# Methods for Estimating Low-Flow Statistics for Massachusetts Streams

←

**Page content transcription**

If your browser does not render page correctly, please read the page content below

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

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

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

73°00´ 72°30´ 72°00´ VERMONT 01333000 01169801 01332000 01167200 01333100 01164300 01162500 01332900 01170100 01168300 01165090 1 01169000 01163250 01331400 01168400 01168650 3 01165500 01166105 7 01359967 01331380 01163298 01169600 01165250 01169900 011197015 01162900 42°30´ 01178200 01174000 01170575 01174050 01178300 01169800 K YOR 01197120 01179900 8 01172810 2 6 01174565 NEW 01197140 01178490 01173260 01197300 4 01180650 Western Region 01174900 01180000 01171500 01197180 01175710 01197230 01171800 01171947 01173420 01175850 01180500 01180800 01173450 01175670 01171970 01198000 01181000 01175890 01176000 01176100 01198060 5 01176780 01124390 01183210 01176200 01123161 1 01198160 01185490 01177360 01176300 01123140 10 01198200 01186300 01187400 01184282 01184200 01176415 01184277 9 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 AT NEW HAMPSHIRE 01101100 13 16 LA 01095928 01096505 01096515 NT 01089400 01096000 01096504 01100608 17 IC 01094396 15 OC 01095915 01094340 01102053 01097300 18 EA 11 01097280 01096910 01102490 19a N 01096935 01095220 01094760 01103015 Massachusetts 01095380 14a 01096855 14b BOSTON Bay 01096805 01103440 Eastern Region 01103435 01105630 01103445 01105582 01109460 20 01104960 01105575 19c 01105830 01105670 01104980 01105600 01111142 01104840 12 01103253 19b 01105568 01105820 01111200 01105270 01103330 01112190 21a 70°00´ 01107000 01111225 9 01108600 01106460 01105861 01111300 RHODE ISLAND 27 25 01108140 01108180 01107400 21b 01109200 70°30´ 01109087 01109225 011058839 01109090 011059106 Southeast 24 22 26 01105937 01105930 Coastal 01105947 01106000 01105935 Region 41°30´ Nantucket Sound 23 0 50 MILES 0 50 KILOMETERS 23 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

sy discharges at the LFPR station and a nearby gaging Yˆ i = Y + ---- ( X i – X ) , (1) sx station is linear. The method is applied by first calculating logarithms-base 10 of the same-day flows for the LFPR and gaging stations and graphing the and then retransforming the estimates by values to ascertain the linearity of the relation. The exponentiating the values ( 10 Ŷ i ) to convert the correlation coefficient is also computed as an indicator estimates into their original units of measurement. of linearity. If the relation appears linear, the MOVE.1 The MOVE.1 relation between an LFPR station, method is used; if not, a graphical method is used, as explained below. Hemlock Brook near Williamstown, Mass., and a streamgaging station, Green River at Williamstown, When the graph of the data appears linear, the Mass., is shown as an example in figure 2. The line means (Y and X) and standard deviations (sy and sx) of through the data points was determined by inserting the the logarithms-base 10 of the same-day flows for the LFPR and gaging stations and the logarithms-base 10 same-day flows for the gaging station into the MOVE.1 of the streamflow statistics (Xi) for the gaging station equation as the Xi values to obtain estimated same-day are calculated. Estimates of the streamflow statistics flows for the LFPR station, then connecting the points ( Ŷ i ) for the LFPR station are obtained by inserting the to illustrate how the MOVE.1 estimates fit the original calculated values into the MOVE.1 equation: data. 10 CORRELATION COEFFICIENT = 0.974 HEMLOCK BROOK AT WILLIAMSTOWN, MASS. DISCHARGE, IN CUBIC FEET PER SECOND 1 SAME-DAY DISCHARGES MOVE.1 RELATION 0.1 1 10 100 GREEN RIVER NEAR WILLIAMSTOWN, MASS. DISCHARGE, IN CUBIC FEET PER SECOND Figure 2. Example MOVE.1 relation between a low-flow partial-record station, Hemlock Brook near Williamstown, Mass., and a streamgaging station, Green River at Williamstown, Mass. 10 Methods for Estimating Low-Flow Statistics for Massachusetts Streams

