Methods for Estimating Low-Flow Statistics for Massachusetts Streams

Methods for Estimating Low-Flow
Statistics for Massachusetts Streams
By Kernell G. Ries, III, and Paul J. Friesz

Abstract                                                Regression equations were developed to estimate
                                                        the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-,
        Methods and computer software are               75-, 70-, 60-, and 50-percent duration flows; the
described in this report for determining flow-          7-day, 2-year and the 7-day, 10-year low flows;
duration, low-flow frequency statistics, and August     and the August median flow for ungaged sites in
median flows. These low-flow statistics can be          Massachusetts. Streamflow statistics and basin
estimated for unregulated streams in Mass-              characteristics for 87 to 133 streamgaging
achusetts using different methods depending on          stations and low-flow partial-record stations
whether the location of interest is at a stream-        were used to develop the equations. The stream-
gaging station, a low-flow partial-record station, or   gaging stations had from 2 to 81 years of record,
an ungaged site where no data are available. Low-       with a mean record length of 37 years. The
flow statistics for streamgaging stations can be        low-flow partial-record stations had from 8 to
estimated using standard U.S. Geological Survey         36 streamflow measurements, with a median of
methods described in the report.                        14 measurements.
        The MOVE.1 mathematical method and a
                                                               All basin characteristics were determined
graphical correlation method can be used to
                                                        from digital map data. The basin characteristics
estimate low-flow statistics for low-flow partial-
record stations. The MOVE.1 method is recom-            that were statistically significant in most of the
mended when the relation between measured               final regression equations were drainage area, the
flows at a partial-record station and daily mean        area of stratified-drift deposits per unit of stream
flows at a nearby, hydrologically similar stream-       length plus 0.1, mean basin slope, and an indicator
gaging station is linear, and the graphical method      variable that was 0 in the eastern region and 1 in
is recommended when the relation is curved.             the western region of Massachusetts.
Equations are presented for computing the                      The equations were developed by use of
variance and equivalent years of record for esti-       weighted-least-squares regression analyses, with
mates of low-flow statistics for low-flow partial-      weights assigned proportional to the years of
record stations when either a single or multiple        record and inversely proportional to the variances
index stations are used to determine the estimates.     of the streamflow statistics for the stations.
        The drainage-area ratio method or regres-       Standard errors of prediction ranged from 70.7 to
sion equations can be used to estimate low-flow         17.5 percent for the equations to predict the 7-day,
statistics for ungaged sites where no data are          10-year low flow and 50-percent duration flow,
available. The drainage-area ratio method is            respectively. The equations are not applicable for
generally as accurate as or more accurate than          use in the Southeast Coastal region of the State, or
regression estimates when the drainage-area ratio       where basin characteristics for the selected
for an ungaged site is between 0.3 and 1.5 times        ungaged site are outside the ranges of those for the
the drainage area of the index data-collection site.    stations used in the regression analyses.

                                                                                                   Abstract    1
A World Wide Web application was devel-                    and to provide estimates of the statistics for selected
oped that provides streamflow statistics for data-                locations on ungaged streams. These studies were done
collection stations from a data base and for                      in cooperation with the Massachusetts Department of
ungaged sites by measuring the necessary basin                    Environmental Management, Office of Water
characteristics for the site and solving the regres-              Resources (MOWR) and are referred to as the Basin
                                                                  Yield studies. The MOWR uses the streamflow statis-
sion equations. Output provided by the Web appli-
                                                                  tics to develop water-resources management plans for
cation for ungaged sites includes a map of the
                                                                  each of the 27 major river basins in Massachusetts
drainage-basin boundary determined for the site,                  (fig. 1) and provides the streamflow statistics to other
the measured basin characteristics, the estimated                 State and local agencies to support their decision-
streamflow statistics, and 90-percent prediction                  making processes.
intervals for the estimates.                                             Five other reports have been published as a result
       An equation is provided for combining                      of the Basin Yield studies (Ries, 1994a, 1994b, 1997,
regression and correlation estimates to obtain                    1999, 2000). The first three reports describe studies
improved estimates of the streamflow statistics                   done to develop regression equations for use in
for low-flow partial-record stations. An equation                 estimating low-flow statistics for ungaged sites. The
is also provided for combining regression and                     fourth report describes and provides data for a network
drainage-area ratio estimates to obtain improved                  of 148 low-flow partial-record (LFPR) stations that was
estimates of the streamflow statistics for ungaged                established in 1988 at the beginning of the first Basin
                                                                  Yield study and continued through 1996, during the
                                                                  third Basin Yield study. The fifth report describes a
                                                                  World Wide Web application that enables users to
INTRODUCTION                                                      select sites of interest on streams and then to obtain
                                                                  estimates of streamflow statistics and basin characteris-
        Low-flow statistics indicate the probable                 tics for the sites.
availability of water in streams during times when
conflicts between water supply and demand are most                Purpose and Scope
likely to arise. Because of this, low-flow statistics are
needed by Federal, State, regional, and local agencies                    This report, the final report of the Basin Yield
for water-use planning, management, and regulatory                study series, presents methods that can be used to
activities. These activities include (1) developing               estimate low-flow statistics for streams in Massachu-
environmentally sound river-basin management plans,               setts, and describes the analyses done to develop and
(2) siting and permitting new water withdrawals,                  evaluate the methods. Methods are presented for esti-
interbasin transfers, and effluent discharges,                    mating statistics for locations where various amounts
(3) determining minimum streamflow thresholds for                 of streamflow data are available and for locations
maintenance of aquatic biota, and (4) land-use                    where no data are available. Previously documented
planning and regulation. Low-flow statistics are also             and generally accepted methods are presented for
needed by commercial, industrial, and hydroelectric               estimating low-flow statistics for locations where
facilities to determine availability of water for water           streamflow data are available. Analyses done to
supply, waste discharge, and power generation.                    develop and evaluate methods for estimating stream-
        Low-flow statistics can be calculated from                flow statistics for locations where no data are available
streamflow data collected at locations where the U.S.             are described. The physical setting of Massachusetts,
Geological Survey (USGS) operates data-collection                 as it relates to the occurrence of low streamflows, is
stations, but it is not possible to operate stations at           also briefly described.
every site where the statistics are needed. Because of                    Equations that can be used to estimate the 99-,
this, methods are needed for estimating low-flow                  98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent
statistics for streams for which no data are available.           duration flows; the 7-day, 2-year and the 7-day, 10-year
        In 1988, the USGS began the first of three                low flows; and the August median flow are presented
studies to develop and evaluate methods for estimating            here. An evaluation of the accuracy of the equations
low-flow statistics for ungaged Massachusetts streams             and limitations for their use is also provided, along

