Methods for Estimating Low-Flow Statistics for Massachusetts Streams

U.S. Department of the Interior U.S. Geological Survey Methods for Estimating Low-Flow Statistics for Massachusetts Streams

By KERNELL G. RIES, III and PAUL J. FRIESZ

Water-Resources Investigations Report 00-4135

Prepared in cooperation with the MASSACHUSETTS DEPARTMENT OF ENVIRONMENTAL MANAGEMENT, OFFICE OF WATER RESOURCES

Northborough, Massachusetts 2000

U.S. DEPARTMENT OF THE INTERIOR BRUCE BABBITT, Secretary

U.S. GEOLOGICAL SURVEY Charles G. Groat, Director

The use of trade or product names in this report is for identiﬁcation purposes only and does not constitute endorsement by the U.S. Geological Survey.

For additional information write to: Copies of this report can be purchased from:

Chief, Massachusetts–Rhode Island District U.S. Geological Survey U.S. Geological Survey Branch of Information Services Water Resources Division Box 25286 10 Bearfoot Road Denver, CO 80225-0286 Northborough, MA 01532 or through our web site at http://ma.water.usgs.gov

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 streamgaging 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 sion equations. Output provided by the Web appli- Yield studies. The MOWR uses the streamflow statistics 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 sites. 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) provides an equation for estimating August median Previous Studies streamflows. This statistic is used by the U.S. Fish and Wildlife Service (1981) and some State agencies as the Low-flow statistics for most streamgaging minimum summertime streamflow required for maintenance 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´

VERMONT 01333000 01169801 01332000 01167200 01333100 01164300 01162500 01332900 01170100 01168300 01169000 01165090 1 01163250 01331400 01168400 01168650 01165500 01166105 7 01331380 3 01163298 01359967 01169600 01165250 01169900 011197015 ° 01162900 42 30´ 01178200 01174000 01170575 01174050 01178300 01169800 01197120 01172810 01179900 8 6 01174565 01178490 2 01197140 01173260 01197300 NEW YORK 4 01180650 Western Region 01174900 01180000 01171500 01197180 01175710 01197230 01171800 01171947 01173420 01175850 01180500 01180800 01173450 01175670 01171970 01198000 01175890 01181000 01176000 01176100 01198060 5 01176780 01183210 01176200 01124390 01198160 01176300 01123161 01177360 01123140 1 01185490 10 01198200 01186300 01184282 01176415 01187400 01184277 9 01184200 01123200 CONNECTICUT 42°00´

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°00´

01073860

71°30´ 01100700 01101000 ATLANTIC OCEAN NEW HAMPSHIRE 16 01101100 01095928 01096505 01096515 13 01089400 01096000 01096504 01100608 17 01094396 15 01095915 01094340 01102053 01097300 01097280 01102490 18 11 01096910 01096935 01095220 19a 01094760 01103015 Massachusetts 01095380 14a 01096855 14b BOSTON Bay 01096805 01103440 Eastern Region 01103435 01103445 01105582 01105630 01109460 01105830 20 01104960 01105575 19c 01105670 01104980 01105600 01111142 01103253 01104840 12 01105820 01111200 19b 01105568 01103330 01105270 01112190 21a 70°00´ 01107000 01111225

01105861 9 01108600 01106460 01111300 RHODE ISLAND 27 25 01108140 01108180 21b 01107400 01109200 70°30´ 01109087 01109225 011058839 01109090 011059106 Southeast

01105937 24 22 26 01105930 Coastal 01105947

01105935 Region 01106000

41°30´ Nantucket Sound 23

0 50 MILES

23 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 http://waterdata.usgs.gov/nwis-w/MA/, 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: http://water.usgs.gov/software/surface_water.html. 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

s discharges at the LFPR station and a nearby gaging Yˆ = Y + ----y()X – X , (1) i s i station is linear. The method is applied by first x calculating logarithms-base 10 of the same-day flows for the LFPR and gaging stations and graphing the and then retransforming the estimates by ˆ values to ascertain the linearity of the relation. The exponentiating the values (10Y 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 equation as the X values to obtain estimated same-day of the streamflow statistics (Xi) for the gaging station i are calculated. Estimates of the streamflow statistics flows for the LFPR station, then connecting the points (Yˆ 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 DISCHARGE, IN CUBIC FEET PER SECOND

HEMLOCK BROOK AT WILLIAMSTOWN, MASS. MOVE.1 RELATION

0.1 110100 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.

100

0.1 SAME-DAY DISCHARGES

DISCHARGE, IN CUBIC FEET PER SECOND GRAPHICAL RELATION HOPPING BROOK NEAR WEST MEDWAY, MASS. WEST MEDWAY, NEAR HOPPING BROOK

0.10 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 2 2 V R 1 z M SESG, M 2 are generalized from Hardison and Moss (1972): V S, U = ------1 +++------------------M M – 3 M – 3 sBG, M – 3 1. The true relation between the logarithms of the

2 base-flow measurements at the LFPR station + b V SG, , (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(s /s ), where r is the B,U B,G 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 equation. 1 when MOVE.1 is used to obtain the 4. The logarithms of the measured streamflows at estimate), and sB,U is the standard deviation 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 2 2 2s When estimates are obtained for LFPR stations N = R I k ------BU, U S SG, s from relations with more than one streamflow-gaging BG, 2 2 2 2 station, the individual estimates, Q , , (where i = 1, V b R I SUi ⁄ R1 + z S SG, ------------+ ------, (6) ..., n, and n is the number of individual estimates of M K N G 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- QSU, , for each of the statistics from the equation record station; w n ∑ ()Q ⁄ V NG is the years of record at the streamflow-gaging SU, i SU, i i = 1 station used in the relation; QSU, = ------n - . (3) w IS,G is the standard deviation of the logarithms-base ∑ ()1 ⁄ V SU, i 10 of the observed flows (annual series for i = 1 frequency statistics or daily flows for duration statistics) at the streamflow-gaging Weighted variances, V SU, , can be determined for the weighted estimates from thew equation station k is from equation 9 of Hardison and Moss n (1972), V = 11⁄ ∑ ()⁄ V . (4) SU, w SU, i i = 1 2 M – 4 2 kr= + ------()1 – r ; and (7) M – 2 Standard errors, SE , , in percent, for the weighted SUw estimates can be obtained from the equation (Stedinger K is from equation 3 of Hardison and Moss and Thomas, 1985, p. 18) (1972),

K = ()1 + z2 SE , = 100exp() 5.3018V – 1 . (5) SUw w SE 2 1 z2M SG, M Equation 2 does not account for errors inherent in the ⁄ 1 +++------------; (8) M – 3 M – 3 s M – 3 discharge measurements made at the LFPR station or B,G 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 RS = SESG, N ISG, , (9) variances and standard errors are somewhat larger than those obtained using equations 4 and 5. with the equation 2 The equivalent years of record also can be 1 + k ⁄ 2 SE = I ------S (10) computed for estimates of streamflow statistics for the SG, SG, N 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 + kS 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 71o00' A. SQUANNACOOK 73o00' 72o00'

RIVER BASIN 42o30'

70o00'

0 50 MILES 42o00'

50 KILOMETERS 0 41o30'

71o50' 71o40'

42o45'

01095977 01095930 01095928

01095990

01096000

01096035

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 71o00' B. WADING 73o00' 72o00' RIVER BASIN 42o30' 70o00'

0 50 MILES 42o00'

50 KILOMETERS 0 41o30'

71o20' 71o10'

42o05'

01108440

01108470

01108490

01108500

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

01108700 01109000

EXPLANATION o 41 55' 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

Estimating Methods for Ungaged Stream Sites 17 71o00' C. QUABOAG 73o00' 72o00' RIVER BASIN 42o30' 70o00'

0 50 MILES 42o00'

50 KILOMETERS 0 41o30'

72o20' 72o00'

42o20'

01175660

01175670

01175695 01175905

01176435 01176000

01176350

EXPLANATION

BASIN BOUNDARY

01176000 STREAMFLOW GAGING STATION AND NUMBER 0 5 10 MILES 01175905 LOW-FLOW PARTIAL- RECORD STATION AND NUMBER 42o00 0 5 10 KILOMETERS

18 Streamflow Statistics and Basin Characteristics for Low-Flow Stations in Massachusetts 71o00' D. GREEN 73o00' 72o00' RIVER BASIN 42o30' 70o00'

0 50 MILES 42o00'

50 KILOMETERS 0 41o30'

72o50' 72o40'

42o50'

01170020

01170030 01170025

01170055 VERMONT MASSACHUSETTS

01170100

01170121

42o40' EXPLANATION 01170141

BASIN BOUNDARY

01170100 STREAMFLOW GAGING STATION AND NUMBER 0 1.0 2 MILES 01170030 LOW-FLOW PARTIAL- RECORD STATION AND NUMBER 0 1.0 2 KILOMETERS

Estimating Methods for Ungaged Stream Sites 19 71o00' E. WESTFIELD 73o00' 72o00' RIVER BASIN 42o30' 70o00' 42o00' 0 50 MILES

41o30' 0 50 KILOMETERS

73o10' 72o55'

42o25'

01180660

01180750 01180780 01180821 01180800

o 42 15' 01181000

EXPLANATION

BASIN BOUNDARY

01180800 STREAMFLOW GAGING 0 2.5 5 MILES STATION AND NUMBER

01180660 LOW-FLOW PARTIAL- RECORD STATION 0 2.5 5 KILOMETERS AND NUMBER

20 Streamflow Statistics and Basin Characteristics for Low-Flow Stations in Massachusetts ow ow ows ows fl fl fl ows for this station ows ows for this station ows ows for this station ows fl fl fl 0 is eastern; 1 western. No., obtained by subtracting from 01108500. upstream. upstream. from basin for Diversions municipal supplies. from basin for Diversions municipal supplies. to and from basin for Diversions municipal supplies. obtained by subtracting from 01108500. obtained by subtracting from 01108440 and 01108470. method for estimating method for estimating Region: Region Remarks tion Mini- mum mum basin eleva- All stations are in Massachusetts except as otherwise indicated. All stations are in Massachusetts except tion Mean basin eleva- ed fi drift area Strati- Station name: Total Total length stream refers to the year of publication for this report (2000). ” age area 43.4 85.4 25.7 180 68 0 Natural 64.4 130 17.1 618 247 0 by mill Occasional regulation Drain- present “ ow partial-record stations. ow fl 86 19.6 42.6 11.2 247 146 0 and ponds. by lakes Regulation – – – present present record The word Period of Period ---- 44.3 57.6 87.3-- 119 8.19 725 13.8 69.9 295 139 649 0 262 19.6 0 595 224 0 by mill Occasional regulation -- 4.83 12.4 1.96 270 180 0 and ponds. by lakes Regulation -- 18.7 40.3 10.3 251 148 0 Natural eld -- 3.83 8.37 2.49 175 128 0 eld 1954 fi Continued fi — Period of record: Period Wading River Basin (subbasin of Taunton River Basin) River Taunton of Basin (subbasin River Wading Squannacook River Basin (subbasin of Nashua River Basin) of Nashua River Basin (subbasin Squannacook River Station name eld fi Townsend Harbor Groton West Route 225 at Mans South Foxboro ″

′

° Longitude ″

′

Station numbers for streamgaging stations are in bold; all others low- Station numbers for streamgaging ° 41 56 51 71 10 38 near Norton River Wading 1926 42 38 03 71 39 30 GrotonWest near Squannacook River 1950 42 00 71 15 38 Mans West at River Wading Latitude Descriptions of low-flow partial-record and streamgaging stations used to analyze the applicability drainage-area ratio Descriptions of low-flow partial-record and streamgaging stations used to analyze the applicability drainage-area ratio No. USGS station 01108700 41 57 06 71 13 27 at Chartley River Wading -- 29.2 62.9 16.8 214 95 0 Natural 01109000 01095928 42 40 2401095930 71 46 39 42 40 2701095977Ashby Brook near Trapfall 71 46 14 42 40 41Townsend West Brook near Willard 71 43 2901095990 -- West near Squannacook River 42 39 08 71 40 2201096000 -- Townsend at Squannacook River 12.3401096035 42 36 07 31.8 71 37 43 5.89 State below Squannacook River 2.12 14.6 878 0.66 44201108470 858 42 01 39 0 71 17 57 480 Brook at Shepardville Hawthorne 01108490 42 01 07 0 -- 71 16 02 Street, near West at River Wading 5.3201108600 41 59 11 8.49 71 14 27 Mans West 2.48 Hodges Brook at 268 192 0 and ponds. by lakes Regulation 01108440 42 02 18 71 16 32 Street, near West at River Wading 01108500 USGS station No.: Table 1. streamflow statistics for ungaged Massachusetts streams Table 1. [ streamflow statistics for ungaged Massachusetts streams -- , no continuous data] number; USGS, U.S. Geological Survey; Areas are in square miles; lengths are in miles; elevations are in feet. Areas are in square miles; lengths elevations

Estimating Methods for Ungaged Stream Sites 21 upstream. upstream. upstream. upstream. method for estimating Region Remarks tion Mini- mum mum basin elevation Mean basin eleva- ed fi drift area Strati- Total Total length stream 8.69 16.7 1.11 871 636 1 age area 41.3 83.8 1.48 1,360 499 1 Drain- 149 319 31.7 809 397 1 Flood-retarding reservoirs – – – present present present record Period of Period ---- 5.79 31.8 10.8-- 0.11 61.6 1,520 1.23 47.8 899 1,470 99.3-- 1 597 1.80 1 1,290 6.07-- 397 11.5 1 0.53 40.6 904 80.8 686 4.55 1 891 607 1 -- 51.9 110 2.11 1,240 298 1 eld 1913 fi Continued — Green River Basin (subbasin of Deerfield River Basin) of Deerfield River Basin (subbasin River Green Quaboag River Basin (subbasin of Chicopee River Basin) of Chicopee River Basin (subbasin Quaboag River eld eld fi fi Station name Guilford, Vt. Vt. near Green River, Brook near Colrain near Green East Brook near Spencer ″

′

° Longitude ″

′

° 42 12 72 40 16 near Colrain Green River 1968 42 15 54 72 00 19 near Spencer River Sevenmile 1961 42 10 56 72 15 51 Brim West at Quaboag River Latitude Descriptions of low-flow partial-record and streamgaging stations used to analyze the applicability drainage-area ratio No. USGS station 01170020 42 48 5101170025 72 44 53 42 47 4301170030Vt. at Harrisville, Green River 72 39 52 42 47 54Vt. Guilford, West at Green River 72 39 3301170055 West Brook at Hinesburg 42 44 27 -- -- 72 40 2701170100 Roaring Brook above Green River 01170121 16.9 42 40 43 5.18 72 39 1001170141 34.4 Stafford 0.4 miles below Green River 42 39 12 9.60 72 37 32 0.66 0.30 Brook Workman below Green River 1,610 1,790 1,450 89901175670 1 1 01175695 42 13 26 72 02 4201175905 at Podunk Street River Sevenmile 42 12 45 72 12 1401176000 Warren near Quaboag River 01176350 42 08 37 -- 72 18 5001176435 near Palmer Quaboag River 42 10 43 72 21 53Three Rivers at Quaboag River 138 -- -- 298 180 29.9 212 815 374 415 594 41.4 50.5 1 796 777 Flood-retarding reservoirs 393 341 1 1 Flood-retarding reservoirs Flood-retarding reservoirs 01175660 42 17 30 72 00 04 at State Route 31, River Sevenmile Table 1. streamflow statistics for ungaged Massachusetts streams

22 Methods for Estimating Low-Flow Statistics for Massachusetts Streams method for estimating Region Remarks tion Mini- mum mum basin elevation Mean basin eleva- ed fi drift area Strati- Total Total length stream age area 94.0 161 3.91 1,420 397 1 Drain- 76 2.95 6.99 .12 1,560 1,300 1 – – present record Period of Period -- 53.8-- 83.01936 1.19 72.5 1,530 117 597 2.58 1 1,510 596 1 -- 12.8 21.9 0.27 1,670 1,230 1 Continued — eld River at eld River at eld River eld River at eld River fi fi fi West Branch Westfield River Basin (subbasin of Westfield River Basin) River Westfield of Basin (subbasin River Westfield Branch West Station name Chester Huntington Chester Becket ″

′

° Longitude ″

′

° 42 15 49 73 02 48 Center Brook near Becket Walker 42 14 1963 72 53 46West Branch West Latitude Descriptions of low-flow partial-record and streamgaging stations used to analyze the applicability drainage-area ratio No. USGS station 01180780 42 16 2601180800 73 04 0901180821 Center Hamilton Brook at Becket 42 16 40 72 58 49 --01181000 Brook at State Route 20 Walker 1.15 1.47 .0 1,730 1,570 1 01180750 42 16 47 72 58 52West Branch West 01180660 42 20 00 73 05 02West Branch West Table 1. streamflow statistics for ungaged Massachusetts streams

Estimating Methods for Ungaged Stream Sites 23 Absolute percent differences between the The LOWESS curves indicate that differences drainage-area ratio estimates and regression estimates, between the data-based estimates and the drainage-area and the data-based estimates (correlation estimates for ratio method estimates are generally smaller than the LFPR stations and calculated statistics for gaging differences between data-based estimates and the stations) were determined for each of the streamﬂow regression equation estimates when the ratio of the drainage area for the LFPR station is within about 0.3 statistics for each station. These absolute percent and 1.5 times the drainage area of the index gaging differences for the four statistics were averaged for station. This range of drainage area ratios was used to each station to obtain the average percent difference for separate the data into four groups based on estimation the estimation method at the station (table 7). The method and whether the drainage-area ratio for the average absolute percent differences from the data- location was within the noted range. The groups were based estimates for the drainage-area ratio method and (1) drainage-area ratio estimates for stations with the regression equations are plotted against the drainage-area ratios less than 0.3 and greater than 1.5, drainage-area ratio for the station (the drainage area for (2) drainage-area ratio estimates for stations with the LFPR station divided by the drainage area for the drainage-area ratios between 0.3 and 1.5, (3) regression index gaging station) in ﬁgure 5. Smoothed curves are estimates for stations with drainage-area ratios less plotted through each set of data to indicate the range of than 0.3 and greater than 1.5, and (4) regression estimates for stations with drainage-area ratios between ratios in which the drainage-area ratio method provides 0.3 and 1.5. Medians and standard deviations of the generally better results than the regression equations. absolute percent differences are presented for each The smoothed curves were obtained by use of a group in table 2, along with the medians and standard LOWESS (LOcally-WEighted Scatter plot Smoother) deviations for all of the estimates, for all drainage-area algorithm (Minitab, Inc., 1998b, pp. 15–20 to 15–25, ratio estimates, and for all regression-equation Cleveland, 1979). estimates.

POINT OMITTED FROM PLOT AT RATIO = 0.0915, LOWESS CURVE THROUGH DRAINAGE-AREA RATIO ESTIMATES REGRESSION DIFFERENCE = 6.41, DRAINAGE- LOWESS CURVE THROUGH REGRESSION ESTIMATES AREA RATIO DIFFERENCE = 11.05 DRAINAGE-AREA RATIO ESTIMATES REGRESSION ESTIMATES 3

1 ABSOLUTE PERCENT DIFFERENCE, DIVIDED BY 100

0 0.01 0.02 0.05 0.1 0.2 0.5 1 2 5 10 20 50 100 RATIO OF LOW-FLOW PARTIAL-RECORD STATION DRAINAGE AREA TO GAGING STATION DRAINAGE AREA

Figure 5. Relation of drainage-area ratio to average absolute percent difference in streamflow statistics between data-based estimates and estimates derived from the drainage-area ratio method (solid curve), and from the regression equations (dashed curve).

24 Methods for Estimating Low-Flow Statistics for Massachusetts Streams Table 2. Medians and standard deviations of absolute percent than the median difference for the regression equation differences between streamflow statistics estimated using estimates when the drainage-area ratio is less than 0.3 available data and by using the drainage-area ratio method or greater than 1.5. The test also showed that the and regression equations median difference of the drainage-area ratio estimates [<, actual value is less than value shown; >, actual value is greater than value is significantly less than (p=0.003) the median shown] difference of the regression equation estimates when Median Drainage- the drainage-area ratio is between 0.3 and 1.5. Number absolute Standard Group area in group percent deviation ratio range On the basis of the above analysis, it should be difference expected that the drainage-area ratio method will All estimates All 72 40.3 151.6 provide estimates of streamflow statistics that are, on Drainage- All 36 34.9 186.0 average, as good as or better than estimates obtained area ratio < 0.3 and > 1.5 20 65.7 240.8 using the regression equations tested when the method 0.3 to 1.5 16 15.5 37.7 drainage-area ratio is between about 0.3 and 1.5. It Regression All 36 43.2 108.9 should be noted, however, that this finding is based on equations < 0.3 and > 1.5 20 40.3 140.4 a comparison of differences between two types of 0.3 to 1.5 16 45.5 48.6 estimates (drainage-area ratio estimates and regression equation estimates) and a third type of estimate Table 2 shows that the median absolute percent difference for the drainage-area ratio method is about 8 (correlation estimates) for the LFPR stations used in percent lower than that for the regression equations the analysis. It was not possible to test the estimation when all the data are considered; however, the standard methods against only observed statistics for deviation for the drainage-area ratio method is much streamgaging stations, as would be preferred, because larger than that for the regression equations. When there were too few streamgaging stations available for drainage-area ratios for the stations are between 0.3 the analysis that were located on the same, unregulated and 1.5, the median difference for the drainage-area streams. The finding was also based on a comparison of ratio method is about 30 percent less and the standard drainage-area ratio estimates with estimates from deviation is about 11 percent less than the regression equations that are now superseded by the corresponding values for the regression equations. equations provided later in this report. Results would When drainage-area ratios for the stations are less than likely differ somewhat if the new equations were used; 0.3 or greater than 1.5, the median difference for the however, time and funding were not available to update drainage-area ratio method is about 25 percent greater the analysis. and the standard deviation is about 100 percent greater than the corresponding values for the regression The upper limit of the drainage-area ratio range equations. in which the drainage-area ratio estimation method is Statistical tests were done on the grouped data to recommended for use over use of regression equations test for significant differences in the variances and is poorly defined because there are only two data points medians of the groups. Differences in variance were (at 4.33 and 4.67) between ratios of 1.42 and 15.9. tested by use of Levene’s test for homogeneity of Absolute percent differences were larger for the variances (Minitab, Inc., 1998b, p. 3–48 to 3–51). drainage-area ratio estimates than for the regression Levene’s test was used because the data were not estimates at the drainage-area ratios of 4.33 and 4.67, normally distributed, and this test is applicable for any but the upper limit of the recommended range of continuous distribution. Although there are substantial drainage-area ratios could be anywhere between 1.42 differences in variance among the groups, none of the groups could be considered significantly different from and 4.33. In addition, users of the drainage-area ratio the others based on the test. Differences in medians method also should consider that potential errors of were tested by use of the Mann-Whitney rank-sum test estimates for individual sites cannot be quantified. If a (Minitab, Inc., 1998b, p. 5–11 to 5–13). This test standard error of estimate or confidence intervals are showed that the median difference for the drainage- needed, then it may be useful to use the regression area ratio estimates is significantly larger (p=0.052) equations to obtain the estimates.

