available in the statewide 

database, but distances between groundwater withdrawal and 

discharge locations and the nearest surface-water body are 

provided in the MA SYE tool. Approximately one-half of 

the groundwater withdrawal and discharge locations in the 

statewide database are within 250 feet of the nearest surfacewater body. The ArcHydro raindrop tool (Maidment, 2002) 

was used to identify the nearest surface-water body (stream or 

lake) within the contributing basin. The raindrop tool traces 

the surface path of a drop of water on the landscape to the 

receiving surface-water body. Once the nearest surface-water 

body was identified, the perpendicular distance between the 

withdrawal or discharge location and the surface-water body 

was computed. Distances between groundwater discharge or 

withdrawal sources and the nearest surface-water body have 

been pre-calculated for 3,029 locations, and these distances are 

stored in the spatially referenced database. 

Table 8. Source of water withdrawals, towns, and years of 

monthly data used to determine characteristic demand curves 

for public water supply groundwater and surface–water 

withdrawals in Massachusetts.

Source of water 

withdrawal Town Years of monthly data

Surface water Ashburnham 1993–2000

Gardner 1993–2000

Lynnfield 1994–1999

Wakefield 1994–1999

Winchendon 1996–2003

Worcester 1996–2001

Groundwater Acton 2000–2004

Auburn 1996–2001

Bellingham 1996–2001

Blackstone 1996–2003

Boylston 1996–2001

Byfield 1993–2001

Douglas 1996–2001

Georgetown 1990–2001

Grafton 1996–2001

Hopedale 1996–2001

Hopkinton 1996–1999

Mendon 1996–2001

Millbury 1996–2001

Millville 1996–2001

Natick 1996–2003

North Attleboro 1996–2001

Northbridge 1996–2001

Rowley 1995–2000

Shrewsbury 1996–2001

Sutton 1996–2001

Templeton 1993–2000

Upton 1996–2001

Uxbridge 1993–1998

Whitinsville 1998–2001

Wrentham 1996–2001
Calculation of Sustainable Yields Using the Massachusetts Sustainable-Yield Estimator (MA SYE) Tool 27

Estimation of Streamflow when 

Groundwater and Surface-Water 

Divides are not Coincident

It is assumed when using the MA SYE tool that the contributing basin to the user-selected stream location has coincident groundwater and surface-water divides. This assumption 

is true for a large portion of Massachusetts; however, for many 

areas in southeastern Massachusetts, groundwater and surfacewater divides differ. For these areas, existing, calibrated 

groundwater-flow models (Masterson and others, 2009; Walter 

and others, 2004; Walter and Whelan, 2004) were used to 

simulate average monthly streamflows at fixed locations near 

the mouths of major streams (fig. 15). For each fixed location, 

withdrawals and discharges in the groundwater-flow model 

were removed to simulate unregulated, average monthly 

streamflow. A second set of average monthly streamflows also 

was simulated using present day (as specified in the respective 

reports) withdrawal and discharge volumes. In the MA SYE 

tool, users can select from one of the fixed stream locations 

in these areas for calculation of sustainable yield. Results are 

served to the user through the MA SYE tool user interface, as 

described in the MA SYE user’s manual located at 

http://pubs.usgs.gov/sir/2009/5227/.

Calculation of Sustainable Yields 

Using the Massachusetts SustainableYield Estimator (MA SYE) Tool

The MA SYE tool provides estimates of unregulated, 

daily mean streamflow and adjusted daily streamflows for 

groundwater and surface-water withdrawals and discharges. 

Users can quickly and easily compute the screening-level 

values of sustainable yield by specifying time-varying flow 

targets (the quantities of water to be left in the stream). The 

flow targets can be entered as monthly user-specified values 

in cubic feet per second, cubic feet per second per mile, or 

daily percentage of the unregulated streamflows to remain in 

the stream. These flow targets are then subtracted from the 

unregulated, daily streamflow to provide an estimate of the 

sustainable yield for the contributing basin at the location on 

the stream of interest. Calculations are based not only on userspecified flow targets but also on a user-specified time period 

between 1960 and 2004. 

Users can also adjust the unregulated, daily mean streamflow by subtracting and adding the reported groundwater and 

surface-water withdrawal and discharge volumes, respectively. 

The user can adjust each selected year of unregulated, daily 

mean streamflow by the withdrawal and discharge volumes 

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

5,000 10,000 15,000 20,000 25,000 30,000 35,000

DIFFUSIVITY, IN FEET SQUARED PER DAY 

STREAMFLOW DEPLETON, 

AS FRACTION OF WITHDRAWAL 

10

250

500

750

1,000

Distance between withdrawal 

location and stream, in feet

Figure 14. Streamflow depletion estimated by the STRMDEPL program for a range of diffusivity values and distances between a 

hypothetical withdrawal location and stream (STRMDEPL program from Barlow, 2000).
28 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts Base from U.S. Geological Survey, DLG, 1:2,000,000, 2005 Massachusetts State Plane projection, North American Datum 1983 

0 20 KILOMETERS 100 20 MILES 10

#

Lakes and pondsMassachusetts townsRivers and streamsLocation where streamflowis simulated

EXPLANATION

Eel River

Red Brook

West Brook

Town Brook

Jones River

Indian Creek

Beaver Brook

Agawam River Wankinco River

Weweantic River

Red River

Red Brook

Hawes Run

Quaker Run

Little River Childs River

Bourne River

Backus River

Herring River

Santuit River

Mashpee River

Pocasset River

Phlashes Brook

Swan Pond Inlet

Nye Pond Outlet Long Pond Outlet

Long Pond

Outlet

Squeteague Brook

Johns Pond Outlet

Hoxie Pond Outlet

Coonamesset

River

Seymour Pond Outlet

Hinckley Pond Outlet

Herring River Inlet

Lower Mill Pond Outlet

Upper Mill Pond Outlet

Coonamesset

Pond Outlet

Upper Shawme Pond Outlet

Quashnet River

Santuit Pond Outlet Mashpee Pond Outlet

Marston Mills River

Lower Shawme Pond Outlet

BUZZARDS

BAY

CAPE COD

BAY

ATLANTIC OCEAN

MASSACHUSETTS

41°40'

