Regional regression equations based on channel-width characteristics to estimate peak-flow frequencies at ungaged sites in Montana using peak-flow frequency data through water year 2011

The U.S. Geological Survey, in cooperation with the Montana Department of Transportation, developed regression equations based on channel width to estimate peak-flow frequencies at ungaged sites in Montana. The equations are based on peak-flow data at streamgages through September 2011 (end of water year 2011), and channel widths measured in the field and from aerial photographs.

Active-channel width and bankfull width (channel widths) were measured in the field at 64 sites across Montana in 2017. Channel widths also were measured near 515 streamgages from aerial photographs. These new channel-width data, along with more than 438 historical channel-width measurements, are published in a separate data release.

Regression equations were developed using generalized least squares regression or weighted least squares regression. The channel-width regression equations can be used to estimate peak-flow frequencies (peak-flow magnitudes associated with annual exceedance probabilities of 66.7, 50, 42.9, 20, 10, 4, 2, 1, 0.5, and 0.2 percent) at ungaged sites in each of the eight hydrologic regions in Montana. Methods are presented for weighting estimates from the channel-width equations with estimates from equations using basin characteristics. The weighting technique can be used to reduce the standard error of prediction relative to that obtained using a single method. Several example problems covering a range of estimation scenarios also are included.