Estimating Methods for Ungaged Stream Sites 25 … Regression Equations logY i = b0 +++b1logX1 b2logX2 ε ++bnlogXn i . (13) Multiple linear-regression analysis (regression analysis) has been used by the USGS and other The algebraically equivalent form when logarithms- researchers throughout the United States and elsewhere base 10 are used in the transformations and the to develop equations for estimating streamflow statis- equation is retransformed to original units is: tics for ungaged sites. In regression analysis, a streamflow statistic (the dependent variable) for a group of ε Y = 10b0()X b1 ()…X b2 ()X bn 10 i . (14) data-collection stations is statistically related to one or i 1 2 n more physical or climatic characteristics of the drainage areas for the stations (the independent variables). The Generalized-Least-Squares (GLS) This results in an equation that can be used to estimate regression algorithm (Tasker, 1989) was developed the statistic for sites where no streamflow data are for use in regression analysis of peak- and low-flow available. Equations can be developed by use of several frequency statistics, such as the 100-year peak flow different regression analysis algorithms. The various and the 7-day, 10-year low flow, because streamflow algorithms use different methods for minimizing differ- data are correlated spatially and in time. Thus, ences between the values of the dependent variable for assumption 5 for use of regression is not strictly the stations used in the analysis (the observed values) satisfied in hydrologic regressions when the most and the corresponding values provided by the resulting commonly used form of regression analysis, Ordinary- regression equation (the estimated or fitted values). Least-Squares (OLS), is used. Tasker and Stedinger Choice of one algorithm over another depends on the (1989) demonstrated that GLS analysis is theoretically characteristics of the data used in the analysis and on most appropriate and generally provides the best the underlying assumptions for use of the algorithm. results when used for hydrologic regressions. GLS allows the weight given to each station used in the Equations obtained by use of regression analysis analysis to be adjusted to compensate for spatial take the general form correlation and differences in record length among the stations. Because GLS was developed specifically for use with flow-frequency statistics, however, it requires Y = b +++++b X b X … b X ε , (12) i 0 1 1 2 2 n n i substantial extra effort to use it for regression with flow-duration statistics (Ries, 1994b) where Yi is the estimate of the dependent variable for Vogel and Kroll (1990) used GLS to develop site i, X1 to Xn are the n independent variables, b0 to bn a regression equation to predict 7-day, 10-year low ε are the n + 1 regression model coefficients, and i is the flows for Massachusetts streams; however, they found residual error (difference between the observed and that the equation parameters (b0 to bn) were nearly estimated value of the dependent variable) for site i. identical when either OLS or GLS was used to develop Assumptions for use of regression analysis are the equation even though OLS does not correct for (1) equation 12 adequately describes the relation differences in record length or cross-correlation among between the dependent and the independent variables, the stations used in the analysis. In addition, Vogel and ε ε (2) the mean of the i is zero, (3) the variance of the i Kroll (1990) found that prediction errors obtained is constant and independent of the values of Xn, (4) the when GLS was used were only marginally smaller than ε ε i are normally distributed, and (5) the i are those obtained when OLS was used. independent of each other (Iman and Conover, 1983, Weighted-Least-Squares regression analysis p. 367). Regression analysis results must be evaluated (WLS) was used to develop the equations presented in to assure that these assumptions are met. this report for estimating the 99-, 98-, 95-, 90-, 85-, Streamflow and basin characteristics used 80-, 75-, 70-, 60-, and 50-percent duration flows; the in hydrologic regression usually are log-normally 7-day, 10- and 2- year low flows; and the August distributed; therefore, transformation of the variables median flow. WLS can compensate for differences in to logarithms is usually necessary to satisfy regression record length, but it does not correct for cross- assumption 2. Transformation results in a model of correlation among the stations used in the analysis. the form Stedinger and Tasker (1985) concluded that gains in

26 Methods for Estimating Low-Flow Statistics for Massachusetts Streams model precision when GLS is used instead of WLS Equation 13 provides unbiased estimates of the increase with decreasing standard error of estimate and mean response of the dependent variable, meaning that increasing cross correlation. WLS and GLS models the expected value of εi is zero. However, equation 13 with large standard errors and low cross correlations yields estimates of the logarithm-base 10 of the were nearly identical. Because Vogel and Kroll (1990) dependent variable when what is desired is estimates in found cross correlation of data they used in their their original units of measure. Equation 14 is a analysis was only 0.35, equations for predicting low- retransformation of equation 13 that produces flow statistics for Massachusetts streams using WLS estimates in the desired units, but it predicts the median should have model precision that is nearly the same as rather than the mean response of the dependent equations developed using GLS. Additionally, the WLS variable, and thus it is biased. In the case of streamflow algorithm can easily be used to adjust the weights for data, the median tends to be lower than the mean. stations used in the analysis to compensate for non- Several investigators have discussed the constant variance of the regression residuals when this problems of bias in retransformed logarithmic is necessary to avoid a violation of regression equations and proposed various bias-correction factors assumption 3. (BCF) as solutions (Bradu and Mundlak, 1970; Duan, When several independent variables are being 1983; Ferguson, 1986; Koch and Smillie, 1986; Cohn considered for use in a regression analysis, usually a and others, 1989; Gilroy and others, 1990). Duan’s variable-selection algorithm is necessary to aid in “smearing estimate” was used as the BCF in previous determining which combination of the independent Basin Yield studies (Ries, 1994a, 1994b, 1997) by variables provides the best estimates of the dependent replacing the error term of equation 14 with the mean variable. Neter and others (1985, p. 421–429) describe error of the retransformed residuals. This BCF is an all-possible-regressions algorithm that examines all advantageous in that it does not require normally possible combinations of the independent variables and distributed regression residuals and is simple to ranks them according to some criterion. This algorithm calculate. was used for the Basin Yield studies to select subsets of Cohn and others (1989) show that if the residuals the independent variables for inclusion in the final are normally distributed a BCF developed by Bradu regression equations, with minimization of Mallow’s and Mundlak (1970) is optimal, in that it provides Cp used as the selection criterion (Neter and others, Minimum Variance Unbiased Estimates (MVUE) of 1985, p. 426–428). These subsets were further the dependent variable. Gilroy and others (1990) analyzed using WLS regression analysis to select a demonstrate that the MVUE estimator and Duan’s final model for each analyzed streamflow statistic. The smearing estimator are about equally effective at final models were selected on the basis of the following eliminating retransformation bias, however the MVUE statistical parameters: (1) Mallow’s Cp statistic; estimator has the advantage of being unbiased 2 (2) Radj , the percentage of the variation in the regardless of the number of stations used in the dependent variable explained by the independent analysis. Equations for computing the MVUE variables, adjusted for the number of stations and the estimator are provided in Cohn and others (1989) and number of independent variables used in the regression in Gilroy and others (1990). Because of their analysis; (3) the mean square error (MSE), the sample complexity, they are not reproduced here. Cohn and model error variance of the estimates for the stations others (1989) also provided a FORTRAN program for included in the analysis; and (4) the PRESS statistic, an computing the MVUE BCF. This program was used to estimate of the prediction error sum of squares determine MVUE factors for the regression equations (Montgomery and Peck, 1982, p. 255). Diagnostic provided later in this report. Smearing estimate BCFs checks were done to test for model adequacy and were also determined for the regression equations. violations of assumptions for regression analysis. The Estimated streamflow statistics for the stations used in independent variables selected for the final models had the regression analyses were determined from to be statistically significant at the 95-percent equations using both types of BCFs, and the means of confidence level, and the signs and magnitudes of the the estimates were compared against the means of the coefficients had to be hydrologically reasonable. observed data. The means of the MVUE estimates were

Estimating Methods for Ungaged Stream Sites 27 generally closer to the means of the observed data than miles; maximum, minimum, and mean basin elevation, the means of the smearing estimates, thus the MVUE in feet; maximum, minimum, and mean elevation in estimates were used in the final equations. stratified drift, in feet; and mean basin slope, in percent. The measured basin characteristics for the Data Base Development stations used in the regression analyses are provided in table 10 (at back of the report). Streamflow statistics and basin characteristics All basin characteristics were measured from were included in the regression analyses for 37 gaging digital-map data using an automated GIS procedure stations and 107 LFPR stations. Streamflows at all of developed for the Basin Yield studies. The automated the stations included in the analyses were essentially procedure was created using the AML programming unregulated during low streamflow periods. Thirty-four language of the ARC/INFO GIS software streamgaging stations were in Massachusetts and three (Environmental Systems Research Institute, Inc., were in bordering states (two in Rhode Island and one 1990). The automated procedure determines the in Connecticut) but had more than two-thirds of their drainage-basin boundary for any selected site on a drainage areas in Massachusetts. Available records Massachusetts stream and creates a digital data layer of through climatic year 1995 were used to compute the the basin boundary. The procedure determines the streamflow statistics for the gaging stations. Record drainage-basin boundary for the site, then overlays the lengths range from 2 to 83 years, with a median of 27 boundary on the other digital data layers to determine years (table 3). Streamflow statistics were also the other basin characteristics for the site. The digital computed for 14 other streamgaging stations that were data layers used by the procedure include (1) drainage not used in the analyses but were used to estimate subbasins at 1:24,000 scale, (2) hydrography at streamflow statistics for the LFPRs. Names and 1:25,000 scale, (3) surficial geology at 1:125,000 scale, descriptions of the streamgaging stations are in table 3. and (4) Digital Elevation Models (DEMs) at 1:25,000 Locations of the streamgaging stations and the LFPR scale and 1:250,000 scale. These data layers are stations are shown in figure 1. documented by and are available from MassGIS All 107 LFPR stations used in the analyses were (http://www.state.ma.us/mgis) as separate products. in Massachusetts. Names and descriptions of the LFPR They have also been packaged into a watershed library stations are in table 8 (at back of report). The LFPRs (http://www.state.ma.us/mgis/ix_wat.htm), which also had from 8 to 36 streamflow measurements available contains several derivative data layers needed for using for relation to streamgaging-station discharge records, the automated procedure. with a median of 14 measurements. One-quarter of the LFPR stations had 10 or fewer measurements, and one- The drainage subbasins data layer includes quarter had 18 or more measurements. Calculated drainage-basin boundaries for about 2300 locations in streamflow statistics in cubic feet per second for the Massachusetts and areas in other states that contribute streamgaging stations and estimated streamflow streamflow to Massachusetts. Subbasin boundaries for statistics for the LFPR stations used in the analyses, most USGS data-collection stations are included in the along with variances in base-10 logarithms, standard data layer. The subbasin boundaries were delineated by errors in percent, and years of record for streamgaging the USGS and digitized by MassGIS, and average 2 stations or equivalent years of record for LFPR stations about 4 mi in extent. are provided in table 9 (at back of report). These The hydrography data comprise three layers, statistics were calculated or estimated using the one each for streams, water bodies, and wetlands. methods described earlier in this report. These data were scanned from Mylar separates of the Basin characteristics measured for use in the three types of blue-line features from 1:25,000-scale analyses were selected on the basis of their theoretical USGS topographic quadrangle maps. The streams relation to differences in flow magnitudes of streams, were enhanced by adding centerlines through the results of previous studies in similar hydrologic water bodies, wetlands, and streams represented on environments, and on the ability to measure them. The the maps by double lines. This enhancement allows characteristics measured were drainage area, in square accurate measurements of total stream length to be miles; areas of stratified drift, wetlands, and water obtained, and also creates a stream network that bodies, in square miles; total length of streams, in enables flow routing.

28 Methods for Estimating Low-Flow Statistics for Massachusetts Streams Table 3. Descriptions of streamgaging stations used in the regression analysis and for correlation with low-flow partial record stations, or both Table 3. Descriptions of streamgaging stations used in the regression analysis and for correlation with low-flow partial record [stations,Period of record:or both Periods—Continued of record shown are based on climatic years, which begin on April 1 of the year noted. The word “present” refers to the year of publication for this report (2000). No., number]

Station Latitude Longitude Period of Station name Remarks No. ° ′ ″ ° ′ ″ record Streamgaging stations used in the regression analysis and for correlation with low-ﬂow partial-record stations

01096000 42 38 03 71 39 30 Squannacook River near West Groton, 1950–present Occasional regulation by mill upstream Mass. 01096910 42 27 04 71 13 43 Boulder Brook at East Bolton, Mass. 1972–82 -- 01097300 42 30 39 71 24 25 Nashoba Brook near Acton, Mass. 1964–present -- 01100700 42 48 41 71 01 59 East Meadow Brook near Haverhill, 1963–73 -- Mass. 01101000 42 45 10 70 56 46 Parker River at Byfield, Mass. 1946–present Occasional regulation by mill and ponds 01105600 42 11 25 70 56 43 Old Swamp River near South 1966–present -- Weymouth, Mass. 01106000 41 33 30 71 07 47 Adamsville Brook at Adamsville, R.I. 1941–77 -- 01107000 42 03 41 71 03 59 Dorchester Brook near Brockton, Mass. 1963–73 -- 01109200 41 52 46 71 15 18 West Branch Palmer River near 1962–73 -- Rehoboth, Mass. 01111200 42 06 17 71 36 28 West River at West Hill Dam near 1962–89 Flood-control dam upstream Uxbridge, Mass. 01111300 41 58 52 71 41 11 Nipmuc River near Harrisville, R.I. 1964–90, -- 1994–present 01162500 42 40 57 72 06 56 Priest Brook near Winchendon, Mass. 1919–present No daily record during August 1936 01165500 42 36 10 72 21 36 Moss Brook at Wendell Depot, Mass. 1917–81 01166105 42 35 39 72 21 41 Whetstone Brook at Wendell Depot, 1986–90 -- Mass. 01169000 42 38 18 72 43 32 North River at Shattuckville, Mass. 1940–present Occasional small diurnal fluctuation 01169900 42 32 31 72 41 39 South River near Conway, Mass. 1967–present Small diurnal fluctuation since 1982 01170100 42 42 12 72 40 16 Green River near Colrain, Mass. 1968–present -- 01171500 42 19 05 72 39 21 Mill River at Northampton, Mass. 1939–present -- 01171800 42 18 09 72 41 16 Bassett Brook near Northampton, Mass. 1963–73 -- 01173260 42 23 52 72 08 51 Moose Brook near Barre, Mass. 1963–73 -- 01174000 42 28 42 72 20 05 Hop Brook near New Salem, Mass. 1948–81 -- 01174050 42 28 49 72 13 27 East Branch Fever River near Petersham, 1984–85 -- Mass. 01174565 42 27 18 72 22 56 West Branch Swift River at Shutesbury, 1984–85 -- Mass. 01174900 42 20 08 72 22 12 Cadwell Creek near Belchertown, Mass. 1962–present -- 01175670 42 15 54 72 00 19 Sevenmile River near Spencer, Mass. 1961–present Occasional regulation by ponds upstream 01176000 42 10 56 72 15 51 Quaboag River at West Brimfield, Mass. 1913–present Flood-retarding reservoirs upstream 01180000 42 17 27 72 52 15 Sykes Brook at Knightville, Mass. 1946–72 -- 01180500 42 15 31 72 52 23 Middle Branch Westfield River at Goss 1910–89 Data for August 1965–66 not used due Heights, Mass. to construction of flood-control reservoir upstream

Estimating Methods for Ungaged Stream Sites 29 Table 3. Descriptions of streamgaging stations used in the regression analysis and for correlation with low-flow partial record stations, or both—Continued

01180800 42 15 49 73 02 48 Walker Brook near Becket Center, Mass. 1963–76 -- 01181000 42 14 14 72 53 46 West Branch Westfield River at 1936–present -- Huntington, Mass. 01187400 42 02 03 72 55 49 Valley Brook near West Hartland, Conn. 1941–71 -- 01197015 42 31 12 73 13 48 Town Brook at Bridge Street, 1981–82 -- Lanesborough, Mass. 01197300 42 20 59 73 17 56 Marsh Brook at Lenox, Mass. 1963–73 -- 01198000 42 11 31 73 23 28 Green River near Great Barrington, 1952–70, 1994, -- Mass. 1995 01331400 42 35 20 73 06 48 Dry Brook near Adams, Mass. 1963–73 -- 01332000 42 42 08 73 05 37 North Branch Hoosic River at North 1932–89 Infrequent small diurnal fluctuation Adams, Mass. 01333000 42 42 32 73 11 50 Green River at Williamstown, Mass. 1950–present Infrequent small diurnal fluctuation Streamgaging stations used for correlation with low-flow partial-record stations, but not used in the regression analysis

01073000 43 08 55 70 57 56 Oyster River near Durham, N.H. 1935–present -- 01105730 42 06 02 70 49 23 Indian Head River at Hanover, Mass. 1967–present Some regulation by mills and ponds 01105870 41 59 27 70 44 03 Jones River at Kingston, Mass. 1967–present Regulation by pond and cranberry bogs. Ground- and surface-water drainage boundaries do not coincide 011058837 41 35 32 70 30 30 Quashnet River at Waquoit Village, 1989–present Some regulation by cranberry bog. Mass. Ground- and surface-water drainage boundaries do not coincide 01109000 41 56 51 71 10 38 Wading River near Norton, Mass. 1926–present Regulation by lakes and ponds. Diversions to and from basin for municipal supplies 01109403 41 49 51 71 21 06 Ten Mile River at East Providence, R.I. 1987–present Regulations and diversions from reservior 01118000 41 29 53 71 43 01 Wood River at Hope Valley, R.I. 1942–present Seasonal regulation by pond since 1968. Regulation at low ﬂow until 1952 01121000 41 50 37 72 10 10 Mount Hope River near Warrenville, 1941–present Occasional regulation by ponds Conn. 01184490 41 54 50 72 33 00 Broad Brook at Broad Brook, Conn. 1962–present Regulation by reservoir and mill 01187300 42 02 14 72 56 22 Hubbard River near West Hartland, 1939–55, -- Conn. 1957–present 01188000 41 47 10 72 57 55 Burlington Brook near Burlington, 1932–present -- Conn. 01197000 42 28 10 73 11 49 East Branch Housatonic River at 1936–present Flow regulated by powerplants and Coltsville, Mass. reservoir. Diversion for municipal supply 01198500 42 01 26 73 20 32 Blackberry Brook at Canaan, Conn. 1950–71 -- 01199050 41 56 32 73 23 29 Salmon Creek at Lime Rock, Conn. 1962–present --

30 Streamflow Statistics and Basin Characteristics for Low-Flow Stations in Massachusetts The surficial geology data layer includes seven computed by dividing the total stream length by the categories: (1) sand and gravel deposits, (2) till or basin area; (5) percentage of water bodies, computed bedrock outcrops, (3) sandy till over sand, (4) end by dividing the area of water bodies by the basin area, moraines, (5) large sand deposits, where distinguished and multiplying the result by 100; (6) percentage of from sand and gravel deposits, (6) fine-grained wetlands, computed by dividing the area of wetlands deposits, and (7) floodplain alluvium. The automated by the basin area, and multiplying the result by 100; procedure determines the total area in each category (7) percentage of storage, computed by adding the within the drainage-basin area. Each category was areas of wetlands and water bodies, dividing by the tested separately as a basin characteristic and in basin area, and multiplying the result by 100; (8) total combination with other categories in preliminary percentage of stratified drift, computed by dividing the regression analyses. total area of surficial geology categories 1, 5, 6, and 7 The 1:25,000-scale DEM data were used to by the basin area, and multiplying the result by 100; define or aid in defining drainage-basin boundaries for (9) total drift per unit stream length, in square miles per locations on streams where basin characteristics and mile, computed by dividing the total area of surficial streamflow statistics were needed. The DEM data used geology categories 1, 5, 6, and 7 by the total stream for the boundary delineations were processed so that length; (10) percent coarse-grained drift, computed by the stream network derived from the DEMs would con- dividing the area of surficial geology categories 1, 5, form exactly with the data layer of streams derived and 7 by the basin area, and multiplying the result by from the USGS topographic maps. This was necessary 100; and (11) coarse-grained drift per unit stream to assure correct automatic delineation of drainage length, in square miles per mile, computed by dividing boundaries. When a user of the automated procedure the area of surficial geology categories 1, 5, and 7 by selects a location on a stream for which no boundary the total stream length. exists in the subbasin boundary data layer, the modified Several of the stations that were used in the DEMs are used to determine the boundary for the loca- regression analyses were also used in the drainage- tion up to the points at which the new boundary inter- area-ratio analysis described previously. In some cases, sects existing boundaries in the subbasin boundary data the streamflow statistics shown for these stations in layer. The previously defined boundaries are then used table 7 differ from those shown in table 10, and the to define the remainder of the boundary and the drain- basin characteristics shown in table 9 differ from those age area for the new location. This process minimizes shown in table 1. The streamflow statistics differ reliance on the DEMs for determining drainage bound- because the regression analyses were done two years aries for selected locations, however drainage bound- after the drainage-area-ratio analysis was done, and aries for some small basins are determined entirely during that time period the methods for determining from the modified DEMs. The original (un-processed) streamflow statistics for the LFPR sites was improved, and in some cases additional streamflow measurements 1:25,000-scale DEMs were used to determine mini- were made at the sites. The basin characteristics differ mum, mean, and maximum elevations in the drainage because the data layers, GIS methods, and regression basin and also in the stratified-drift areas in the basin. equations used for the drainage-area ratio analysis were The 1:250,000-scale DEMs were used to compute those described by Ries (1994b, 1997), and they differ mean basin slopes, in percent. from the data layers, GIS methods, and equations Some of the measured basin characteristics were described in this report. Values shown in tables 9 and combined to determine additional characteristics for 10 supersede those shown in tables 1 and 7. use in the analyses. These characteristics included (1) relief, in feet, computed by subtracting the mini- Development of the Equations mum from the maximum basin elevation; (2) relief in Regression equations for predicting the 99-, 98-, stratified-drift areas, in feet, computed by subtracting 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent the minimum from the maximum elevation in the strat- duration flows; the 7-day, 10- and 2- year low flows; ified-drift areas within the basin; (3) GWHEAD, in and the August median flow were developed using feet, a surrogate used in previous Basin Yield studies WLS regression, as described above. The equations are for the effective head in the stratified drift, computed presented in table 4, along with the number of stations by subtracting the minimum from the mean basin ele- used in the analysis and several measures of model vation; (4) drainage density, in miles per square mile, adequacy.

Estimating Methods for Ungaged Stream Sites 31 Table 4. Summary of regression equations developed for estimating low-flow statistics for Massachusetts streams

[Statistic: Pxx is the xx-percent duration flow, Q7,y is the 7-day, y-year low flow, Aug50 is the August median flow, all in cubic feet per second. Equation: DA is drainage area (square miles); SL is mean basin slope (percent); DR/ST is area of stratified drift per unit of total stream length (square miles 2 per mile); REG is region, 0 for eastern, 1 for western. Radj: Coefficient of determination (percent). SEr and SEp: Average standard errors of estimate and prediction, respectively (percent). MAD: Median absolute deviation (percent)] Number 2 Statistic Equation of Radj SEr SEp MAD stations

1.020 P50 0.955(DA) 87 98.1 17.3 17.6 13.4 1.050 0.123 P60 0.763(DA) (DR/ST + 0.1) 97 97.6 19.2 19.8 15.5 1.070 0.357 0.121(REG) P70 0.607(DA) (DR/ST + 0.1) 10 115 96.7 22.7 23.5 17.8 1.080 0.432 0.158(REG) P75 0.509(DA) (DR/ST + 0.1) 10 123 95.9 25.0 25.8 20.6 1.060 0.191 0.693 0.145(REG) P80 0.507(DA) (SL) (DR/ST + 0.1) 10 129 95.2 27.3 28.4 18.8

1.080 0.255 0.746 0.159(REG) P85 0.365(DA) (SL) (DR/ST + 0.1) 10 133 95.0 30.8 31.9 21.0 1.080 0.396 0.985 0.160(REG) P90 0.329(DA) (SL) (DR/ST + 0.1) 10 132 94.0 35.2 36.6 26.8 1.120 0.457 0.999 0.190(REG) P95 0.171(DA) (SL) (DR/ST + 0.1) 10 126 92.1 43.7 45.6 31.0 1.130 0.412 1.030 0.247(REG) P98 0.116(DA) (SL) (DR/ST + 0.1) 10 124 87.8 57.9 60.3 35.1 1.160 0.427 1.050 0.255(REG) P99 0.082(DA) (SL) (DR/ST + 0.1) 10 119 86.7 62.4 65.1 37.3

1.130 0.272 0.858 0.199(REG) Q7,2 0.173(DA) (SL) (DR/ST + 0.1) 10 119 88.5 47.3 49.5 28.0 1.170 0.514 1.180 0.260(REG) Q7,10 0.080(DA) (SL) (DR/ST + 0.1) 10 114 84.4 67.7 70.8 36.7 1.080 0.175 0.745 0.192(REG) Aug50 0.418(DA) (SL) (DR/ST + 0.1) 10 131 95.1 31.5 33.2 23.1

The measures of model adequacy include (1) the 133 (34 streamgaging stations and 99 LFPR stations) coefficient of determination, otherwise known as the for the equations for the 85- percent duration. The 2 adjusted R-squared (Radj ); (2) the average standard number of stations differed because limits were placed error of estimate, SEr, in percent; (3) the average on the standard errors of estimate allowed for the LFPR standard error of prediction, SEp, in percent; and stations used in the analysis, and because some stations (4) the median absolute deviation (MAD), in percent. were removed from the analyses because they were 2 The Radj is a measure of the proportion of the variation outliers. Limits of standard errors of estimate set for in the dependent variable that is explained by the inclusion of LFPR stations in the analyses were 30 independent variables, adjusted for the number of percent for the 99-percent duration flow and the 7-day, stations and the number of independent variables used 10-year low flow; 25 percent for the 98-percent in the analysis. The SEr is a measure of the average duration flow; 20 percent for the 95-percent duration precision with which the regression equations estimate flow and the 7-day, 2-year low flow; and 15 percent for the streamflow statistics for stations used in the all other statistics. The limits were set higher for the analyses, whereas the SEp indicates the average lower flows because, for the same error in flow in cubic precision with which the equations can be used to feet per second, the percentage error increases as the estimate streamflow statistics for ungaged sites with actual flow decreases. Streamflow statistics were basin characteristics similar to those for the stations omitted from table 9 for stations not used in the used in the regression analyses. About 68 percent of regression analyses. streamflows estimated by using regression equations will have errors within the noted average standard Weighting Procedure errors. Half of the regression-equation estimates for According to Montgomery and Peck (1982, stations used in the analyses had absolute errors, in p. 99), when observations of the dependent variable in percent, that were greater than the MAD, and half of a regression analysis have different accuracies, the them were less than the MAD. individual observations should be assigned weights that The number of stations used in the analyses are inversely proportional to their variances. Because ranged from 87 (34 streamgaging stations and 53 LFPR of this, weights for the stations used in the regression stations) for the equation for the 50-percent duration to

