The Souris River Basin is a 61,000-square-kilometer basin in the Provinces of Saskatchewan and Manitoba in Canada and the State of North Dakota in the United States. Greater than average snowpack during the winter of 2010–11, along with record-setting rains in May and June 2011, resulted in historically unprecedented flooding in the Souris River Basin. The severity of the 2011 flood led the United States and Canada to request a review of the operating plan for any improvements of reservoir operations and flood control measures in the basin, and the Souris River Basin Task Force was formed. The International Souris River Study Board was then formed in 2017 to carry out the recommendations of the Souris River Basin Task Force laid out in a plan of study. To support the International Souris River Study Board, the U.S. Geological Survey (USGS), in cooperation with the North Dakota State Water Commission and the International Joint Commission, used the previously developed unregulated and regulated streamflow models and data for stochastic streamflow in the Souris River Basin to characterize climate and streamflow and support selection of streamflow traces based on their characterization. Components of the original stochastic hydrology models and their outputs were used in this phase of the study to (1) characterize historical and stochastic climate and streamflow for the Souris River Basin, (2) disaggregate monthly stochastic streamflow spatially and temporally to meet the needs of the U.S. Army Corps of Engineers, Hydrologic Engineering Center, Reservoir System Simulation model for the Souris River Basin, and (3) discuss selection of disaggregated streamflow traces (simulations) using the characteristics of climate and streamflow. A trace is a time series of a stochastic variable such as streamflow, potential evapotranspiration, or precipitation.

To characterize climate conditions, precipitation, potential evapotranspiration (PET), and moisture deficit for the Souris River Basin and individual points at Rafferty, Grant Devine, and Lake Darling Reservoirs were determined annually and seasonally. The annual basin (November 1–October 31) precipitation for the 50-percent nonexceedance probability is 452 millimeters (mm). Spring (March–May) is the wettest season, followed by summer (June–August), fall (September–November), and winter (December–February). Annual moisture deficit was largest at Lake Darling Reservoir, followed by Rafferty Reservoir, and then Grant Devine Reservoir.

Annual maximum monthly mean streamflow was determined for the Souris River below Rafferty Reservoir, Saskatchewan (Canadian streamgage 05NB036); Long Creek near Noonan (above Boundary Reservoir), North Dakota (USGS streamgage 05113600); Moose Mountain Creek near Oxbow, Saskatchewan (Canadian streamgage 05ND004); the Souris River near Sherwood, N. Dak. (USGS streamgage 05114000); the Des Lacs River at Foxholm, N. Dak. (USGS streamgage 05116500); and the Souris River above Minot, N. Dak. (USGS streamgage 05117500). When the seasonal maximum monthly mean streamflows are evaluated in contrast to annual maximum monthly mean streamflows separated by their seasonal occurrence, summer months of annual maximum monthly mean streamflows have a higher 50-percent exceedance probability of streamflow compared to annual maximum monthly mean streamflows that occur in spring, seasonal maximum monthly mean streamflows that occur in spring, and seasonal maximum monthly mean streamflows that occur in summer. When annual maximum monthly mean streamflows in summer are compared to annual maximum monthly mean streamflows in spring, they are consistently higher in streamflow but occur in less than 4.2 percent of years. Evaluation of whether the annual maximum monthly mean streamflows that occur in summer can be described as a separate population from annual maximum monthly mean streamflows that occur in spring was outside the scope of this study, and the summer and spring annual maximum monthly mean streamflows were not tested for statistical differences in mean or variance. Further investigation of seasonal weather patterns that induce flooding could lead to a better understanding of the seasonal differences in flooding.

Long-term hydrologic drought was characterized by evaluating multiyear mean streamflow. Shorter averaging periods have greater streamflow variability than longer periods and hence have a wider range of values. As the averaging period is extended to a longer period, the variability of mean streamflow decreases, and the more extreme streamflow volumes seen in shorter averaging periods cannot be sustained. Stochastic streamflow time series were disaggregated spatially and temporally for use in a HEC–ResSim model. The combination of monthly and daily stochastic streamflow data was used to select traces with qualities that could be used to test alternatives focused on water supply, summer flooding, and apportionment.