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Equations for estimating selected streamflow statistics in Rhode Island

April 1, 2014

Regional regression equations were developed for estimating selected natural—unaffected by alteration—streamflows of specific flow durations and low-flow frequency statistics for ungaged stream sites in Rhode Island. Selected at-site streamflow statistics are provided for 41 long-term streamgages, 21 short-term streamgages, and 135 partial-record stations in Rhode Island, eastern Connecticut, and southeastern and south-central Massachusetts. The regression equations for estimating selected streamflow statistics and the at-site statistics estimated for each of the 197 sites may be used by Federal, State, and local water managers in addressing water issues in and near Rhode Island.

Multiple and simple linear regression equations were developed to estimate the 99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, 50-, 40-, 30-, 25-, 20-, 15-, 10-, 5-, 2-, and 1-percent flow durations and the 7Q2 (7-day, 2-year) and 7Q10 (7-day, 10-year) low-flow-frequency statistics. An additional 49 selected statistics, for which regression equations were not developed, also were estimated for the long- and short-term streamgages and partial-record stations for flow durations between the 99.99 and 0.01 percent and for the mean annual, mean monthly, and median monthly streamflows. A total of 70 selected streamflow statistics were estimated for 41 long-term streamgages, 21 short-term streamgages, and 135 partial-record stations in and near Rhode Island. Estimates of the long-term streamflow statistics for the 21 short-term streamgages and 135 partial-record stations were developed by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique.

The equations used to estimate selected streamflow statistics were developed by relating the 19 flow-duration and 2 low-flow-frequency statistics to 31 different basin characteristics (physical, land-cover, and climatic) at the 41 long-term and 19 of 21 short-term streamgages (a total of 60 streamgages) in and near Rhode Island. The 135 partial-record stations were not used in the regression analyses. The regression analyses were done by using a user-weighted least-squares technique in the weighted-multiple-linear regression program for the 90- to 1-percent flow-duration statistics. For the 99-, 98-, and 95-percent flow durations and the 7Q2 and 7Q10 statistics, left-censored regression analyses were used to account for zero flows at a few streamgages. The regression analyses determined that two basin characteristics—drainage area and stream density—were the only significant explanatory variables for 16 of the 19 flow-duration and the 2 low-flow regression equations. For the 10-, 15-, and 20-percent flow-duration regression equations, drainage area was the only significant explanatory variable. The standard error of the estimate for the 21 regression equations ranged from 17.58 to 141.83 percent. The 99- to 85-percent flow durations and the low-flow statistics 7Q2 and 7Q10 had the highest standard errors of the estimate, ranging from 48.68 to 141.83 percent. The standard error of the estimate for the medium- to high-flow statistics—the 80- to 1-percent flow durations—ranged from 17.58 to 37.65 percent, with the standard errors for the 60- to 1-percent flow durations all being less than about 21 percent. Data also are provided to allow the user to calculate the 90-percent prediction intervals for the 21 streamflow statistics.

The equations, which are based on data from streams with little to no flow alterations, will provide an estimate of the natural flows for a selected site. They will not estimate flows for altered sites with dams, surface-water withdrawals, groundwater withdrawals (pumping wells), diversions, and wastewater discharges. If the equations are used to estimate streamflow statistics for altered sites, the user should adjust the flow estimates for the alterations. The regression equations should be used only for ungaged sites with drainage areas between 0.52 and 294 square miles and stream densities between 0.94 and 3.49 miles per square mile; these are the ranges of the explanatory variables in the equations.