Graphical Method Combining Estimates Determined from Multiple Index Sites The graphical method (Searcy, 1959; Riggs, 1972) is used when curvature is apparent in the plot of Selection of individual gaging stations for logarithms-base 10 of the same-day flows. The method relation to a LFPR station is based on distance between is applied by first plotting the original (non-log) values the stations and similarity of basin characteristics of the same-day flows on log-log paper and drawing a between the stations. In Massachusetts, the measured smooth curve through the plotted points that appears to streamflows at a LFPR station usually will correlate best fit the data. Next, the calculated streamflow well with more than one gaging station. When this statistics for the gaging station are entered into the happens, MOVE.1 or graphical relations between a curve of relation and corresponding values for the given LFPR station and each of several gaging stations LFPR station are read from the graph. Log-log plots can be developed to estimate the streamflow statistics sometimes have extreme curvature in the very low for the LFPR station. This process results in multiple end of the relation. Because of this, it is sometimes estimates of the streamflow statistics for a single LFPR necessary to replot the data on arithmetic paper to station, when only a single best estimate is desired. adequately define the relation in this range and to avoid long downward extrapolations that would otherwise be Tasker (1975) stated that when independent necessary with log-log plots. multiple estimates of streamflow statistics are available The graphical relation between an LFPR station, for a single station, the best estimate can be obtained Hopping Brook near West Medway, Mass., and a by weighting each individual estimate by its variance streamgaging station, West River near Uxbridge, and averaging the weighted estimates. This final Mass., is shown as an example in figure 3. The curve weighted estimate is best because its variance is less was fit through the data visually to minimize overall than or equal to the variances of each of the differences between the observed and fit values. individual estimates. 100 HOPPING BROOK NEAR WEST MEDWAY, MASS. DISCHARGE, IN CUBIC FEET PER SECOND 10 1 0.1 SAME-DAY DISCHARGES GRAPHICAL RELATION 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 VR 2 SE S, G 2 M 2 are generalized from Hardison and Moss (1972): V S, U = ------ 1 + -------------- + -------------- + -------------- -------------- 1 z M M M – 3 M – 3 s B, G M – 3 1. The true relation between the logarithms of the 2 base-flow measurements at the LFPR station + b V S, G , (2) and the same-day mean streamflows at the gaging station is the same as the true relation where: between the logarithms of the data from which VS,U is the sample variance of the streamflow the low streamflow statistics are calculated. In statistic at the LFPR station, in log units; the case of the 7-day low-flow statistics, the VS,G is the sample variance of the streamflow data are calculated from an annual series of statistic at the gaging station, in log units; minimum 7-day mean flows. In the case of the VR is the variance about the MOVE.1 or graphical flow-duration and August median statistics, the line of relation; data are calculated from the daily mean flows. M is the number of base-flow measurements; 2. The relation between the logarithms of the data SES,G is the standard error of the streamflow statistic from which the low-flow statistics are at the gaging station, which equals the square calculated is the same as the relation between root of VS,G; the flow statistics for the stations. b is computed as r(sB,U/sB,G), where r is the 3. The time-sampling errors in the streamflow correlation coefficient between the low statistics that are used to enter the regression streamflow measurements made at the LFPR equation are independent of the variation in the station and the same-day mean discharges at base-flow measurements used to define the the gaging station (the value of r can be set to equation. 1 when MOVE.1 is used to obtain the estimate), and sB,U is the standard deviation 4. The logarithms of the measured streamflows at of the logarithms-base 10 of the low the LFPR station and the same-day mean streamflow measurements made at the LFPR streamflows at the gaging station follow a station; bivariate normal distribution. sB,G is the standard deviation of the logarithms-base 5. The M measurements made at the LFPR station 10 of the mean discharges at the gaging are statistically independent estimates of the station on the same days the low-flow base-flow relation. measurements were made at the ungaged Hardison and Moss noted that the first four site; and assumptions appeared to be reasonable under the z is the number of standard deviation units conditions in which application of the original equation between the mean of the logarithms-base 10 2 was intended. These assumptions are reasonable for of the same-day mean discharges at the the modified equation 2 as well. Hardison and Moss gaging station and the logarithm-base 10 of also noted that assumption 5 could be satisfied by the streamflow statistic at the gaging station. applying criteria for using only those measurements Equation 2 is modified from an equation that can be reasonably assumed independent to define developed by Hardison and Moss (1972) to determine the relation. The criterion usually applied is that the the variance of estimates of 7-day, T-year low flows base-flow measurements used in the relation should be obtained from an ordinary-least-squares (OLS) separated by significant storm events (Stedinger and regression of the logarithms-base 10 of base-flow Thomas, 1985). Collection of low streamflow measurements at a LFPR station to the logarithms-base measurements at LFPR stations in Massachusetts has 10 of same-day mean discharges at a nearby, generally followed that criterion. 12 Methods for Estimating Low-Flow Statistics for Massachusetts Streams