32 Methods for Estimating Low-Flow Statistics for Massachusetts Streams analyses were initially assigned as the reciprocal of the result, the variances of a statistic for two LFPR stations variances of the streamflow statistics, shown for each can be the same, but their equivalent years of record statistic for each station in table 9. However, weighted can be very different. residuals from initial regression analyses using these Equation 6 tends to produce estimates of weights were not normally distributed, as stations with equivalent years of record that are higher, on average, very large or small variances relative to the others than the actual years of record for a streamgaging tended to be outliers. Plots of the weighted residuals station with the same variance as that of the LFPR showed that the LFPR stations mostly formed a large, station. Because of this, if years of record (actual and dense cluster, whereas the gaging stations were more equivalent) were to be used alone as the weights in the scattered. This clustering of LFPR stations was more regression analysis, the LFPR stations would have pronounced for the lower (in flow) flow-duration larger influence in the analysis than the streamgaging statistics than for the higher flow-duration statistics; stations in relation to the accuracies of the statistics for this was caused by the fact that variances for the flow- the stations. duration statistics for the LFPR stations were mostly substantially higher than those for the streamgaging Several potential weighting schemes were tested. stations. Variances for the streamgaging stations and The weights used in the regression analyses for the the LFPR stations were similar for the 7-day, 2- and flow-duration statistics and the August median were 10-year low-flow frequency statistics, but very high or computed using the equation low variances for individual stations still caused those stations to be outliers, thus causing non-normal N ⁄ mean()N W = ------(15) residuals. Because of this, another weighting scheme ⁄ () V c mean V c was needed that was theoretically reasonable, would reduce the number of weight-induced outliers, and where W is the weight, N is either the actual years of would not cause the weighted residuals for the LFPR record for streamgaging stations or the equivalent years and streamgaging stations to form separate clusters. of record computed using equation 6 for LFPR Record length often has been used in hydrologic stations, and Vc is the variance of the streamflow regression analyses as an easily calculated surrogate to statistic for the station computed from regression weight the stations according to differences in the equations that relate the variance to the magnitude of accuracy of their streamflow statistics. Record length is the streamflow statistics. A separate regression used to adjust the weights for the stations in the GLS equation was computed for each statistic. Dividing N regression algorithm (Tasker, 1989). Record length can and Vc by their means removes differences in the scales be used for the weights because the variance of a of the variables, yet maintains their spread. Use of streamflow statistic at a streamgaging station is highly variances computed from regression equations in place inversely related to the record length for the station. of the actual calculated variances resulted in (1) similar When LFPR stations are used along with streamgaging variances for a given magnitude of streamflow for both stations in a regression analysis, however, appropriate the streamgaging stations and the LFPR stations, (2) a weighting of the LFPR stations becomes a problem. single population of weighted statistics rather than Equivalent years of record, computed using separate populations for streamgaging stations and equation 6, could be used to weight the LFPR stations LFPR stations, (3) elimination of outliers created by used in the regression analyses, but equivalent years of some stations having much larger or smaller variances record is not highly related to the variance of a statistic than the others, and (4) correction for non-constant for a LFPR station. For example, based on a linear variance of the regression residuals resulting from regression, the reciprocal of the variance of the greater spread of the data for stations with small flows 75-percent duration flow explains about 80 percent of than for stations with large flows. the variation in the years of record for the streamgaging The weights used in the regression analyses for stations used in this study, but it explains only about the 7-day, 2- and 10-year low flows were computed by 17 percent of the variation in the equivalent years of use of the equation record for the LFPR stations. The other parameters in equation 6 explain most of the remaining variation in ⁄ ()⁄ () equivalent years of record for the LFPR stations. As a W = 1 V c mean V c . (16)

Estimating Methods for Ungaged Stream Sites 33 These weights proved to be adequate for The value of Si is computed using the equation developing the equations for the 7-day, 2- 0.5 and 10-year low flows because the S = []γ 2 + x Ux ' (19) variances of the flow statistics for the i i i LFPR stations and the streamgaging 2 where γ is the model error variance; xi is a row vector of the stations used in the analyses were similar, logarithms of the basin characteristics for site i, augmented by a 1 and clustering of the weighted LFPR as the first element; U is the covariance matrix for the regression stations did not occur. coefficients; and xi′ is the transpose of xi (Ludwig and Tasker, 2 1993). The values of BCF, t(α/2,n-p), γ , and U needed to determine Prediction Intervals prediction intervals for estimates obtained from the equations in table 4 are presented in table 5. Prediction intervals at the 90-percent confidence level can be calculated for Example Computations estimates obtained from the regression The procedure necessary to obtain the estimates is explained equations. Prediction intervals indicate the by an example computation of the 95-percent duration low flow for uncertainty inherent in use of the the selected site on the Hawes Brook at Norwood, Mass. (LFPR equations. Assurance is 90 percent that the station number 01104980). First, the necessary basin characteristics true value of the streamflow statistic for an for the site are measured from the various GIS data layers. Values ungaged site will be within the prediction for drainage area, mean basin slope, area of stratified drift, total interval. length of streams, and region are 8.64 mi2, 2.27 percent, 2.20 mi2, 15.5 mi, and zero (eastern region = 0), respectively. DRT/TST is Tasker and Driver (1988) have computed by dividing the stratified-drift area by the total stream shown that a 100(1-α) prediction interval length, and adding a constant of 0.1, to obtain a value of 0.242 mi. for the true value of a streamflow statistic Substituting these values into the equation to predict the 95-percent obtained for an ungaged site by use of duration low flow (table 4) yields weighted regression equations corrected 1.120 0.457 0.999 0.190(0) for bias can be computed by Q95 = 0.171(8.64) (2.27) (0.142+0.1) 10 = 0.675 ft3/s. 1 Q <<Q To determine a 90-percent prediction interval for this estimate, the --- ------QT------, (17) T BCF BCF xi vector is where Q is the streamflow statistic for the xi = {1, log10(8.64), log10(2.27), log10(0.242), 0}, site, BCF is the bias correction factor for γ2 the equation, and T is computed as: the model error variance from table 3 is = 0.03302, and the covariance matrix, U, for the 95-percent duration low flow is [] t()α ⁄ , Si 0.154371– 0.038763 0.024844 0.178711 0.016523 T = 10 2 np– . (18) –0.038763 0.045306– 0.026013 –0.010435 –0.009947 U = 0.024844– 0.026013 0.215936 0.141923– 0.060291 In equation 18, t(α/2,n-p) is the critical value 0.178711– 0.010435 0.141923 0.386539 0.015753 from the students t-distribution at alpha- 0.016523– 0.009947 –0.060291 0.015753 0.071684 level α (α = 0.10 for 90-percent prediction intervals); n-p is the degrees of freedom The standard error of prediction computed from equation 19 0.5 with n stations used in the regression is Si = [0.03302 + 0.0255] = 0.2419, and T computed from analysis and p parameters in the equation equation 18 is T = 101.654(0.2419) = 2.512. The 90-percent prediction (the number of basin characteristics plus interval is estimated from equation 17 as one); and Si is computed from equation 19 1 0.675 0.675 ------<

34 Streamflow Statistics and Basin Characteristics for Low-Flow Stations in Massachusetts Table 5. Values needed to determine 90-percent prediction intervals for estimates obtained from the equations

[Dependent variable: Pxx is the xx-percent duration flow; Q7,y is the 7-day, y-year low flow; Aug50 is the August median flow. BCF: The bias correction factor usedTable in equation5. Values 17. neededt: The critical to determine value from the 90-percent Students t distribution prediction used intervals in equation for estimates6. γ2: The regression obtained model from error the variance equations used —in Continuedequation 19. U: The covariance matrix used in equation 19]

Dependent BCF t γ2 U variable

P50 1.003 1.662 0.00556 0.0854720 -0.0560165 -0.0560165 0.0424162

P60 1.003 1.660 0.00684 0.207555 -0.037260 0.210624 -0.037260 0.041084 0.019092 0.210624 0.019092 0.326740

P70 1.005 1.657 0.00944 0.163451 -0.038750 0.179908 0.029080 -0.038750 0.042838 0.005409 -0.014309 0.179908 0.005409 0.321624 0.064405 0.029080 -0.014309 0.064405 0.054811

P75 1.006 1.656 0.01141 0.149847 -0.041152 0.157830 0.026810 -0.041152 0.043708 0.002937 -0.013412 0.157830 0.002937 0.284083 0.059967 0.026810 -0.013412 0.059967 0.051001

P80 1.007 1.655 0.01360 0.118875 -0.038593 0.009972 0.124035 0.019158 -0.038593 0.046913 -0.024336 -0.006071 -0.006589 0.009972 -0.024336 0.183858 0.099280 -0.057213 0.124035 -0.006071 0.099280 0.284838 0.020611 0.019158 -0.006589 -0.057213 0.020611 0.067052

P85 1.009 1.654 0.01706 0.136687 -0.034752 0.018759 0.159536 0.018791 -0.034752 0.039592 -0.015993 -0.005497 -0.011277 0.018759 -0.015993 0.192606 0.135772 -0.053629 0.159536 -0.005497 0.135772 0.366356 0.016069 0.018791 -0.011277 -0.053629 0.016069 0.065965

P90 1.011 1.654 0.02202 0.114435 -0.032504 0.004651 0.120264 0.019455 -0.032504 0.039590 -0.013401 -0.001500 -0.012562 0.004651 -0.013401 0.183669 0.112504 -0.053751 0.120264 -0.001500 0.112504 0.300342 0.018315 0.019455 -0.012562 -0.053751 0.018315 0.068902

P95 1.017 1.654 0.03302 0.154371 -0.038763 0.024844 0.178711 0.016523 -0.038763 0.045306 -0.026013 -0.010435 -0.009947 0.024844 -0.026013 0.215936 0.141923 -0.060291 0.178711 -0.010435 0.141923 0.386539 0.015753 0.016523 -0.009947 -0.060291 0.015753 0.071684

P98 1.028 1.655 0.05447 0.146494 -0.039856 0.024356 0.169566 0.019479 -0.039856 0.047367 -0.027332 -0.010335 -0.009705 0.024356 -0.027332 0.220827 0.140684 -0.063551 0.169566 -0.010335 0.140684 0.374380 0.017814 0.019479 -0.009705 -0.063551 0.017814 0.073700

P99 1.031 1.656 0.06196 0.155123 -0.041195 0.027513 0.180199 0.019040 -0.041195 0.050395 -0.033160 -0.011029 -0.008574 0.027513 -0.033160 0.251192 0.159684 -0.067073 0.180199 -0.011029 0.159684 0.402732 0.016396 0.019040 -0.008574 -0.067073 0.016396 0.074477

Estimating Methods for Ungaged Stream Sites 35 Table 5. Values needed to determine 90-percent prediction intervals for estimates obtained from the equations—Continued

Dependent BCF t γ2 U variable

Q7,2 1.019 1.657 0.03810 0.158738 -0.046861 0.027795 0.181537 0.018992 -0.046861 0.058491 -0.031551 -0.005478 -0.006372 0.027795 -0.031551 0.223389 0.145159 -0.065982 0.181537 -0.005478 0.145159 0.407552 0.016782 0.018992 -0.006372 -0.065982 0.016782 0.072663

Q7,10 1.036 1.658 0.07122 0.165118 -0.044475 0.027261 0.193316 0.022249 -0.044475 0.054996 -0.029584 -0.004231 -0.008217 0.027261 -0.029584 0.248129 0.168050 -0.069078 0.193316 -0.004231 0.168050 0.452158 0.019891 0.022249 -0.008217 -0.069078 0.019891 0.077525

Aug50 1.009 1.656 0.01785 0.148786 -0.037505 0.015571 0.169781 0.024324 -0.037505 0.039103 -0.017540 -0.011161 -0.011969 0.015571 -0.017540 0.192826 0.127179 -0.053990 0.169781 -0.011161 0.127179 0.364703 0.024260 0.024324 -0.011969 -0.053990 0.024260 0.069070

Thus, the most probable estimate of the 95-percent entirely underlain by coarse-grained stratified-drift duration low flow for station 01104980 is 0.675 ft3/s, deposits, are not adequately represented by sites in the and there is a 90-percent probability that the true value regression analyses. Streams in these areas 3 of Q95 is between 0.264 and 1.67 ft /s. commonly have ground-water drainage divides that are not coincident with topographic drainage divides. Limitations for Use of the Equations Estimates obtained by use of the regression equations for selected sites in these areas could Regression equations can be used to estimate have substantial errors. streamflow statistics for ungaged sites with natural flow conditions in most of Massachusetts. If the equations World Wide Web Application for are used to estimate streamflow statistics for sites Use of the Equations where human influences on streamflows are present, such as water-supply withdrawals and dam regulations, The automated procedure for measuring basin the user should adjust the estimates for the human characteristics, described in the Data Base influences. Development section, was modified for use in a World Applicability of the equations is limited by the Wide Web (Web) application that serves streamflow range of data used to develop the equations and by the statistics for user-selected stream sites. The Web accuracy of the estimates. Ranges of applicability for application (http://ma.water.usgs.gov/streamstats) was each equation are shown in table 6. The measures of Table 6. Ranges of basin characteristics used to develop the model adequacy listed in table 4, and the prediction regression equations intervals calculated using equations 17 to 19, indicate 2 potential errors that can be expected when basin [mi, mile; mi , square mile; --, not applicable] Name characteristics for the selected sites are within the Mini- Maxi- Basin characteristic in Mean ranges of those for the sites used in the regression mum mum equations analyses. The equations generally are not applicable in Drainage area (mi2) ...... DA 1.61 14.9 149 almost all of the South Coastal Shore subbasin of the Total basin stream length (mi)... -- 1.79 27.9 319 South Coastal Basin, the eastern part of the Buzzards Mean basin slope (percent) ...... SL .32 5.28 24.6 Bay Basin, Cape Cod, and the islands of Martha’s Area of stratified drift per DR/ST .00 .144 1.29 2 Vineyard and Nantucket. These areas, which are almost unit stream length (mi /mi) ... Region ...... REG 0--1

36 Methods for Estimating Low-Flow Statistics for Massachusetts Streams developed jointly by the USGS and MassGIS and it where the terms are as previously defined, except incorporates a data base of previously published Q is the regression equation estimate of SU, r streamflow statistics as well as the automated streamflow statistic S for the LFPR station and SEr is procedure for measuring basin characteristics and the standard error of the regression equation estimate obtaining regression equation estimates of streamflow determined for the station from (a) equation 19, (b) the statistics for ungaged sites. The previously developed regression equation standard error of estimate from automated procedure was translated from an AML table 4 if the station was used in the regression script to an Avenue script (Environmental Systems analysis, or (c) the regression equation standard error Research Institute, Inc., 1996a) to enable it to function of prediction from table 4 if the station was not used in in the Web application, and a subroutine was added to the regression analysis. The standard error of estimate solve the regression equations and calculate the determined from equation 19 will provide the most prediction intervals presented in this report. precise weighted estimate, but it is difficult to calculate. A user interface was developed for the Use of the standard errors from table 4 should be application by Syncline, Inc., of Cambridge, Mass., adequate for most needs. under contract to the USGS. The user interface is a Java When an ungaged site is on the same stream as a applet that delivers interactive maps to users using the streamgaging or LFPR station and the drainage area for ArcView Internet Map Server (Environmental Systems the ungaged site is between 0.3 and 1.5 times the Research Institute, Inc., 1996–97) software drainage area of the streamgaging or LFPR station, extension to ArcView (Environmental Systems improved estimates of the streamflow statistics for the Research Institute, Inc., 1996b). Users locate sites on ungaged site can be obtained using a weighting streams for which they want streamflow statistics by procedure to combine the estimates from regression using the interface to add various digital map data and equations with the streamflow statistics determined for to move around and zoom in to the area of interest. the data-collection station. The procedure is modified Users can obtain streamflow statistics for a data- from that of Pope and Tasker (1999, p. 16) and collection station by selecting its location marker on Choquette (1988, p. 42). The estimates are combined the map. The data base provides any previously by first computing the correction factor, determined streamflow statistics for the selected site, including peak-flow statistics not discussed in this C = Q , ⁄ Q , (21) report. Users can also obtain estimated streamflow D SDw SD, r statistics for any location along a stream (within the areas of applicability) by running the automated where CD is the correction factor for D, the data- procedure. Further documentation for the Web collection station (streamgaging or LFPR station), application is provided in a fact sheet (Ries and others, QSD, w is the streamflow statistic S determined from 2000), and in help pages and other links within the available data for the data-collection station, and Q is the streamflow statistic determined from the application. SD, r regression equation. Next, a correction factor, CU, is determined for the ungaged site. If the drainage area COMBINING ESTIMATES DETERMINED for the ungaged site (DAU) is less than 1.5 times larger BY DIFFERENT METHODS than the drainage area for the data-collection station (DAD), use the equation Improved estimates of streamflow statistics for ∆ () LFPR stations can be obtained by combining the DA CD – 1 CU = CD – ------, (22) weighted correlation-based estimates determined from 0.5DAD equation 3 with those obtained from the regression equations. The estimates are weighted by the where ∆DA is the absolute value of the difference reciprocals of their standard errors and averaged by between DAU and DAD. If DAU is smaller than and using the equation within 0.3 times DAD, use the equation

()Q ⁄ ()SE + ()Q ⁄ ()SE ∆ () SU, w w SU, r r DA CD – 1 QSU, = ------()⁄ ()()⁄ () - , (20) CU = CD – ------. (23) w' 1 SEw + 1 SEr 0.7DAD

Combining Estimates Determined by Different Methods 37 The effect of the correction factor is that more weight station by the drainage area for the station, then is given to the streamflow statistic for the data- multiplying these values by the drainage area of the collection station the closer the ungaged site is to it. If ungaged site of interest to obtain estimates of the DAU is greater than 1.5 times or less than 0.3 times streamflow statistics for the site. A comparison of DAD, no correction is necessary. streamflow statistics estimated using the drainage-area ratio method and regression equations to those determined from available data for 25 LFPR and 8 SUMMARY streamgaging stations in 5 Massachusetts river basins indicated that drainage-area ratio estimates generally This report is the sixth and final report of the are as accurate or more accurate than regression Basin Yield series of reports prepared in cooperation estimates when the drainage-area ratio for an ungaged with the Massachusetts Department of Environmental site is between 0.3 and 1.5 times the drainage area of Management. The report provides methods for the index data-collection site. Regression equations can estimating low-flow statistics for Massachusetts be used to obtain estimates for most ungaged sites. streams. Different methods are provided depending on Regression equations were developed to estimate whether the location of interest is a streamgaging the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-, 75-, station, a low-flow partial-record station, or an ungaged 70-, 60-, and 50-percent duration flows; the 7-day, site where no data are available. Standard USGS 2-year and the 7-day, 10-year low flows; and the methods and computer software are described for August median flow for ungaged sites in determining flow-duration and low-flow frequency Massachusetts. As many as 37 streamgaging stations statistics for streamgaging stations. Two methods are and 107 LFPR stations were included in the analyses. described for determining August median flows for Streamflow statistics and basin characteristics for these streamgaging stations. References are provided to stations were presented in the report. The number of reports that describe methods for extending or stations used to develop the individual equations augmenting records for streamgaging stations with ranged from 87 for the 50-percent duration flow to 133 short records to reflect long-term conditions. for the 98-percent duration flow. The gaging stations Mathematical and graphical correlation methods had from 2 to 81 years of record, with a mean record are presented for estimating low-flow statistics for low- length of 37 years. The LFPRs had from 8 to 36 flow partial-record stations. The MOVE.1 streamflow measurements, with a median of 14 mathematical method is recommended for use when measurements. the relation between measured flows at the low-flow All physical characteristics of the basins for the partial-record (LFPR) station and daily mean flows at a stations used in the regression analyses were nearby, hydrologically similar streamgaging station is determined from digital data bases using GIS computer linear. A widely used graphical method is software. Drainage area, the area of stratified-drift recommended when this relation is curved. The report deposits per unit of stream length plus 0.1, mean basin contains equations for computing the variance and slope, and an indicator variable that was 0 in the equivalent years of record for estimates of low-flow eastern region and 1 in the western region of statistics determined using the two methods. Estimates Massachusetts were used in 9 of the 13 final regression of low-flow statistics for LFPR stations can be equations. Mean basin slope was not used in the improved by combining estimates determined from equations for the 50- through 75-percent duration multiple index stations. The report contains equations flows. The indicator variable for region was not used in for calculating combined estimates and the variances, the equations for the 50- and 60-percent duration flows. standard errors, and equivalent years of record of these Only drainage area was used in the equation for the estimates. 50-percent duration flow. All basin characteristics that Two methods are presented for estimating low- appeared in the equations were positively correlated to flow statistics for ungaged sites where no data are the streamflow statistics used as the dependent available -- the drainage-area ratio method and use of variables. regression equations. The drainage-area ratio method is The equations were developed by use of applied by dividing the streamflow statistics for a weighted-least-squares regression analyses. Weights in nearby, hydrologically similar index streamgaging the analyses were assigned proportional to the actual

38 Methods for Estimating Low-Flow Statistics for Massachusetts Streams (for streamgaging stations) or equivalent (for LFPR REFERENCES CITED stations) years of record and inversely proportional to the variances of the streamflow statistics for the Bent, G.C., 1995, Streamflow, ground-water recharge and discharge, and characteristics of surficial deposits in stations. Standard errors of prediction ranged from 70.8 Buzzards Bay Basin, southeastern Massachusetts: U.S. to 17.6 percent for the equations to predict the 7-day, Geological Survey Water-Resources Investigations 10-year low flow and 50-percent duration flow, Report 95-4234, 56 p. respectively. The proportion of the variation in the Bisese, J.A., 1995, Methods for estimating the magnitude dependent variables that is explained by the and frequency of peak discharges of rural, unregulated 2 stream in Virginia: U.S. Geological Survey Water- independent variables (Radj ) ranged from 84.4 to 98.1 Resources Investigations Report 94-4148, 70 p., 1 pl. percent for the 7-day, 10-year low flow and 50-percent Bradu, D. and Mundlak, Y., 1970, Estimation in lognormal duration flow, respectively. The equations are not linear models: Journal of the American Statistical applicable in the Southeast Coastal region of the State, Association, v. 65, no. 329, p.198–211. or where basin characteristics for the selected ungaged Bratton, Lisa, and Parker, G.W., 1995, Estimated availability of water from stratified-drift aquifers in the Concord site are outside the ranges of those for the stations used River Basin, Massachusetts: U.S. Geological Survey in the regression analyses. If the equations are used to Water-Resources Investigations Report 94-4256, 35 p. estimate streamflow statistics for sites where human Cervione, M.A., Jr., 1982, Streamflow information for influences on streamflows are present, such as water- Connecticut with application to land-use planning: supply withdrawals and dam regulations, the user Connecticut Department of Environmental Protection Bulletin 35, p. 16. should adjust the estimates for the human influences. Choquette, A.F., 1988, Regionalization of peak discharges A World Wide Web application is described that for streams in Kentucky: U.S. Geological Survey enables users to obtain streamflow statistics for most Water-Resources Investigations Report 88-4209, 105 p., stream locations in Massachusetts. The Web 1 pl. application provides streamflow statistics for data- Cleveland, W.S., 1979, Robust locally weighted regression and smoothing scatterplots: Journal of the American collection stations from a data base and for ungaged Statistical Association, v. 74, p. 829–836. sites by measuring the necessary basin characteristics Cohn, T.A., DeLong, L.L., Gilroy, E.J., Hirsch, R.M., and for a selected site and solving the regression equations. Wells, D.K., 1989, Estimating constituent loads: Water- Output provided by the Web application for ungaged Resources Research, v. 25, no. 5, p. 937–942. sites includes a map of the drainage-basin boundary deLima, Virginia, 1991, Stream-aquifer relations and yield of determined for the site, the measured basin stratified-drift aquifers in the Nashua River Basin, Massachusetts: U.S. Geological Survey Water- characteristics, the streamflow statistics estimated Resources Investigations Report 88-4147, 47 p. from the equations in this report, and 90-percent Dingman, S.L., 1978, Synthesis of flow-duration curves for prediction intervals for the estimates. unregulated streams in New Hampshire: Water- Resources Bulletin, v. 14, no. 6, p. 1481–1502. Finally, the report presents an equation that Duan, Naihua, 1983, Smearing estimate: a non-parametric can be used to combine regression and correlation retransformation method: Journal of the American estimates to obtain improved estimates of the Statistical Association, v. 78, no. 383, p. 605–610. streamflow statistics for LFPR stations. The report Environmental Systems Research Institute, Inc., 1990, also presents equations that can be used to combine Understanding GIS, the ARC/INFO method: Redlands, regression and drainage-area ratio estimates to obtain Calif., 10 chaps., various pagination. improved estimates of the streamflow statistics for _____1996a, Avenue: Customization and application development for ArcView GIS: Redlands, Calif., 239 p. ungaged sites. These equations are applicable when _____1996b, Getting to know ArcView: New York, N.Y., the drainage area of the ungaged site is between 0.3 John Wiley, various pagination. and 1.5 times the drainage area of a streamgaging or _____1996–1997, ArcView Internet Map Server: Redlands, LFPR station. Calif., 60 p.

