Peak-flow (flood) frequency analysis is essential to water-resources management applications, including the design of critical infrastructure such as bridges and culverts, and floodplain mapping. Federal guidelines for performing peak-flow flood frequency analyses are presented in a U.S. Geological Survey Techniques and Methods Report known as Bulletin 17C. A basic assumption within Bulletin 17C, which documents the guidelines for determining annual peak streamflow frequency, is that, for basins without major hydrologic alterations (for example, regulation, diversion, and urbanization), statistical properties of the distribution of annual peak streamflows are stationary; that is, the mean, variance, and skew are constant through time. Nonstationarity is a statistical property of a peak-flow series such that the long-term (on the order of decades) distributional properties change one or more times either gradually or abruptly through time. Individual nonstationarities may be attributed to one source such as flow regulation, land-use change, or climate but are often the result of a combination of sources, making detection and attribution of nonstationarities challenging.

In response to a growing concern regarding nonstationarity in peak streamflows in the region, the U.S. Geological Survey, in cooperation with the Departments of Transportation of Illinois, Iowa, Michigan, Minnesota, Missouri, South Dakota, and Wisconsin; the Montana Department of Natural Resources and Conservation; and the North Dakota Department of Water Resources, assessed the potential nonstationarity in peak streamflows in the north-central United States. This chapter characterizes the effects of natural hydroclimatic shifts and potential climate change on annual peak streamflows in the State of South Dakota. Annual peak and daily streamflow as well as model-simulated gridded climatic data were examined for temporal monotonic trends, change points, and other statistical properties indicative of changing climatic and environmental conditions.

Changes in annual peak and daily flows were evaluated among 13, 35, and 81 qualifying U.S. Geological Survey streamgages for the 75-, 50-, and 30-year trend periods through water year 2020 (the period from October 1, 2019, to September 30, 2020) in South Dakota, respectively. No qualifying streamgages were in the 100-year trend period in the State. Statistical tests for autocorrelation (independent and identically distributed assumption), monotonic trends, and change points in the median and scale are analyzed to evaluate potential stationarity violations (nonstationarity) for performing at-site peak-flow flood-frequency analysis. The trends are reported using a likelihood approach as an alternative to simply reporting significant trends with an arbitrary p-value cutoff point.

A distinct east-west spatial pattern of likely upward and downward monotonic trends and change points, respectively, was detected in 75- and 50-year trend periods, but an inconsistent spatial pattern was detected in the 30-year trend period. Additionally, change points in the median annual peak streamflows were detected in the late 1970s and early 1980s in the western part of the State, but in the east, the change point was more commonly detected in 1992–93. A similar east-west spatial pattern of likely upward and downward trends was detected in the annual peak-flow timing, the day of the year of the annal peak streamflow. In the western part of the State, the annual peak streamflows are arriving earlier, but in the east, the annual peak streamflows are arriving later. A peaks-over-threshold (POT) analysis where, on average, there are two events per year (POT2) and four events per year (POT4) was also used to evaluate changes in the frequency (count) of daily streamflows exceeding the threshold. Similar to detected changes in the annual peak streamflow, an east-west likely upward or downward change corresponding to an increase or decrease, respectively, in the frequency of daily streamflow greater than a POT2 and POT4 threshold was detected.

A monthly water-balance model was used to evaluate hydroclimatic variation in annual and seasonal precipitation, snowfall, potential evapotranspiration, and soil moisture storage for all qualifying streamgages in the 75-, 50-, and 30-year trend periods. Detected trends in the annual hydroclimatic metrics for the 75- and 50-year trend periods indicate a spatially consistent statewide increase in precipitation, decrease in snowfall, increase in potential evapotranspiration, and increase in soil moisture storage. Furthermore, detected trends in seasonal precipitation in the 75- and 50-year trend periods highlight a pronounced change in precipitation in winter and later into the summer season, especially in the 50-year trend period in the eastern part of the State. Statewide increases in seasonal soil moisture storage were also detected, highlighting year-round increasing flood magnitudes, particularly in the eastern part of the State.

Based on the results of these stationarity tests for the qualifying streamgages in South Dakota among the 75-, 50-, and 30-year trend periods, consistent temporal and spatial patterns of nonstationarity were detected among the 75- and 50-year trend periods. Furthermore, when nonstationarity is detected in daily streamflow, increased streamflow and volume (increasing frequency in POT), as well as potentially bridge scour, may have implications on culvert and highway design in the eastern part of South Dakota. Thus, when performing at-site peak-flow flood-frequency analyses in South Dakota, potential nonstationarities and alternative approaches are important considerations.