2 2 s B, U N U = R S I S, G k ---------- 2 2 When estimates are obtained for LFPR stations s B, G from relations with more than one streamflow-gaging 2 2 2 station, the individual estimates, Q S, U i , (where i = 1, V R 1 + z 2 b RS I S, G ⁄ ------- -------------- + ---------------------- , (6) ..., n, and n is the number of individual estimates of M K NG statistic S for LFPR station U) can be weighted by the reciprocals of their variances, determined from where all variables are as previously defined, and: equation 2, to obtain minimum-variance estimates, NU is the equivalent years of record at the partial- Q S, U , for each of the statistics from the equation record station; w n ∑ ( Q S, U ⁄ V S, U ) i i NG is the years of record at the streamflow-gaging station used in the relation; i=1 Q S, U = ----------------------------------------- n - . (3) IS,G is the standard deviation of the logarithms-base ∑ w ( 1 ⁄ V S, U ) 10 of the observed flows (annual series for i i=1 frequency statistics or daily flows for Weighted variances, V S, U , can be determined for the duration statistics) at the streamflow-gaging w weighted estimates from the equation station k is from equation 9 of Hardison and Moss n (1972), V S, U w = 1⁄ ∑ ( 1 ⁄ V S, U i ) . (4) r + -------------- ( 1 – r ) ; and i=1 2 M–4 2 k = M – 2 (7) Standard errors, SE S, U , in percent, for the weighted w estimates can be obtained from the equation (Stedinger K is from equation 3 of Hardison and Moss and Thomas, 1985, p. 18) (1972), 2 SE S, U = 100 exp ( 5.3018V w ) – 1 . (5) K = (1 + z ) w 2 z M S ,G M 2 SE 1 Equation 2 does not account for errors inherent in the ⁄ 1 + -------------- + -------------- + ------------- - -------------- ; (8) M – 3 M – 3 sB ,G M – 3 discharge measurements made at the LFPR station or in the mean daily discharges determined for the gaging RS is a correction factor that depends on the stations. In addition, the estimates obtained for an streamflow statistic being estimated, and is LFPR station by use of the MOVE.1 or graphical determined by combining the equation that method with multiple gaging stations are not truly appears in table 1 of Hardison and Moss independent because of cross correlation of the (1972), streamflow records at the gaging stations. As a result, the final estimates obtained using equations 2 and 3 may not truly be the best possible, and the true R S = ( SE S, G N ) ⁄ I S ,G , (9) variances and standard errors are somewhat larger than those obtained using equations 4 and 5. with the equation 2 The equivalent years of record also can be 1 + kS ⁄ 2 computed for estimates of streamflow statistics for the SE S, G = I S ,G --------------------- (10) 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 + k S ⁄ 2 . (11) accuracy. The equivalent years of record for LFPR stations is computed from an equation developed by Subscripts have been changed from their original combining equations 7, 8, and 9 in Hardison and Moss appearance in equations 6 to 11 to generalize from (1972) and solving for the number of years of record. T-year statistics to other streamflow statistics. In The resulting equation is: equations 10 and 11 above, kS is the number of Estimating Methods for Data-Collection Stations 13