70°40'

42°00'

70°00'

Figure 15. Locations in Massachusetts near the mouths of major streams for which unregulated and regulated streamflows were simulated using a groundwater-flow model because groundwater and surface-water divides are not coincident.
Limitations 29

reported for a particular year from 2000 through 2004 or 

by an average year. Results of the unregulated and adjusted 

streamflows, as well as the user-specified flow targets, are 

summarized on a two-page report that graphically displays 

the unregulated and adjusted streamflows along with the flow 

targets for the user-specified time period. Average, monthly 

unregulated streamflow values are calculated and compared 

to the flow targets. General information about the calculation 

of the unregulated and adjusted streamflows also is provided 

in the summary report, such as the physical and climate basin 

characteristics, reference streamgage used to compute the 

unregulated streamflows, and the number of withdrawal and 

discharge locations in the basin.

The MA SYE tool was designed as a desktop application 

that employs the Environmental Systems Research Institute, 

Inc. (ESRI) ArcMap GIS software (Environmental Systems 

Research Institute, Inc., 2009) coupled with Microsoft Excel 

and Access, commonly used and widely available spreadsheet 

and database programs, respectively. Available options are

• Select the period of analysis, 

• Select an average or single year of withdrawal and discharge volumes to adjust the unregulated streamflow,

• Select a different reference streamgage,

• Edit withdrawal and discharge volumes for any wateruse point within the basin,

• Apply STRMDEPL (Barlow, 2000) to a groundwater 

withdrawal or discharge volume,

• Add or edit aquifer properties used in the computation 

of streamflow depletion,

• Add a volume or percent of total withdrawals returned 

to the basin from septic-system discharge,

• Enter custom flow targets or choose from a predefined 

list of targets, and 

• Export results to text files compatible with the Indicators of Hydrologic Alteration (IHA) (The Nature 

Conservancy, 2005) tool and the National Hydrologic 

Assessment Tool (NAHAT) (Hendrickson and others, 

2006), which allow for the computation of over 151 

streamflow statistics. Unregulated and adjusted streamflows can be readily output to these programs for a 

comparison of a wide variety of flow statistics.

Once a user selects the location on a stream of interest from the MA SYE GIS user interface, a spreadsheet 

template guides the user through the remaining functions 

of the MA SYE tool. All related files needed to use the 

MA SYE along with a complete user’s manual with installation instructions for the MA SYE tool is available at 

http://pubs.usgs.gov/sir/2009/5227/.

Limitations

There are several limitations to the use of the MA SYE 

tool for estimating unregulated, daily mean streamflow time 

series. In particular, the use of the regression equations is 

limited to the range of basin characteristics used to develop 

the regression equations (fig. 5). The MA SYE tool provides 

warnings for all basin characteristics with values outside the 

range for which the regression equations were developed. 

Spatial correlation between streamflows could be accommodated through a generalized least-squares approach, but that 

is beyond the scope of this report. Prediction and confidence 

intervals associated with estimates of unregulated, daily mean 

streamflows could be used to make comparisons using existing methods to estimate unregulated streamflow at ungaged 

sites or to determine whether significant differences exist 

between estimated unregulated and regulated streamflows. 

The three components— (1) regression equations, (2) reference-streamgage selection criteria, and (3) the assumption of 

equivalent exceedence probabilities on the same day—all contribute to the uncertainty associated with MA SYE estimates 

of unregulated, daily mean streamflows; however, there does 

not currently exist a theoretical framework from which prediction or confidence intervals for the MA SYE-estimated daily 

streamflows can be derived. A lack of theoretical framework 

for error documentation also limits the understanding of, and 

ability to model, the unregulated, daily mean FDC. 

Estimates of adjusted, daily mean streamflow have 

several important limitations. Adjusted streamflow estimates 

consider only withdrawal and discharge locations that are part 

of the statewide water-use database. Limitations of the quality 

and resolution of the statewide database affect the estimates of 

adjusted streamflow. The use of a constant daily withdrawal 

pattern for non-public-water-supply withdrawal volumes does 

not take into account the seasonal withdrawals, such as golf 

course watering, which will lead to underestimation of the 

effects of withdrawals during the summer low-flow period. 

The MA SYE tool addresses these data quality and resolution 

limitations by allowing the user to override reported withdrawal and discharge volumes in the statewide database and 

provide more detailed information.

A change in withdrawal or discharge volumes at one location may have an affect on withdrawal or discharge volumes 

at other locations in the basin. For example, an increase in a 

withdrawal volume at one location might result in increases in 

the discharge volume at other locations within the basin. Additionally, if monthly data are redistributed within a particular 

year, no warnings are provided if the new annual total dischage or withdrawal volume differs from the annual volume 

reported in the MA SYE water-use database.

Adjusted streamflow estimates do not account for the 

effects of impoundments; septic-system discharge; private 

domestic withdrawals; non-public-water-supply withdrawals 

of less than 100,000 gallons per day; and impervious area, 
30 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

which can affect streamflow. To address the limitation of 

septic-system discharge, the MA SYE allows the user to enter 

a percentage of total withdrawals that is returned to the basin 

or a volume that is added to the adjusted streamflow. Withdrawals from surface-water reservoirs are directly subtracted 

from the unregulated streamflows, and the storage effects 

of reservoirs are not included in the adjusted-streamflow 

estimates. Users have the option of removing surface-water 

reservoirs from the adjusted-streamflow calculations by choosing to ignore the withdrawal location, which entirely removes 

the effects of these withdrawals on the adjusted-streamflow 

values.

The MA SYE tool does not contain data on withdrawal 

and discharge volumes for locations outside of Massachusetts. Therefore, if a user-selected point on a stream has a 

contributing area outside of Massachusetts, the MA SYE tool 

warns the user that the adjusted streamflows will not include 

the withdrawal and discharge volumes located outside of 

Massachusetts. An updated version of STRMDEPL, termed 

“STMDEPL08” (Reeves, 2008) has been developed to address 

some of the simplifying assumptions in STRMDEPL; however 

STMDEPL08 has not been incorporated into the MA SYE 

tool.