References Cited 39 Fennessey, Neil, and Vogel, R.M., 1990, Regional flow- Koltun, G.F., and Roberts, J.W., 1990, Techniques for duration curves for ungauged sites in Massachusetts: estimating flood-peak discharges of rural, unregulated Journal of Water Resources Planning and Management, stream in Ohio: U.S. Geological Survey Water- v. 116, no. 4, p. 530–549. Resources Investigations Report 89-4126, 68 p., 1 pl. Ferguson, R.I., 1986, River loads underestimated by rating Koltun, G.F., and Schwartz, R.R., 1986, Multiple-regression curves: Water Resources Research, v. 22, no. 1, p. 74- equations for estimating low flows at ungaged stream 76. sites in Ohio: U.S. Geological Survey Water-Resources Flynn, K.M., Hummel, P.R., Lumb, A.M., and Kittle, J.L., Investigations Report 86-4354, 39 p., 6 pls. Jr., 1995, User's manual for ANNIE, version 2, a Ku, H.F., Randall, A.D., and MacNish, R.D., 1975, computer program for interactive hydrologic data Streamflow in the New York part of the Susquehanna management: U.S. Geological Survey Water-Resources River Basin: New York State Department of Investigations Report 95-4085, 211 p. Environmental Conservation Bulletin 71, 130 p. Friesz, P.J., 1996, Geohydrology of stratified drift and Kulik, B.H., 1990, A method to refine the New England streamflow in the Deerfield River Basin: U.S. Aquatic Base Flow Policy: Rivers, v. 1, no. 1, p. 8–22. Geological Survey Water-Resources Investigations Report 96-4115, 49 p., 1 pl. Lapham, W.W., 1988, Yield and quality of ground water Gadoury, R.A., Socolow, R. S., Girouard, G.G., and from stratified-drift aquifers, Taunton River Basin, Ramsbey, L.R., 1995, Water resources data for Massachusetts: U.S. Geological Survey Water- Massachusetts and Rhode Island, water year 1994: U.S. Resources Investigations Report 86-4053, 69 p., 2 pls. Geological Survey Water-Data Report MA-RI-94-1, Loaiciga, H.A., 1989, Variability of empirical flow quantiles: 314 p. Journal of Hydraulic Engineering, American Society of Gilroy, E.J., Hirsch, R.M., and Cohn, T.A., 1990, Mean Civil Engineers, 115(1), p. 82–100. square error of regression-based constituent transport Ludwig, A.H., and Tasker, G.D., 1993, Regionalization of estimates: Water Resources Research, v. 26, no. 9, p. low-flow characteristics of Arkansas streams: U.S. 2069–2077. Geological Survey Water-Resources Investigations Hardison, C.H., 1969, Accuracy of streamflow Report 93-4013, 19 p. measurements: U.S. Geological Survey Professional Lumb, A.M., Kittle, J.L., Jr., and Flynn, K.M., 1990, Users Paper 650-D, p. 210–214. manual for ANNIE, a computer program for interactive Hardison, C.H., and Moss, M.E., 1972, Accuracy of low- hydrologic analyses and data management: U.S. flow characteristics estimated by correlation of base- Geological Survey Water-Resources Investigations flow measurements, in Manual of Hydrology—Part 2. Report 89-4080, 236 p. Low-Flow Techniques: U.S. Geological Survey Water- Lumia, Richard, 1991, Regionalization of flood discharges Supply Paper 1542-B, p. 35–55. for rural, unregulated streams in New York, excluding Hansen, B.P., and Lapham, W.W., 1992, Geohydrology and Long Island: U.S. Geological Survey Water-Resources simulated ground-water flow, Plymouth–Carver aquifer, Investigations Report 90-4197, 119 p., 2 pls. southeastern Massachusetts: U.S. Geological Survey Male, J.W., and Ogawa, Hisashi, 1982, Low flow of Water-Resources Investigations Report 90-4204, 69 p., Massachusetts streams: Amherst, Mass., University of 2 pls. Massachusetts, Water Resources Research Center Hirsch, R.M., 1982, A comparison of four streamflow record Publication 125, 152 p. extension techniques: Water Resources Research, v. 18, Minitab, Inc., 1998a, User’s guide 1—Data, graphics, and no. 4., p. 1081–1088. macros: State College, Penn, 33 chapters, various Iman, R.L., and Conover, W.J., 1983, A modern approach to pagination. statistics: New York, John Wiley, 497 p. Johnson, C.G., 1970, A proposed streamflow data program Minitab, Inc., 1998b, User’s guide 2—Data analysis and for central New England: U.S. Geological Survey quality tools: State College, Penn, 22 chapters, various Open-File Report, 38 p. pagination. Klinger, A.R., 1996, Estimated short-term yields of and Montgomery, D.C., and Peck, E.A., 1982, Introduction to quality of ground water in stratified-drift aquifer areas linear regression analysis: New York, John Wiley, in the Neponset River Basin, Massachusetts: U.S. 504 p. Geological Survey Water-Resources Investigations Myette, C.F., and Simcox, A.C., 1992, Water resources and Report 93-4142, 30 p. aquifer yields in the Charles River Basin, Koch, R.W., and Smillie, G.M., 1986, Bias in hydrologic Massachusetts: U.S. Geological Survey Water- prediction using log-transformed regression models: Resources Investigations Report 88-4173, Revised Water Resources Bulletin, v. 22, no. 5, p. 717–723. 1991, 50 p.

40 Methods for Estimating Low-Flow Statistics for Massachusetts Streams Neter, John, Wasserman, William, and Kutner, M.H., 1985, Searcy, J.K., 1959, Flow-duration curves, Manual of Applied linear statistical models: Homewood, Illinois, hydrology—Part 2. Low-flow techniques: U.S. Irwin, 1127 p. Geological Survey Water-Supply Paper 1542-A, p. 1– Olimpio, J.C., and deLima, Virginia, 1984, Ground-water 33. resources of the Mattapoisett River Valley, Plymouth Socolow, R.S., Comeau, L.Y., Casey, R.G., and Ramsbey, County, Massachusetts: U.S. Geological Survey Water- L.R., 1996, Water resources data for Massachusetts and Resources Investigations Report 84-4043, 83 p. Rhode Island, water year 1995: U.S. Geological Survey Parker, G.W., 1977, Methods for determining selected flow Water-Data Report MA-RI-95-1, 428 p. characteristics for streams in Maine: U.S. Geological Socolow, R.S., Murino, Domenic, Jr., Casey, R.G., and Survey Open-File Report 78-871, 31 p. Ramsbey, L.R., 1997, Water resources data for Persky, J.H., 1993, Yields and water quality of stratified-drift Massachusetts and Rhode Island, water year 1996: U.S. aquifers in the Southeast Coastal Basin, Cohassett to Geological Survey Water-Data Report MA-RI-96-1, Kingston, Massachusetts: U.S. Geological Survey 367 p. Water-Resources Investigations Report 91-4112, 47 p., Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic 2 pl. analysis 1. Ordinary, weighted, and generalized least Pope, B.F., and Tasker, G.D., 1999, Estimating the squares compared: Water Resources Research, v. 21, magnitude and frequency of floods in rural basin of no. 9, p. 1421–1432. North Carolina: U.S. Geological Survey Water- Stedinger, J.R., and Thomas, W.O., 1985, Low-flow Resources Investigations Report 99-4114, 44 p. frequency estimation using base-flow measurements: Randall, A.D., 1996, Mean annual runoff, precipitation, and U.S. Geological Survey Open-File Report 85-95, p. 22. evapotranspiration in the glaciated northeastern United Tasker, G.D., 1972, Estimating low-flow characteristics of States, 1951-80: U.S. Geological Survey Open-File streams in southeastern Massachusetts from maps of Report 96-395, 2 pls., scale 1:1,000,000. ground water availability, in Geological Survey Ries, K.G., III, 1994a, Estimation of low-flow duration Research, 1972: U.S. Geological Survey Professional discharges in Massachusetts: U.S. Geological Survey Paper 800-D, p. D217–D220. Water-Supply Paper 2418, 50 p. _____1975, Combining estimates of low-flow characteristics _____1994b, Development and application of generalized- of streams in Massachusetts and Rhode Island: Journal least-squares regression models to estimate low-flow of Research of the U.S. Geological Survey, v. 3, no. 1, duration discharges in Massachusetts: U.S. Geological p. 107–112. Survey Water-Resources Investigations Report 94- _____1989, An operational GLS model for hydrologic 4155, 33 p. regression: Journal of Hydrology, v. iii, p. 361–375. _____1997, August median streamflows in Massachusetts: Tasker, G.D., and Driver, N.E., 1988, Nationwide regression U.S. Geological Survey Water-Resources Investigations models for predicting urban runoff water quality at Report 97-4190, 27 p. unmonitored sites: Water Resources Bulletin, v. 24, _____1999, Streamflow measurements, basin characteristics, no. 5, p. 1091–1101. and streamflow statistics for low-flow partial-record Tasker, G.D., and Stedinger, J.R., 1989, An operational GLS stations operated in Massachusetts from 1989 through model for hydrologic regression: Journal of Hydrology, 1996: U.S. Geological Survey Water-Resources v. 3, p. 361–375. Investigations Report 99-4006, 162 p. Thomas, M.P., 1966, Effect of glacial geology upon the time _____2000, Obtaining streamflow statistics for distribution of streamflow in eastern and southeastern Massachusetts streams on the World Wide Web: U.S. Connecticut: U.S. Geological Survey Professional Geological Survey Fact Sheet 104-00, 4 p. Paper 550-B, p. B209–B212. Riggs, H.C., 1972, Low-flow investigations: U.S. Geological U.S. Commerce Department, National Oceanic and Survey Techniques of Water-Resources Investigations, Atmospheric Administration, 1989, Climatological book 4, chap. B1, 18 p. data, annual summary, New England, v. 101, no. 13, Risley, J.C., 1994, Estimating the magnitude and frequency 51 p. of low flows of streams in Massachusetts: U.S. _____1994, Climatological data, annual summary, New Geological Survey Water-Resources Investigations England, v. 106, no. 13, 52 p. Report 94-4100, 29 p. U.S. Fish and Wildlife Service, 1981, Interim regional policy Ritzi, Charles, and Associates, 1987, Computation of for New England stream flow recommendations: USFWS Aquatic Base Flow for Regulated Streams. Region I, Concord, NH: U.S. Fish and Wildlife Service, Winthrop, Maine, 15 p. 3 p.

References Cited 41 Vogel, R.M., and Fennessey, N.M, 1994, Flow-duration _____1991, The value of streamflow record augmentation curves. I: New interpretation and confidence intervals: procedures in low-flow and flood-flow frequency Journal of Water Resources Planning and Management, analysis: Journal of Hydrology, v. 125, pp. 259–276 v. 120, no. 4, p. 485–504. Wandle, S.W., Jr., and Randall, A.D., 1994, Effects of Vogel, R.M., and Kroll, C.N., 1989, Low-flow frequency surficial geology, lakes and swamps, and annual water analysis using probability-plot correlation coefficients: availability on low flows of streams in central New Journal of Water Resources Planning and Management, England, and their use in low-flow estimation: U.S. v. 115, no. 3, p.338–357. Geological Survey Water-Resources Investigations Report 93-4092, 57 p. _____1990, Generalized low-flow frequency relationships for ungaged sites in Massachusetts: Water Resources Bulletin, v. 26, no. 2, p. 241–253.

42 Methods for Estimating Low-Flow Statistics for Massachusetts Streams TABLES 7–10

cent differences between cent differences between the Remarks e to applicability of the drainage- applicability of the drainage-area ows at the index streamgaging station.] streamgaging at the index ows fl ow statistics are the 99-, 98-, and 95-percent duration and the August median statistics are the 99-, 98-, and 95-percent duration ow percent percent Absolute fl difference Low- Data-based estimates were calculated for streamgaging stations from the daily mean Data-based estimates were calculated for streamgaging /s) 3 (ft Continued Estimate Regression equations — ows to same-day mean ows fl Low-flow statistic: Low-flow percent percent Absolute Data-based estimates: difference method /s) 3 (ft Drainage-area ratio ow statistics. ow Estimate fl /s) 3 (ft Squannacook River Basin (subbasin of Nashua River Basin) of Nashua River Basin (subbasin Squannacook River estimate Data-based ow ow partial-record stations by correlating measured ow fl fl 9895 .046 .15 .72 1.04 1,472 612 .44 .62 852 327 9895 .76 1.2298 1.51 2.1895 99.7 3.22 78.7 5.08 1.27 5.44 1.7098 7.8495 67.5 68.9 39.1 6.10 54.3 8.97 5.36 7.07 7.02 10.2 66.6 15.9 38.1 13.7 7.33 9.56 20.2 6.6 August .86 1.83August 114 2.53 1.00 3.83August 16.5 51.4 10.2 2.52 13.8August 0.4 35.3 16.2 11.0 17.9 7.5 10.5 15.3 5.9 Average .27 1.05Average 1,105 1.28 .61 2.19Average 641 85.0 5.27 1.64 7.90Average 46.9 58.6 9.08 6.93 10.3 45.5 14.2 9.50 12.3 statistic Low- /s); average is the average of the four stream is the average /s); average area ratio 3 Drainage- No. Index gaging station stream- Station numbers for streamgaging stations are in bold the station number column. Station numbers for streamgaging Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01095928 01096000 0.092 99 0.026 0.60 2,223 0.38 1,369 01095930 01096000 .192 9901095977 01096000 .688 .60 99 1.2601095990 01096000 110 .895 2.58 1.08 4.54 99 80.5 76.0 5.05 4.38 5.90 69.9 16.8 5.89 16.6 ows, in cubic feet per second (ft ows, ows for the period of record and estimated low- ows Station No.: Table 7. the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams fl fl data-based estimates and from the drainage-area ratio method regression equations for stations used to analyze ratio method for estimating low-flow statistics ungaged Massachusetts streams Table 7. [

Table 7 45 cent differences between Remarks ) divided by unregulated area for by unregulated ) divided ). 2 2 e to applicability of the drainage- 01108490 (8.55 mi 01109000 (23.8 mi Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) Wading River Basin (subbasin of Taunton River Basin) River Taunton of Basin (subbasin River Wading 3 (ft estimate Data-based Squannacook River Basin (subbasin of Nashua River Basin)— of Nashua River Basin (subbasin Squannacook River ow ﬂ 9895 7.90 11.4 ------8.86 11.4 12.2 0.1 9895 8.19 12.2 8.58 12.4 4.8 1.6 10.1 12.9 23.8 6.1 9895 1.19 1.41 .83 1.15 30.6 18.4 .34 .59 71.7 58.0 9895 .38 .44 .37 .52 2.12 15.7 .19 .32 48.7 27.6 August 20.0 --August 22.5 -- 21.7 17.9 3.6 10.4 20.1 10.7 August 1.94 2.16August 11.3 .61 1.69 .97 12.7 58.6 .76 24.1 Average 11.5 --Average 12.4 -- 12.5 11.3 4.0 7.3 12.8 14.8 Average 1.42 1.22Average 23.4 .45 .72 .55 54.7 20.7 .36 39.7 statistic Low- area ratio Drainage- -- 1.000 99 6.60 -- -- 7.03 6.5 No. Index gaging station stream- Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01096000 01096035 01096000 1.085 9901108490 01109000 6.74 0.359 7.16 99 6.2 1.13 7.99 0.75 18.5 33.3 0.26 76.6 area for Drainage-area ratio computed as unregulated 01108600 01109000 .161 99 .36 .34 6.37 .15 58.4 Table 7. the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams

46 Methods for Estimating Low-Flow Statistics for Massachusetts Streams 86. – cent differences between Remarks ) divided by unregulated area for by unregulated ) divided ). 2 2 e to applicability of the drainage- 01108700 (9.60 mi 01109000 (23.8 mi period of record for station 01108500, 1954 Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) Green River Basin (subbasin of Deerfield River Basin) of Deerfield River Basin (subbasin River Green 3 (ft estimate Data-based Wading River Basin (subbasin of Taunton River Basin)— River Taunton of Basin (subbasin River Wading ow fl 9895 2.30 3.20 ------1.40 2.26 39.0 29.4 9895 .62 .7798 .9495 1.15 52.4 3.34 50.1 4.02 3.06 .30 .45 3.75 51.2 8.4 41.3 6.7 1.59 2.12 52.5 47.2 9895 1.17 1.47 .93 1.29 20.7 12.2 .48 .79 59.3 46.1 August 6.00 --August -- 1.38 5.75 2.01August 4.2 45.7 6.62 1.08 6.53 21.9 1.4 4.28 35.3 August 2.25 2.42 7.6 2.1 10.5 Average 3.40 --Average -- .82 2.63 1.23Average 30.1 50.5 4.22 .52 3.99 40.9 6.6 2.35 46.7 Average 1.50 1.37 15.9 .91 45.4 statistic Low- area ratio Drainage- -- 1.000 99 2.10 -- -- 1.10 47.7 Statistics computed for the period corresponding to No. Index gaging station stream- Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01170020 01170100 0.125 9901170025 01170100 0.52 .408 0.80 99 53.9 2.90 0.26 2.61 49.3 10.0 1.40 51.9 01108700 01109000 0.403 99 1.10 0.85 23.0 0.38 65.6 area for Drainage-area ratio computed as unregulated 01109000 Table 7. the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams

Table 7 47 cent differences between Remarks e to applicability of the drainage- Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 (ft estimate Data-based Green River Basin (subbasin of Deerfield River Basin)— of Deerfield River Basin (subbasin River Green ow fl 9895 7.50 9.20 ------4.42 5.75 41.1 37.5 9895 1.00 1.20 1.0598 1.2995 5.0 5.34 7.5 6.48 .45 5.78 .62 7.09 55.2 8.2 48.3 9.4 3.5898 4.6195 33.0 28.9 8.20 9.97 8.67 10.6 5.7 6.3 5.27 6.81 35.7 31.7 August 1.93 2.24August 16.1 10.9 1.25 12.3August 35.3 12.8 16.0 8.95 --August 17.9 16.9 -- 18.5 11.6 9.5 27.3 13.8 18.6 Average 1.25 1.37Average 7.8 6.83 .68 7.52Average 48.2 9.4 9.78 5.06 --Average 28.1 10.5 -- 11.3 6.40 6.6 36.6 7.59 30.5 statistic Low- area ratio Drainage- -- 1.000 99 6.40 -- -- 3.81 40.5 No. Index gaging station stream- Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01170030 01170100 0.140 9901170055 01170100 0.87 .771 0.90 9901170100 2.6 4.60 0.40 4.9301170121 01170100 54.1 7.2 1.156 3.09 99 32.8 7.05 7.40 5.0 4.52 35.9 Table 7. the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams

48 Methods for Estimating Low-Flow Statistics for Massachusetts Streams cent differences between Remarks e to applicability of the drainage- those based on both gaging stations in the basin. those based on both gaging Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 Quaboag River Basin (subbasin of Chicopee River Basin) of Chicopee River Basin (subbasin Quaboag River (ft estimate Data-based Green River Basin (subbasin of Deerfield River Basin)— of Deerfield River Basin (subbasin River Green ow fl 9895 8.6 10.6 9.42 11.6 9.5 9.4 6.09 7.76 29.2 26.7 9895 .16 .34 .25 .43 55.9 25.7 .2798 .4395 65. 25.7 .36 .61 1.16 1.74 222 185 .50 .76 37.8 23.9 9895 .16 .34 .81 1.22 405 260 .27 .43 65.2 25.7 August 18.6 20.1 8.1 15.3 17.6 August 1.46 1.26August 13.7 1.46 1.22 2.60August 16.4 78.1 1.80 1.22 3.72 16.4 107 2.01 11.7 Average 1.3 12.3 9.2 8.59 25.6 Average .52 .54Average 41.8 .52 .54 1.32Average 298 50.6 .76 .54 1.89 184 50.6 .92 30.2 statistic Low- area ratio Drainage- No. Index gaging station stream- 01176000 .058 99 .29 .93 221 .43 47.2 Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01170141 01170100 1.256 99 7.32 8.04 9.8 5.20 29.0 01175660 01175670 0.698 99 0.12 0.20 72.0 0.23 94.9 of are the weighted averages Correlation estimates shown 01175660 01176000 .041 9901175670 .12 .65 451 .23 94.9 the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams Table 7.

Table 7 49 cent differences between Remarks e to applicability of the drainage- those based on both gaging stations in the basin. those based on both gaging stations in the basin. those based on both gaging Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 (ft estimate Data-based Quaboag River Basin (subbasin of Chicopee River Basin)— of Chicopee River Basin (subbasin Quaboag River ow ﬂ 9895 2.88 4.68 1.68 2.85 41.7 39.1 2.32 3.539895 19.4 24.6 21.5 30.6 5.73 9.71 73.3 68.3 8.69 13.2 59.6 56.9 9895 2.88 4.68 5.43 8.15 88.5 74.1 2.32 3.539895 19.4 24.6 21.5 30.6 18.5 27.8 14.0 9.2 8.69 13.2 59.6 56.9 August 11.9 8.40August 29.4 11.9 10.5 17.4August 11.8 46.2 62.5 10.5 28.6August 11.8 54.2 62.5 43.6 59.3 30.2 5.1 43.6 30.2 Average 5.43 3.57Average 37.6 5.43 4.58 8.83Average 17.1 75.3 33.2 4.58 12.2Average 17.1 67.6 33.2 18.1 30.1 52.0 11.6 18.1 52.0 statistic Low- area ratio Drainage- No. Index gaging station stream- Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01175695 01175670 4.669 99 2.26 1.35 40.3 1.98 12.5 of are the weighted averages Correlation estimates shown 01175695 01176000 .272 9901175905 0175670 15.92 2.26 4.35 9901175905 01176000 92.5 18.1 .926 1.98 4.62 99 12.5 74.5 18.1 7.01 14.8 61.3 18.2 of are the weighted averages Correlation estimates shown 7.01 61.3 the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams Table 7.

50 Methods for Estimating Low-Flow Statistics for Massachusetts Streams 1996. cent differences between – Remarks e to applicability of the drainage- period of record available at the time of analysis for period of record available station 01175670, 1961 those based on both gaging stations in the basin. those based on both gaging analyses to station used in the regression those for any determine the equations. stations in the basin. those based on both gaging analyses to station used in the regression those for any determine the equations. Some basin characteristics for this station are larger than Some basin characteristics for this station are larger than Some basin characteristics for this station are larger Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 (ft estimate Data-based Quaboag River Basin (subbasin of Chicopee River Basin)— of Chicopee River Basin (subbasin Quaboag River ow ﬂ 9895 20.0 30.0 6.19 10.5 69.1 65.0 17.0 22.7 14.7 24.4 9895 32.1 44.3 7.46 12.6 76.8 71.6 21.7 28.69895 32.4 35.3 39.2 54.6 8.79 14.9 77.6 72.7 29.8 38.2 23.9 30.1 9895 32.1 44.3 24.1 36.2 24.9 18.3 21.7 28.69895 32.4 35.3 39.2 54.6 28.4 42.6 27.6 22.0 29.8 38.2 23.9 30.1 August 64.0 30.9 51.7 55.4 13.4 August 84.7 37.3August 56.0 84.7 70.0 77.2August 17.4 105 8.9 70.0 43.9August 17.4 58.2 105 88.3 90.9 15.9 13.4 88.3 15.9 Average 32.5 13.1 63.7 27.2 17.0 Average 47.1 15.8Average 70.6 47.1 34.3 39.2Average 30.7 20.3 58.0 34.3 18.7Average 30.7 71.8 58.0 44.8 46.2 25.2 23.7 44.8 25.2 statistic Low- area ratio Drainage- No. Index gaging station stream- 01175670 17.19 99 16.0 4.98 68.9 13.5 15.6 Statistics computed for the period corresponding to Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01176000 01176350 01175670 20.72 99 27.3 6.01 78.0 17.0 37.8 of are the weighted averages Correlation estimates shown 01176350 01176000 1.206 9901176435 01175670 24.41 27.3 19.3 9901176435 01176000 29.3 33.4 1.42 17.0 7.08 99 37.8 78.8 33.4 23.0 22.7 31.0 of are the weighted averages Correlation estimates shown 32.0 23.0 31.0 the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams Table 7.

Table 7 51 cent differences between Remarks e to applicability of the drainage- those based on both gaging stations in the basin. those based on both gaging stations in the basin. those based on both gaging percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 (ft estimate Data-based West Branch Westfield River Basin (subbasin of Westfield River Basin) River Westfield of Basin (subbasin River Westfield Branch West ow fl 9895 .68 1.03 1.30 1.73 90.9 68.0 .70 1.059895 2.9 1.9 3.67 5.23 5.47 7.29 49.0 39.4 5.86 7.57 59.5 44.8 9895 .68 1.03 1.21 1.63 77.7 58.3 .70 1.059895 2.9 1.9 3.67 5.23 5.09 6.86 38.7 31.2 5.86 7.57 59.5 44.8 August 2.45 3.46August 41.2 2.45 2.69 2.99August 10.0 22.0 10.9 2.69 14.6August 10.0 33.9 10.9 15.4 12.6 41.5 15.6 15.4 41.5 Average 1.17 1.90Average 80.0 1.17 1.27 1.70Average 9.5 62.5 5.67 1.27 8.02Average 9.5 46.9 5.67 8.47 7.17 55.2 32.3 8.47 55.2 statistic Low- area ratio Drainage- No. Index gaging station stream- Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01180600 01180800 4.325 99 0.51 1.12 120 0.627 23.2 of are the weighted averages Correlation estimates shown 01180600 01181000 .136 9901180750 01180800 18.22 .51 99 .9801180750 01181000 2.87 91.9 .572 4.74 .627 99 65.2 23.2 2.87 5.02 4.12 75.1 of are the weighted averages Correlation estimates shown 43.6 5.02 75.1 the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams Table 7.

52 Methods for Estimating Low-Flow Statistics for Massachusetts Streams cent differences between Remarks e to applicability of the drainage- those based on both gaging stations in the basin. those based on both gaging stations in the basin. those based on both gaging Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 (ft estimate Data-based ow fl 9895 .14 .18 .12 .16 19.3 13.8 .02298 .04195 84.8 77.3 .30 .4098 .2895 .38 2.77 7.0 3.53 6.0 7.37 .11 9.83 .18 166 62.7 178 54.3 8.40 10.8 203 205 9895 .14 .18 .11 .15 24.8 18.8 .022 .041 84.8 77.3 West Branch Westfield River Basin (subbasin of Westfield River Basin)— River Westfield of Basin (subbasin River Westfield Branch West August .29 .31August 9.1 .29 .14 .27August 49.3 5.9 .80 .14 .69August 49.3 13.8 5.84 19.6 .51 236 36.6 22.1 278 Average .18 .17Average 15.2 .18 .054 .15Average 76.1 19.6 .44 .054 .39Average 76.1 10.0 3.62 1.8 .22 188 54.3 12.1 223 statistic Low- area ratio Drainage- No. Index gaging station stream- 01181000 .031 99 .26 .23 13.1 .095 63.5 Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01180780 01180800 0.390 99 0.12 0.10 18.5 0.009 92.7 of are the weighted averages Correlation estimates shown 01180780 01181000 .012 9901180800 .12 .08801180821 01180800 24.57 29.0 .009 99 92.7 2.34 6.39 173 7.1 204 of are the weighted averages Correlation estimates shown the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams Table 7.

