The climatic conditions of the specific time period during which peak-flow data were collected at a given streamflow-gaging station (hereinafter referred to as gaging station) can substantially affect how well the peak-flow frequency (hereinafter referred to as frequency) results represent long-term hydrologic conditions. Differences in the timing of the periods of record can result in substantial inconsistencies in frequency estimates for hydrologically similar gaging stations. Potential for inconsistency increases with decreasing peak-flow record length. The representativeness of the frequency estimates for a short-term gaging station can be adjusted by various methods including weighting the at-site results in association with frequency estimates from regional regression equations (RREs) by using the Weighted Independent Estimates (WIE) program. Also, for gaging stations that cannot be adjusted by using the WIE program because of regulation or drainage areas too large for application of RREs, frequency estimates might be improved by using record extension procedures, including a mixed-station analysis using the maintenance of variance type I (MOVE.1) procedure. The U.S. Geological Survey, in cooperation with the Montana Department of Transportation and the Montana Department of Natural Resources and Conservation, completed a study to provide adjusted frequency estimates for selected gaging stations through water year 2011.

The purpose of Chapter D of this Scientific Investigations Report is to present adjusted frequency estimates for 504 selected streamflow-gaging stations in or near Montana based on data through water year 2011. Estimates of peak-flow magnitudes for the 66.7-, 50-, 42.9-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities are reported. These annual exceedance probabilities correspond to the 1.5-, 2-, 2.33-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals, respectively.

The at-site frequency estimates were adjusted by weighting with frequency estimates from RREs using the WIE program for 438 selected gaging stations in Montana. These 438 selected gaging stations (1) had periods of record less than or equal to 40 years, (2) represented unregulated or minor regulation conditions, and (3) had drainage areas less than about 2,750 square miles.

The weighted-average frequency estimates obtained by weighting with RREs generally are considered to provide improved frequency estimates. In some cases, there are substantial differences among the at-site frequency estimates, the regression-equation frequency estimates, and the weighted-average frequency estimates. In these cases, thoughtful consideration should be applied when selecting the appropriate frequency estimate. Some factors that might be considered when selecting the appropriate frequency estimate include (1) whether the specific gaging station has peak-flow characteristics that distinguish it from most other gaging stations used in developing the RREs for the hydrologic region; and (2) the length of the peak-flow record and the general climatic characteristics during the period when the peak-flow data were collected. For critical structure-design applications, a conservative approach would be to select the higher of the at-site frequency estimate and the weighted-average frequency estimate.

The mixed-station MOVE.1 procedure generally was applied in cases where three or more gaging stations were located on the same large river and some of the gaging stations could not be adjusted using the weighted-average method because of regulation or drainage areas too large for application of RREs. The mixed-station MOVE.1 procedure was applied to 66 selected gaging stations on 19 large rivers.

The general approach for using mixed-station record extension procedures to adjust at-site frequencies involved (1) determining appropriate base periods for the gaging stations on the large rivers, (2) synthesizing peak-flow data for the gaging stations with incomplete peak-flow records during the base periods by using the mixed-station MOVE.1 procedure, and (3) conducting frequency analysis on the combined recorded and synthesized peak-flow data for each gaging station. Frequency estimates for the combined recorded and synthesized datasets for 66 gaging stations with incomplete peak-flow records during the base periods are presented. The uncertainties in the mixed-station record extension results are difficult to directly quantify; thus, it is important to understand the intended use of the estimated frequencies based on analysis of the combined recorded and synthesized datasets. The estimated frequencies are considered general estimates of frequency relations among gaging stations on the same stream channel that might be expected if the gaging stations had been gaged during the same long-term base period. However, because the mixed-station record extension procedures involve secondary statistical analysis with accompanying errors, the uncertainty of the frequency estimates is larger than would be obtained by collecting systematic records for the same number of years in the base period.