The MA SYE tool is unable to estimate streamflow for 

locations on the main stems of the Connecticut and Merrimack 

Rivers because large portions of these drainage basins are outside of Massachusetts and the methods developed for the MA 

SYE tool do include streamgages or basin characteristics for 

the northern portions of these basins. Furthermore, basin characteristics for these basins cannot presently be summarized in 

a consistent manner and are outside the scope of the MA SYE 

tool. If a user clicks on the main stems of the Connecticut and 

Merrimack Rivers, the MA SYE tool delineates a drainage 

basin but displays a message that the MA SYE tool is unable 

to continue.

Summary

To quantify the sustainable yield of a basin—the unregulated, daily mean streamflow less some user-specified flow 

targets–at ungaged sites in Massachusetts, the U.S. Geological 

Survey, in cooperation with the Massachusetts Department of 

Environmental Protection (MassDEP), developed the Massachusetts Sustainable-Yield-Estimator (MA SYE) tool. The MA 

SYE tool is designed to be a flexible, statewide, screeninglevel decision-support system to compute the sustainable yield 

of a basin and to evaluate the effects of water withdrawals 

and discharges on streamflow. The MA SYE tool estimates 

both the unregulated, daily mean streamflow and streamflow 

adjusted for water withdrawals and discharges within the basin 

for a user-selected location on a stream in Massachusetts.

The MA SYE tool estimates an unregulated, daily mean 

time series of streamflow for a 44-year period (October 1, 

1960, through September 30, 2004) using statistically based 

methods. First, streamflow quantiles are calculated at six 

exceedence probabilities by regressing streamflow against 

readily measureable climate and physical basin characteristics. Next streamflow quantiles at 11 additional exceedence 

probabilities are solved by use of regression to quantify the 

structure of the streamflow quantiles. A continuous daily flowduration curve (FDC) at the ungaged site is then obtained by 

log-linear interpolation among the 17 regression-estimated 

streamflow quantiles. Lastly, a reference streamgage is used to 

transform the FDC into daily mean streamflow. The reference 

streamgage is determined from the estimated correlation of the 

logarithms of the daily streamflows between the ungaged location and one of 66 potential reference streamgages.

The MA SYE tool estimates an adjusted daily mean time 

series of streamflow at ungaged sites from reported withdrawal and discharge volumes at locations within the basin. 

Withdrawal and discharge volumes used in the MA SYE tool 

are obtained from a spatially referenced statewide database 

of groundwater and surface-water withdrawals, groundwater 

discharges, and National Pollutant Discharge Elimination 

System (NPDES) surface-water discharges. For a user-selected 

basin, groundwater and surface-water withdrawal and discharge volumes are subtracted and added, respectively, from 

the unregulated, daily streamflow. Time-varying groundwater 

withdrawals and discharges can be optionally modified using 

an analytical program, STRMDEPL, which simulates the 

effects of the aquifer properties on the timing and magnitude 

of streamflow alteration.

For the MA SYE tool, it is necessary that groundwater 

and surface-water divides are coincident for the contributing 

basin; however, in southeastern Massachusetts and Cape Cod, 

groundwater-flow models have shown that the surface and 

subsurface divides differ. In the MA SYE tool, streamflows are 

obtained from existing groundwater-flow model simulations 

for these areas, which computed streamflows with and without 

inclusion of the groundwater and surface-water withdrawals 

in the model simulations. For the MA SYE tool, it is assumed 

that groundwater and surface-water divides are coincident for 

all other areas in Massachusetts.

The user interface of the MA SYE tool was designed 

as a desktop application that employs Environmental Systems Research Institute, Inc. ArcMap software, a geographic 

information system, coupled with Microsoft Excel and Access. 

On the basis of user-defined constraints such as existing water 

withdrawals and discharges in the basin and flow targets, the 

MA SYE tool estimates the sustainable yield of the basin by 

subtracting the flow targets from the unregulated, daily mean 

streamflow. The MA SYE tool supplies the user with graphical 

and numerical comparisons of the unregulated and adjusted 

streamflows relative to any user-specified flow targets. Users 

can compute the water availability in the basin for any number 

of water-management scenarios (by changing the withdrawal 

and discharge volumes, the time period of analysis, or flow 

targets). Results of each water-management scenario are summarized in a two-page report that displays the unregulated and 

adjusted streamflow hydrographs for the user-specified time 
References Cited 31

period and presents selected streamflow statistics calculated 

from these hydrographs in tabular format.

Acknowledgments

The authors thank Paul Blain, Thomas Lamonte, Kari 

Winfield, and Robert Hames of the Massachusetts Department 

of Environmental Protection for their reviews of the report 

and decision-support tool and Phillip Zarriello, David Armstrong, and Gardner Bent of the U.S. Geological Survey for 

their participation in the technical reviews of the project. The 

authors also thank Jery Stedinger of Cornell University for 

providing technical insights on the estimation of streamflow at 

ungaged sites; Amy Lavoie of the U.S. Environmental Protection Agency for providing insights into the way withdrawals 

vary temporally and spatially across Massachusetts; Leslie 

DeSimone, John Masterson, and Jeff Barbaro of the U.S. 

Geological Survey for providing detailed water-use data; Mark 

Smith and Colin Apse of The Nature Conservancy for their 

helpful comments related to the decision-support tool; and 

Nigel Pickering of the Charles River Watershed Association 

and Christian Jacques at MassGIS for initiating the development of, and contributions to, a statewide database of permitted groundwater and surface-water withdrawals and discharges 

in Massachusetts.

