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 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 sion equations. Output provided by the Web appli- Yield studies. The MOWR uses the streamflow statis- 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 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) pro- vides 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 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.