Table 7 53 77. – cent differences between Remarks e to applicability of the drainage- period of record for station 01180800, 1963 Continued percent percent Absolute difference /s) 3 (ft Continued Estimate Regression equations — percent percent Absolute difference method /s) 3 (ft Drainage-area ratio Estimate /s) 3 (ft estimate Data-based ow fl 9895 8.9 12.0 9.56 12.7 7.4 5.8 12.4 15.4 38.8 28.6 9895 2.77 3.53 6.86 9.25 148 162 8.40 10.8 203 205 West Branch Westfield River Basin (subbasin of Westfield River Basin)— River Westfield of Basin (subbasin River Westfield Branch West August 22.0 25.5 15.9 30.4 38.3 August 5.84 17.0 191 22.1 278 Average 12.5 14.0 11.0 17.1 37.2 Average 3.62 9.66 160 12.1 223 statistic Low- area ratio Drainage- No. Index gaging station stream- 01180800 31.86 99 7.2 8.28 15.0 10.3 43.3 Statistics computed for the period corresponding to Low-flow statistics estimated using available data, the drainage-area ratio method, and regression equations; absolute per No. Station 01180821 01181000 0.771 9901181000 2.34 5.55 137 7.1 204 Table 7. the data-based estimates and from drainage-area ratio method regression equations for stations used to analyz area ratio method for estimating low-flow statistics ungaged Massachusetts streams

54 Methods for Estimating Low-Flow Statistics for Massachusetts Streams correlation Gaging stations used for Gaging 01111200 01111200 01111200 01111200 Number of measurements Continued — Station name No. Basin gure 1. No., number] ﬁ ″

′

° Longitude ″

′

° Number refers to Latitude Descriptions of low-flow partial-record stations used in the regression analyses Descriptions of low-flow partial-record stations used in the regression analyses No. Station 01073860 42 51 0001094340 42 33 35 70 51 59 71 52 02 18 Mass. 11 Smallpox Brook at Salisbury, Mass.Westminster, near Whitman River 13 10 01109000, 01097300, 01105600, 01105730, 01111300, 01101000, 01097300, 01096000, 01073000 01094396 42 34 2801094760 42 23 49 71 50 1501095220 42 24 39 71 46 48 1101095380 71 47 30 42 23 00 Mass. 11 Philips Brook at Fitchburg, 01095915 Mass. Boylston, 42 34 26 71 50 12West Brook near 11 Waushacum 01095928 42 40 24 71 37 43 near Sterling, Mass. River Stillwater 01096504 11 42 40 03 71 46 3901096505 Brook near Holden, Mass. 11 Trout 42 41 23 71 33 55 Mass. 11 Mulpus Brook near Shirley, 01096515 71 32 54 Mass. 42 40 41Ashby, Brook near 11 Trapfall 01096805 10 42 21 15 71 29 38 Brook at East Pepperell, Mass. 11 Reedy Meadow 01096855 01097300, 01096000, 01111300, 01175670 42 23 57 71 37 40 Brook near Pepperell, Mass. Unkety 13 71 34 00 1001096935 14 Salmon Brook at Main Street Dunstable, Mass. 42 25 4701097280 23 14 North Brook near Berlin, Mass. 01096000, 01097300, 01162500, 01175670, 01101000 42 28 07 71 30 56 Danforth Brook at Hudson, Mass. 1701099400 01096000, 01097300, 01175670, 01162500, 01111200 71 24 31 42 37 29 1401100608 19 01096000, 01097300, 01162500, 01101000 42 37 14 71 19 11 Mass. 17Wheeler Street at Stow, 14 Elizabeth Brook at 1101101100 42 43 31 71 12 44 Concord, Mass.West Pond Brook at Fort 01175670, 01097300, 01096000, 01162500, 01111200 1801102053 01162500, 01101000, 01096000, 01073000, 01097300 14 01097300, 01096000, 01162500, 01175670 42 33 34 70 54 01102490 Mass. Brook at Lowell, Meadow 15 River 22 01162500, 01175670, 01096000, 01097300 42 28 16 70 56 55 Mass.Tewksbury, Brook near 16 Meadow 01103015 12 71 10 34 01096000, 01097300, 01162500, 01101000 42 25 20 Mass. near Rowley, 18 Mill River 01103253 01097300, 01096000, 01175670, 01111200, 01111300 42 08 27 71 08 59 Mass. 18 Crane Brook at Danvers, 01103435 42 17 13 Mass. 71 25 26 16Woburn, Glen Brook near Shaker 1601103440 20 42 17 45 71 18 05 1601104960 01175670, 01097300, 01162500, 01096000 Arlington, Mass. 20 Mill Brook at 0107300, 01096000, 01175670, 01105600, 01111300, 42 11 04 71 17 18 Mass. Medway, 01097300, 01105600, 01109000, 01111300, 01111200 West 20 Brook near Chicken 01104980 71 13 29 13 Mass. 42 10 26Wellesley, Brook at 20 Waban 15 Mass. 71 12 31Wellesley, 19 Fuller Brook at 01097300, 01096000, 01101000, 01105600 01105100 42 09 36 01073000, 01096000, 01097300, 01105600, 01101000 Mass. Brook near Norwood, Germany 01105270 19 42 08 59 71 11 47 13 Mass. Brook at Norwood, Hawes 71 08 5801105568 19 9 01097300, 01105600, 01101000 42 09 19 10 2201105575 Mass. Brook near Norwood, 19 Traphole 42 11 02 71 01 37 01101000, 01097300, 01073000 Massapoag Brook at Canton, Mass. 01073000, 01096000, 01097300, 01105600, 01101000 01109000, 01073000, 01111300, 01111200 71 00 42 19 20 at Holbrook, Mass. 19 Cochato River 11 01097300, 01105600, 01101000 Cranberry Brook at Braintree Highlands, Mass. 18 18 01109000, 01097300, 01111300, 01111200, 01175670 01111200, 01111300, 01109000, 01105730, 01101000 01097300, 01111300, 01111200, 01109000 20 26 01109000, 01097300, 01105600, 01105730, 01111300, 16 01101000, 01111300, 01105730, 01105870, 01109000 9 01105600, 01097300, 01105730, 01109000 01109000, 01097300, 01105600, 01105730, 01111300, 9 01105600, 01097300, 01105730, 01109000 Basin number: Table 8. Table 8. [

Table 8 55 correlation Gaging stations used for Gaging 01106000 01111300 01106000 01175670 01111200 01184490 23 01109000, 01105600, 01105730, 01111200, 01106000 Number of measurements Continued — eld, Mass. 27 01109000, 01105730, 01105870, 01111200, 01111300 ﬁ Station name eld, Mass. 9 01111300, 01121000, 01174900, 01175670, 01176000, ﬁ Mass. No. Basin ″

′

° Longitude ″

′

° Latitude Descriptions of low-flow partial-record stations used in the regression analyses No. Station 01105935 41 34 2001105937 71 00 47 41 40 5501105947 41 38 00 71 01 05 24 71 03 46 Destruction Brook near South Dartmouth, Mass.01106460 24 42 02 43 near North Dartmouth, Mass. 24 Shingle Island River 70 58 1701107400 Mass.Westport, Bread and Cheese Brook at Head of 41 51 5501108140 25 41 54 20 70 54 32 24 Mass. Brook near East Bridgewater, Beaver 01108180 70 59 19 25 41 52 57 25 2401108600 01109000, 01105600, 01105870, 01105730, 01111200 41 59 11 71 02 54 Brook near Middleboro, Mass. 25 Fall 01109000, 01105600, 01105730, 01111200, 01106000 01109087 01109000, 01105600, 01105870, 01105730, 01111200, 41 47 57 71 14 27 Brook near North Middleboro, Mass. Poquoy 01109090 25 41 46 36 71 03 37 Mass. Taunton, at East River 25 Cotley 71 05 2301109225 Mans West 25 Hodges Brook at 21 41 46 52Assonet, Mass. at 25 Assonet River 01109460 71 15 03 01109000, 01118000, 01105730, 01105870, 01111200, 42 12 20Assonet, Mass. Brook near Rattlesnake 16 71 50 06 2601111142 42 11 25 Run near Rehoboth, Mass. Rocky 01109000, 01105600, 01111300, 01105730 01111225 12 42 02 40 71 39 23 3601112190 Mass.Auburn, Dark Brook at 42 05 35 71 37 2101123140 01105600, 01111300, 01105730, 01109000 12 14 42 06 35 71 31 11 12 Miscoe Brook near Grafton, Mass. 72 11 51 01109000, 01105600, 01111300, 01105730 12 Emerson Brook near Uxbridge, Mass. 11 10 Muddy Brook at South Milford, Mass. 22 Mill Brook at Brim 01109000, 01111200, 01105730, 01118000, 01105870, 01109000, 01105730, 01097300, 01111200, 01111300 36 01109000, 01118000, 01111200, 01111300, 01106000 18 11 12 13 01097300, 01105600, 01109000, 01111200, 01111300, 01097300, 01105600, 01109000, 01175670 01097300, 01109000, 01111300, 01175670 01097300, 01109000, 01111300, 01175670 01105582 42 13 2501105630 42 12 53 70 59 49 70 53 06 19 at Braintree, Mass. 19 Monatiquot River Mass. near Hingham Center, River Meadow Crooked 15 01109000, 01097300, 01105600, 01105730, 01111300, 10 01105600, 01097300, 01105730, 01109000 01105670 42 11 3501105820 42 09 36 70 43 4401105830 42 11 30 70 47 20 2101105861 70 46 49 41 59 47 at Scituate, Mass. 21 Satuit River 70 47 18 21 Second Herring Brook at Norwell, Mass. Mass. First Herring Brook near Scituate Center, 01105930 21 41 40 43 Brook near Kingston, Mass. Jones River 70 58 39 24 Bedford, Pond near New Turner at 16 River Paskamanset 15 01105600, 01111200, 01111300, 01109000, 01105730 01105600, 01105730, 01105870, 01109000 14 9 01105600, 01109000, 01105870, 01097300 01105600, 01105730, 01105870 011058839 41 46 21011059106 41 44 35 70 33 46 70 52 04 21 at Bournedale, Mass. 13 Herring River Mass. #1 near Rochester, tributary Mattapoisett River 13 01109000, 01105870, 01111200, 01105730 12 01109000, 01158837, 01105870, 01105730 Table 8.

56 Methods for Estimating Low-Flow Statistics for Massachusetts Streams

00 correlation Gaging stations used for Gaging 01096000 01181000 10 01176000, 01175670, 01174900, 01174500, 01184490 Number of measurements Continued — eld, Mass. 11 01174500, 01174900, 01175670, 01176000 fi eld, Mass 15 01171500, 01176000 fi eld, Mass. 14 01171500, 01176000, 01184490, 01121000 eld, Mass. 12 01171500, 01176000, 01175670, 01174900 fi fi eld, Mass. 10 01121000, 01174000, 01175670 Station name fi Longmeadow, Mass. Longmeadow, No. Basin ″

′

° Longitude ″

′

° Latitude Descriptions of low-flow partial-record stations used in the regression analyses No. Station 01123200 42 03 4101124390 42 09 16 72 09 4501162900 42 33 52 71 54 47 10 72 00 43 Brook at Holland, Mass. 10 Stevens at Richardson Corners, Mass. Little River 7 Mass. at Gardner, Otter River 18 01175670, 01176000, 01111200, 01111300, 01121000 22 01176000, 01175670, 01171500, 01187300, 01121000 18 01162500, 01165500, 01174000, 01174900, 01175670, 01123161 42 06 25 72 11 36 10 Brook at Brim Wales 01163298 42 35 4901164300 72 05 28 42 41 1401165090 42 38 45 72 10 3901165250 7 42 32 17 72 15 2501167200 Mass. Brook at Route 20, near Baldwinville, Trout 7 42 41 15 72 14 5101168300 Mass. Brook at Royalston, 7 Lawrence 42 38 12 72 32 43 at North Orange, Mass. River Tulley 01168400 Branch 7 West 72 56 10 42 37 2801168650Athol, Mass. Brook near South 6 Riceville 9 42 36 47 72 54 2701169600 at Bernardston, Mass. River 3 Fall 42 32 45 72 46 10 01096000, 01169000, 01170100, 01174900 01169800 Mass. near Zoar, Cold River 3 42 29 16 72 43 1501169801 9 near Charlemont, Mass. River 3 Chickley 42 43 15 72 44 47 Mass. Falls, 3 Clesson Brook near Shelburne 01096000, 01162500, 01174500, 01175670 72 44 37 Mass. near Conway, 3 Bear River 14 3 Poland Brook near Burkville, Mass. 9 01096000, 01162500, 01174500, 01175670 at North Poland Road near Burkville, Mass. South River 01096000, 01162500, 01174500, 01175670, 01170100 11 16 24 22 01169000, 01169900, 01170100, 01333000, 011715 01169000, 01170100, 01169900, 01162500 01169000, 01169900, 01170100, 01333000, 01171500 01170100, 01169900, 01169000, 01333000 31 01169000, 01333000, 01169900, 01170100 15 17 01169000, 01169900, 01170100, 01333000, 01171500 01169000, 01169900, 01170100, 01171500, 01333000 01170575 42 31 2301171947 42 16 33 72 32 2401171970 42 15 08 72 30 31 6 72 34 26 Brook near Montague, Mass. 6 Sawmill Mass.At Granby, 6 Bachelor Brook Mass. Street at South Hadley, Brook at Morgan Stony 10 01169900, 01171500, 01174900, 01175670, 01176000, 01176200 9 42 09 4101176300 42 07 43 72 16 08 01162500, 01171500, 01169900, 01174900, 01174500 01176415 10 42 05 35 72 15 3101176780 8 42 08 52 72 18 44 01171500, 01174900, 01175670, 01176000, 01184490 01177360 Brim West 8 Kings Brook at 42 05 06 72 24 00 Mass. Mill Stream near Fentonville, 8 Foskett 72 28 50 8 Chicopee Brook at Route 32, South Monson, Mass Mass.Wilbraham, Brook near North 6 Twelvemile at Porter Road near East South Branch Mill River 10 17 01121000, 01174900, 01175670, 01184490 8 01171500, 01176000, 01184490, 01121000 01176000, 01175670, 01171500, 01184490, 01121000 01175890 42 13 3101176100 42 10 13 72 10 12 72 15 41 8 Mass.Warren, 8 Naultaug Brook at Brim West Blodgett Brook near 14 01162500, 01174900, 01175670, 01176000 01172810 42 26 1501173420 42 14 53 72 02 2601173450 72 15 59 42 14 5601175710 8 42 19 39 72 15 5301175850 8 Canesto Brook near Barre, Mass. 42 15 50 72 02 18 Mass.Ware, Muddy Brook at 8 72 09 33 Mass.Ware, 8 Flat Brook near near North Brook Mile River 8 Five Brook West at Mill River 10 01175670, 01162500, 01176000, 01174900 9 15 01176000, 01175670, 01174900, 01174500 01162500, 01096000, 01171500, 01174900, 01175670 Table 8.

Table 8 57 correlation Gaging stations used for Gaging 01197000 01121000 15 01169000, 01169900, 01333000 Number of measurements Continued — eld, Mass. 12 01197000, 01333000, 01181000, 01169900 fi eld, Mass. 8 01169000, 01169900, 01181000, 01187300 fi eld, Mass. 17 01181000, 01188000, 01199050 fi eld, Mass. 14 01181000, 01187300, 01188000, 01180500, 01199050, fi eld, Mass. 9 01187300, 01181000, 01171500, 01184490, 01188000 fi Station name eld Brook at East Windsor, Mass.Windsor, eld Brook at East 17 01169900, 01181000, 01171500, 01180500, 01169000 fi Williamstown, Mass. Williamstown, No. Basin ″

′

° Longitude ″

′

° Latitude Descriptions of low-flow partial-record stations used in the regression analyses No. Station 01179900 42 25 2101180650 42 19 56 72 59 1901183210 73 05 09 42 07 05 4 72 48 01 Mass.Worthington, West Brook at 4 Trout Mass. Mill Brook at Becket, Shaker 4West Munn Brook near 01197120 42 26 28 9 73 17 47 01169900, 01171500, 01181000 9 2 at Pitts Branch Housatonic River West South 01169900, 01171500, 01181000, 01199050 01333100 42 41 1601359967 42 32 19 73 13 50 73 20 01 1 Mass.Williamstown, 1 Hemlock Brook near Kinderhook Creek at Hancock, Mass. 14 01333000, 01332000 9 01197000, 01333000, 01199050, 01198000 01178200 42 28 41 72 59 09 4 West 01178300 42 26 5001178490 42 24 02 72 51 29 72 52 36 4 Mass. at Swift River, 4 Swift River Chester West Branch at West 1801197140 42 22 51 01169900, 01181000, 01171500, 01180500 01197180 42 17 59 73 15 2601197230 42 16 13 73 12 5301198060 2 73 15 06 42 09 17 Brook near Lenox, Mass.01198160 2 Yokun 42 05 26 73 26 5101198200 2 Brook at East Lee, Mass. Greenwater 42 03 11 73 14 4001331380 Hop Brook near South Lee, Mass. 2 42 33 40 73 19 3501332900 2 Fenton Brook near South Egremont, Mass. 42 40 38 73 09 06 at South 2 Umpachene River 73 12 39 Mass. Falls, Ashley at River 1 Konkapot Road at Cheshire, Mass.Windsor 1 South Brook at Hopper Brook at Road near South 14 18 17 01197000, 01181000, 01187300, 01188000 01169900, 01181000, 01199050, 01333000 14 14 01181000, 01187300, 01188000, 01999050 01169000, 01169900, 01197000, 01333000 01181000, 01187300, 01188000, 01169900, 01199050 34 01181000, 01199050, 01198000, 01198500 01184200 42 02 31 72 14 0001184277 42 02 5401184855 6 42 09 40 72 27 1601185490 Mass. Agawam, West Still Brook near 42 06 03 73 04 1901186300 6 73 05 43 42 02 37 near Hampden, Mass. 5 Scantic River 73 08 13 near Otis, Mass. River Branch Farmington 5 West Boston, Mass. New West near Clam River 5 Sandy Brook near Sandis 18 10 01171500, 01181000, 01174900, 01175670, 01184490, 01187300, 01171500, 01188000, 01181000, 01199050 14 9 01181000, 01187300, 01188000 01174900, 01175670, 01176000, 01184490 Table 8.

58 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed mflow statistics are computed low-flow partial-record stations are low-flow partial-record stations are ion not used in analysis because standard error of estimate was too large too large ion not used in analysis because standard error of estimate was Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .030 .054 .16 .36 .65 1.15 1.82 ------.74 .020 .16 ow .44 .61 1.09 1.82 2.52 3.52 4.77 6.16 10.7 17.4 2.73 .39 1.06 ow .061 .10 -- -- .83 1.35 2.09 3.06 -- -- .94 .051 .22 ow 1.23 1.65 2.79 4.39 5.99 7.97 10.1 12.7 19.6 28.9 6.42 1.06 2.73 ow .082 .12 .22 .43 .64 .98 1.42 1.95 3.53 -- .67 .056 .23 ow .44 .58 1.04 1.69 2.20 2.95 ------2.34 .34 1.08 ow 1.05 1.33 2.21 3.78 5.40 7.53 10.0 13.0 -- -- 5.82 .89 2.29 ow 0.17 0.18 0.23 0.28 0.33 0.38 0.44 0.51 -- -- 0.34 0.15 0.23 fl fl fl fl fl fl fl fl Statistic VarianceStandard error 15.8Years .00463 13.4 .00336 38.8 .00204 10.4 41.8 .00182 9.8 .0021 43.5 10.6 .00276 40.4 .00352 12.1 36.6 -- 13.7 32.4 -- 28.6 ------.00236 -- -- .01072 .00479 11.2 -- 24.2 29.6 16.0 22.5 28.1 VarianceStandard error 15.6Years .00454 13.4 .00338 35.5 .0018 9.8 36.4 .001 7.3 38.2 .00078 6.4 39.7 .0008 39.9 6.5 .00102 39.1 .00135 7.4 .00252 36.7 .00403 8.5 .00083 33.9 11.6 .00973 26.4 .00408 14.7 20.6 6.6 34 23.0 19.8 14.8 21.1 VarianceStandard error 19.2Years .00681 15.9 .00472 35.6 -- -- 39 ------.00079 6.5 -- .0012 8.0 49.6 .00195 10.2 43.8 .00289 -- 12.4 37.1 -- -- 31.2 .00093 -- -- .01092 .00357 -- 7.0 24.4 41.2 13.8 13.4 20.8 VarianceStandard errorYears 7.6 .00109 .0009 6.9 42.8 .00061 5.7 43.5 .00042 44 .00034 4.7 .00028 43.9 4.2 .00026 43.8 3.9 .00026 43.8 .0003 3.7 43.7 .00037 .00035 3.7 43.1 .00271 4.0 .00138 41.9 4.4 40.2 4.3 38.4 12.0 25.4 26.1 8.6 VarianceStandard error 18.1Years .0061 15.9 .00468 27.4 12.1 .00272 28.2 .0016 9.2 30.2 .00133 8.4 .00141 31.8 .00176 8.7 31.9 .00228 31.1 9.7 .00381 29.1 -- 11.0 26.4 .00141 14.3 .01201 19.9 -- .00481 -- 8.7 26.1 25.6 13.4 16.1 17.3 VarianceStandard error 22.5Years .0093 18.5 .00636 19.6 12.7 .00301 25.1 .00241 11.3 37.9 .00262 11.8 .00339 33.3 -- 13.5 25.5 -- 19.8 ------.00279 .01167 12.2 -- .00373 25.3 15.8 14.1 5.8 13.2 VarianceStandard error 22.9Years .0096 19.5 .00706 17.2 13.7 .00353 19.3 .00175 9.7 26.7 .00146 .00185 8.8 36 .00269 9.9 37.1 .00384 29.5 12.0 -- 19.9 14.3 -- 13.6 -- .00152 -- .01182 -- .00376 -- 9.0 21.7 25.4 14.2 3.5 7.1 VarianceStandard error 12.7Years .00303 11.1 .00229 27.2 .00118 7.9 27.9 .00063 5.8 .00058 31.3 .00079 5.6 37.3 .00124 37.6 6.5 .00270 30.2 -- 8.1 19.6 -- 12.0 8.0 -- .00061 .01182 -- -- .00123 -- 5.7 17.9 25.4 3.5 8.1 5.5 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea ow is in cubic feet per second; variance is in units of base-10 logarithms; standard error is in percent. No., number; --, stat is in units of base-10 logarithms; is in cubic feet per second; variance ow fl No. Station 01095928 Stream 01095915 Stream 01095380 Stream 01095220 Stream 01094760 Stream 01094396 Stream 01094340 Stream 01073860 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record [Stream an outlier] or it was