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Tables 1–2
34 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts Table 1. Summary of 66 U.S. Geological Survey streamgages, number of streamflow observations, and the periods of observed, mean daily streamflow record, New England study area.—Continued [REG, used to develop regression equations; REF, used as a reference streamgage; VAL, used in validation of methods; SS, used in Massachusetts StreamStats (Ries and Friesz, 2000) comparison; ¥, site not used in Armstrong and others (2008) to classify streamflows in Massachusetts.] Streamgage number Streamgage name Four-letter abbreviation for streamgage Number of daily streamflow values Period of observed streamflow record Use of streamgage in analysis 01106000 Adamsville Brook at Adamsville, RI ADAM 14,105 October 1, 1940–September 30, 1978; February 17, 1987–September 30, 1987 REG, REF 01171800 Bassett Brook near North Hampton, MA BASS 4,352 November 1, 1962–September 30, 1974 REF, SS 010965852 Beaver Brook at North Pelham, NH BBNH 7,234 October 1, 1986–July 24, 2006 REF 01084500 Beard Brook near Hillsboro, NH BEAR 9,131 October 1, 1945–September 30, 1970 REG, REF 01198500 Blackberry River at Canaan, CT BLAB 8,130 October 1, 1949–October 20, 1971 REG, REF 01126600 Blackwell Brook near Brooklyn, CT BLAC 4,754 October 1, 1963–October 5, 1976 REF 01111500 Branch River at Forestdale, RI BRAN 23,719 January 24, 1940–December 31, 2004 REG, REF, VAL 01117468 Beaver River near Usquepaug, RI BRRI 11,556 December 4, 1974–July 24, 2006 REF 01188000¥ Burlington Brook near Burlington, CT BURL 26,756 October 1, 1931–December 31, 2004 REG, REF, VAL 01174900 Cadwell Creek near Belchertown, MA CADW 13,229 July 13, 1961–September 30, 1997 REG, REF, SS 01155000 Cold River at Drewsville, NH COLD 13,979 June 23, 1940–September 30, 1978 REG, REF 01082000 Contocook River at Peterborough, NH CONT 12,962 July 7, 1945–September 30, 1977; October 1, 2001–December 31, 2004 REG, REF 01107000¥ Dorchester Brook near Brockton, MA DORC 4,360 October 24, 1962–September 30, 1974 REF, SS 01331400 Dry Brook near Adams, MA DRYB 4,352 November 1, 1962–September 30, 1974 REF, SS 01194500 East Branch Eightmile River near North Lyme, CT EBEM 17,265 October 1, 1937–October 6, 1981; October 1, 2001–December 31, 2004 REG, REF 01100700 East Meadow River near Haverhill, MA EMEA 4,355 October 29, 1962–September 30, 1974 REF, SS 01170100 Green River near Colrain, MA GREC 14,177 October 1, 1967–July 24, 2006 REF, SS 01333000 Green River at Williamstown, MA GREW 20,192 September 20, 1949–December 31, 2004 REG, REF, VAL, SS
Table 1. Summary of 66 U.S. Geological Survey streamgages 35

Table 1. Summary of 66 U.S. Geological Survey streamgages, number of streamflow observations, and the periods of observed, mean daily streamflow record, New England study area.—Continued[REG, used to develop regression equations; REF, used as a reference streamgage; VAL, used in validation of methods; SS, used in Massachusetts StreamStats (Ries and Friesz, 2000) comparison; ¥, site not used in Armstrong and others (2008) to classify streamflows in Massachusetts.]

Streamgage 

number Streamgage name

Four-letter 

abbreviation for 

streamgage

Number of daily 

streamflow values Period of observed streamflow record Use of streamgage in analysis

01198000 Green River near Great Barrington, MA GRGB 8,227 October 1, 1951–September 30, 1971; 

March 24, 1994–September 30, 1996

REG, REF, SS

01120000 Hop Brook near Columbia, CT HOPC 14,250 October 1, 1932–October 6, 1971 REG, REF01174000 Hop Brook near New Salem, MA HOPM 12,735 November 19, 1947–September 30, 1982 REG, REF, SS01187300 Hubbard River near West Hartland, CT HUBB 16,587 August 4, 1959–December 31, 2004 REG, REF, VAL01105730 Indian Head River at Hanover, MA IHEA 14,625 July 8, 1966–July 24, 2006 REF, SS01195100 Indian River near Clinton, CT INDI 9,029 November 4, 1981–July 24, 2006 REF01123000 Little River near Hanover, CT LITT 19,451 October 1, 1951–December 31, 2004 REG, REF, VAL01171500 Mill River at Northampton, MA MILL 24,151 November 18, 1938–December 31, 2004 REG, REF, VAL, SS01165500 Moss Brook at Wendell Depot, MA MOSS 24,470 June 4, 1909–October 16, 1909; 

April 25, 1910–June 30, 1910; July 19, 1910–August 27, 1910; June 1, 1916–September 30, 1982

REG, REF, SS

01121000 Mount Hope River near Warrenville, CT MOUN 23,468 October 1, 1940–December 31, 2004 REG, REF, VAL01097300 Nashoba Brook near Acton, MA NASH 15,135 July 26, 1963–December 31, 2004 REG, REF, SS01332000 North Branch Hoosic River at North Adams, MA NBHO 21,651 June 22, 1931–September 30, 1990 REG, REF, SS01111300 Nipmuc River near Harrisville, RI NIPM 14,185 March 1, 1964–September 30, 1991; 

