Methods for estimating low-flow statistics for Massachusetts streams

1 Methods for Estimating Low-Flow Statistics for Massachusetts Streams By Kernell G. Ries, III, and Paul J. Friesz Abstract Methods and computer software are described in this report for determining flowduration, low-flow frequency statistics, and August median flows. These low-flow statistics can be estimated for unregulated streams in Massachusetts using different methods depending on whether the location of interest is at a streamgaging station, a low-flow partial-record station, or an ungaged site where no data are available. Lowflow statistics for streamgaging stations can be estimated using standard U.S. Geological Survey methods described in the report. The MOVE.1 mathematical method and a graphical correlation method can be used to estimate low-flow statistics for low-flow partialrecord stations. The MOVE.1 method is recommended when the relation between measured flows at a partial-record station and daily mean flows at a nearby, hydrologically similar streamgaging station is linear, and the graphical method is recommended when the relation is curved. Equations are presented for computing the variance and equivalent years of record for estimates of low-flow statistics for low-flow partialrecord stations when either a single or multiple index stations are used to determine the estimates. The drainage-area ratio method or regression equations can be used to estimate low-flow statistics for ungaged sites where no data are available. The drainage-area ratio method is generally as accurate as or more accurate than regression estimates when the drainage-area ratio for an ungaged site is between 0.3 and 1.5 times the drainage area of the index data-collection site. Regression equations were developed to estimate the natural, long-term 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent duration flows; the 7-day, 2-year and the 7-day, 10-year low flows; and the August median flow for ungaged sites in Massachusetts. Streamflow statistics and basin characteristics for 87 to 133 streamgaging stations and low-flow partial-record stations were used to develop the equations. The streamgaging stations had from 2 to 81 years of record, with a mean record length of 37 years. The low-flow partial-record stations had from 8 to 36 streamflow measurements, with a median of 14 measurements. All basin characteristics were determined from digital map data. The basin characteristics that were statistically significant in most of the final regression equations were drainage area, the area of stratified-drift deposits per unit of stream length plus 0.1, mean basin slope, and an indicator variable that was 0 in the eastern region and 1 in the western region of Massachusetts. The equations were developed by use of weighted-least-squares regression analyses, with weights assigned proportional to the years of record and inversely proportional to the variances of the streamflow statistics for the stations. Standard errors of prediction ranged from 70.7 to 17.5 percent for the equations to predict the 7-day, 10-year low flow and 50-percent duration flow, respectively. The equations are not applicable for use in the Southeast Coastal region of the State, or where basin characteristics for the selected ungaged site are outside the ranges of those for the stations used in the regression analyses. 2 Methods for Estimating Low-Flow Statistics for Massachusetts Streams A World Wide Web application was developed that provides streamflow statistics for datacollection stations from a data base and for ungaged sites by measuring the necessary basin characteristics for the site and solving the regression equations. Output provided by the Web application for ungaged sites includes a map of the drainage-basin boundary determined for the site, the measured basin characteristics, the estimated streamflow statistics, and 90-percent prediction intervals for the estimates. An equation is provided for combining regression and correlation estimates to obtain improved estimates of the streamflow statistics for low-flow partial-record stations. An equation is also provided for combining regression and drainage-area ratio estimates to obtain improved estimates of the streamflow statistics for ungaged sites. INTRODUCTION Low-flow statistics indicate the probable availability of water in streams during times when conflicts between water supply and demand are most likely to arise. Because of this, low-flow statistics are needed by Federal, State, regional, and local agencies for water-use planning, management, and regulatory activities. These activities include (1) developing environmentally sound river-basin management plans, (2) siting and permitting new water withdrawals, interbasin transfers, and effluent discharges, (3) determining minimum streamflow thresholds for maintenance of aquatic biota, and (4) land-use planning and regulation. Low-flow statistics are also needed by commercial, industrial, and hydroelectric