Table 9 59 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .91 1.07 1.54 2.39 3.19 4.05 5.24 6.69 10.5 -- 3.36 .76 1.55 ow .040 .060 .10 .15 .24 .34 .47 .69 1.30 2.20 .22 -- -- ow .16 .18 .26 .39 .50 .65 .82 1.02 -- -- .53 .14 .25 ow .65 .77 1.19 1.85 2.62 3.50 4.53 5.61 8.34 11.7 2.73 .54 1.09 ow 2.55 3.06 4.32 5.98 7.41 9.18 11.2 13.3 18.6 25.0 7.76 2.34 4.49 ow .50 .64 .97 1.41 1.82 2.34 2.89 3.50 4.98 6.80 1.94 .46 .97 ow .26 .31 .45 .63 .77 .92 1.08 1.25 1.60 2.00 .81 .24 .46 ow 6.40 7.80 11.0 15.0 18.0 22.0 27.0 32.0 48.0 69.0 19.0 6.52 11.7 fl fl fl fl fl fl fl fl Statistic VarianceStandard error 19.8Years .00726 17.4 .0056 16.1 12.8 .00307 17.1 .00136 8.5 21.7 .00082 .00068 6.6 29.9 .00089 6.0 34.3 .00141 36.2 6.9 .00312 -- 30.9 8.7 23.9 .00078 12.9 .0098 12.8 -- .00348 -- 6.4 26.6 23.1 3.6 13.6 6.1 VarianceStandard errorYears 4.5 .00039 .00032 4.2 11 .00025 3.6 .00019 11 .00016 3.2 11 .00014 2.9 .00013 11 2.7 .00012 11 .00011 2.6 11 .00010 .00088 2.5 -- 11 2.4 -- 11 2.4 11 6.8 11 -- 11 ------VarianceStandard error 17.2Years .00549 14.8 .00408 18.5 .00206 10.5 20.6 .00119 8.0 .00121 27.8 .00162 8.0 32.9 .00239 9.3 30 .00337 -- 23.4 11.3 16 13.4 -- -- 11.3 .00129 .00728 -- -- .00247 8.3 -- 19.8 18.5 11.5 4.4 7.4 VarianceStandard error 14.9Years .00413 13.2 .00327 29.1 .00177 9.7 29.4 .00095 7.1 .00078 32 .00091 6.4 35.6 .00125 7.0 38.3 .0017 38.6 .00287 8.2 .00408 32.1 9.5 .00084 26.7 .00687 12.4 .00287 19.7 14.8 16.4 6.7 32 19.3 11.2 12.4 13.3 VarianceStandard error 11.8Years .00262 10.2 .00196 34.9 .00114 7.8 37.1 .00081 6.6 .00081 42.2 .00096 6.6 41.7 .00125 37.1 7.1 .00162 31.6 .00261 8.2 .00378 25.5 .00084 9.3 20.5 .00337 11.8 .00132 12.6 14.2 8.5 6.7 21.7 13.4 8.3 8.4 11.8 VarianceStandard error 12.0Years .0027 10.4 .00203 36.9 .00118 7.9 38.9 .00071 6.1 43.1 .00057 .00056 5.5 46.8 .00064 48 5.5 .00078 46.3 .00123 5.8 .00181 42.3 6.4 .00057 37.4 .00395 8.1 .00161 27.9 9.8 21.1 5.5 34.8 14.5 15.8 9.3 18.4 VarianceStandard error 12.8Years .00307 10.5 .00207 26.9 .00078 6.4 31.1 .00029 3.9 .00032 46.5 .00056 4.1 65.1 .00092 57.5 5.5 .00138 40.7 .00242 7.0 .00359 27.3 .00037 8.6 18.7 .00405 11.4 .00095 10 13.9 6.7 4.4 36.8 14.7 9.4 7.1 18.3 VarianceStandard errorYears 1.6 .00005 .00004 1.5 47 .00003 1.3 .00002 47 .00002 1.1 47 .00002 1.0 .00002 47 1.0 .00001 47 .00001 .9 47 .00001 .00007 47 .9 .00467 .00256 .8 47 .8 47 2.0 47 15.8 47 11.7 47 47 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01096935 Stream 01096910 Stream 01096855 Stream 01096805 Stream 01096515 Stream 01096505 Stream 01096504 Stream 01096000 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

60 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed .00003 ------low-flow partial-record stations are .0000298 .0000271 Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .46 .49 .57 .69 .78 .94 1.13 1.36 2.00 2.85 .84 -- .58 ow .45 .53 .77 1.20 1.55 1.93 2.32 2.81 3.76 4.75 1.64 .39 .81 ow ------6.00 8.70 15.0 23.0 ------ow .15 .22 .41 .60 .78 1.10 1.40 1.80 3.20 4.90 .67 .15 .36 ow .18 .24 .36 .55 .73 .96 1.23 1.52 -- -- .78 .15 .36 ow 1.17 1.61 2.54 4.22 5.93 8.28 11.0 14.2 -- -- 6.52 .98 2.45 ow .19 .29 .71 1.40 2.10 3.10 4.10 5.20 7.90 12.0 2.30 .12 -- ow 1.11 1.33 1.78 2.60 3.42 4.40 5.49 6.77 -- 13.0 3.65 0.89 1.83 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 7.4 .00104 .00074 6.3 28.6 .00038 4.5 30.8 .00026 .00031 35.6 3.7 .00045 38.1 4.1 .00067 35.9 4.9 .00091 30.9 .00154 6.0 .00224 24.6 .00035 7.0 -- 19.9 9.1 11.7 .00066 10.9 7.8 4.3 26.7 -- -- 16.6 5.9 VarianceStandard error 13.4Years .00337 11.6 .00254 31.9 .00128 8.3 33.2 .0006 5.6 37.3 .00059 .0008 5.6 42 .00113 6.5 40.7 .00164 36.5 7.8 .00271 31.1 .00382 9.3 .00066 25.4 .00537 12.0 .00188 18.7 14.3 15 5.9 31.4 17.0 12.3 10.0 18.9 VarianceStandard errorYears ------1.3 .0000322 50 1.3 1.2 50 1.2 50 -- 50 ------VarianceStandard errorYears 4.2 .00033 .00028 3.9 11 .00021 3.4 .00016 11 .00014 2.9 11 .00012 2.7 .00011 11 2.5 .00010 11 .00009 2.4 11 .00009 .00046 2.3 11 .01102 .00605 2.2 11 2.2 11 5.0 11 24.5 11 18.1 11 11 VarianceStandard error 17.0Years .00535 14.4 .00387 29.8 .00218 10.8 32 .00148 8.9 .00154 37 .00196 9.1 39.9 .00262 10.2 34.8 .00343 11.8 -- 26.5 13.5 -- 18.9 -- 14.1 .00162 .0071 -- -- .00248 9.3 -- 19.6 19.7 11.5 4.6 7.6 VarianceStandard error 25.1Years .01153 20.9 .0081 16.8 14.6 .00399 19.1 .00175 9.7 24.7 .00128 .00151 8.3 33 .00221 9.0 37.8 .00322 39.6 10.9 -- 28.3 13.1 -- 19.6 -- .00134 -- .01505 -- .00483 -- 8.4 27.6 28.8 16.1 3.8 7 VarianceStandard errorYears 2.5 .00012 .00010 2.3 32 .00008 2.0 .00006 32 .00005 1.8 32 .00004 1.6 .00004 32 1.5 .00004 32 .00003 1.5 32 .00003 .00036 1.4 32 .01480 -- 1.3 32 1.3 32 4.4 32 28.6 32 -- 32 -- VarianceStandard error 14.3Years .00382 12.5 .00292 21.6 .00176 9.7 22.7 .0009 6.9 26 .00063 .00062 5.8 32 .00079 5.7 34.9 .00113 -- 33.7 6.5 29 .00316 7.8 .00063 22.9 -- .00574 .002 -- 13.0 5.8 10 17.6 25.6 10.3 4 7.2 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01102053 Stream 01101100 Stream 01101000 Stream 01100700 Stream 01100608 Stream 01099400 Stream 01097300 Stream 01097280 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 61 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow ------1.86 2.04 2.26 -- 2.84 3.40 3.99 2.13 -- -- ow .38 .47 .67 1.05 1.51 2.07 2.71 3.60 5.85 8.93 1.71 .29 .66 ow .10 .13 .19 .28 .37 .49 .63 .81 1.19 1.66 .40 .079 .19 ow .15 .19 .30 .50 .70 .95 1.27 1.70 2.74 -- .74 .11 .31 ow .25 .33 .51 .96 1.46 2.05 2.94 4.68 10.1 -- 1.51 .13 .54 ow .26 .32 .46 .72 .99 1.36 1.86 2.53 4.18 6.41 1.04 .18 .48 ow .45 .57 .87 1.29 1.64 2.04 2.41 2.79 3.60 4.48 1.76 .38 .84 ow 0.19 0.24 0.36 0.58 0.77 0.99 1.20 1.45 -- -- 0.83 0.17 0.37 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears ------2.4 -- .00011 .00009 2.2 33.4 .00009 2.2 33.3 -- 33 -- .00012 -- .00018 2.5 .00025 30.4 3.1 .0001 -- 25.1 3.6 20.7 -- 2.3 26.3 ------VarianceStandard error 10.7Years .00214 9.8 .00179 25.6 .0013 8.3 25.6 .00085 6.7 26.1 .00059 .00043 27.2 5.6 .00033 28.3 4.8 .00027 29.1 .00028 4.2 29.7 .00042 .00058 3.8 29.9 .00418 3.9 .00206 29.1 4.7 27.3 24.7 5.5 11.2 15.0 11.2 10.5 VarianceStandard error 11.2Years .00237 10.2 .00196 27 .00139 8.6 .00092 27.1 7.0 .0007 28.1 .00057 6.1 29.7 .00053 5.5 31 .00054 32 .00068 5.3 .00093 32.5 5.4 .00069 .00369 32.1 6.0 .00176 28.6 7.0 24.4 6.1 23.9 14.1 7.8 9.7 9.6 VarianceStandard error 14.6Years .00397 12.9 .00309 29.7 .00192 10.1 30.6 .00129 8.3 .00117 33.9 .0013 7.9 35.2 .00162 8.3 34.1 .00215 31.6 9.3 .00349 -- 27.8 10.7 23.5 .00121 13.7 .00675 16.7 -- .00259 -- 8.0 24.7 19.1 7.8 11.8 12.4 VarianceStandard error 21.7Years .00867 19.2 .00685 22.3 .00442 15.4 22.7 .00236 11.2 .00167 23.9 .00142 9.4 27.7 .00147 8.7 29.3 .00207 29.7 8.8 .0042 -- 28.7 10.5 25.3 .00164 15.0 .01605 19.3 -- .00612 -- 9.3 24.9 29.8 7.1 18.2 10.2 VarianceStandard errorYears 9.9 .00185 .00146 8.8 34.6 .00098 7.2 34.8 .00062 .00052 36.8 5.7 .00055 38.2 5.3 .0007 38.7 5.4 .00097 37.2 .00168 6.1 33.7 .00252 .00056 7.2 29.6 .00408 .00176 9.5 23.3 11.6 19.3 31.1 5.5 11.8 14.8 15.6 9.7 VarianceStandard error 15.4Years .00441 13.2 .00326 20.7 .00172 9.6 22.3 .00087 6.8 .00064 26.8 .00061 5.8 31.9 .00071 33.7 5.7 .00087 33 .00135 6.1 .00194 30.2 .00064 6.8 .00618 26.4 8.5 .00227 19.6 10.2 15 5.8 27.2 18.3 5.8 11.0 9.3 VarianceStandard error 15.4Years .0044 13.1 .00321 26.6 .00172 9.6 28.1 .00108 7.6 32.6 .00121 .00167 8.0 35.8 .00223 31.9 9.4 .00293 25.8 -- 10.9 20.6 12.5 -- 16.2 -- .00134 -- .00623 -- .00217 -- 8.4 22 18.3 10.8 8.3 12.6 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01105100 Stream 01104980 Stream 01104960 Stream 01103440 Stream 01103435 Stream 01103253 Stream 01103015 Stream 01102490 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

62 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .047 .071 .14 .26 .41 .62 ------.53 .033 .14 ow .14 .17 .23 .30 .36 .43 .50 .58 -- -- .41 -- -- ow .35 .46 .73 1.08 1.40 1.92 2.50 3.19 -- -- 1.55 .27 .71 ow .20 .29 .48 .83 1.20 1.70 2.20 2.71 4.10 5.40 1.40 .16 .44 ow ------6.92 9.83 12.4 ------8.15 -- -- ow .015 .025 .062 .13 .22 .33 .47 .64 1.16 1.87 .25 .009 .055 ow 0.12 0.15 0.25 0.38 0.53 ------0.093 0.25 ow ------2.43 2.87 3.50 -- -- 2.10 -- -- fl fl fl fl fl fl fl fl Statistic VarianceStandard error 24.2Years .0107 19.9 .0073 27.5 14.1 .00371 29.8 .00218 10.8 35.1 .00226 11.0 .00315 37.8 13.0 -- 37.2 -- 32.1 ------.00279 .01612 12.2 -- .00485 29.9 24.2 16.1 5.7 10.1 VarianceStandard error 19.9Years .00729 16.3 .00492 13.8 .0026 11.8 15.9 .00145 8.8 19.4 .00134 .00169 8.4 22.7 .00226 9.5 22.3 .00316 19.5 11.0 -- 15.8 13.0 -- 11.2 -- .00147 ------8.8 15.4 ------VarianceStandard error 14.0Years .00368 11.2 .00234 24.9 .00104 7.4 28.4 .00069 6.1 .00083 34.6 .00145 6.6 35.2 .00231 31.1 8.8 .00336 23.3 -- 11.1 16.6 -- 13.4 12.1 -- .001 -- .0061 -- .00145 -- 7.3 20.2 18.1 5.3 8.8 11.6 VarianceStandard errorYears 2.3 .00010 .00008 2.1 30 .00006 1.8 .00005 30 .00004 1.6 30 .00004 1.5 .00003 30 1.4 .00003 30 .00003 1.3 30 .00003 .00029 1.2 30 .00525 .00288 1.2 30 1.2 30 3.9 30 16.8 30 12.4 30 30 VarianceStandard errorYears ------14.6 -- .00399 13.8 .00357 31.3 .00349 13.7 30.2 -- -- 33.4 ------.00371 14.1 ------24.5 ------VarianceStandard error 20.9Years .00805 18.6 .0064 24.9 15.1 .00424 25.2 .00293 12.5 26.2 .00237 11.2 .00205 27 10.5 .00192 27.4 .00192 10.1 27.7 .00221 10.1 .00272 27.9 .00233 10.9 27.8 .01309 12.1 .00627 26.1 11.1 23.7 26.8 23.4 18.4 9 10.5 VarianceStandard error 20.5Years .00773 17.0 .00535 25.8 .003 12.7 27.9 .00266 11.9 29.9 .00357 13.8 -- 25.5 -- 19.3 ------.01132 24.9 .00366 -- 14.0 4.6 7.3 VarianceStandard errorYears ------13.3 -- .00332 12.5 17.2 .00292 .00304 12.7 17.2 -- -- 16.7 ------.00392 14.5 ------10.4 ------Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01105820 Stream 01105670 Stream 01105630 Stream 01105600 Stream 01105582 Stream 01105575 Stream 01105568 Stream 01105270 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 63 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .18 .26 .47 .82 1.21 1.65 2.24 3.04 5.21 8.41 1.52 .14 .46 ow .085 .13 .28 .60 1.05 1.76 2.80 4.25 8.78 -- 1.29 .062 .28 ow -- .48 -- .98 ------4.27 ------ow .41 .54 .91 1.53 2.29 3.34 4.63 ------2.71 .32 .94 ow .090 .11 .15 .22 .32 .41 .52 .64 -- -- .41 .076 .15 ow ------5.95 -- 8.45 ------10.6 ------ow 0.60 .79 1.23 1.81 2.38 2.97 3.93 5.09 -- -- 3.11 .49 1.24 ow -- 0.021 0.043 0.085 0.14 0.23 0.34 0.49 0.95 1.60 0.17 0.010 0.044 fl fl fl fl fl fl fl fl Statistic VarianceStandard error 19.3Years .00693 17.1 .00543 25.8 .00356 13.8 27 .00231 11.1 .00176 30.2 .00156 9.7 32.8 .00151 9.1 33.8 .00166 33 9.0 .00239 .00347 30.8 9.4 .00161 .00919 11.3 27.7 .00396 13.6 22.1 9.3 17.4 22.3 24.7 14.6 5.1 6.9 VarianceStandard error 16.2Years .00491 14.5 .00395 35.6 .00257 11.7 35.6 .00155 9.1 .00111 36.8 .00093 7.7 37.7 .00097 7.0 38.3 .00117 38.5 .00183 7.2 -- 38.1 7.9 .00114 36.6 9.9 .00818 31.6 .00382 -- -- 7.8 34 21.1 12.5 14.3 15 VarianceStandard errorYears -- -- 7.3 -- .00101 -- -- 36.8 -- .00041 4.7 -- -- 38.2 ------.00076 -- -- 6.4 26.3 ------VarianceStandard error 14.5Years .00391 12.8 .00308 36.1 .00196 10.2 36.2 .00122 8.1 .00092 37.7 .00083 7.0 38 .00091 6.6 38.1 -- 37.7 7.0 -- 36.5 ------.00093 -- .00592 -- .00266 -- 7.0 31.7 17.9 10.3 11.9 13 VarianceStandard error 18.1Years .00611 16.5 .00509 22.8 .00368 14.0 23.2 .00267 11.9 .0022 24.8 10.8 .00196 25.4 10.2 .00176 24.4 .00144 9.7 22.6 -- 21.3 8.8 -- 21.6 -- .00225 -- .00819 -- .00413 -- 11.0 21.1 14.4 14.9 4.4 5.4 VarianceStandard errorYears ------12.6 -- .00298 -- -- 44.4 12.3 -- .00284 -- -- 38.3 ------.0028 12.2 ------15.6 ------VarianceStandard error 13.5Years .00343 11.3 .00238 39.8 .00148 8.9 41.3 .00154 9.1 .00194 41.3 .00252 10.2 34.5 .0035 11.6 28.6 .00469 24.5 13.7 -- 19.7 15.9 -- 15.6 -- .00261 -- .00525 -- .00192 -- 11.8 16.8 16.4 10.1 9.2 13.1 VarianceStandard errorYears -- -- 15.1 -- .00427 13.1 .00322 31.9 .0024 11.3 32 .00195 10.2 .00164 31.8 9.3 .00146 31.9 .00136 8.8 32 .00137 8.5 .00152 32.2 .00191 8.5 32.2 .00796 .00437 9.0 31.3 10.1 29.6 20.8 26.1 15.3 11.4 11.6 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01105947 Stream 01105937 Stream 01105935 Stream 01105930 Stream 01105861 Stream 01105830 Stream 011059106 Stream 011058839 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

64 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .84 1.11 1.84 2.99 4.22 5.95 7.98 10.4 16.3 24 4.67 .62 1.91 ow .036 .058 .14 .32 .61 1.05 ------.90 .025 .15 ow .60 .75 1.07 1.48 1.90 2.41 2.99 3.64 -- -- 2.09 .47 1.06 ow ------3.21 3.78 4.42 5.13 5.89 7.45 8.96 4.02 -- -- ow -- 2.06 -- 3.76 4.64 5.72 6.86 ------5.01 1.32 2.73 ow .020 .030 .070 .17 .32 .60 1.00 1.60 3.70 5.50 .19 -- -- ow .40 .50 .74 1.10 1.44 1.81 2.26 2.80 3.99 5.66 1.64 .34 .76 ow 0.070 0.080 0.12 0.30 0.63 1.20 2.20 3.40 6.50 9.20 0.65 0.054 0.15 fl fl fl fl fl fl fl fl Statistic VarianceStandard error 14.0Years .00367 12.9 .0031 27.5 10.9 .00221 27.2 .00155 9.1 27.7 .0012 8.0 .00093 28.2 .00077 7.0 28.9 .00067 29.8 6.4 .00062 30.7 .00069 6.0 .00116 31.4 .00578 5.7 31.6 .00294 6.1 30.4 7.9 22.9 17.6 8.8 12.5 10.1 VarianceStandard error 15.4Years .00441 12.9 .00311 49.5 .00186 10.0 49.4 .0018 9.8 49.5 .00252 11.6 .0035 47.9 -- 13.7 45.3 40.8 ------.00329 .00896 13.3 -- .00354 22.1 32.2 13.8 19.5 25.9 VarianceStandard error 12.8Years .00307 10.7 .00213 27.9 .00116 7.9 30.1 .0008 6.5 34.9 .00091 .00131 7.0 36.3 .0019 32.7 8.3 .00263 26 10.1 -- 19.3 11.8 -- 14.3 -- .00106 -- .00495 -- .00147 -- 7.5 20.8 16.3 5.8 8.8 10.4 VarianceStandard errorYears ------4.2 -- .00033 .00035 4.3 42.2 .00047 5.0 39.3 .00067 33.2 6.0 .00093 25.7 .00154 7.0 .00217 19.4 .0004 9.1 -- 11.8 10.8 -- 8.5 4.6 25.9 ------VarianceStandard errorYears -- -- 5.5 -- .00058 -- -- 35.3 -- .00033 4.2 .00027 3.8 35.3 .00023 35.5 3.5 .0002 35.8 -- 3.3 36.5 ------.00028 -- .00137 -- .00075 3.9 31.2 8.5 16.8 6.3 17 VarianceStandard errorYears 5.6 .00059 .00050 5.1 11 .00038 4.5 .00029 11 .00025 3.9 11 .00022 3.6 .00020 11 3.4 .00018 11 .00017 3.2 11 .00016 .00179 3.1 -- 11 3.0 -- 11 2.9 11 9.8 11 -- 11 ------VarianceStandard errorYears 9.3 .00162 .00112 7.7 42.5 .00063 5.8 45.5 .00057 .00075 48.6 5.5 .00106 45.2 6.3 .00146 37.9 7.5 .00194 29.5 .00293 8.8 .00415 22.2 .0009 10.2 16.8 .00259 12.5 .0009 10.9 14.9 7.9 6.9 21.8 11.8 8.2 6.9 14.9 VarianceStandard errorYears 2.9 .00016 .00013 2.7 37 .00010 2.3 .00008 37 .00007 2.0 37 .00006 1.9 .00005 37 1.8 .00005 37 .00004 1.7 37 .00004 .00050 1.6 37 .01015 .00557 1.5 37 1.5 37 5.2 37 23.5 37 17.3 37 37 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01109087 Stream 01108600 Stream 01108180 Stream 01108140 Stream 01107400 Stream 01107000 Stream 01106460 Stream 01106000 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 65 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .50 .66 1.00 1.80 2.60 3.90 5.60 7.60 12.0 18.0 2.40 .25 1.16 ow .78 .90 1.15 1.49 1.78 2.12 2.46 2.79 3.46 4.18 1.80 .63 1.19 ow 2.10 2.50 3.20 4.50 6.10 7.90 10.0 13.0 20.0 29.0 6.80 1.80 3.23 ow .068 .11 .21 .36 .52 ------.20 ow 1.11 1.36 1.97 2.94 3.84 4.74 5.48 6.29 8.36 10.9 4.13 .94 -- ow .083 .11 .19 .35 .55 ------3.95 6.60 .60 .065 .20 ow -- -- .090 .16 .29 .48 .78 1.50 3.40 5.00 .26 -- -- ow 0.14 0.19 0.34 0.58 0.86 1.24 1.80 2.53 -- -- 1.04 0.11 0.34 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 2.6 .00013 .00011 2.4 29 .00008 2.1 .00006 29 .00005 1.8 29 .00005 1.7 .00004 29 1.6 .00004 29 .00004 1.5 29 .00004 .00034 1.5 29 .01227 .00674 1.4 29 1.4 29 4.2 29 25.9 29 19.1 29 29 VarianceStandard errorYears 7.3 .001 6.1 29 .00071 .00039 4.5 31 .00035 4.3 .00048 34.7 .00074 5.0 31.6 .00106 6.3 25.7 .00141 19.4 .00215 7.5 .00297 14.6 .00051 8.7 .00212 11.4 10.7 .00066 7.8 12.6 5.8 5.2 18.3 10.6 8.2 5.9 14.7 VarianceStandard errorYears 2.3 .00010 .00008 2.1 28 .00006 1.8 .00005 28 .00004 1.6 28 .00004 1.5 .00003 28 1.4 .00003 28 .00003 1.3 28 .00003 .00016 1.3 28 .00290 .00159 1.2 28 1.2 28 2.9 28 12.4 28 9.2 28 28 VarianceStandard error 26.0Years .01236 21.3 .00839 20.2 .00405 14.7 23.6 .00349 13.7 .00422 28.5 -- 15.0 27.4 -- -- 23.3 ------.00554 17.3 -- 9.3 VarianceStandard error 14.0Years .00366 12.4 .00289 17.7 .00176 9.7 18.5 .00097 7.2 .00066 21.3 .00054 5.9 25.5 .0005 28.2 5.4 .00049 29.2 .00066 5.2 29.6 .00102 5.1 .00063 29.5 .00480 5.9 -- 24.9 7.4 18.2 5.8 21.4 16.1 3.4 -- -- VarianceStandard error 19.3Years .00687 17.8 .00591 33.9 .00452 15.6 33.8 .00315 13.0 .00238 34.3 -- 11.3 35.4 -- -- 36.6 ------.00167 .00214 -- 9.4 .00228 10.7 .00893 34.3 .00487 11.0 29.2 22.0 24.9 16.2 6.5 7.2 VarianceStandard errorYears ------2.1 -- .00008 .00006 1.8 10 .00005 1.7 .00005 10 1.6 .00004 10 .00004 1.5 10 .00004 .00003 1.4 10 .00037 -- 1.4 10 -- 1.4 10 4.4 10 -- 10 ------VarianceStandard error 16.5Years .00509 14.1 .00371 29.1 .00212 10.6 31.6 .00149 8.9 .00157 36.5 .00213 9.1 38.7 .00305 10.7 35.3 .00418 28.1 12.8 -- 20.9 15.0 -- 15.7 -- .00185 -- .00716 -- .00254 -- 9.9 22.2 19.7 11.6 5.6 10 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01111300 Stream 01111225 Stream 01111200 Stream 01111142 Stream 01109460 Stream 01109225 Stream 01109200 Stream 01109090 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