October 1, 1993–December 31, 2004

REG, REF

01115630 Nooseneck River at Nooseneck, RI NOOS 6,519 November 26, 1963–September 30, 1981 REF01169000 North River at Shattuckville, MA NORT 23,761 December 13, 1939–December 31, 2004 REG, REF, VAL, SS01105600 Old Swamp River near South Weymouth, MA OLDS 14,676 May 20, 1966–July 24, 2006 REF, SS01073000 Oyster River near Durham, NH OYST 25,585 December 15, 1934–December 31, 2004 REG, REF, VAL
36 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts Table 1. Summary of 66 U.S. Geological Survey streamgages, number of streamflow observations, and the periods of observed, mean daily streamflow record, New England study area.—Continued [REG, used to develop regression equations; REF, used as a reference streamgage; VAL, used in validation of methods; SS, used in Massachusetts StreamStats (Ries and Friesz, 2000) comparison; ¥, site not used in Armstrong and others (2008) to classify streamflows in Massachusetts.] Streamgage number Streamgage name Four-letter abbreviation for streamgage Number of daily streamflow values Period of observed streamflow record Use of streamgage in analysis 01118500 Pawtucket River at Westerly, RI PAWE 23,411 November 27, 1940–December 31, 2004 REG, REF, VAL 01117500 Pawcatuck River at Wood River Junction, RI PAWR 23,401 December 7, 1940–December 31, 2004 REG, REF, VAL 01115098 Peeptoad Brook at Elmdale Road near Westerly, RI PEEP 4,118 June 23, 1994–September 30, 2005 REF 01118300 Pendleton Hill Brook near Clarks Falls, CT PEND 16,894 October 1, 1958–December 31, 2004 REG, REF, VAL 01115187 Ponaganset River at South Foster, RI PONA 4,508 March 22, 1994–July 24, 2006 REF 01162500 Priest Brook near Winchendeon, MA PRIE 31,677 May 25, 1916–September 30, 1917; July 18, 1918–August 31, 1935; October 1, 1936–December 31, 2004 REG, REF, VAL, SS 01176000 Quaboag River at West Brimfield, MA QUAB 33,738 August 19, 1912–December 31, 2004 REG, REF, VAL, SS 01199050 Salmon Creek at Lime Rock, CT SALC 15,798 October 1, 1961–December 31, 2004 REG, REF 01193500 Salmon River near East Hampton, CT SALR 27,851 October 1, 1928–December 31, 2004 REG, REF, VAL 01154000 Saxtons River at Saxtons River, VT SAXT 16,753 June 20, 1940–September 30, 1982; June 1, 2001–December 31, 2004 REG, REF 01091000 South Branch Piscataquog River near Goffstown, NH SBPI 13,945 July 27, 1940–September 30, 1978 REG, REF 01175670 Sevenmile River near Spencer, MA SEVE 16,102 December 1, 1960–December 31, 2004 REG, REF, SS 01089000 Soucook River near Concord, NH SOU1 13,149 October 1, 1951–September 30, 1987 REG, REF 01169900 South River near Conway, MA SOUT 13,880 January 1, 1967–December 31, 2004 REF, SS 01096000 Squannacook River near West Groton, MA SQUA 20,181 October 1, 1949–December 31, 2004 REG, REF, VAL, SS 01184100 Stony Brook near West Suffield, CT STCT 9,210 May 7, 1981–July 24, 2006 REF 01095220 Stillwater River near Sterling, MA STIL 4,476 April 22, 1994–July 24, 2006 REF, SS
Table 1. Summary of 66 U.S. Geological Survey streamgages 37

Table 1. Summary of 66 U.S. Geological Survey streamgages, number of streamflow observations, and the periods of observed, mean daily streamflow record, New England study area.—Continued[REG, used to develop regression equations; REF, used as a reference streamgage; VAL, used in validation of methods; SS, used in Massachusetts StreamStats (Ries and Friesz, 2000) comparison; ¥, site not used in Armstrong and others (2008) to classify streamflows in Massachusetts.]

Streamgage 

number Streamgage name

Four-letter 

abbreviation for 

streamgage

Number of daily 

streamflow values Period of observed streamflow record Use of streamgage in analysis

01093800 Stony Brook tributary near Temple, NH STON 15,129 May 1, 1963–September 30, 2004 REG, REF01180000¥ Sykes Brook at Knightville, MA SYKE 10,621 June 20, 1945–July 18, 1974 REG, REF, SS01161500 Tarbell Brook near Winchendon, MA TARB 24,572 May 29, 1916–September 6, 1983 REG, REF, SS01108000 Taunton River near Bridgewater, MA TAUN 21,160 October 1, 1929–April 23, 1976; 

April 19, 1985–May 31, 1988; October 1, 1996–December 31, 2004

REG, REF, SS

01200000 Ten Mile River, CT TENM 25,820 October 1, 1930–April 4, 1988; 

April 12, 1988–Febraury 7, 1989; November 2, 1990–December 19, 1990; October 1, 1991–September 30, 1999; October 1, 2000–December 31, 2004

REG, REF

01187400 Valley Brook near West Hartland, CT VALL 11,688 October 1, 1940–September 30, 1972 REG, REF01109000 Wading River near Norton, MA WADI 29,069 June 1, 1925–December 31, 2004 REG, REF, VAL, SS01086000¥ Warner River at Davisville, NH WARN 15,433 October 1, 1939–September 30, 1978; 

October 1, 2001–December 31, 2004

REG, REF

01109200¥ West Branch Palmer River near Rehoboth, MA WBPA 4,357 October 27, 1962–September 30, 1974 REF, SS01174565 West Branch Swift River near Shutesbury, MA WBSW 4,529 November 8, 1983–September 30, 1985; 

April 1, 1995–September 30, 2005

REF, SS

01085800 West Branch Warner River near Bradford, NH WBWA 15,473 May 22, 1962–September 30, 2004 REG, REF01181000 West Branch Westfield at Huntington, MA WBWE 25,325 September 1, 1935–December 31, 2004 REG, REF, VAL, SS01117800 Wood River near Arcadia, RI WOOA 14,589 January 23, 1964–September 30, 1981; 

October 1, 1982–December 31, 2004

REG, REF

01118000 Wood River Hope Valley, RI WOOH 23,306 March 12, 1941–December 31, 2004 REG, REF
38 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Table 2. Streamflow quantiles corresponding to 17 exceedence probabilities estimated from the observed period of record at 47 U.S. 

Geological Survey streamgages, New England study area.