2   Methods for Estimating Low-Flow Statistics for Massachusetts Streams
with an example application. The equations provide         estimated streamflow statistics and basin characteris-
estimates of low-flow statistics for streams with          tics were provided. The equations provided in the
natural flow conditions, and supersede those from          second report superseded those from the first report.
earlier reports.                                                   The third Basin Yield report (Ries, 1997) pro-
                                                           vides an equation for estimating August median
                                                           streamflows. This statistic is used by the U.S. Fish and
Previous Studies
                                                           Wildlife Service (1981) and some State agencies as the
       Low-flow statistics for most streamgaging           minimum summertime streamflow required for mainte-
                                                           nance of habitat for aquatic biota in New England. The
stations and many LFPR stations in Massachusetts
                                                           report also provides estimates of August median
were published by the USGS in a series of gazetteers
                                                           streamflows for sites on unregulated streams in Massa-
published as Water-Resources Investigations Reports,
                                                           chusetts where the values could be determined from
in a series of Hydrologic Atlas reports (see U.S.
                                                           available data, and describes how the August median
Geological Survey, 1987, for a complete listing of both
                                                           streamflow per square mile of drainage area varies
series), and in a series of ground-water assessment
                                                           throughout the State.
reports published as Water-Resources Investigations
                                                                   The LFPR network described in the fourth Basin
Reports (Olimpio and DeLima, 1984; Lapham, 1988;
                                                           Yield report (Ries, 1999a) was established to provide
Myette and Simcox, 1992; DeLima, 1991; Hanson and          additional data for use in the regression analyses and to
Lapham, 1992; Persky, 1993; Bratton and Parker, 1995;      provide a better understanding of the physical
Bent, 1995; Friesz, 1996; Klinger, 1996). Statistics       mechanisms that cause streamflow to vary in time and
provided in this report supersede those from the           space. The report provides streamflow measurements
previous reports.                                          collected systematically at the 148 LFPR stations in the
       Studies that used regression analysis to            network between 1989 and 1996, and also includes any
regionalize low-flow frequency statistics in the           historical streamflow measurements available for the
northeastern United States include those for               stations. In addition, the report provides estimated
Connecticut (Cervione, 1982), central New England          streamflow statistics, basin characteristics, location and
(Wandle and Randall, 1994), Pennsylvania and New           other descriptive information for each of the stations.
York (Ku and others, 1975), Maine (Parker, 1977),          The estimated streamflow statistics include the 99-,
Massachusetts, New Hampshire, Rhode Island and             98-, 97-, 95-, 93-, 90-, 85-, 80-, 75-, 70-, 65-, 60-, 55-,
Vermont (Johnson, 1970), southeastern Massachusetts        and 50-percent duration flows; the 7-day, 2-year and
(Tasker, 1972), and Massachusetts (Male and Ogawa,         the 7-day, 10-year low flows; and the August median
1982; Vogel and Kroll, 1990; Risley, 1994). Studies        flow. Basin characteristics measured include drainage
that regionalized flow-duration statistics include those   area; total stream length; mean basin slope; area of
for Connecticut (Thomas, 1966), New Hampshire              surficial stratified drift; area of wetlands; area of water
(Dingman, 1978), southeastern Massachusetts (Tasker,       bodies; and mean, maximum, and minimum basin
                                                           elevation. The basin characteristics were measured for
1972), and Massachusetts (Male and Ogawa, 1982;
                                                           the stations from digital maps by use of a Geographic
Fennessey and Vogel, 1990; Ries, 1994a, 1994b).
                                                           Information System (GIS).
       Reports for the first two Basin Yield studies               The fifth Basin Yield report (Ries and others,
(Ries, 1994a, 1994b) provided equations for estimating     2000), a fact sheet, describes a World Wide Web
the 99-, 98-, and 95-percent duration streamflows and      application that includes (1) a mapping tool that allows
also provided estimates of the streamflow statistics and   users to specify locations on streams where low-flow
measured basin characteristics for selected ungaged        statistics are needed, (2) a database that includes
streams in eastern Massachusetts river basins. The         streamflow statistics, basin characteristics, location,
equations were developed for these studies by use of       and descriptive information for all data-collection
regression analyses, which statistically relate the        stations in Massachusetts for which streamflow
streamflow statistics to measured basin characteristics    statistics were published previously, and (3) an
for the stations used in the analyses. The studies         automated GIS procedure that determines the required
differed in the methods of regression analysis used to     basin characteristics and solves the regression
develop the equations, the number of stations included     equations provided in this report to estimate low-flow
in the analyses (more stations were used in the second     statistics for the user-selected site. The World Wide
study), and the locations of ungaged streams for which     Web application is further described later in this report.

                                                                                                       Introduction   3
73°00´                                       72°30´                                    72°00´

                                                                01332000                                          01167200
                                     01333100                                                                                    01164300            01162500
                                                     01332900                                 01170100
                                                                      01168300                                               01165090
                                                     1                                         01169000
                                                01331400                01168400            01168650
                                                                                                                               01166105      7
                                         01359967          01331380                                                                          01163298
                                                                                   01169600                                        01165250
                                                    011197015                                                                                     01162900
                    42°30´                                       01178200                                                 01174000
                                                                                                             01170575                    01174050
                                                                         01178300 01169800

                                                                 01179900                                                                   8        01172810

                                        2                                                                6                 01174565

                                                01197140                           01178490
                                   01197300                            4
                                                                01180650          Western Region                               01174900
                                                                           01180000                    01171500
                                                    01197180                                                                                    01175710
                                   01197230                                                       01171800
                                                                                                                    01171947    01173420 01175850
                                                            01180800                                                      01173450                   01175670
                                     01198000                              01181000                                                              01175890
                               01198060                     5                                                      01176780
                                                                                 01183210                                  01176200
                         1              01198160
                                                                                                               01177360 01176300          01123140               10
                                                           01186300         01187400                 01184282

       Figure 1. Locations of streamgaging stations and low-flow partial-record stations used to develop equations for
       estimating low-flow statistics for ungaged Massachusetts streams and locations of streamgaging stations outside
       Massachusetts used for correlation with low-flow partial-record stations, and boundaries of the 27 major river
       basins and three hydrologic regions in the State.

