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Peak-flow variability, peak-flow informational needs, and consideration of regional regression analyses in managing the crest-stage gage network in Montana

July 28, 2021

The U.S. Geological Survey (USGS), in cooperation with the Montana Department of Transportation (MDT), has operated a crest-stage gage (CSG) network in Montana to collect peak-flow data since 1955. The CSG network is vital to collecting peak-flow data on small drainage basins that typically are not addressed by continuous streamflow operations. Discussions between USGS and MDT identified a need for evaluating the CSG network to allow for better decision making in the management of the network. The purpose of this report is to (1) generally describe peak-flow variability in Montana, (2) assess peak-flow informational needs relevant to MDT activities, and (3) consider the characteristics of the active CSG network in relation to addressing the informational needs. The evaluation of the CSG network is intended to assist in prioritization for discontinuation of CSGs and other activities involving changes to the CSG network.

Peak-flow variability was investigated by analysis of selected peak-flow characteristics of 659 unregulated streamgages in or near Montana. A generalized peak-flow variability index (PFVI) was developed to provide large-scale representation of peak-flow variability in Montana. For unregulated Montana streamgages, PFVI generally monotonically decreases with increasing drainage area, although there is somewhat large (but generally consistent) variability about the locally weighted scatterplot smooth line. Presumably, highly variable small-scale hydroclimatic processes are integrated with increasing drainage area such that variability in many hydrologic characteristics is reduced. PFVI also decreases with increasing mean basin elevation and mean annual precipitation. Presumably, higher elevation and wetter hydroclimatic settings in Montana contribute to reduced variability in hydrologic characteristics. Intuitively, PFVI might be expected to generally decrease with increasing years of record because the standard deviation might typically be expected to decrease with increasing sample size. However, relations among PFVI and years of record are more complex and variable than drainage area, elevation, and precipitation. PFVI variably increases from 10 to about 40 years of record and then generally monotonically decreases from about 40 to about 105 years of record. Relations among PFVI and the years of record might be confounded by effects of drainage area because streamgages with long periods of record (greater than about 60 years) generally have large drainage areas (greater than about 100 square miles).

The relations between PFVI and drainage area, mean basin elevation, mean annual precipitation, and years of record substantially differ among the eight hydrologic regions in Montana. As such, the PFVI relations were further investigated within each hydrologic region.

A major use of peak-flow information by MDT is for design of road and highway infrastructure, including bridges, culverts, and roadside drainage ditches. As such, basin characteristics (including drainage area, mean basin elevation, and mean annual precipitation) of the Montana streamgage network (735 regulated and unregulated streamgages) were statistically investigated in relation to basin characteristics of 12,639 road and stream intersections in Montana. Both regulated and unregulated streamgages were investigated because the road and stream intersections are on both regulated and unregulated streams. Exploratory analyses indicated that the various relations substantially differ among the hydrologic regions. As such, the relations between the Montana streamgage network and the road and stream intersections were further investigated within each hydrologic region.

An important objective of the CSG network is to provide data for developing regional regression equations (RREs) for estimating frequencies at ungaged sites in Montana. Various characteristics of the RREs substantially differ among the eight hydrologic regions in Montana. As such, the RRE characteristics were further investigated within each hydrologic region.

For each of the eight hydrologic regions, various characteristics of peak-flow variability, peak-flow informational needs, and regional regression analyses were investigated in detail. Possible shortcomings of the streamgage network in each hydrologic region are identified and possible future improvements to the CSG network are presented.

Citation Information

Publication Year 2021
Title Peak-flow variability, peak-flow informational needs, and consideration of regional regression analyses in managing the crest-stage gage network in Montana
DOI 10.3133/sir20215063
Authors Steven K. Sando
Publication Type Report
Publication Subtype USGS Numbered Series
Series Title Scientific Investigations Report
Series Number 2021-5063
Index ID sir20215063
Record Source USGS Publications Warehouse
USGS Organization WY-MT Water Science Center