[**, observed streamflow record does not contain enough observations to estimate; QX, streamflow value at the X divided by 100 exceedence probability]

USGS 

streamgage 

number

Streamgage name Code

Estimated 

Q99.9938, in 

cubic feet 

per second

Estimated 

Q99, in 

cubic feet 

per second

Estimated 

Q95, in 

cubic feet 

per second

Estimated 

Q90, in 

cubic feet 

per second

01106000 Adamsville Brook at Adamsville, RI ADAM ** 0.07 0.13 0.3

01084500 Beard Brook near Hillsboro, NH BEAR ** 1.2 2.7 4.3

01198500 Blackberry River at Canaan, CT BLAB ** 3.4 6.1 8.7

01111500 Branch River at Forestdale, RI BRAN 2.6 13 20 26

01188000 Burlington Brook near Burlington, CT BURL 0.17 0.65 1 1.3

01174900 Cadwell Creek near Belchertown, MA CADW ** 0.11 0.21 0.34

01155000 Cold River at Drewsville, NH COLD ** 4.7 7.3 9.9

01082000 Contocook River at Peterborough, NH CONT ** 6 11 15

01194500 East Branch Eightmile River near North Lyme, CT EBEM 0.03 0.75 2 3.4

01333000 Green River at Williamstown, MA GREW 3.3 4.9 8.1 11

01198000 Green River near Great Barrington, MA GRGB ** 3.3 4.8 6.6

01120000 Hop Brook near Columbia, CT HOPC ** 4.3 7.8 11

01174000 Hop Brook near New Salem, MA HOPM ** 0.02 0.14 0.32

01187300 Hubbard River near West Hartland, CT HUBB 0.19 0.59 1.5 2.5

01123000 Little River near Hanover, CT LITT 3.4 4.9 7.2 9

01171500 Mill River at Northampton, MA MILL 3.8 6.4 10 14

01165500 Moss Brook at Wendell Depot, MA MOSS 0.3 0.7 1.2 1.7

01121000 Mount Hope River near Warrenville, CT MOUN 0.2 1.2 2.6 4.1

01097300 Nashoba Brook near Acton, MA NASH ** 0.14 0.6 1.2

01332000 North Branch Hoosic River at North Adams, MA NBHO 3.2 5.7 8.5 11

01111300 Nipmuc River near Harrisville, RI NIPM ** 0.39 1 1.7

01169000 North River at Shattuckville, MA NORT 5.2 9.4 16 21

01073000 Oyster River near Durham, NH OYST 0.02 0.54 0.85 1.2

01118500 Pawtucket River at Westerly, RI PAWE 25 68 98 127

01117500 Pawcatuck River at Wood River Junction, RI PAWR 15 28 40 50

01118300 Pendleton Hill Brook near Clarks Falls, CT PEND 0.01 0.07 0.31 0.59

01162500 Priest Brook near Winchendeon, MA PRIE 0.1 0.6 1.5 2.4

01176000 Quaboag River at West Brimfield, MA QUAB 5 16 29 40

01199050 Salmon Creek at Lime Rock, CT SALC ** 3.9 6.5 8.8

01193500 Salmon River near East Hampton, CT SALR 1.1 6.8 13 19

01154000 Saxtons River at Saxtons River, VT SAXT 2.4 4.8 7.7 11

01091000 South Branch Piscataquog River near Goffstown, NH SBPI ** 4.5 8.3 12

01175670 Sevenmile River near Spencer, MA SEVE ** 0.25 0.57 1.1

01089000 Soucook River near Concord, NH SOU1 ** 4 7.2 10

01096000 Squannacook River near West Groton, MA SQUA 0.53 6.4 11 15

01093800 Stony Brook tributary near Temple, NH STON ** 0.14 0.28 0.45

01180000 Sykes Brook at Knightville, MA SYKE ** 0.07 0.12 0.17

01161500 Tarbell Brook near Winchendon, MA TARB 0.15 1.1 2.3 3.3

01108000 Taunton River near Bridgewater, MA TAUN 9 28 52 69

01200000 Ten Mile River, CT TENM 7.2 15 26 36

01187400 Valley Brook near West Hartland, CT VALL ** 0.3 0.5 0.8

01109000 Wading River near Norton, MA WADI 0.38 2.4 4.6 6.8

01086000 Warner River at Davisville, NH WARN ** 6.2 12 18

01085800 West Branch Warner River near Bradford, NH WBWA ** 0.21 0.41 0.66

01181000 West Branch Westfield at Huntington, MA WBWE 3.4 7.2 12 18

01117800 Wood River near Arcadia, RI WOOA ** 7.7 12 15

01118000 Wood River Hope Valley, RI WOOH 10 19 28 35
Table 2. Streamflow quantiles 39

Table 2. Streamflow quantiles corresponding to 17 exceedence probabilities estimated from the observed period of record at 47 U.S. 

Geological Survey streamgages, New England study area.—Continued

[**, observed streamflow record does not contain enough observations to estimate; QX, streamflow value at the X divided by 100 exceedence probability]

