Methods for estimating magnitudes of peak flows at various recurrence intervals, needed for highway-structure and water-control design and planning, were developed for gaged and ungaged sites on streams throughout Idaho. Recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years were selected for analysis of peak flows. For gaged sites in Idaho, peak-flow estimates were calculated by fitting a log-Pearson Type III distribution to the annual peak-flow data for each site. Annual peak flows through 1997 were used in the analysis. Basin and climatic characteristics for these gaged sites were calculated from 1:24,000 digitalelevation models and various thematic data coverages using a geographic information system. Peak- flow data and basin and climatic characteristics for 333 gaged sites were combined to develop a database that was used for the analysis. To estimate the magnitude of peak flows at ungaged sites near gaged sites on the same stream, a method was developed on the basis of drainage-area ratios. To estimate the magnitude of peak flows for ungaged sites on unregulated and undiverted streams, two regional regression methods were developed. The first regression method, termed the regional regression method, used generalized least-squares regression to develop a set of predictive equations for estimating peak flows at selected recurrence intervals for seven hydrologic regions in Idaho. These regional regression equations related basin and climatic characteristics to peak flows. The regional regression equations were all functions of drainage area plus one or two other basin characteristics. Average errors of prediction for these regression equations ranged from +143 percent to 58.8 percent. The range of errors was narrowest,
from about +51.9 to about 34.2, for region 5. Error ranges were usually narrower for the middle recurrence intervals than for the lower and upper recurrence intervals. A computer program was developed to calculate the magnitude of peak flows at each recurrence interval, the average error of prediction, and the 90-percent confidence interval for each ungaged site. The second regression method, termed the region-of-influence method, was used to develop a unique regression equation for each estimate that is based on a subset of gaged sites with values of basin and climatic characteristics similar to those for the ungaged sites. All 333 gages in the database were used to select the subset. Root-mean-squared errors for this method ranged from 55.5 percent to 72.4 percent. Differences in root-mean-squared errors between regional regression equations and the region-of-influence method were quite large. The average difference in root-mean-squared errors for the region-of-influence method was more than 10 percent greater than the average differences for the regional regression equations. For region 5, the average difference was greater than 20 percent. However, for region 8, the root-mean-squared errors were, in general, only slightly smaller for the region-of-influence method than for the regional regression equations.
The region-of-influence method is not recommended for use in determining flood-frequency estimates for ungaged sites in Idaho because the results, overall, are less accurate and the calculations are more complex than those of regional regression equations. The regional regression equations were considered to be the primary method of estimating the magnitude and frequency of peak flows for ungaged sites in Idaho.