4   Methods for Estimating Low-Flow Statistics for Massachusetts Streams


                                    71°30´                                01100700

          NEW HAMPSHIRE                                                                        01101100
                                                                13                     16

            01095928 01096505

             01096000          01096504                              01100608

             01094396                                          15

        01094340                                                                     01102053

                   11                   01097280


                                                                 01103015                            Massachusetts
            01095380       14a 01096855 14b
                                                                     BOSTON                              Bay
             Eastern Region                                    01103435
                                                    01103445                    01105582
                                                     20         01104960 01105575        19c         01105830
                                                                     01104980                   01105600
                        01111142                                      01104840
                   12                    01103253
                                                           19b                       01105568          01105820
                          01111200                                     01105270
                                         01112190                                                    21a                                                 70°00´

                     9                                         01108600              01106460        01105861
                         RHODE ISLAND
                                                      27                          25
                                                        01109200                                                              70°30´
                                                          01109225                                                011058839
                                                                                01109090 011059106                               Southeast
                                                                                                     24                                             22
                                                                            01105937 01105930

                                                                              01105935                                             Region
                                                        41°30´                                                                          Nantucket
0                                                                                 50 MILES

0                                              50 KILOMETERS

    Figure 1. Locations of streamgaging stations and low-flow partial-record stations used to develop equations for
    estimating low-flow statistics for ungaged Massachusetts streams, locations of streamgaging stations outside
    Massachusetts used for correlation with low-flow partial-record stations, and boundaries of the 27 major river
    basins and three hydrologic regions in the State—Continued.

                                                                                                                                                    Introduction   5
Physical Setting                                                  surrounded by upland areas underlain by till with
                                                                  exposed bedrock outcrops. Till is an unsorted glacial
        Massachusetts encompasses an area of 8,093 mi2            deposit that consists of material ranging in size from
in the northeastern United States. State environmental            clay to large boulders. Till yields little water to adjacent
agencies divide Massachusetts into 27 major river                 streams in comparison to yields from coarse-grained
basins for planning and regulatory purposes (fig. 1).             stratified drift. As a result, during summertime, streams
Some of these designated river basins are actually part           in till areas tend to have less flow per unit of drainage
of larger river basins that extend into neighboring               area than streams in areas of coarse-grain stratified
states. The Millers, Deerfield, Chicopee, and Westfield           drift, and some small streams in till areas may go dry
River Basins are part of the Connecticut River Basin.             (Wandle and Randall, 1994).
The Nashua, Concord, and Shawsheen River Basins are                       Ries (1997) defined three hydrologic regions in
part of the Merrimack River Basin. Several designated             Massachusetts based on differences in August median
basins in coastal areas of Massachusetts were                     streamflow per square mile of drainage area (fig. 1).
comprised by grouping land areas drained by multiple              These regions were the Western, the Eastern, and the
streams that discharge to the same receiving body of              Southeast Coastal regions. The Western region was
salt water, such as Boston Harbor and Buzzards Bay.               defined by all major basins that drain to the
        The climate of Massachusetts is humid.                    Connecticut River plus those west of the Connecticut
Precipitation is distributed fairly evenly throughout the         River Basin (basins 1 through 8 on fig. 1). The Eastern
State and throughout the year, and averages about                 region was defined as all basins east of the Western
45 in. annually. Average annual temperatures range                region except Cape Cod, the Islands, the southern part
from 50˚F in coastal areas to 45˚F in the western                 of the South Coastal Basin, and the eastern part of the
mountains. Average monthly temperatures range from                Buzzards Bay Basin, which define the Southeast
about 30˚F in February to about 71˚F in July in coastal           Coastal region. August median flows per square mile
areas, and from about 20˚F in January to about 68˚F in            were significantly higher, on average, in the Western
July in the western parts of the State (U.S. Commerce             region than in the Eastern region.
Department, National Oceanic and Atmospheric                              Differences in August median streamflow per
Administration, 1989). Average evapotranspiration                 unit area between the Western and Eastern regions
ranges from 19 in. in southeastern Massachusetts to               appeared to be more a function of climate and
22 in. in the western Mountains (Randall, 1996).                  physiography than surficial geology. Percentages of
        Several physical characteristics vary from east to        stratified-drift deposits were generally lower in the
west in Massachusetts. Elevations range from sea level            Western region than in the Eastern region, but August
along the coast in eastern Massachusetts to almost                median streamflows were higher in the Western region
3,500 ft in the western mountains. Basin relief and               than in the Eastern region. The higher low flows per
mean basin slope, which are highly related, also tend to          unit area in the Western region than in the Eastern
increase from east to west in Massachusetts. The extent           region is likely explained by the combination of lower
of lakes, ponds, and wetlands, as a proportion of total           mean annual temperatures, higher mean elevations,
basin area, generally decreases from east to west in              higher relief, higher precipitation, lower evapo-
Massachusetts. The extent of coarse-grained stratified            transpiration, and lower areal percentages of wetlands
drift, as a proportion of total basin area, also generally        and water bodies in western Massachusetts than in
decreases from east to west.                                      eastern Massachusetts.
        Except during and for a short time after storms,                  The Southeast Coastal region is underlain
summertime flow in Massachusetts streams comes                    entirely by stratified-drift deposits, which are mostly
from ground water discharged by aquifers in                       coarse grained. Surface-water drainage boundaries in
unconsolidated deposits adjacent to the streams. This             this region often do not coincide with contributing
discharge is termed base flow. High-yielding aquifers             areas of ground water for streams in the area. In
usually are in stratified drift, sand and gravel deposits         addition, dam regulations, diversions, or controls by
that are located primarily along the valley floors of             cranberry bogs affect most streams in the region. As a
inland river basins and in coastal areas of southeastern          result, insufficient data were available to define the
Massachusetts. The stratified-drift deposits usually are          natural flow characteristics of streams in this region.