USGS 

streamgage 

number

Streamgage name Code

Estimated 

Q85, in 

cubic feet 

per second

Estimated 

Q80, in 

cubic feet 

per second

Estimated 

Q70, in 

cubic feet 

per second

Estimated 

Q60, in 

cubic feet 

per second

01106000 Adamsville Brook at Adamsville, RI ADAM 0.64 1.2 3.3 6.4

01084500 Beard Brook near Hillsboro, NH BEAR 6.2 8.6 17 27

01198500 Blackberry River at Canaan, CT BLAB 11 14 21 30

01111500 Branch River at Forestdale, RI BRAN 32 38 60 87

01188000 Burlington Brook near Burlington, CT BURL 1.7 2 2.8 3.8

01174900 Cadwell Creek near Belchertown, MA CADW 0.52 0.72 1.3 2.1

01155000 Cold River at Drewsville, NH COLD 14 17 27 37

01082000 Contocook River at Peterborough, NH CONT 19 23 36 50

01194500 East Branch Eightmile River near North Lyme, CT EBEM 5 6.9 12 20

01333000 Green River at Williamstown, MA GREW 15 19 28 38

01198000 Green River near Great Barrington, MA GRGB 9 12 20 32

01120000 Hop Brook near Columbia, CT HOPC 15 21 36 52

01174000 Hop Brook near New Salem, MA HOPM 0.58 0.81 1.6 2.5

01187300 Hubbard River near West Hartland, CT HUBB 3.7 5.1 9 15

01123000 Little River near Hanover, CT LITT 11 13 19 26

01171500 Mill River at Northampton, MA MILL 17 21 30 42

01165500 Moss Brook at Wendell Depot, MA MOSS 2.3 3 4.8 7.4

01121000 Mount Hope River near Warrenville, CT MOUN 6 8.2 14 22

01097300 Nashoba Brook near Acton, MA NASH 2 3 5.1 7.7

01332000 North Branch Hoosic River at North Adams, MA NBHO 14 19 27 37

01111300 Nipmuc River near Harrisville, RI NIPM 2.6 3.8 7.4 12

01169000 North River at Shattuckville, MA NORT 27 34 50 70

01073000 Oyster River near Durham, NH OYST 1.6 2.1 3.8 6.4

01118500 Pawtucket River at Westerly, RI PAWE 155 182 248 338

01117500 Pawcatuck River at Wood River Junction, RI PAWR 59 70 92 122

01118300 Pendleton Hill Brook near Clarks Falls, CT PEND 0.92 1.3 2.5 4

01162500 Priest Brook near Winchendeon, MA PRIE 3.6 5 8.4 12

01176000 Quaboag River at West Brimfield, MA QUAB 52 64 92 126

01199050 Salmon Creek at Lime Rock, CT SALC 11 14 19 25

01193500 Salmon River near East Hampton, CT SALR 25 32 55 83

01154000 Saxtons River at Saxtons River, VT SAXT 14 18 28 40

01091000 South Branch Piscataquog River near Goffstown, NH SBPI 16 22 36 60

01175670 Sevenmile River near Spencer, MA SEVE 1.8 2.6 4.3 6.6

01089000 Soucook River near Concord, NH SOU1 13 17 28 43

01096000 Squannacook River near West Groton, MA SQUA 18 22 32 47

01093800 Stony Brook tributary near Temple, NH STON 0.66 0.9 1.6 2.5

01180000 Sykes Brook at Knightville, MA SYKE 0.23 0.3 0.6 0.91

01161500 Tarbell Brook near Winchendon, MA TARB 4.5 5.7 8.7 12

01108000 Taunton River near Bridgewater, MA TAUN 87 107 170 253

01200000 Ten Mile River, CT TENM 48 60 95 142

01187400 Valley Brook near West Hartland, CT VALL 1 1.6 3 5

01109000 Wading River near Norton, MA WADI 9.3 12 21 34

01086000 Warner River at Davisville, NH WARN 24 32 52 78

01085800 West Branch Warner River near Bradford, NH WBWA 0.92 1.3 2.3 3.6

01181000 West Branch Westfield at Huntington, MA WBWE 24 31 48 72

01117800 Wood River near Arcadia, RI WOOA 19 23 32 45

01118000 Wood River Hope Valley, RI WOOH 41 49 67 92
40 The Massachusetts Sustainable-Yield Estimator: A decision-support tool to assess water availability in Massachusetts

Table 2. Streamflow quantiles corresponding to 17 exceedence probabilities estimated from the observed period of record at 47 U.S. 

Geological Survey streamgages, New England study area.—Continued

[**, observed streamflow record does not contain enough observations to estimate; QX, streamflow value at the X divided by 100 exceedence probability]

