Frequency analysis on annual peak streamflow (hereinafter, peak flow) is essential to water-resources management applications, including critical structure design (for example, bridges and culverts) and floodplain mapping. Nonstationarity is a statistical property of a peak-flow series such that the distributional properties (the mean, variance, or skew) change either gradually (monotonic trend) or abruptly (shift, step change or change point) through time. Not incorporating or accounting for observed nonstationarity into peak-flow frequency analysis might result in a poor representation of the true probability of large floods and thus misrepresent the actual flood risks to life and property. This report summarizes how hydroclimatic variability might affect the temporal and spatial distributions of peak-flow data in the State of Montana (and northern Wyoming) and is part of a larger study to document peak-flow nonstationarity and hydroclimatic changes across a nine-State region consisting of Illinois, Iowa, Michigan, Minnesota, Missouri, Montana, North Dakota, South Dakota, and Wisconsin. A wide range of analyses and statistical approaches are applied to document the primary mechanisms controlling floods and characterize temporal changes in hydroclimatic variables and peak flows. This study was completed in cooperation with the Montana Department of Natural Resources and Conservation.

The purpose of this report is to characterize temporal and spatial patterns of nonstationarity in peak flows and hydroclimatology in Montana and northern Wyoming. In this evaluation, peak-flow, daily streamflow, and model-simulated gridded climatic data were examined for monotonic trends, change points, and other statistical properties that might indicate changing climatic and environmental conditions. This report includes background information on the study area, the history of U.S. Geological Survey peak-flow data collection and frequency analysis in Montana, and the review of research relating to hydroclimatic variability and change in Montana. This study might help provide a framework for addressing potential nonstationarity issues in peak-flow frequency updates that commonly are completed by the U.S. Geological Survey in cooperation with other agencies throughout the Nation.

The analytical structure of this study includes analyses of monotonic trends and change points in numerous hydroclimatic variables in assigned 30-, 50-, 75-, and 100-year analysis periods. For Montana and part of Wyoming, the 30-, 50-, 75, and 100-year analyses included 157, 70, 48, and 12 streamgages, respectively. For those streamgages, nonstationarities were analyzed in the following variables: (1) climatic variables, including annual and seasonal (winter, spring, summer, and fall) temperature and precipitation; (2) daily streamflow variables, including the annual center of volume duration, annual center of volume median, and peaks over threshold with a mean of four events per year; and (3) annual peak-flow variables, including peak-flow timing and magnitude. A likelihood approach was used to express statistical confidence and assign the nonstationarity results as likely upward or downward (highest statistical confidence), somewhat likely upward or downward (less statistical confidence), or about as likely as not (little statistical confidence; hereinafter, neutral). For the nonstationarity analyses of the climatic, daily streamflow, and peak-flow variables, the results are presented in detail and discussed with respect to statewide patterns and geographic variability. For each of the 30-, 50-, and 75-year analyses, peak-flow change-point and monotonic trend analyses were compiled for streamgages classified with likely downward or likely upward trends. For those streamgages, the associated basin characteristics and nonstationarity results for peak-flow timing, daily streamflow, and climatic variables were investigated and statistically compared to discern associations among other variables that might contribute to the peak-flow nonstationarity results.

The 50- and 75-year peak-flow nonstationarities identified in this study are mostly downward, in association with mostly upward temperature and potential evapotranspiration:precipitation monotonic trends. For the 50-, 75-, and 100-year analyses, the peak-flow change points are predominantly downward and are concentrated in the 1970s and 1980s, which indicates general consistency among the longer trend periods. These findings are in association with substantial research documenting globally rising temperature and atmospheric greenhouse gas concentrations that might be largely attributed to anthropogenic activities. Anthropogenic effects might represent long-term (on the order of several decades to more than a century) climate changes that might happen within highly variable natural climate fluctuations. Several paleo studies in the north-central United States have indicated that hydroclimatic extremes (that is, low- and high-streamflow conditions) before European settlement have been outside of extremes since the 1900s. Depending on the interactions of anthropogenic effects and natural climate variability, extreme high-streamflow conditions might occur in the future, even in the presence of long-term downward peak-flow trends.