6   Methods for Estimating Low-Flow Statistics for Massachusetts Streams
Acknowledgments                                            as part of the three Basin Yield projects. Data for many
                                                           of the network stations are used in the analyses
        The authors would like to thank the MOWR           described here.
for its long-term support of this work. Thanks also                Miscellaneous-measurement stations usually are
to Aleda Freeman, Christian Jacqz, and the rest of         established to obtain streamflow data for hydrologic
the staff of MassGIS, to John Rader, formerly of           studies of limited regional extent and short duration.
MassGIS and USGS, and to Peter Steeves of USGS.            The number and streamflow range of measurements
These people worked together to prepare numerous           made at these stations varies depending on the
digital data layers needed for measuring the basin         objectives of the study. High-flow as well as low-flow
characteristics used in the regression analyses, and to    measurements commonly are made at miscellaneous-
develop methods for automating measurements of the         measurement stations. Low-flow statistics can be
basin characteristics. The authors would also like to      estimated for miscellaneous-measurement stations
express their appreciation to the many other USGS          when the number and range of low-flow measurements
employees who assisted with collection and analysis        collected at the stations approximates the requirements
of streamflow data, measurements of basin                  for measurements at a LFPR station.
characteristics, and preparation of this report.                   Many stations in Massachusetts have been
                                                           operated at different times as both LFPR stations and
                                                           miscellaneous-measurement stations. Methods used in
ESTIMATING METHODS FOR                                     this study to estimate low-flow statistics for LFPR
DATA-COLLECTION STATIONS                                   stations and miscellaneous-measurement stations were
                                                           the same and are described in the section “Low-flow
                                                           statistics for low-flow partial-record stations.” Because
        The USGS operates three types of data-
                                                           the data and analysis methods were the same, both
collection stations for which low-flow statistics can
                                                           station types are referred to as LFPR stations for the
be estimated. These include (1) streamgaging stations,
                                                           remainder of this report.
(2) low-flow partial record (or LFPR) stations, and
(3) miscellaneous-measurement stations. Methods
used to estimate streamflow statistics at data-
                                                           Low-Flow Statistics for
collection stations differ depending on the type of
                                                           Streamgaging Stations
statistic and on the type of station. Continuous records
of streamflow are obtained at streamgaging stations.
                                                                  Daily mean flows for all complete climatic
Streamflow statistics generally are determined directly
                                                           years of record are used to determine flow-duration
from the records for these stations using methods
                                                           and low-flow frequency statistics for streamgaging
described in the section “Low-flow statistics for          stations. A climatic year begins on April 1 of the year
streamgaging stations.”                                    noted and ends on March 31 of the following year.
       Low-flow partial-record and miscellaneous-          Daily mean flows for all complete Augusts for the
measurement stations are often established where           period of record are used to determine August median
streamflow information is needed, but either (1) it is     flows. Daily mean flows for USGS streamgaging
not physically or economically feasible to continuously    stations in Massachusetts can be obtained by
monitor streamflows at the location, or (2) the amount     downloading them from the World Wide Web address:
or accuracy of the streamflow information needed does, or by
not require continuous monitoring at the location. At      contacting the Massachusetts–Rhode Island District
LFPR stations, a series of streamflow measurements         information officer at the address provided on the
are made during independent low-flow periods when          back of the title page of this report.
all or nearly all streamflow is from ground-water                 The USGS has established standard methods
discharge. Usually about 10 low-flow measurements          for estimating flow-duration (Searcy, 1959) and
are obtained systematically over a period of years. Ries   low-flow frequency statistics (Riggs, 1972) for
(1999) summarized a network of LFPR stations               streamgaging stations. The computer software
operated in Massachusetts during 1989 through 1996         programs IOWDM, ANNIE, and SWSTAT can be used

                                                                      Estimating Methods for Data-Collection Stations   7
to format input data, manage and display data, and                statistics and probabilities of recurrence (recurrence
complete the statistical analyses, respectively, required         intervals) of individual annual values can be analyzed.
to determine flow-duration and low-flow frequency                 A disadvantage of the approach is that generally at
statistics for streamgaging stations (Lumb and others,            least 10 years of record are needed to determine the
1990; Flynn and others, 1995). These programs can be              statistics with reasonable confidence.
downloaded from the World Wide Web address:
                                                                  Low-Flow Frequency Statistics
Flow-Duration Statistics                                                 Low-flow frequency statistics are determined for
        A flow-duration curve is a graphical                      streamgaging stations from series of annual minimum
representation of the percentage of time streamflows              mean flows for a given number of days. The statistics
for a given time step (usually daily) are equaled or              can be computed for any combination of days of
exceeded over a specified period (usually the                     minimum mean flow and years of recurrence. For
complete period of record) at a stream site. Flow-                example, the 7-day, 10-year low flow is determined
duration curves usually are constructed by first ranking          from the annual series of minimum 7-day mean flows
all of the daily mean discharges for the period of record         at a station. The mean flow for each consecutive 7-day
at a gaging station from largest to smallest, next                period is computed from the daily records, and the
computing the probability for each value of being                 lowest mean value for each year represents that year in
equaled or exceeded, then plotting the discharges                 the annual series. The 7-day minimum mean flows are
against their associated exceedance probabilities                 usually fit to a log-Pearson Type III distribution to
(Loaiciga, 1989, p. 82). The daily mean discharges
                                                                  determine the recurrence interval for an individual
are not fit to an assumed distribution. Flow-duration
                                                                  7-day minimum mean flow (Riggs, 1972), although
analysis can be done by use of the USGS software
described above or by use of most commercially                    other researchers sometimes have used other
available statistical software.                                   distributions (Vogel and Kroll, 1989). The value that
                                                                  recurs, on average, once in 10 years is the 7-day,
        Flow-duration statistics are points along a flow-
                                                                  10-year low flow. The 7-day, 10-year low flow is used
duration curve. For example, the 99-percent duration
streamflow is equaled or exceeded 99 percent of the               by the U.S. Environmental Protection Agency and by
time, whereas the 50-percent duration streamflow is               many state and local agencies to regulate waste-water
equaled or exceeded 50 percent of the time. Strictly              discharges into surface waters.
interpreted, flow-duration statistics reflect only the                    The USGS has, to a large extent, automated the
period for which they are calculated; however, when               process of determining low-flow frequency statistics
the period of record used to compute the statistics is            for streamgaging stations. The computer program
sufficiently long, the statistics often are used as an            SWSTAT (Lumb and others, 1990, p. 141) determines
indicator of probable future conditions (Searcy, 1959).
                                                                  the annual series of minimum mean flows, ranks them,
        Vogel and Fennessey (1994) presented an                   fits them to a log-Pearson type III distribution, and
alternative method for determining flow-duration                  plots the resulting line of fit through the annual values.
statistics that indicate future conditions. This method           How well the data fit the distribution, and the ultimate
requires determining flow-duration statistics for each
                                                                  low-flow frequency values to be used, are left to the
individual year of record at a gaging station, then using
                                                                  judgment of the individual hydrologist. Usually at least
the median of the annual values to represent the long-
term flow-duration statistics. Median annual flow-                10 years of record are needed to determine the statistics
duration statistics determined by use of this alternative         with reasonable confidence. The annual series should
method tend to be higher than those calculated from the           be checked for trends, and corrected if necessary,
entire period of record by use of the traditional                 before the log-Pearson analysis is done. The output
approach. The advantages of using the alternative                 from the analysis should be checked for outliers, and
method over the traditional approach are that                     corrected if necessary, before the frequency curve is
confidence intervals can easily be attached to the                finalized.