USGS 

streamgage 

number

Streamgage name Code

Estimated 

Q50, in 

cubic feet 

per second

Estimated 

Q40, in 

cubic feet 

per second

Estimated 

Q30, in 

cubic feet 

per second

Estimated 

Q20, in 

cubic feet 

per second

01106000 Adamsville Brook at Adamsville, RI ADAM 9.2 12 16 22

01084500 Beard Brook near Hillsboro, NH BEAR 41 58 84 130

01198500 Blackberry River at Canaan, CT BLAB 40 52 71 101

01111500 Branch River at Forestdale, RI BRAN 119 156 196 256

01188000 Burlington Brook near Burlington, CT BURL 5 6.3 8 11

01174900 Cadwell Creek near Belchertown, MA CADW 3 4 5.2 7

01155000 Cold River at Drewsville, NH COLD 52 71 105 165

01082000 Contocook River at Peterborough, NH CONT 69 90 120 170

01194500 East Branch Eightmile River near North Lyme, CT EBEM 29 39 50 67

01333000 Green River at Williamstown, MA GREW 50 66 87 121

01198000 Green River near Great Barrington, MA GRGB 44 62 88 122

01120000 Hop Brook near Columbia, CT HOPC 73 100 133 183

01174000 Hop Brook near New Salem, MA HOPM 3.6 4.9 6.6 9.2

01187300 Hubbard River near West Hartland, CT HUBB 20 27 37 55

01123000 Little River near Hanover, CT LITT 36 47 60 80

01171500 Mill River at Northampton, MA MILL 57 76 100 140

01165500 Moss Brook at Wendell Depot, MA MOSS 10 14 20 30

01121000 Mount Hope River near Warrenville, CT MOUN 31 42 56 75

01097300 Nashoba Brook near Acton, MA NASH 11 16 22 31

01332000 North Branch Hoosic River at North Adams, MA NBHO 48 64 87 125

01111300 Nipmuc River near Harrisville, RI NIPM 18 25 34 45

01169000 North River at Shattuckville, MA NORT 94 126 172 249

01073000 Oyster River near Durham, NH OYST 9.8 14 19 29

01118500 Pawtucket River at Westerly, RI PAWE 448 561 703 892

01117500 Pawcatuck River at Wood River Junction, RI PAWR 155 192 237 296

01118300 Pendleton Hill Brook near Clarks Falls, CT PEND 5.7 7.5 9.8 13

01162500 Priest Brook near Winchendeon, MA PRIE 17 23 33 49

01176000 Quaboag River at West Brimfield, MA QUAB 167 221 295 391

01199050 Salmon Creek at Lime Rock, CT SALC 32 41 53 70

01193500 Salmon River near East Hampton, CT SALR 116 156 204 273

01154000 Saxtons River at Saxtons River, VT SAXT 56 76 109 164

01091000 South Branch Piscataquog River near Goffstown, NH SBPI 88 120 163 240

01175670 Sevenmile River near Spencer, MA SEVE 9.2 12 17 23

01089000 Soucook River near Concord, NH SOU1 60 82 112 165

01096000 Squannacook River near West Groton, MA SQUA 66 89 118 162

01093800 Stony Brook tributary near Temple, NH STON 3.5 4.8 6.8 10

01180000 Sykes Brook at Knightville, MA SYKE 1.3 1.8 2.6 3.8

01161500 Tarbell Brook near Winchendon, MA TARB 17 22 30 43

01108000 Taunton River near Bridgewater, MA TAUN 349 455 583 750

01200000 Ten Mile River, CT TENM 195 260 343 463

01187400 Valley Brook near West Hartland, CT VALL 7.2 9.6 13 19

01109000 Wading River near Norton, MA WADI 50 68 89 117

01086000 Warner River at Davisville, NH WARN 119 168 243 364

01085800 West Branch Warner River near Bradford, NH WBWA 5 6.9 10 15

01181000 West Branch Westfield at Huntington, MA WBWE 99 132 178 258

01117800 Wood River near Arcadia, RI WOOA 58 74 92 115

01118000 Wood River Hope Valley, RI WOOH 119 151 187 233
Table 2. Streamflow quantiles 41

Table 2. Streamflow quantiles corresponding to 17 exceedence probabilities estimated from the observed period of record at 47 U.S. 

Geological Survey streamgages, New England study area.—Continued

[**, observed streamflow record does not contain enough observations to estimate; QX, streamflow value at the X divided by 100 exceedence probability]

USGS 

streamgage 

number

Streamgage name Code

Estimated 

Q15, in 

cubic feet 

per second

Estimated 

Q10, in 

cubic feet 

per second

Estimated 

Q5, in 

cubic feet 

per second

Estimated 

Q1, in 

cubic feet 

per second

Estimated 

Q006, in 

cubic feet 

per second

01106000 Adamsville Brook at Adamsville, RI ADAM 26 34 47 95 **

01084500 Beard Brook near Hillsboro, NH BEAR 170 230 364 777 **

01198500 Blackberry River at Canaan, CT BLAB 122 160 240 556 **

01111500 Branch River at Forestdale, RI BRAN 304 377 514 951 3,870

01188000 Burlington Brook near Burlington, CT BURL 13 17 26 61 477

01174900 Cadwell Creek near Belchertown, MA CADW 8.6 11 17 40 **

01155000 Cold River at Drewsville, NH COLD 215 293 447 933 **

01082000 Contocook River at Peterborough, NH CONT 210 272 393 730 **

01194500 East Branch Eightmile River near North Lyme, CT EBEM 81 101 139 287 1,490

01333000 Green River at Williamstown, MA GREW 146 187 271 525 2,100

01198000 Green River near Great Barrington, MA GRGB 150 195 281 566 **

01120000 Hop Brook near Columbia, CT HOPC 223 283 400 785 **

01174000 Hop Brook near New Salem, MA HOPM 11 14 20 42 **

01187300 Hubbard River near West Hartland, CT HUBB 70 94 148 350 1,310

01123000 Little River near Hanover, CT LITT 93 115 167 360 1,870

01171500 Mill River at Northampton, MA MILL 172 219 319 674 3,440

01165500 Moss Brook at Wendell Depot, MA MOSS 37 48 69 140 786

01121000 Mount Hope River near Warrenville, CT MOUN 90 113 165 355 2,250

01097300 Nashoba Brook near Acton, MA NASH 38 49 66 121 **

01332000 North Branch Hoosic River at North Adams, MA NBHO 160 220 348 753 4,080

01111300 Nipmuc River near Harrisville, RI NIPM 53 67 98 200 **

01169000 North River at Shattuckville, MA NORT 318 428 672 1,460 7,580

01073000 Oyster River near Durham, NH OYST 36 47 70 138 681

01118500 Pawtucket River at Westerly, RI PAWE 1,020 1,200 1,490 2,180 5,940

01117500 Pawcatuck River at Wood River Junction, RI PAWR 340 395 487 702 1,780

01118300 Pendleton Hill Brook near Clarks Falls, CT PEND 15 19 26 50 251

01162500 Priest Brook near Winchendeon, MA PRIE 62 81 119 225 1,240

01176000 Quaboag River at West Brimfield, MA QUAB 458 551 713 1,130 7,540

01199050 Salmon Creek at Lime Rock, CT SALC 83 101 141 280 **

01193500 Salmon River near East Hampton, CT SALR 324 402 568 1,150 8,230

01154000 Saxtons River at Saxtons River, VT SAXT 215 290 450 954.6 3,340

01091000 South Branch Piscataquog River near Goffstown, NH SBPI 305 403 600 1,150 **

01175670 Sevenmile River near Spencer, MA SEVE 27 34 48 87 **

01089000 Soucook River near Concord, NH SOU1 207 275 405 765 **

01096000 Squannacook River near West Groton, MA SQUA 199 252 365 700 3,330

01093800 Stony Brook tributary near Temple, NH STON 13 17 26 57 **

01180000 Sykes Brook at Knightville, MA SYKE 4.7 6.2 9.3 19 **

01161500 Tarbell Brook near Winchendon, MA TARB 54 70 103 185 1,390

01108000 Taunton River near Bridgewater, MA TAUN 880 1,060 1,390 2,200 4,700

01200000 Ten Mile River, CT TENM 550 681 941 1,800 10,200

01187400 Valley Brook near West Hartland, CT VALL 24 30 51 109 **

01109000 Wading River near Norton, MA WADI 137 168 223 360 1140

01086000 Warner River at Davisville, NH WARN 457 590 866 1,620 **

01085800 West Branch Warner River near Bradford, NH WBWA 20 27 47 109 **

01181000 West Branch Westfield at Huntington, MA WBWE 328 440 675 1,530 9,800

01117800 Wood River near Arcadia, RI WOOA 131 155 197 319 **

01118000 Wood River Hope Valley, RI WOOH 265 314 401 650 2,040

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
Archfield and others—The Massachusetts Sustainable-Yield Estimator—Scientific Investigations Report 2009–5227