66 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .94 1.56 2.29 3.16 3.67 4.65 5.72 7.06 10.3 -- 4.02 .90 2.07 ow 2.79 3.33 4.61 6.33 8.18 10.1 12.2 14.3 19.5 25.0 8.32 2.57 4.52 ow ------17.0 -- .45 -- ow .26 .33 .50 .84 1.25 1.77 2.4 3.23 -- -- 1.38 .20 .52 ow .10 .15 .28 .50 .79 ------4.04 6.64 .78 .086 .25 ow ------1.38 2.22 2.99 ------2.25 -- -- ow 1.44 1.64 2.16 2.84 3.54 4.28 4.89 5.67 7.40 -- 3.85 1.29 2.20 ow 0.19 0.24 0.36 0.57 0.78 1.05 1.37 1.74 2.56 -- 0.79 0.14 0.39 fl fl fl fl fl fl fl fl Statistic VarianceStandard error 10.4Years .00201 8.5 .00136 33.5 .00065 5.9 35.6 .00043 .00054 4.8 40 .00089 5.4 42.5 .00147 40.6 6.9 .00221 34.1 .00409 8.8 -- 26.2 10.9 .00061 19.9 14.8 .00324 12 .0012 -- -- 5.7 28.4 13.2 10.2 8.0 15.5 VarianceStandard errorYears 7.5 .00106 .00085 6.7 37.5 .00057 5.5 38 .00041 .00036 4.7 38.9 .00038 39 4.4 .00043 4.5 38.1 .0005 36.3 .00072 4.8 .00097 33.6 .00037 5.2 .00148 30.5 .00076 6.2 24.2 7.2 19.8 4.4 28.2 8.9 11.7 12.4 6.4 VarianceStandard errorYears ------.8 .00001 -- -- 76 .00357 13.8 ------76 -- VarianceStandard error 20.7Years .00789 18.3 .00618 23.9 .00394 14.5 25.6 .00247 11.5 .00207 30.8 10.5 .00218 34.6 .00263 10.8 33.3 .00341 11.8 29.5 -- 13.5 25 -- -- 20.6 .00206 -- .01033 -- .00422 10.5 -- 23.7 20.8 15.0 4.3 6.1 VarianceStandard error 10.3Years .002 8.8 51.1 .00145 .00083 6.6 52.8 .00059 5.6 55.6 .00063 -- 56.6 5.8 55.1 ------.00228 -- .00328 11.0 .00066 31.2 .00325 13.2 .00141 24.9 5.9 45.6 13.2 17 8.7 21.1 VarianceStandard errorYears ------13.5 -- .00342 10.5 .00207 30.5 .00272 12.1 33.4 -- -- 29 ------.00227 11.0 ------28.2 ------VarianceStandard error 13.5Years .00342 11.6 .00253 14.9 .00133 8.4 17 .00079 6.5 .00081 23.1 .00116 6.6 28 .00159 7.9 25.9 .00222 .00378 19.1 9.2 -- 15.3 10.9 .00096 14.2 10.8 .00439 .00138 -- 5.9 -- 7.1 15.3 12.6 8.6 2.4 5.3 VarianceStandard error 16.5Years .00505 14.6 .00396 23.5 .0025 11.6 24.1 .00167 9.4 26.1 .00155 .00178 9.1 27.4 .00227 9.7 26.7 .00292 24.5 11.0 .00446 -- 20.9 12.5 17.2 .00162 15.5 .00877 12 -- .00326 -- 9.3 19.5 21.8 13.2 6.2 9.6 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01163250 Stream 01162900 Stream 01162500 Stream 01124390 Stream 01123200 Stream 01123161 Stream 01123140 Stream 01112190 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 67 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow -- 4.06 5.05 6.52 7.91 9.44 11.1 13.1 17.1 22.2 8.14 3.24 4.84 ow 1.97 2.39 3.27 4.70 6.11 7.77 9.72 12.3 17.8 25.3 6.36 1.69 3.05 ow 1.91 2.43 3.48 5.21 6.58 7.71 8.66 9.61 -- -- 6.63 1.46 2.89 ow .99 1.10 1.40 2.00 2.50 2.90 3.40 4.00 5.10 6.30 2.60 -- -- ow .70 .87 ------7.40 10.0 ------ow -- -- .52 .96 1.28 1.98 ------.50 ow .15 .20 ------ow 0.35 0.52 1.02 1.77 2.65 3.80 5.11 ------2.87 0.32 1.01 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears -- -- 5.5 -- .00057 .0003 4.0 49.2 .00019 3.2 55.5 .00025 61 .00041 3.6 .00063 56.4 4.7 .00096 45.6 5.8 .00165 35.3 .00252 7.1 .00028 26.6 .0012 9.4 17 .00045 11.6 11.9 3.9 39.1 8.0 8.1 4.9 12 VarianceStandard errorYears 6.1 .00071 .00055 5.4 43.8 .00036 4.4 44.1 .00024 .00021 45.7 3.6 .00024 47.2 3.3 .0003 47.5 3.6 .00041 46.4 .00066 4.0 44.2 .001 4.7 .00024 41.6 .00127 5.9 36 .00063 7.3 30.8 3.6 41.6 16.9 8.2 18.7 5.8 VarianceStandard errorYears 7.6 .0011 7.2 .00097 42.2 .00088 6.8 42.1 .00094 41.1 .00103 7.1 .00109 38.6 7.4 .00113 36.2 7.6 .00112 34.7 -- 7.8 34.1 -- 7.7 34.2 .00107 -- -- .00225 .00144 -- -- 7.5 27.8 11.0 20.9 17.5 8.8 VarianceStandard errorYears 4.0 .00030 .00025 3.6 5 .00019 3.2 .00015 5 .00012 2.8 .00011 5 2.6 .00010 5 2.4 .00009 .00008 5 2.3 .00008 .00133 5 2.2 -- 2.1 5 -- 2.1 5 8.4 5 -- 5 -- 5 -- -- VarianceStandard errorYears 1.6 .00005 .00004 1.4 65 -- -- 65 ------.00001 -- .8 .00001 -- 65 .8 -- -- 65 ------VarianceStandard errorYears ------9.2 -- .00159 .00124 8.1 46.9 .00165 9.4 43.9 .00259 -- 39.2 11.8 34.2 ------.0043 -- 15.2 25.1 VarianceStandard error 22.6Years .00941 18.6 .00641 22 -- -- 26.4 ------VarianceStandard error 22.9Years .00965 19.3 .0069 27 14.4 .00389 29.7 .00274 12.1 .00265 34.9 11.9 .00309 35.9 12.9 .00382 33.2 -- 14.3 28.1 -- -- 22.9 ------.00274 -- -- .01163 12.1 .0046 -- 25.2 21.6 15.7 8.1 10.9 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01168400 Stream 01168300 Stream 01167200 Stream 01166105 Stream 01165500 Stream 01165250 Stream 01165090 Stream 01164300 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

68 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow 3.80 4.20 5.33 6.50 7.48 8.60 9.79 11.0 13.7 -- 7.73 3.48 5.05 ow -- 7.10 8.80 12.0 14.6 17.6 21.0 26.0 36.0 49.0 15.0 4.81 7.61 ow 3.70 4.32 5.70 7.40 9.10 11.0 13.0 16.0 22.0 30.0 9.60 3.32 5.37 ow 2.41 2.75 3.44 4.24 4.95 5.79 6.69 7.77 9.98 12.8 5.07 2.17 3.10 ow .22 .29 .44 .69 .96 1.32 1.78 2.42 4.12 -- 1.02 .19 .39 ow .80 .96 1.29 1.80 2.32 2.92 3.62 4.48 6.41 9.07 2.41 .70 1.20 ow 9.20 11.0 15.0 21.0 27.0 33.0 40.0 49.0 68.0 92.0 27.4 8.46 13.9 ow -- -- 4.39 5.55 6.57 7.72 8.94 10.3 13.3 17.1 6.78 2.89 4.25 fl fl fl fl fl fl fl fl Statistic VarianceStandard error 11.6Years .00253 9.8 .00181 22.7 .00088 6.8 24.9 .00066 .00082 5.9 31.4 .00118 29.2 6.6 .00172 23.2 7.9 .00235 16.3 .00399 9.6 -- 11 11.2 .00088 7.7 14.6 .00323 .00105 4.2 -- -- 6.8 13.5 13.1 2.3 7.5 3.8 VarianceStandard errorYears -- -- 1.9 -- .00007 .00005 1.6 29 .00004 1.4 .00003 29 .00003 1.3 29 .00003 1.2 29 .00002 .00002 1.2 29 .00002 1.1 .00013 29 .00179 1.1 .00098 29 1.1 29 2.6 29 9.8 29 7.2 29 29 VarianceStandard errorYears 1.9 .00007 .00006 1.8 30 .00004 1.5 .00003 30 .00003 1.3 30 .00003 1.2 .00002 30 1.2 .00002 30 .00002 1.1 30 .00002 .00014 1.1 30 .00165 .00091 1.0 30 1.0 30 2.7 30 9.4 30 6.9 30 30 VarianceStandard errorYears 3.0 .00017 .00011 2.4 33.6 .00007 1.9 34.1 .00008 .00013 36.1 2.1 .0002 39.4 2.6 .0003 37.2 3.3 .00043 32.1 .00069 4.0 27.4 .00103 .00016 4.8 23.6 .00051 6.1 18.3 .00021 15 7.4 2.9 28.4 14.5 5.2 17.9 3.3 VarianceStandard errorYears 9.1 .00155 .00108 7.6 40.7 .00059 5.6 42 .00047 .00066 5.0 45.5 .00103 49.2 5.9 .00156 47.1 7.4 .00226 41.2 .00389 9.1 -- 34.2 11.0 .00075 27.9 14.4 .0026 18.7 .00103 -- -- 6.3 35.9 11.8 11.2 7.4 16.3 VarianceStandard errorYears 8.0 .0012 6.6 .00082 44.5 .00041 4.7 46.8 .00025 52.3 .00034 3.6 .00058 60.5 4.2 .00092 56.6 5.5 .0014 45.4 .00244 7.0 35.6 .00376 .00039 8.6 27.5 .00179 11.4 17.9 .00063 14.2 12.7 4.5 39.7 9.8 8.8 13.7 5.8 VarianceStandard errorYears 1.5 .00004 .00004 1.4 57 .00003 1.2 .00002 57 .00002 1.1 57 .00002 1.0 .00001 57 .00001 .9 57 .00001 57 .9 .000012 .00007 .00118 57 .8 .00065 57 .8 57 .8 2.0 57 7.9 57 5.9 57 57 VarianceStandard errorYears ------3.9 -- .00028 .0002 3.3 68 .00026 3.7 76 .0004 4.6 67.1 .0006 50.7 5.6 .00087 .00149 36.6 6.8 .00228 .00028 26.2 8.9 .00096 15.2 11.0 .00036 10 3.9 37.1 7.1 7.7 4.4 11.3 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01170575 Stream 01170100 Stream 01169900 Stream 01169801 Stream 01169800 Stream 01169600 Stream 01169000 Stream 01168650 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 69 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .22 .27 .44 .71 1.03 1.37 1.78 2.22 3.58 5.33 1.09 .20 .42 ow 2.37 2.68 3.69 4.96 6.08 7.40 8.82 10.2 13.5 17.1 6.47 2.17 3.56 ow -- -- .040 .15 .34 .56 .88 1.40 2.60 3.60 .26 -- -- ow 1.38 1.55 2.05 2.64 3.18 3.69 4.19 4.70 -- -- 3.36 1.29 2.02 ow .85 1.11 1.91 3.38 5.12 7.17 9.62 ------5.65 -- -- ow 1.61 1.97 3.06 4.62 6.02 7.42 8.75 10.5 14.7 20.4 6.96 1.49 3.03 ow .55 .63 .79 1.10 1.40 1.70 2.00 2.30 3.60 4.80 1.50 .46 .89 ow 6.70 7.80 10.0 14.0 17.0 21.0 25.0 29.0 40.0 55.0 18.0 6.31 10.0 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 8.4 .00133 .00105 7.5 37 .00062 5.7 .00044 37.9 .00048 4.8 39.7 .0006 41 5.0 .00077 5.6 40.4 .00097 37.9 .00159 6.4 .0023 34.7 .00053 7.2 .00239 31.4 9.2 .00111 24.2 11.1 19 5.3 32.1 11.3 15.3 7.7 17.7 VarianceStandard error 13.1Years .00319 11.6 .00251 22 .00136 8.5 .00075 22.8 6.3 .00055 27.2 .0005 5.4 31.7 .00061 5.2 34.8 .00079 36.9 .00133 5.7 .00199 33.7 6.5 .00054 28.9 .00398 8.4 .00165 20 10.3 14.4 5.4 29.5 14.6 4.3 9.4 6.1 VarianceStandard errorYears ------5.6 -- .00058 .00045 4.9 9 .00038 4.5 .00033 9 4.2 .00030 9 .00028 4.0 .00025 9 .00025 3.9 .00288 9 -- 3.7 -- 3.6 9 12.4 9 -- 9 -- 9 -- -- VarianceStandard error 15.9Years .0047 13.7 .00352 13.4 .00176 9.7 14.6 .00108 7.6 21.7 .00113 .00149 7.8 25.8 .00202 20 8.9 .00268 13.9 -- 10.4 9.8 12.0 -- -- 7.1 .00122 .0055 -- -- .00191 -- 8.1 17.2 11.1 10.1 1.7 3.1 VarianceStandard error 21.5Years .00851 18.5 .00637 24.1 .00333 13.3 26.7 .00189 10.0 .0021 34.1 10.6 .00291 41.6 12.5 .00402 34.3 -- 14.7 25.4 -- -- 18.9 ------.00226 ------11.0 ------20.9 ------VarianceStandard error 14.4Years .00386 12.7 .00301 34.2 .00169 9.5 35.7 .00102 7.4 .00088 39.8 .0009 6.8 42.7 .00101 44.4 6.9 .00121 45.4 .00188 7.3 44.1 .00282 8.0 .00086 40.5 .00477 10.0 .00195 31.9 12.3 24.4 6.8 34.1 16.0 8.3 10.2 11 VarianceStandard errorYears 3.2 .00019 .00016 2.9 11 .00012 2.6 .00010 11 .00008 2.3 11 .00007 2.1 .00006 11 1.9 .00006 11 .00005 1.8 11 .00005 .00039 1.8 11 .00883 .00485 1.7 11 1.7 11 4.5 11 21.9 11 16.1 11 11 VarianceStandard errorYears 1.4 .00004 .00003 1.3 57 .00002 1.1 .00002 57 .00002 1.0 57 .00001 .9 .00001 57 .00001 .9 57 .00001 57 .00001 .8 .00007 57 .00087 .8 .00048 57 .7 57 .7 57 2.0 57 6.8 5.0 57 57 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01173450 Stream 01173420 Stream 01173260 Stream 01172810 Stream 01171970 Stream 01171947 Stream 01171800 Stream 01171500 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

70 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .12 .16 .30 .48 .66 .86 1.08 1.35 2.06 3.03 .74 .10 .29 ow 1.05 1.24 1.83 2.70 3.69 4.72 5.78 6.92 9.80 13.2 3.96 .97 1.81 ow .32 .42 .82 1.52 2.18 3.10 4.14 5.34 8.49 -- 2.52 .30 .83 ow .28 .35 .61 1.10 1.80 2.60 3.40 4.30 6.70 9.40 1.90 .23 .56 ow .11 .13 .21 .34 .52 .72 1.00 1.30 2.10 3.00 .55 0.092 0.18 ow .90 1.00 1.40 2.09 2.94 4.10 5.49 6.15 8.12 11.9 3.24 -- -- ow .16 .19 .27 .50 .91 1.21 1.57 1.91 2.98 4.44 1.85 -- -- ow 0.020 0.050 0.14 0.31 0.56 0.81 1.14 1.55 2.50 3.60 0.50 -- -- fl fl fl fl fl fl fl fl Statistic VarianceStandard error 14.3Years .00383 12.4 .00288 37.9 .00153 9.0 41.4 .00088 6.8 .00066 49.3 .00061 5.9 52.1 .00067 50.2 5.7 .00082 50.7 .00134 6.0 .00207 50.9 .00063 6.6 48.9 .00493 8.4 .00194 40.4 10.5 31.3 5.8 43.9 16.3 10.3 10.2 16.4 VarianceStandard errorYears 7.5 .00107 .00086 6.8 36.1 .0005 5.2 37 .00031 .0003 4.1 39 .00036 4.0 40.2 .00047 4.4 40.2 .0006 39.1 .00095 5.0 .00136 36.5 5.6 .00034 32.9 .00174 7.1 .00081 25.7 8.5 20.6 4.2 33.1 9.6 12.4 15 6.6 VarianceStandard error 22.4Years .0092 19.9 .00729 32.1 15.2 .00431 32.3 .00274 12.1 34.9 .0024 11.3 .00253 36.3 11.6 .00286 33.8 12.4 .00319 32.3 .00394 13.1 30.5 -- 14.5 29 .00239 -- .01102 26.3 .00527 11.3 -- 24.5 25.5 16.8 8.4 8.8 VarianceStandard errorYears 2.2 .00009 .00008 2.0 35 .00006 1.8 .00005 35 .00004 1.6 35 .00003 1.4 .00003 35 1.3 .00003 35 .00003 1.3 35 .00003 .00026 1.2 35 .00523 .00287 1.2 35 1.2 35 3.7 35 16.8 35 12.4 35 35 VarianceStandard errorYears 2.2 .00009 .00008 2.0 35 .00006 1.8 .00005 35 .00004 1.6 35 .00003 1.4 .00003 35 1.3 .00003 35 .00003 1.3 35 .00003 .00026 1.2 35 .00523 .00287 1.2 35 1.2 35 3.7 35 16.8 35 12.4 35 35 VarianceStandard errorYears 2.3 .00010 .00008 2.1 2 .00006 1.8 .00005 2 .00004 1.6 .00004 2 1.5 .00003 2 1.4 .00003 .00040 2 1.3 .000026 .00028 2 1.3 -- 4.6 2 -- 1.2 2 3.8 2 -- 2 -- 2 -- -- VarianceStandard errorYears 9.5 .00170 .00143 8.7 2 .00108 7.6 .00084 2 .00071 6.7 .00062 2 6.1 .00056 2 5.8 .00052 .00047 2 5.5 .00046 .00369 2 5.3 -- 5.0 2 -- 4.9 2 14.0 2 -- 2 -- 2 -- -- VarianceStandard errorYears 2.7 .00014 .00011 2.5 34 .00009 2.1 .00007 34 .00006 1.9 34 .00005 1.7 .00004 34 1.6 .00004 34 .00004 1.5 34 .00004 .00052 1.5 -- 34 1.4 -- 34 1.4 34 5.3 34 -- 34 ------Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01175890 Stream 01175850 Stream 01175710 Stream 01175670 Stream 01174900 Stream 01174565 Stream 01174050 Stream 01174000 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 71 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .62 .79 1.16 1.82 2.43 3.21 4.11 5.20 8.18 12.6 2.55 .54 1.11 ow 2.74 2.97 3.61 4.32 4.95 5.58 5.91 6.50 7.79 9.25 5.57 -- -- ow 1.75 2.10 3.00 4.20 5.41 6.76 7.70 9.16 13.1 -- 6.42 1.68 3.18 ow 3.31 3.58 4.26 5.02 5.78 6.48 6.93 7.61 9.08 10.5 6.05 3.11 4.17 ow ------3.48 3.90 4.30 4.61 4.97 5.79 6.74 4.09 -- -- ow .74 .89 1.18 1.58 1.94 2.30 2.59 2.95 3.81 4.97 2.08 .69 1.22 ow -- -- .82 1.47 1.97 ------.11 .91 ow 16.0 20.0 30.0 42.0 52.0 65.0 78.0 93.0 126 168 65.0 15.8 32.8 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 6.9 .00089 .00064 5.8 58.8 .00043 4.8 61 .00041 .00054 4.7 59.3 .00077 55.3 5.4 .00107 52.1 6.4 .00144 47.6 .00234 7.5 .00345 42.6 .0006 8.8 37.9 .00166 11.2 .0007 29.5 13.6 23.3 5.6 40.6 9.4 18.8 6.1 23.6 VarianceStandard error 12.1Years .00272 10.5 .00207 12.1 .00112 7.7 13.3 .00057 5.5 .00038 17 .00036 4.5 22.3 .00041 4.4 26.1 .00055 27.2 .00103 4.7 .00176 24.2 .00041 5.4 -- 20.3 7.4 -- 12.6 9.7 7 4.7 19 ------VarianceStandard error 18.9Years .0066 16.3 .00497 17 12.1 .00274 18.5 .00138 8.6 .00091 23.2 .00088 7.0 29.1 .00105 6.8 31.5 .00137 29.8 7.5 .00265 -- 26 8.5 .00091 11.9 22.1 .00764 14.2 .00271 -- -- 7.0 21.1 20.3 12.0 2.8 5.1 VarianceStandard errorYears 6.2 .00072 .00055 5.4 25.2 .00029 3.9 26.9 .00015 .00012 31.4 2.8 .00016 34.3 2.5 .00021 32.6 2.9 .0003 28.7 .00057 3.3 24.9 .0009 .00014 4.0 21 .00100 5.5 .00038 14.1 6.9 9.5 2.7 27.2 7.3 4.7 4.5 7.9 VarianceStandard errorYears ------2.8 -- .00015 .00018 3.1 53.1 .00024 3.6 48 .0003 40.3 4.0 .0004 33.6 .00068 4.6 .00106 27.4 .00022 6.0 -- 17.7 7.5 11.8 -- 3.4 27.6 ------VarianceStandard errorYears 7.5 .00105 .00078 6.4 40.3 .00048 5.0 41.7 .00036 .00037 45 4.4 .00045 45.2 4.4 .00055 42.1 4.9 .00068 37 .00103 5.4 .00153 31.5 .00041 6.0 .0015 26.9 .00064 7.4 20.2 9.0 15.6 4.7 30.9 8.9 10.4 14 5.8 VarianceStandard errorYears ------17.1 -- .00542 14.7 .00402 60.2 .00409 14.8 -- 61.1 -- 57.1 ------.01378 27.5 -- .00608 18.1 11.8 16 VarianceStandard errorYears 1.1 .00002 .00002 1.0 83 .00001 .9 .00001 83 .00001 .8 83 .00001 .00001 83 .7 .00001 83 .7 .00001 83 .00001 .6 .00005 83 .00124 .6 .00068 83 .6 83 .6 83 1.7 83 8.1 83 6.0 83 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01178200 Stream 01177360 Stream 01176780 Stream 01176415 Stream 01176300 Stream 01176200 Stream 01176100 Stream 01176000 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

72 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow 7.10 8.90 12.0 18.0 24.0 30.0 38.0 46.0 70.0 96.0 23.0 5.79 11.0 ow .26 .30 .40 .54 .74 1.00 1.30 1.60 2.50 3.40 .80 .21 .34 ow .30 .37 .55 .86 1.28 ------1.31 .24 .55 ow 2.90 -- 5.30 8.20 11.0 15.0 19.0 24.0 36.0 50.0 11.2 1.40 5.33 ow .070 .080 .11 .16 .22 .28 .38 .53 0.86 1.20 .21 .058 .11 ow -- -- .21 .55 1.04 1.74 2.97 ------1.04 -- -- ow .73 1.06 1.99 ------4.77 .59 1.67 ow 1.51 1.90 2.87 4.37 5.68 7.36 9.33 11.6 -- -- 5.91 1.32 2.71 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 1.6 .00005 .00004 1.4 60 .00003 1.3 .00002 60 .00002 1.1 60 .00002 1.0 .00002 60 1.0 .00001 60 .00001 .9 60 .00001 .00010 60 .9 .00155 .00085 .8 60 .8 60 2.3 60 9.1 60 6.7 60 60 VarianceStandard errorYears 3.3 .00021 .00018 3.0 14 .00013 2.7 .00010 14 .00009 2.3 14 .00008 2.1 .00007 14 2.0 .00006 14 .00006 1.9 14 .00006 .00051 1.8 14 .00329 .00181 1.8 14 1.7 14 5.2 14 13.3 14 9.8 14 14 VarianceStandard error 22.4Years .00922 18.7 .00646 26.4 .00338 13.4 30.8 .00193 10.1 .00272 41.3 -- 12.1 51.7 -- -- 41.7 ------.0029 .01298 12.4 -- .0039 26.7 29.3 14.5 3.1 5.6 VarianceStandard errorYears 1.5 .00004 -- -- 79 .00003 1.2 -- .00002 1.0 .00002 79 .00002 1.0 79 .00001 .9 79 .00001 .00001 79 .9 .00001 .00009 79 .8 .00326 .00179 79 .8 79 .8 79 2.1 13.2 79 9.8 79 79 VarianceStandard errorYears 2.6 .00013 .00011 2.4 28 .00008 2.1 .00006 28 .00005 1.8 28 .00005 1.7 .00004 28 1.6 .00004 28 .00004 1.5 28 .00003 .00022 1.4 28 .00306 .00168 1.4 28 1.3 28 3.4 28 12.8 28 9.5 28 28 VarianceStandard errorYears ------15.0 -- .00422 10.7 .00215 52.5 .00168 9.5 55.4 .00184 9.9 56.5 .00248 -- 55.9 11.5 54.1 ------.00205 ------10.5 -- 51.4 ------VarianceStandard error 20.8Years .00796 16.9 .00533 29.6 .00253 11.6 -- 31.3 -- 35.3 ------.0017 9.5 -- .01096 24.5 .00386 30 14.4 5.5 9 VarianceStandard error 10.2Years .00194 8.5 .00135 56.5 .00086 6.8 60 .00081 .00114 6.6 58.3 .00172 7.8 52.2 .00246 46.4 9.6 .00334 -- 38.6 11.5 31.3 -- 13.4 25.8 -- .00126 .00309 -- -- .00115 -- 8.2 30.8 12.9 10.2 7.8 15.6 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01181000 Stream 01180800 Stream 01180650 Stream 01180500 Stream 01180000 Stream 01179900 Stream 01178490 Stream 01178300 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 73 ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow 1.20 1.30 1.40 1.60 2.17 2.70 3.60 4.40 8.34 9.90 2.35 -- -- ow .30 .40 .50 .80 1.00 1.60 2.20 3.00 5.00 7.20 -- .24 .46 ow .51 .70 1.17 1.83 2.55 3.38 4.34 5.49 8.76 -- 2.61 .40 1.11 ow 2.17 2.99 ------10.3 1.75 4.47 ow 3.13 4.03 5.94 8.50 11.5 14.9 18.6 22.9 -- -- 12.0 2.70 5.81 ow 1.41 2.25 4.32 6.36 7.82 8.90 9.46 10.2 11.5 -- 8.44 -- 4.21 ow .48 .57 .78 1.12 1.47 1.83 2.17 2.55 3.52 4.70 1.56 .43 .78 ow 2.95 4.43 7.26 8.77 10.5 11.7 12.2 13.3 15.4 16.8 11.9 1.94 7.44 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 7.9 .00117 .00098 7.2 2 .00074 6.3 .00057 2 .00048 5.5 .00043 2 5.1 .00039 2 4.8 .00036 .00032 2 4.5 .00031 .00066 2 4.4 -- 4.2 2 -- 4.1 2 5.9 2 -- 2 -- 2 -- -- VarianceStandard errorYears 2.5 .00012 .00010 2.3 31 .00008 2.0 .00006 31 .00005 1.8 31 .00004 1.6 .00004 31 1.5 .00004 31 .00003 1.4 31 .00003 -- 1.4 31 .00435 1.3 .00239 31 1.3 31 -- 31 15.3 -- 11.3 31 31 VarianceStandard error 13.6Years .00346 11.3 .00241 39.6 .00126 8.2 42.9 .00082 6.6 .00084 51.1 .00108 6.7 54.1 .00146 49.3 7.6 .00195 41.3 .00328 8.8 -- 32.9 10.2 .00089 26.3 13.2 .00493 16.7 .0016 -- -- 6.9 34.3 16.3 6.7 9.2 12.1 VarianceStandard error 18.6Years .00643 15.2 .00432 45.1 -- -- 49.8 ------.00315 13.0 -- .00847 21.4 24.2 .00317 13.0 6.4 9.5 VarianceStandard error 13.7Years .00349 11.5 .00249 32.6 .00148 8.9 35.1 .00106 7.5 .00113 39 .00148 7.8 39.9 .00199 8.9 36.5 .00264 -- 30.5 10.3 24.2 -- 11.9 19.2 -- .00119 .00456 -- -- .00174 -- 8.0 23.7 15.6 4.8 9.6 7.3 VarianceStandard error 11.3Years .00239 9.9 .00184 31.3 .00094 7.1 32.3 .00055 .00058 5.4 36.9 .00085 39.3 5.5 .00117 36.9 6.7 .00165 31.6 .00294 7.9 -- 26.2 9.4 .00075 21.5 -- 12.5 14.5 -- .00128 -- 6.3 27.3 -- -- 8.3 11.8 VarianceStandard errorYears 6.4 .00076 .00064 5.8 38.8 .0005 5.2 38.7 .00043 37.9 .00044 4.8 .0005 36.5 4.8 .00057 34.3 5.2 .00065 31.5 .00088 5.5 28.6 .00116 .00047 5.9 26 .00113 6.8 .00067 21.1 7.9 17.6 5.0 25.4 10.9 7.8 10.4 6.0 VarianceStandard error 11.5Years .00249 9.7 .00175 45.3 .00096 7.1 48.3 .00065 .00051 5.9 54.1 .00054 51.5 5.2 .00064 46.8 5.4 .00085 41.2 .00169 5.8 .00313 35.5 .00058 6.7 31.4 .0035 9.5 .00117 23.7 12.9 16.9 5.5 36.4 13.7 8.4 7.9 14.6 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01197015 Stream 01187400 Stream 01186300 Stream 01185490 Stream 01184855 Stream 01184277 Stream 01184200 Stream 01183210 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