8   Methods for Estimating Low-Flow Statistics for Massachusetts Streams
August Median Flows                                          to extend the records for short-term streamgaging
                                                             stations to estimate flow-duration statistics that reflect
       August median flows at streamgaging stations
                                                             long-term conditions for the stations. These methods
can be determined by two methods. The U.S. Fish and
                                                             are similar to those described below for estimating
Wildlife Service (USFWS) (1981) recommends
                                                             low-flow statistics for LFPR stations.
calculating August median streamflows as the median
value of the annual series of August monthly mean
streamflows for the period of record at a gaging station.    Low-Flow Statistics for
The USFWS uses the August median flow calculated in
                                                             Low-Flow Partial-Record Stations
this manner as the minimum streamflow required for
summertime maintenance of habitat for biota in New                  Streamflow statistics for LFPR stations are
England streams.                                             estimated by relating the low streamflow measurements
       Charles Ritzi and Associates (1987) suggested         made at the stations to daily mean discharges on the
calculating August median flows as the median of the         same days at nearby, hydrologically similar
daily mean flows for all complete Augusts during the         streamgaging stations. Lines or curves of correlation
period of record at a streamgaging station. Kulik            are developed between the same-day discharges at
(1990) and Ries (1997) also used this method for             the LFPR stations and the selected streamgaging
calculating August median flows. This method                 stations, and then the streamflow statistics for the
typically results in values of August median flows that      gaging stations are entered into the relations to
are somewhat lower than those determined by use of           determine the corresponding streamflow statistics for
the method suggested by the USFWS. The monthly               the LFPR stations. A mathematical correlation method
mean values used by the USFWS to calculate August            described by Hirsch (1982) is used when the relations
median flows tend to be skewed by infrequent storm           are linear. A graphical correlation method described
events that cause the monthly means to be larger than        by Riggs (1972) and Searcy (1959) is used when
the medians, thus “the median is a more useful statistic     the relations are nonlinear. These methods were
than the mean for describing the central tendency” of        recommended for use by the USGS Office of Surface
the daily data (Kulik, 1990).                                Water in Technical Memorandum No. 86.02, Low-
                                                             Flow Frequency Estimation at Partial-Record Sites,
Streamflow Statistics for                                    issued December 16, 1985. Both methods assume that
Streamgaging Stations with Short Records                     the relation between the discharges at the LFPR station
                                                             and the streamgaging station remains constant with
       Streamflow statistics are often needed for
                                                             time, thus the relation between the same-day flows can
streamgaging stations with short records that may not
                                                             be used to estimate streamflow statistics that represent
reflect long-term conditions, and thus may not be
                                                             long-term conditions.
useful as indicators of future conditions. Streamflow
                                                                    Medium- to high-range streamflow measure-
record extension or augmentation can be used to adjust
                                                             ments made at some LFPR stations can be useful for
the records for these stations to reflect a longer period.
                                                             estimating flow statistics near the median flow.
This is usually done by developing a relation between
                                                             Commonly, however, measurements made in these
the daily mean streamflows or the streamflow statistics
                                                             ranges need to be excluded from the analyses because
at the short-term station and the daily mean
                                                             the measurements were made at times when flow was
streamflows or the streamflow statistics for the same
                                                             rapidly changing, thus the measurements correlate
period at a nearby and hydrologically similar gaging
                                                             poorly with same-day mean flows at gaging stations.
station with a long record.
       Vogel and Kroll (1991) demonstrated the value
                                                             Mathematical Method
of augmenting streamflow records to obtain improved
estimates of low- and peak-flow frequency statistics                A mathematical record-extension method known
for streamgaging stations. They also described methods       as the Maintenance Of Variance Extension, Type 1
that can be used for augmenting records to estimate          (MOVE.1) method (Hirsch, 1982) can be used to
these statistics. Searcy (1959, p.12–14) and Ries            estimate streamflow statistics for LFPR stations when
(1994a, p. 21–22) described methods that can be used         the relation between the logarithms of the same-day

                                                                        Estimating Methods for Data-Collection Stations   9
discharges at the LFPR station and a nearby gaging                                                           Yˆ i = Y + ---- ( X i – X ) ,           (1)
station is linear. The method is applied by first
calculating logarithms-base 10 of the same-day flows
for the LFPR and gaging stations and graphing the                                             and then retransforming the estimates by
values to ascertain the linearity of the relation. The                                        exponentiating the values ( 10 Ŷ i ) to convert the
correlation coefficient is also computed as an indicator                                      estimates into their original units of measurement.
of linearity. If the relation appears linear, the MOVE.1
                                                                                                     The MOVE.1 relation between an LFPR station,
method is used; if not, a graphical method is used, as
explained below.                                                                              Hemlock Brook near Williamstown, Mass., and a
                                                                                              streamgaging station, Green River at Williamstown,
          When the graph of the data appears linear, the
                                                                                              Mass., is shown as an example in figure 2. The line
means (Y and X) and standard deviations (sy and sx) of
                                                                                              through the data points was determined by inserting the
the logarithms-base 10 of the same-day flows for the
LFPR and gaging stations and the logarithms-base 10                                           same-day flows for the gaging station into the MOVE.1
of the streamflow statistics (Xi) for the gaging station                                      equation as the Xi values to obtain estimated same-day
are calculated. Estimates of the streamflow statistics                                        flows for the LFPR station, then connecting the points
( Ŷ i ) for the LFPR station are obtained by inserting the                                   to illustrate how the MOVE.1 estimates fit the original
calculated values into the MOVE.1 equation:                                                   data.


                                                            CORRELATION COEFFICIENT = 0.974


                                                                                                                      SAME-DAY DISCHARGES
                                                                                                                      MOVE.1 RELATION

                                                      1                                       10                                             100

                                                          GREEN RIVER NEAR WILLIAMSTOWN, MASS. DISCHARGE, IN CUBIC FEET PER SECOND

         Figure 2. Example MOVE.1 relation between a low-flow partial-record station, Hemlock Brook near
         Williamstown, Mass., and a streamgaging station, Green River at Williamstown, Mass.