standard deviation units between the streamflow topographic maps. Streamflow statistics are computed statistic and the mean of the data from which it is for the index station, then the statistics (numerical calculated. From assumption 4 above, the annual series values) are divided by the drainage area to determine of 7-day low flows and the daily mean streamflows streamflows per unit area at the index station. These from which the flow-duration statistics and the August values are multiplied by the drainage area at the median streamflows are calculated are distributed log- ungaged site to obtain estimated statistics for the site. normally, and thus kS can be obtained from a table of This method is most commonly applied when the index standard normal deviates as appears in most statistical gaging station is on the same stream as the ungaged site textbooks. Values for the 99-, 98-, 95-, 90-, 85-, 80-, because the accuracy of the method depends on the 75-, 70-, 60-, and 50-percent duration streamflows, the proximity of the two, on similarities in drainage area August median streamflow, and the 7-day, 10- and and on other physical and climatic characteristics of 2-year streamflows are 2.3263, 2.0537, 1.6449, 1.2816, their drainage basins. 1.0364, 0.8416, 0.6745, 0.5244, 0.2533, 0.0, 0.0, Several researchers have provided guidelines as 1.2816, and 0.0, respectively (Iman and Conover, 1983, to how large the difference in drainage areas can be p. 434–435). When estimates for LFPR stations are before use of regression equations is preferred over use obtained from relations with more than one of the drainage-area ratio method. Guidelines have streamgaging station, the individual calculations of been provided for estimating peak-flow statistics, and equivalent years of record can be weighted by the usually the recommendation has been that the drainage reciprocals of the variances of the estimated streamflow area for the ungaged site should be within 0.5 and 1.5 statistics, determined from equation 2, then the times the drainage area of the index station (Choquette, individual weighted equivalent years of record can be 1988, p. 41; Koltun and Roberts, 1990, p. 6; Lumia, averaged to obtain the final weighted equivalent years 1991, p. 34; Bisese, 1995, p. 13). One report (Koltun of record for the LFPR station by substituting the and Schwartz, 1986, p.32) recommended a range of equivalent years of record estimates for the discharge 0.85 to 1.15 times the drainage area of the index station estimates in equation 3 above. for estimating low flows at ungaged sites in Ohio. None of these researchers provided any scientific basis for use of these guidelines. R.E. Thompson, Jr. (U.S. ESTIMATING METHODS FOR Geological Survey, written commun., 1999), however, UNGAGED STREAM SITES recently completed a study that provides evidence supporting use of ratios between 0.33 and 3.0 for Estimates of streamflow statistics often are streams in Pennsylvania. needed for sites on streams where no data are available. The two methods used most commonly to estimate Because of uncertainty in an appropriate range statistics for ungaged sites are the drainage-area ratio for use of the drainage-area ratio method for streams in method and regression equations. The drainage-area Massachusetts, an experiment was designed to ratio method is most appropriate for use when the determine the ratio range in which the method is likely ungaged site is near a streamgaging station on the same to provide better estimates of low streamflow statistics stream (nested). Regression equations can be used to than use of regression equations. Five river basins with obtain estimates for most ungaged sites. Additional one or more continuous gaging stations in each basin details on application of these methods is provided were chosen for the experiment to represent the varied below. topography, geology, and precipitation of Massachusetts. Two basins, the Green and the West Branch Westfield, are in the mountainous western part Drainage-Area Ratio Method of the State; two basins, the Quaboag and the Squannacook, are in the foothills of the central part of The drainage-area ratio method assumes that the the State; and one basin, the Wading, is in the flat, streamflow at an ungaged site is the same per unit area low-lying landscape typical of eastern Massachusetts. as that at a nearby, hydrologically similar streamgaging A total of 25 LFPR stations were established station used as an index. Drainage areas for the upstream and downstream from 8 streamgaging ungaged site and the index station are determined from stations in the 5 basins. Most of the LFPR stations have 14 Methods for Estimating Low-Flow Statistics for Massachusetts Streams