74 Methods for Estimating Low-Flow Statistics for Massachusetts Streams ow fl 7-Day, 2-year low low ow fl 7-Day, 7-Day, 10-year low low August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow .68 .80 1.03 1.34 1.67 2.00 2.33 2.70 3.57 4.50 1.70 .59 1.02 ow ------.017 .092 ow 3.20 3.70 4.70 6.40 8.50 12.0 15.0 19.0 30.4 42.0 9.10 3.11 -- ow .010 .020 .060 .21 .38 .55 .83 1.10 1.60 2.40 .47 -- -- ow 1.70 2.09 2.84 -- 4.91 6.06 7.26 8.63 11.9 15.5 4.98 1.50 2.77 ow -- 1.85 2.25 2.68 3.13 3.54 4.00 4.43 5.45 6.47 3.13 1.49 2.17 ow .16 .21 .36 .63 .95 1.39 1.94 ------1.02 .12 .34 ow 1.63 1.96 2.76 4.15 5.57 7.16 9.05 11.3 -- -- 5.90 1.45 2.67 fl fl fl fl fl fl fl fl Statistic VarianceStandard errorYears 8.7 .00142 .00111 7.7 44.6 .0008 6.5 46.2 .00069 46.9 .00078 6.1 .00097 45.3 6.4 .00122 40.4 7.2 .00152 34.9 .0023 8.1 29 .00313 .00081 9.0 24.2 .00212 11.1 .00101 16.7 12.9 12.9 6.6 29 10.6 9.6 7.3 11.2 VarianceStandard errorYears ------26.9 -- .01321 18.6 .00643 11.2 12.6 VarianceStandard errorYears 2.7 .00014 .00012 2.5 21 .00009 2.2 .00007 21 .00006 1.9 21 .00005 1.8 .00005 21 1.7 .00004 21 .00004 1.6 21 .00004 .00020 1.5 21 .00320 -- 1.4 21 1.4 21 3.3 21 13.1 21 -- 21 -- VarianceStandard errorYears 5.8 .00064 .00053 5.3 9 .00040 4.6 .00031 9 .00026 4.1 .00023 9 3.7 .00021 9 3.5 .00020 .00018 9 3.3 .00017 .00275 9 3.2 -- 3.1 9 -- 3.0 9 12.1 9 -- 9 -- 9 -- -- VarianceStandard errorYears 6.8 .00088 .00062 5.7 47.6 .00043 -- 4.8 49.7 49.4 -- .00063 -- .0009 5.8 37.8 .0012 6.9 30.6 .00156 8.0 .00239 24.3 .00328 9.1 .00067 19.6 .00138 11.3 13.3 .00062 13.2 10.1 6.0 26.4 8.6 11.9 15 5.7 VarianceStandard errorYears -- -- 5.5 -- .00057 .00035 4.3 52.8 .00032 4.1 60.9 .00042 .00059 54.8 4.7 .00082 42.3 5.6 .00107 31.7 .00174 6.6 23.3 .00245 7.5 .00043 17.8 .00111 9.6 10.9 .00042 11.4 7.8 4.8 25.3 7.7 7 4.7 9.8 VarianceStandard error 19.3Years .00692 16.8 .00528 37.5 .00328 13.2 39.2 .00216 10.7 .00209 42 10.6 .00258 44.9 .00343 11.7 43.3 -- 13.5 38.4 -- -- 31.4 ------.00219 -- -- .00957 .00391 10.8 -- 22.8 29.8 14.5 6.4 8.6 VarianceStandard error 11.0Years .00225 9.3 .00164 39.7 .00083 6.6 41.2 .00068 .00101 6.0 47.1 .0016 44.2 7.3 .00238 35.1 9.2 .00337 27.7 -- 11.3 21.8 -- 13.4 17.2 -- .00118 -- .00325 -- .00118 -- 7.9 22.9 13.2 7.1 7.9 13.5 Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01198160 Stream 01198060 Stream 01198000 Stream 01197300 Stream 01197230 Stream 01197180 Stream 01197140 Stream 01197120 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

Table 9 75 ow fl 7-Day, 2-year low low ow fl .0007938 .0004359 7-Day, 7-Day, 10-year low low 0000834 August August median mflow statistics are computed low-flow partial-record stations are Flow-duration percentile Flow-duration Continued 99 98 95 90 85 80 75 70 60 50 — ow 2.43 2.75 3.66 4.74 4.94 5.11 5.77 6.80 9.09 11.3 4.96 2.29 3.74 ow ------1.26 1.67 2.68 4.29 -- .10 .22 ow 4.80 5.60 7.80 11.0 14.0 18.2 23.0 27.0 36.0 48.0 15.0 4.57 8.19 ow ------1.67 2.01 2.70 ------7.98 2.13 1.34 1.45 ow 5.70 6.50 8.50 11.0 14.4 19.0 23.0 -- -- 49.0 14.0 5.21 7.77 ow .17 .27 .57 1.10 1.60 2.00 2.60 3.37 5.20 7.30 1.90 -- -- ow .48 .54 .72 .96 1.17 1.44 1.78 2.16 3.20 -- 1.22 .44 .70 ow -- -- 19.1 24.5 29.6 35.7 41.3 47.4 61.0 75.9 30.6 -- -- fl fl fl fl fl fl fl fl Statistic VarianceStandard error 12.5Years .00291 10.7 .00214 24.4 .00093 7.0 27.2 .00051 5.2 .00057 42.4 .00041 5.5 57.5 .0005 28.7 4.7 .00088 21.4 .00214 5.2 19.3 .00354 6.8 .00057 16.1 .00366 10.7 .00099 9.6 13.8 6.6 5.5 17.3 14.0 4 7.3 9.9 VarianceStandard errorYears ------7.7 .00111 45.9 .00136 8.5 .00201 10.4 43.8 .00295 -- 12.6 39.4 -- 34.9 .00564 .00301 -- 17.4 12.7 16.1 17.7 VarianceStandard errorYears 1.6 .00005 .00004 1.4 47 .00003 1.2 .00002 47 .00002 1.1 47 .00002 1.0 .00002 47 .00001 .9 47 .00001 47 .9 .00001 .00009 47 .00171 .9 .00094 47 .8 47 .8 2.2 47 9.5 47 7.1 47 47 VarianceStandard errorYears ------3.9 -- .00029 .00026 3.7 57.1 .00032 4.1 56.6 -- 54.4 ------.00166 -- .00029 9.4 .00202 33.4 3.9 .00086 49.7 10.4 19.2 6.8 23.6 VarianceStandard errorYears 1.5 .0000409 .0000343 1.3 .000026 58 .0000201 .000017 1.2 58 .0000149 .0000135 1.0 58 -- .9 58 -- .9 58 .00001 58 .8 . 58 ------.8 2.1 58 6.5 58 4.8 58 58 VarianceStandard errorYears 4.8 .00044 .00037 4.4 10 .00028 3.9 .00022 10 .00018 3.4 10 .00016 3.1 .00015 10 2.9 .00014 10 .00012 2.8 10 .00012 .00209 2.7 -- 10 2.6 -- 10 2.5 10 10.6 10 -- 10 ------VarianceStandard error 13.5Years .00343 11.6 .00253 39.7 .00131 8.3 41.4 .00069 6.1 .00058 46.1 .0007 5.5 51.8 .00107 52.8 6.1 .00159 49.4 .00288 7.5 -- 42.6 9.2 35.7 .00061 12.4 .00446 25.1 .00169 -- -- 5.7 40.8 15.5 7 9.5 10 VarianceStandard errorYears ------3.0 -- .00017 .00014 2.7 37.3 .00012 2.5 36.9 .00011 36.6 2.4 .0001 36.2 .0001 2.3 35.8 .0001 2.3 .00011 35.3 .00013 2.3 -- 34.3 2.5 33.3 -- 2.6 31.8 ------Streamflow statistics, variances, standard errors, and years of record for stations included in the regression analyses; strea No. Station 01359967 Stream 01333100 Stream 01333000 Stream 01332900 Stream 01332000 Stream 01331400 Stream 01331380 Stream 01198200 Stream computed from equation 14 Table 9. from daily records for streamgaging stations and estimated low-flow partial-record stations; equivalent years of record

76 Methods for Estimating Low-Flow Statistics for Massachusetts Streams Region basin elevation Maximum Maximum elevation Mean basin basin elevation Minimum 0 is eastern; 1 western; No., number; -- , no data] Region: feet. Area of wetlands water bodies Area of Continued — ed- ﬁ drift area Strati Mean basin slope Total length stream area Drainage Basin characteristics for stations used in the regression analyses Basin characteristics for stations used in the regression analyses 01073860010943400109439601094760 1.83 21.701095220 15.801095380 7.4101095915 30.4 4.2101095928 38.601096000 32.3 6.79 15.701096504 12.7 50.7 5.89 0.8401096505 64.4 4.5701096515 11.6 1.92 6.4101096805 23.6 3.8101096855 13.3 6.84 1.80 125 18.2 5.8001096910 3.78 15.4 3.9901096935 3.26 1.40 6.62 3.0201097280 12.7 1.62 1.61 4.93 0.0001097300 30.7 5.41 17.201099400 5.07 42.6 .77 1.95 24.9 1.9301100608 18.5 .25 4.53 12.9 2.28 .5201100700 2.99 0.00 25.6 .66 2.86 .4701101000 17.1 42.4 4.09 4.5401101100 .70 57.4 1.52 .02 3.7101102053 .40 33.7 5.54 .50 4.62 21.4 3.6601102490 .23 48.1 11.3 22 .02 .80 10.2 7.70 3.9201103015 .40 3.43 670 2.72 2.28 .0201103253 .41 10.1 1.76 567 3.05 2.3901103435 .02 56.4 423 .02 .18 65 2.0101103440 25.6 5.35 403 1,000 .91 .22 5.55 1.35 1.3701104960 7.23 1,050 .15 4.88 7.70 532 10.2 .30 2.78 .05 5.06 7.45 241 615 3.91 15.8 1,150 1,340 5.52 108 .52 10.5 .00 482 2.37 1,580 4.67 252 .36 18.5 2.17 .37 806 1.99 .57 19.0 181 .49 1.72 312 2,000 3.21 806 .57 0 .09 0 7.03 9.92 177 893 3.21 0 .47 .00 4.18 5.51 855 174 1,080 2.29 .13 .71 1.72 216 300 1.56 1.81 0 403 0 234 .07 .34 1,300 332 1.58 .96 1,500 .50 298 2.26 1.60 234 1.65 0 .07 1.09 205 450 428 .12 126 .01 0 6.24 446 0 514 .21 2.35 158 0 .01 2.16 441 397 98 .05 .67 422 701 0 .56 104 .06 295 661 .02 .50 0 314 95 .01 582 .04 0 32 249 640 0 .13 .07 229 26 470 0 .36 26 463 .48 213 0 193 50 403 .47 0 354 15 0 130 .10 172 0 96 110 334 354 0 202 118 0 194 252 113 306 167 236 0 0 364 214 377 0 213 445 0 370 0 336 0 334 0 0 0 0 Station No. Table 10. Table 10. are in are in cubic feet per second; areas square miles; lengths slopes percent; elevations [Flows

Table 10 77 Region basin elevation Maximum Maximum elevation Mean basin basin elevation Minimum Area of wetlands water bodies Area of Continued — ed- ﬁ drift area Strati Mean basin slope Total length stream area Drainage Basin characteristics for stations used in the regression analyses 01104980011051000110527001105568 8.6401105575 3.40 10.401105582 4.3101105600 15.5 1.7201105630 5.84 27.401105670 29.401105820 4.47 6.53 4.91 2.2701105830 1.79 1.61 3.0301105861 48.7 3.17 2.50 8.03 1.30 10.9 1.72 2.20 2.1301105930 4.74 2.47 1.96 2.3301105935 6.09 6.45 1.2701105937 2.04 3.19 8.09 1.63 0.4601105947 7.92 .0001106000 2.64 10.8 .81 .01 1.1401106460 8.59 .72 1.50 17.4 9.25 .0501107000 3.64 .61 0.31 7.99 1.0601107400 .01 5.76 8.94 1.01 .1501108140 .05 15.3 .7701108180 .73 18.3 4.71 .00 1.2401108600 .05 17.6 9.30 59 .06 .08 4.22 17.3 8.20 1.8201109087 .09 1.86 79 .00 7.48 1.5201109090 104 .05 9.61 3.8301109200 .26 15.4 3.63 118 .90 222 20.7 1.5101109225 .21 .00 16.0 .06 115 1.44 1.5001109460 11.6 271 4.22 59 3.27 .06 284 11.4 4.33 1.10 .28 180 1.43 75 396 7.21 1.04 .16 37.0 11.1 .18 29 182 .20 1.09 .00 3.30 .01 484 330 6.19 490 .96 .02 9.25 6 42 241 .88 0 11.6 137 .96 7.21 2.40 .01 31.1 104 -- 1.42 259 6.98 62 0 39 630 1.81 .19 0 .43 3.69 0 .76 154 .32 65 200 2.49 .04 1.11 1.03 75 .45 180 0 9.37 3.46 131 0 .18 -- 94 1.51 41 .91 .05 221 0 124 2.78 70 2.85 .01 155 0 .25 19 1.32 200 2.91 .15 170 .89 109 .03 55 0 10 0 170 .61 .02 236 118 155 .02 .19 0 49 2.53 0 .51 179 32 175 178 .11 270 15 0 209 296 .42 124 1.18 111 27 0 .44 259 82 227 0 23 301 0 92 101 214 173 19 138 491 0 0 131 172 0 183 160 305 0 109 249 680 0 326 0 255 0 200 0 869 0 0 0 0 011058839011059106 6.87 2.58 5.34 3.46 2.21 .61 6.87 1.64 1.10 .02 .02 .50 42 52 118 70 193 88 0 0 Station No. Table 10.

78 Methods for Estimating Low-Flow Statistics for Massachusetts Streams Region basin elevation Maximum Maximum elevation Mean basin basin elevation Minimum Area of wetlands water bodies Area of Continued — ed- ﬁ drift area Strati Mean basin slope Total length stream area Drainage Basin characteristics for stations used in the regression analyses 01111142011112000111122501111300 5.67 27.801112190 7.2601123140 16.001123161 11.7 6.1701123200 69.9 13.801124390 17.201162500 30.0 6.57 16.2 4.39 3.9801162900 8.58 4.4301163298 39.2 19.2 3.1501164300 15.3 19.2 3.1401165090 12.9 1.30 3.3801165250 28.5 7.22 8.45 15.6 13.9 6.3301165500 2.60 14.1 5.9601166105 32.2 4.60 7.08 4.63 0.0501167200 10.9 .95 12.1 3.8201168300 26.8 .27 3.27 3.6801168400 20.8 5.24 .08 1.88 -- 22.3 11.2 2.8201168650 0.65 29.6 .18 3.0901169000 15.0 .02 27.1 .00 1.77 4.0601169600 10.6 2.01 .17 18.1 7.6401169800 .19 38.6 .16 6.17 89.8 4.34 350 --01169801 57.0 2.59 .02 10.5 55.5 247 6.9301169900 .17 2.80 .16 6.69 7.39 .0101170100 .57 36.7 1.45 270 15.6 10.6 17501170575 .24 505 1.45 .45 11.0 24.101171500 348 21.4 .09 .20 424 12.1 200 1.92 41.301171800 13.6 .54 .50 1.24 652 456 21.7 11.1 .52 31.2 .05 1.15 653 659 54.0 1.19 .16 9.70 48.1 572 .20 690 659 371 5.56 8.49 .21 84.2 .14 .91 564 943 8.22 641 .73 39.7 851 .00 2.17 0 100 915 8.72 .18 913 .05 5.41 773 .17 0 986 9.45 587 9.17 1.06 834 .17 1,250 828 1,280 9.52 0 .17 856 .14 1,180 .24 6.86 1,110 .05 1.89 560 .04 1,290 0 .03 6.91 623 0 .08 3.20 1,090 995 1,870 5.20 0 1,360 .01 .20 1.48 511 0 1,310 .13 4.43 478 .02 977 0 .09 .07 395 9.52 961 1,160 0 1,880 1 2.04 .20 .10 751 999 1 .01 .01 1,400 613 983 .32 .07 1,300 483 858 1 .08 1 .53 1,940 475 1,620 .03 .08 1,790 587 1,300 1 .03 1,330 1,400 1 776 .10 820 2,830 1,350 1 .54 2,510 1,070 485 1 .11 1,900 1,310 475 1 1,280 2,230 296 1 1,550 1,150 1 141 209 1,700 1,360 1 1,830 1 907 1,830 1 848 2,400 1 514 1 1,300 1 1,690 1 829 1 1 1 Station No. Table 10.

Table 10 79 Region basin elevation Maximum Maximum elevation Mean basin basin elevation Minimum Area of wetlands water bodies Area of Continued — ed- ﬁ drift area Strati Mean basin slope Total length stream area Drainage Basin characteristics for stations used in the regression analyses 011719470117197001172810 18.401173260 18.801173420 12.701173450 4.6201174000 34.4 19.001174050 31.201174565 17.8 6.6001174900 3.39 4.01 33.4 5.03 3.4601175670 12.5 1.4101175710 10.8 2.89 3.6101175850 7.97 1.6601175890 8.69 6.29 8.20 13.8 5.4401176000 27.9 10.9 11.5 4.2701176100 5.99 2.47 3.55 6.5301176200 149 16.74 .00 4.60 0.2501176300 28.8 4.54 7.4701176415 25.6 9.34 .10 1.00 5.9601176780 3.96 .03 7.68 5.46 319 .07 6.5701177360 1.31 .03 15.3 .72 3.87 .2501178200 20.8 1.94 13.6 4.6701178300 .88 .02 4.91 .02 5.6401178490 .59 6.92 1.11 8.76 .01 11.1 29201179900 18.9 4.51 .58 2.16 1.23 .17 22.9 22.0 4.88 .0801180000 1.93 167 12.3 7.0701180500 .46 12.5 0.67 713 .00 6.46 8.54 .2101180650 394 19.2 31.7 .00 927 432 5.8001180800 38.8 1.74 .43 .25 2.86 401 52.8 5.5701181000 .04 26.0 1,010 .08 1.08 432 6.35 3.20 .01 .01 6.78 1.41 1,070 797 730 .30 2.95 5.79 4.36 699 3.54 94.0 2.54 706 1,310 4.86 643 .83 97.8 2.83 593 .03 699 5.78 .52 13.21 1,220 .01 539 4.57 1,000 1 5.34 .09 650 .05 6.98 986 8.28 161 .22 931 9.72 1 .32 1 664 823 .80 8.50 .08 986 .52 613 1,300 1 4.74 .26 860 .17 609 .03 864 .19 1 1,220 387 4.76 .13 1,040 .01 908 .00 .28 8.78 1 1.50 373 1 .17 1,160 880 .26 1,080 .00 373 .01 857 1 792 .54 408 .01 1,150 1 .12 396 3.91 .10 1,160 .01 775 1 260 .46 .48 1,100 1 684 1,220 .01 .00 243 806 1 .07 1,360 .05 819 1,220 1 1.15 647 .15 1,040 1 961 .51 1 1,210 747 332 1,460 .11 1,860 1,260 1 .03 1,050 1.30 1,410 1 637 1,410 412 1 1,830 1,220 2,300 850 1 1,280 1,870 1 1,010 393 2,070 1,320 2,120 1,700 1 1 1,550 1,340 1,320 1 2,240 1 2,140 1 1,820 2,240 1 1 1 1 1 Station No. Table 10.

80 Methods for Estimating Low-Flow Statistics for Massachusetts Streams Region basin elevation Maximum Maximum elevation Mean basin basin elevation Minimum Area of wetlands water bodies Area of Continued — ed- ﬁ drift area Strati Mean basin slope Total length stream area Drainage Basin characteristics for stations used in the regression analyses 011832100118420001184277 22.20118485501185490 5.27 24.401186300 30.301187400 43.2 29.101197015 13.601197120 49.6 9.8701197140 42.7 7.37 10.6 46.8 8.3901197180 20.4 2.7901197230 15.9 5.95 7.7001197300 12.2 5.2601198000 20.8 7.62 5.02 22.2 6.6901198060 36.2 3.00 2.18 3.8301198160 7.50 5.58 51.0 11.001198200 2.42 11.1 8.91 2.91 0.2801331380 25.6 .19 8.0901331400 8.46 .04 1.87 61.0 8.5901332000 .59 76.6 .07 12.4 .70 7.03 .9201332900 3.19 0.29 10.7 .54 7.6801333000 18.9 .71 40.9 .11 9.2901333100 .31 94.0 .03 .09 9.4901359967 .25 12.8 -- 6.70 19.0 1.39 42.6 209 .78 9.60 2.79 .01 58.5 5.25 6.22 .89 190 .40 14.1 .01 6.78 5.13 399 1,160 .03 .79 10.5 8.21 829 73.2 -- .08 .16 8.19 10.1 .19 .04 13.5 387 .27 21.4 -- 10.6 1,620 .56 1,280 .02 786 24.6 1,460 .38 .37 18.5 .02 1,110 .00 .18 573 19.4 .21 2,120 583 1,020 .46 1,540 3.10 1,210 17.6 .05 1.23 -- 1 .11 969 .22 .32 1,790 1,060 1,120 4.90 .00 1,600 1,810 1 .00 1 846 .01 -- 1 .44 1.39 1,550 1.28 .27 990 2,630 -- 1,660 1,400 688 2,210 .00 1 1,400 .03 .02 774 2,160 .09 1,010 1,370 .00 682 -- 2,260 1 1,290 1 .02 1 1 1,960 1,400 .00 979 1,160 .00 1,490 1,840 1 1,440 2,060 1 .00 .05 830 2,030 1 1,640 766 1,690 1,850 2,110 629 1 1 837 1,950 979 2,260 1 2,080 2,250 1 2,020 1 1,540 3,080 1,580 3,480 1 1 3,480 2,800 1 2,550 1 1 1 1 Station No. Table 10.

Table 10 81