10   Methods for Estimating Low-Flow Statistics for Massachusetts Streams
Graphical Method                                                                               Combining Estimates Determined
                                                                                               from Multiple Index Sites
        The graphical method (Searcy, 1959; Riggs,
1972) is used when curvature is apparent in the plot of                                               Selection of individual gaging stations for
logarithms-base 10 of the same-day flows. The method                                           relation to a LFPR station is based on distance between
is applied by first plotting the original (non-log) values                                     the stations and similarity of basin characteristics
of the same-day flows on log-log paper and drawing a                                           between the stations. In Massachusetts, the measured
smooth curve through the plotted points that appears to                                        streamflows at a LFPR station usually will correlate
best fit the data. Next, the calculated streamflow                                             well with more than one gaging station. When this
statistics for the gaging station are entered into the
                                                                                               happens, MOVE.1 or graphical relations between a
curve of relation and corresponding values for the
                                                                                               given LFPR station and each of several gaging stations
LFPR station are read from the graph. Log-log plots
                                                                                               can be developed to estimate the streamflow statistics
sometimes have extreme curvature in the very low
                                                                                               for the LFPR station. This process results in multiple
end of the relation. Because of this, it is sometimes
                                                                                               estimates of the streamflow statistics for a single LFPR
necessary to replot the data on arithmetic paper to
                                                                                               station, when only a single best estimate is desired.
adequately define the relation in this range and to avoid
long downward extrapolations that would otherwise be                                                  Tasker (1975) stated that when independent
necessary with log-log plots.                                                                  multiple estimates of streamflow statistics are available
        The graphical relation between an LFPR station,                                        for a single station, the best estimate can be obtained
Hopping Brook near West Medway, Mass., and a                                                   by weighting each individual estimate by its variance
streamgaging station, West River near Uxbridge,                                                and averaging the weighted estimates. This final
Mass., is shown as an example in figure 3. The curve                                           weighted estimate is best because its variance is less
was fit through the data visually to minimize overall                                          than or equal to the variances of each of the
differences between the observed and fit values.                                               individual estimates.




                                                                                                              SAME-DAY DISCHARGES
                                                                                                              GRAPHICAL RELATION

                                                         1                                     10                                           100
                                                             GREEN RIVER NEAR WILLIAMSTOWN, MASS. DISCHARGE, IN CUBIC FEET PER SECOND

         Figure 3. Example graphical relation between a low-flow partial-record station, Hopping Brook near West
         Medway, Mass., and a streamgaging station, West River near Uxbridge, Mass.

                                                                                                         Estimating Methods for Data-Collection Stations   11
Calculated variances for each individual                                                    hydrologically similar gaging station. Modifications
estimate of the streamflow statistics for each LFPR                                                to the Hardison and Moss equation were needed to
station were needed to obtain the final best estimates                                             generalize its use for other streamflow statistics and to
for the stations. Variances were calculated by use of                                              allow for the MOVE.1 or graphical methods of line
the equation                                                                                       fitting to be used rather than the ordinary-least-squares
                                                                                                   method of line fitting. Assumptions for use of equation
          VR                              2              SE S, G 2 M                               2 are generalized from Hardison and Moss (1972):
 V S, U = ------ 1 + -------------- + -------------- +  --------------  --------------
                           1            z M
           M         M – 3 M – 3  s B, G   M – 3                                                 1. The true relation between the logarithms of the
                                              2                                                             base-flow measurements at the LFPR station
                                       + b V S, G ,                                          (2)            and the same-day mean streamflows at the
                                                                                                            gaging station is the same as the true relation
where:                                                                                                      between the logarithms of the data from which
  VS,U is the sample variance of the streamflow                                                             the low streamflow statistics are calculated. In
          statistic at the LFPR station, in log units;                                                      the case of the 7-day low-flow statistics, the
  VS,G is the sample variance of the streamflow                                                             data are calculated from an annual series of
          statistic at the gaging station, in log units;                                                    minimum 7-day mean flows. In the case of the
    VR is the variance about the MOVE.1 or graphical                                                        flow-duration and August median statistics, the
          line of relation;                                                                                 data are calculated from the daily mean flows.
    M is the number of base-flow measurements;                                                       2. The relation between the logarithms of the data
SES,G is the standard error of the streamflow statistic                                                     from which the low-flow statistics are
          at the gaging station, which equals the square                                                    calculated is the same as the relation between
          root of VS,G;                                                                                     the flow statistics for the stations.
     b is computed as r(sB,U/sB,G), where r is the
                                                                                                     3. The time-sampling errors in the streamflow
          correlation coefficient between the low
                                                                                                            statistics that are used to enter the regression
          streamflow measurements made at the LFPR
                                                                                                            equation are independent of the variation in the
          station and the same-day mean discharges at
                                                                                                            base-flow measurements used to define the
          the gaging station (the value of r can be set to
          1 when MOVE.1 is used to obtain the
          estimate), and sB,U is the standard deviation                                              4. The logarithms of the measured streamflows at
          of the logarithms-base 10 of the low                                                              the LFPR station and the same-day mean
          streamflow measurements made at the LFPR                                                          streamflows at the gaging station follow a
          station;                                                                                          bivariate normal distribution.
  sB,G is the standard deviation of the logarithms-base                                              5. The M measurements made at the LFPR station
          10 of the mean discharges at the gaging                                                           are statistically independent estimates of the
          station on the same days the low-flow                                                             base-flow relation.
          measurements were made at the ungaged                                                           Hardison and Moss noted that the first four
          site; and                                                                                assumptions appeared to be reasonable under the
     z is the number of standard deviation units                                                   conditions in which application of the original equation
          between the mean of the logarithms-base 10                                               2 was intended. These assumptions are reasonable for
          of the same-day mean discharges at the                                                   the modified equation 2 as well. Hardison and Moss
          gaging station and the logarithm-base 10 of                                              also noted that assumption 5 could be satisfied by
          the streamflow statistic at the gaging station.                                          applying criteria for using only those measurements
      Equation 2 is modified from an equation                                                      that can be reasonably assumed independent to define
developed by Hardison and Moss (1972) to determine                                                 the relation. The criterion usually applied is that the
the variance of estimates of 7-day, T-year low flows                                               base-flow measurements used in the relation should be
obtained from an ordinary-least-squares (OLS)                                                      separated by significant storm events (Stedinger and
regression of the logarithms-base 10 of base-flow                                                  Thomas, 1985). Collection of low streamflow
measurements at a LFPR station to the logarithms-base                                              measurements at LFPR stations in Massachusetts has
10 of same-day mean discharges at a nearby,                                                        generally followed that criterion.