facilities to determine availability of water for water supply, waste discharge, and power generation. Low-flow statistics can be calculated from streamflow data collected at locations where the U.S. Geological Survey (USGS) operates data-collection stations, but it is not possible to operate stations at every site where the statistics are needed. Because of this, methods are needed for estimating low-flow statistics for streams for which no data are available. In 1988, the USGS began the first of three studies to develop and evaluate methods for estimating low-flow statistics for ungaged Massachusetts streams and to provide estimates of the statistics for selected locations on ungaged streams. These studies were done in cooperation with the Massachusetts Department of Environmental Management, Office of Water Resources (MOWR) and are referred to as the Basin Yield studies. The MOWR uses the streamflow statistics to develop water-resources management plans for each of the 27 major river basins in Massachusetts (fig. 1) and provides the streamflow statistics to other State and local agencies to support their decisionmaking processes. Five other reports have been published as a result of the Basin Yield studies (Ries, 1994a, 1994b, 1997, 1999, 2000). The first three reports describe studies done to develop regression equations for use in estimating low-flow statistics for ungaged sites. The fourth report describes and provides data for a network of 148 low-flow partial-record (LFPR) stations that was established in 1988 at the beginning of the first Basin Yield study and continued through 1996, during the third Basin Yield study. The fifth report describes a World Wide Web application that enables users to select sites of interest on streams and then to obtain estimates of streamflow statistics and basin characteristics for the sites. Purpose and Scope This report, the final report of the Basin Yield study series, presents methods that can be used to estimate low-flow statistics for streams in Massachusetts, and describes the analyses done to develop and evaluate the methods. Methods are presented for estimating statistics for locations where various amounts of streamflow data are available and for locations where no data are available. Previously documented and generally accepted methods are presented for estimating low-flow statistics for locations where streamflow data are available. Analyses done to develop and evaluate methods for estimating streamflow statistics for locations where no data are available are described. The physical setting of Massachusetts, as it relates to the occurrence of low streamflows, is also briefly described. Equations that can be used to estimate the 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, and 50-percent duration flows; the 7-day, 2-year and the 7-day, 10-year low flows; and the August median flow are presented here. An evaluation of the accuracy of the equations and limitations for their use is also provided, along Introduction 3 with an example application. The equations provide estimates of low-flow statistics for streams with natural flow conditions, and supersede those from earlier reports. Previous Studies Low-flow statistics for most streamgaging stations and many LFPR stations in Massachusetts were published by the USGS in a series of gazetteers published as Water-Resources Investigations Reports, in a series of Hydrologic Atlas reports (see U.S. Geological Survey, 1987, for a complete listing of both series), and in a series of ground-water assessment reports published as Water-Resources Investigations Reports (Olimpio and DeLima, 1984; Lapham, 1988; Myette and Simcox, 1992; DeLima, 1991; Hanson and Lapham, 1992; Persky, 1993; Bratton and Parker, 1995; Bent, 1995; Friesz, 1996; Klinger, 1996). Statistics provided in this report supersede those from the previous reports. Studies that used regression analysis to regionalize low-flow frequency statistics in the northeastern United States include those for Connecticut (Cervione, 1982), central New England (Wandle and Randall, 1994), Pennsylvania and New York (Ku and others, 1975), Maine (Parker, 1977), Massachusetts, New Hampshire, Rhode Island and Vermont (Johnson, 1970), southeastern Massachusetts (Tasker, 1972), and Massachusetts (Male and Ogawa, 1982; Vogel and Kroll, 1990; Risley, 1994). Studies that regionalized flow-duration statistics include those for Connecticut (Thomas, 1966), New Hampshire (Dingman, 1978), southeastern Massachusetts (Tasker, 1972), and Massachusetts (Male and Ogawa, 1982; Fennessey and Vogel, 1990; Ries, 1994a, 1994b). Reports for the first two Basin Yield studies (Ries, 1994a, 1994b) provided equations for estimating the 99-, 98-, and 95-percent duration streamflows and also provided estimates of the streamflow statistics and measured basin characteristics for selected ungaged streams in eastern Massachusetts river basins. The equations were developed for these studies by use of regression analyses, which statistical