smaller drainage areas than those for the streamgaging and one discontinued streamgaging station) at which stations because historically most streamgaging streamflow measurements were made in the Wading stations in Massachusetts have been established near River Basin, only three of the stations (01108490, the downstream ends of rivers. Locations and drainage 01108600, and 01108700) were used to compare boundaries for the streamgaging stations and LFPR results of the different estimation methods. Discharges stations are shown for each basin in figures 4A to 4E. and basin characteristics from stations 01108440 and Station descriptions for the stations are in table 1. 01108470 were subtracted from station 01108490, and Seven to ten discharge measurements were made station 01108500 was subtracted from 01108700 to at each of the LFPR stations during 1994 and 1995. determine discharges and basin characteristics The measurements were published in the Mass. annual representative of the naturally flowing areas above data reports for those years (Gadoury and others, 1995; those stations. The adjusted discharges and basin Socolow and others, 1996, 1997). The measurements, characteristics were used to estimate unregulated along with historical measurements available at three streamflow statistics for the stations. Station 01108600 stations, were used to estimate streamflows at the 99-, was not affected by regulation or diversions. 98-, and 95-percent durations and August median flows for the stations using the methods described above for The drainage area for the Wading River below LFPR stations. Estimates of the flow-duration statistics the West Mansfield streamgaging station (station were also derived for the stations using the drainage- 01108500) and above the Norton streamgaging station area ratio method and the regression equations (station 01109000) is not affected by regulation or developed by Ries (1994b, 1997). The regression diversions, whereas the drainage area above the West equations presented later in this report were not used Mansfield station is affected by regulation and because they were not yet available at the time of the diversions. Streamflow statistics for the West Mansfield analysis. station were subtracted from those for the Norton Two gaging stations were available in some station to obtain the streamflow statistics for the basins for the analysis (table 1). To increase the sample naturally flowing part of the drainage area above the size for the analysis of the drainage-area ratio method, Norton station. drainage-area ratio estimates and regression-equation The four streamflow statistics (99-, 98-, and estimates were determined for the streamgaging 95-percent duration and August median streamflows) stations in addition to the estimates determined from estimated by the three different methods (correlation, the records for the stations. The drainage-area ratio drainage-area ratio, and regression equation) for each estimates were determined for each streamgaging of the LFPR and streamgaging stations used in the station by applying the flow per unit area for one streamgaging station to the drainage area for the other analysis are presented in table 7 (back of the report). streamgaging station. The longest common period of The estimates derived by correlation, shown in the record available for the streamgaging stations in each column labeled “Correlation method estimate or basin was used to compute the streamflow statistics for computed,” were considered the best estimates the analysis to avoid differences in the statistics due to available for the LFPR stations for the analysis, differences in record length. and they were compared to the estimates derived by The Wading River Basin, unlike the other four the other methods. The correlation estimates were basins used in the experiment, has water withdrawals considered the best estimates because they were and regulated streamflows in parts of the basin (see derived from actual streamflow data for the stations, table 1, remarks). It was chosen for use in the whereas the drainage-area ratio and regression experiment because the unregulated part of the basin is estimates were derived indirectly based on an the largest unregulated area in southeastern assumed or statistical relation between the basin Massachusetts. Discharges, drainage areas, and other characteristics for the LFPR stations and stream- basin characteristics used to solve the regression gaging stations. Statistics shown for streamgaging equations were adjusted for stations downstream from stations in the column labeled “Correlation method the diversions and regulation to correct for these estimate or computed” were computed from daily- activities. Of the seven stations (including one active flow records. Estimating Methods for Ungaged Stream Sites 15

71o00' A. SQUANNACOOK 73o00' 72o00' RIVER BASIN 42o30' 70o00' 0 50 MILES 42o00' 0 50 KILOMETERS 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' 73o00' B. WADING 72o00' 42o30' RIVER BASIN 70o00' 0 50 MILES 42o00' 0 50 KILOMETERS 41o30' 71o20' 71o10' 42o05' 01108440 01108470 01108490 01108500 SHADED AREAS ARE AFFECTED 01108600 BY REGULATION, DIVERSIONS, OR BOTH 01108700 01109000 EXPLANATION 41o55' BASIN BOUNDARY 01109000 STREAMFLOW GAGING STATION AND NUMBER 01108600 LOW-FLOW PARTIAL- RECORD STATION 0 1.0 2 MILES AND NUMBER 0 1.0 2 KILOMETERS Figure 4. Locations and drainage boundaries of low-flow partial-record stations and gaging stations in the (A) Squannacook, (B) Wading, (C) Quaboag, (D) Green, and (E) West Branch Westfield River Basins, Massachusetts—Continued. Estimating Methods for Ungaged Stream Sites 17

You can also read