12   Methods for Estimating Low-Flow Statistics for Massachusetts Streams
                                                                                                                               2 s B, U
                                                                                                           N U =  R S I S, G k  ---------- 
                                                                                                                     2 2
         When estimates are obtained for LFPR stations
                                                                                                                                s B, G 
from relations with more than one streamflow-gaging                                                                                           2 2 2
station, the individual estimates, Q S, U i , (where i = 1,                                                    V R  1 + z 2 b RS I S, G
                                                                                                            ⁄  ------- -------------- + ---------------------- ,        (6)
..., n, and n is the number of individual estimates of                                                        M K                            NG 
statistic S for LFPR station U) can be weighted by the
reciprocals of their variances, determined from                                         where all variables are as previously defined, and:
equation 2, to obtain minimum-variance estimates,                                         NU is the equivalent years of record at the partial-
 Q S, U , for each of the statistics from the equation                                            record station;
      w                            n

                                 ∑       ( Q S, U ⁄ V S, U )
                                                       i                i
                                                                                          NG is the years of record at the streamflow-gaging
                                                                                                  station used in the relation;
              Q S, U =           -----------------------------------------
                                         n                                -   .   (3)     IS,G is the standard deviation of the logarithms-base
                                              ( 1 ⁄ V S, U )                                      10 of the observed flows (annual series for
                                                                                                  frequency statistics or daily flows for
Weighted variances, V S, U , can be determined for the                                            duration statistics) at the streamflow-gaging
weighted estimates from the equation                                                              station
                                                                                             k is from equation 9 of Hardison and Moss
                                             n                                                    (1972),
               V S, U
                                = 1⁄       ∑ ( 1 ⁄ V S, U i )                 .   (4)
                                                                                                                r +  -------------- ( 1 – r ) ; and
                                          i=1                                                                    2    M–4                    2
                                                                                                      k =
                                                                                                                     M – 2
Standard errors, SE S, U , in percent, for the weighted
estimates can be obtained from the equation (Stedinger                                      K is from equation 3 of Hardison and Moss
and Thomas, 1985, p. 18)                                                                         (1972),

          SE S, U       = 100 exp ( 5.3018V w ) – 1 .                             (5)                                  K = (1 + z )
                                                                                                                      z M  S ,G  M 
                                                                                                                         2             SE
Equation 2 does not account for errors inherent in the                                       ⁄ 1 + -------------- + -------------- +  -------------
                                                                                                                                                   - -------------- ;    (8)
                                                                                                   M – 3 M – 3  sB ,G   M – 3
discharge measurements made at the LFPR station or
in the mean daily discharges determined for the gaging                                     RS is a correction factor that depends on the
stations. In addition, the estimates obtained for an                                             streamflow statistic being estimated, and is
LFPR station by use of the MOVE.1 or graphical                                                   determined by combining the equation that
method with multiple gaging stations are not truly                                               appears in table 1 of Hardison and Moss
independent because of cross correlation of the                                                  (1972),
streamflow records at the gaging stations. As a result,
the final estimates obtained using equations 2 and 3
may not truly be the best possible, and the true                                                            R S = ( SE S, G N ) ⁄ I S ,G ,                                (9)
variances and standard errors are somewhat larger than
those obtained using equations 4 and 5.                                                 with the equation
       The equivalent years of record also can be                                                                          1 + kS ⁄ 2
computed for estimates of streamflow statistics for the                                                   SE S, G = I S ,G ---------------------                         (10)
LFPR stations. The equivalent years of record is the
length of time that a streamgaging station would need                                   from Hardison (1969, p. D212) to obtain
to be operated at the location of the LFPR station to
                                                                                                                       2                2
obtain an estimate of the streamflow statistic with equal                                                         RS = 1 + k S ⁄ 2 .                                     (11)
accuracy. The equivalent years of record for LFPR
stations is computed from an equation developed by                                            Subscripts have been changed from their original
combining equations 7, 8, and 9 in Hardison and Moss                                    appearance in equations 6 to 11 to generalize from
(1972) and solving for the number of years of record.                                   T-year statistics to other streamflow statistics. In
The resulting equation is:                                                              equations 10 and 11 above, kS is the number of

                                                                                                    Estimating Methods for Data-Collection Stations                        13
standard deviation units between the streamflow                   topographic maps. Streamflow statistics are computed
statistic and the mean of the data from which it is               for the index station, then the statistics (numerical
calculated. From assumption 4 above, the annual series            values) are divided by the drainage area to determine
of 7-day low flows and the daily mean streamflows                 streamflows per unit area at the index station. These
from which the flow-duration statistics and the August            values are multiplied by the drainage area at the
median streamflows are calculated are distributed log-            ungaged site to obtain estimated statistics for the site.
normally, and thus kS can be obtained from a table of             This method is most commonly applied when the index
standard normal deviates as appears in most statistical           gaging station is on the same stream as the ungaged site
textbooks. Values for the 99-, 98-, 95-, 90-, 85-, 80-,           because the accuracy of the method depends on the
75-, 70-, 60-, and 50-percent duration streamflows, the           proximity of the two, on similarities in drainage area
August median streamflow, and the 7-day, 10- and                  and on other physical and climatic characteristics of
2-year streamflows are 2.3263, 2.0537, 1.6449, 1.2816,            their drainage basins.
1.0364, 0.8416, 0.6745, 0.5244, 0.2533, 0.0, 0.0,                        Several researchers have provided guidelines as
1.2816, and 0.0, respectively (Iman and Conover, 1983,            to how large the difference in drainage areas can be
p. 434–435). When estimates for LFPR stations are                 before use of regression equations is preferred over use
obtained from relations with more than one                        of the drainage-area ratio method. Guidelines have
streamgaging station, the individual calculations of              been provided for estimating peak-flow statistics, and
equivalent years of record can be weighted by the                 usually the recommendation has been that the drainage
reciprocals of the variances of the estimated streamflow          area for the ungaged site should be within 0.5 and 1.5
statistics, determined from equation 2, then the                  times the drainage area of the index station (Choquette,
individual weighted equivalent years of record can be             1988, p. 41; Koltun and Roberts, 1990, p. 6; Lumia,
averaged to obtain the final weighted equivalent years            1991, p. 34; Bisese, 1995, p. 13). One report (Koltun
of record for the LFPR station by substituting the                and Schwartz, 1986, p.32) recommended a range of
equivalent years of record estimates for the discharge            0.85 to 1.15 times the drainage area of the index station
estimates in equation 3 above.                                    for estimating low flows at ungaged sites in Ohio. None
                                                                  of these researchers provided any scientific basis for
                                                                  use of these guidelines. R.E. Thompson, Jr. (U.S.
ESTIMATING METHODS FOR                                            Geological Survey, written commun., 1999), however,
UNGAGED STREAM SITES                                              recently completed a study that provides evidence
                                                                  supporting use of ratios between 0.33 and 3.0 for
        Estimates of streamflow statistics often are
                                                                  streams in Pennsylvania.
needed for sites on streams where no data are available.
The two methods used most commonly to estimate                           Because of uncertainty in an appropriate range
statistics for ungaged sites are the drainage-area ratio          for use of the drainage-area ratio method for streams in
method and regression equations. The drainage-area                Massachusetts, an experiment was designed to
ratio method is most appropriate for use when the                 determine the ratio range in which the method is likely
ungaged site is near a streamgaging station on the same           to provide better estimates of low streamflow statistics
stream (nested). Regression equations can be used to              than use of regression equations. Five river basins with
obtain estimates for most ungaged sites. Additional               one or more continuous gaging stations in each basin
details on application of these methods is provided               were chosen for the experiment to represent the varied
below.                                                            topography, geology, and precipitation of
                                                                  Massachusetts. Two basins, the Green and the West
                                                                  Branch Westfield, are in the mountainous western part
Drainage-Area Ratio Method                                        of the State; two basins, the Quaboag and the
                                                                  Squannacook, are in the foothills of the central part of
       The drainage-area ratio method assumes that the            the State; and one basin, the Wading, is in the flat,
streamflow at an ungaged site is the same per unit area           low-lying landscape typical of eastern Massachusetts.
as that at a nearby, hydrologically similar streamgaging                 A total of 25 LFPR stations were established
station used as an index. Drainage areas for the                  upstream and downstream from 8 streamgaging
ungaged site and the index station are determined from            stations in the 5 basins. Most of the LFPR stations have

14   Methods for Estimating Low-Flow Statistics for Massachusetts Streams
smaller drainage areas than those for the streamgaging       and one discontinued streamgaging station) at which
stations because historically most streamgaging              streamflow measurements were made in the Wading
stations in Massachusetts have been established near         River Basin, only three of the stations (01108490,
the downstream ends of rivers. Locations and drainage        01108600, and 01108700) were used to compare
boundaries for the streamgaging stations and LFPR            results of the different estimation methods. Discharges
stations are shown for each basin in figures 4A to 4E.       and basin characteristics from stations 01108440 and
Station descriptions for the stations are in table 1.        01108470 were subtracted from station 01108490, and
       Seven to ten discharge measurements were made         station 01108500 was subtracted from 01108700 to
at each of the LFPR stations during 1994 and 1995.           determine discharges and basin characteristics
The measurements were published in the Mass. annual          representative of the naturally flowing areas above
data reports for those years (Gadoury and others, 1995;      those stations. The adjusted discharges and basin
Socolow and others, 1996, 1997). The measurements,           characteristics were used to estimate unregulated
along with historical measurements available at three        streamflow statistics for the stations. Station 01108600
stations, were used to estimate streamflows at the 99-,      was not affected by regulation or diversions.
98-, and 95-percent durations and August median flows
for the stations using the methods described above for              The drainage area for the Wading River below
LFPR stations. Estimates of the flow-duration statistics     the West Mansfield streamgaging station (station
were also derived for the stations using the drainage-       01108500) and above the Norton streamgaging station
area ratio method and the regression equations               (station 01109000) is not affected by regulation or
developed by Ries (1994b, 1997). The regression              diversions, whereas the drainage area above the West
equations presented later in this report were not used       Mansfield station is affected by regulation and
because they were not yet available at the time of the       diversions. Streamflow statistics for the West Mansfield
analysis.                                                    station were subtracted from those for the Norton
       Two gaging stations were available in some            station to obtain the streamflow statistics for the
basins for the analysis (table 1). To increase the sample    naturally flowing part of the drainage area above the
size for the analysis of the drainage-area ratio method,     Norton station.
drainage-area ratio estimates and regression-equation               The four streamflow statistics (99-, 98-, and
estimates were determined for the streamgaging
                                                             95-percent duration and August median streamflows)
stations in addition to the estimates determined from
                                                             estimated by the three different methods (correlation,
the records for the stations. The drainage-area ratio
                                                             drainage-area ratio, and regression equation) for each
estimates were determined for each streamgaging
                                                             of the LFPR and streamgaging stations used in the
station by applying the flow per unit area for one
streamgaging station to the drainage area for the other      analysis are presented in table 7 (back of the report).
streamgaging station. The longest common period of           The estimates derived by correlation, shown in the
record available for the streamgaging stations in each       column labeled “Correlation method estimate or
basin was used to compute the streamflow statistics for      computed,” were considered the best estimates
the analysis to avoid differences in the statistics due to   available for the LFPR stations for the analysis,
differences in record length.                                and they were compared to the estimates derived by
       The Wading River Basin, unlike the other four         the other methods. The correlation estimates were
basins used in the experiment, has water withdrawals         considered the best estimates because they were
and regulated streamflows in parts of the basin (see         derived from actual streamflow data for the stations,
table 1, remarks). It was chosen for use in the              whereas the drainage-area ratio and regression
experiment because the unregulated part of the basin is      estimates were derived indirectly based on an
the largest unregulated area in southeastern                 assumed or statistical relation between the basin
Massachusetts. Discharges, drainage areas, and other         characteristics for the LFPR stations and stream-
basin characteristics used to solve the regression           gaging stations. Statistics shown for streamgaging
equations were adjusted for stations downstream from         stations in the column labeled “Correlation method
the diversions and regulation to correct for these           estimate or computed” were computed from daily-
activities. Of the seven stations (including one active      flow records.

                                                                        Estimating Methods for Ungaged Stream Sites    15
              A. SQUANNACOOK                                73o00'   72o00'

                 RIVER BASIN                       42o30'


                                      0         50 MILES                 42o00'

                                      0    50 KILOMETERS                      41o30'

                                       71o50'                                                                   71o40'






     42o35'                      EXPLANATION

                                      BASIN BOUNDARY

                          01096000    STREAMFLOW GAGING
                                      STATION AND NUMBER
                                                                                        0                 2.5             5 MILES
                          01095930    LOW-FLOW PARTIAL-
                                      RECORD STATION
                                      AND NUMBER
                                                                                        0        2.5            5 KILOMETERS

 Figure 4. Locations and drainage boundaries of low-flow partial-record stations and gaging stations in the (A) Squannacook,
 (B) Wading, (C) Quaboag, (D) Green, and (E) West Branch Westfield River Basins, Massachusetts.

16   Streamflow Statistics and Basin Characteristics for Low-Flow Stations in Massachusetts
           B. WADING                                               72o00'

          RIVER BASIN

                                   0       50 MILES                    42o00'

                                   0    50 KILOMETERS                       41o30'

                                       71o20'                                                                                 71o10'






                      SHADED AREAS ARE AFFECTED                                               01108600
                      BY REGULATION, DIVERSIONS, OR BOTH


 41o55'                            BASIN BOUNDARY

                      01109000     STREAMFLOW GAGING
                                   STATION AND NUMBER

                      01108600     LOW-FLOW PARTIAL-
                                   RECORD STATION                               0                            1.0                  2 MILES
                                   AND NUMBER

                                                                                0             1.0                  2 KILOMETERS

Figure 4. Locations and drainage boundaries of low-flow partial-record stations and gaging stations in the (A) Squannacook,
(B) Wading, (C) Quaboag, (D) Green, and (E) West Branch Westfield River Basins, Massachusetts—Continued.

                                                                                              Estimating Methods for Ungaged Stream Sites   17
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