The Bureau of Reclamation identified eight water-supply alternatives for the Red River Valley Water Supply Project. Of those alternatives, six were considered for this study. Those six alternatives include a no-action alternative, two in-basin alternatives, and three interbasin alternatives. To address concerns of stakeholders and to provide information for an environmental impact statement, the U.S. Geological Survey, in cooperation with the Bureau of Reclamation, developed and applied a water-quality model to simulate the transport of total dissolved solids, sulfate, chloride, sodium, and total phosphorus during unsteady-flow conditions and to simulate the effects of the water-supply alternatives on water quality in the Red River and the Sheyenne River. The physical domain of the model, hereinafter referred to as the Red River model, includes the Red River from Wahpeton, North Dakota, to Emerson, Manitoba, and the Sheyenne River from below Baldhill Dam, North Dakota, to the confluence with the Red River. Boundary conditions were specified for May 15 through October 31, 2003, and January 15 through June 30, 2004. Measured streamflow data were available for August 1 through October 31, 2003, and April 1 through June 30, 2004, but water-quality data were available only for September 15 through 16, 2003, and May 10 through 13, 2004. The water-quality boundary conditions were assumed to be time invariant for the entire calibration period and to be equal to the measured value. The average difference between the measured and simulated streamflows was less than 4 percent for both calibration periods, and most differences were less than 2 percent. The average differences are considered to be acceptable because the differences are less than 5 percent, or the same as the error that would be expected in a typical streamflow measurement. Simulated total dissolved solids, sulfate, chloride, and sodium concentrations generally were less than measured concentrations for both calibration periods. The average absolute differences generally were less than 25 percent. Total phosphorus was simulated as a nonconservative constituent by assuming that concentrations change according to a first-order decay rate. The average difference between the measured and simulated total phosphorus concentrations was 6.2 percent for the 2003 calibration period and -24 percent for the 2004 calibration period. The Red River model demonstrates sensitivity to changes in boundary conditions so a reasonable assumption is that the model can be used to compare relative effects of the various water-supply alternatives. The calibrated Red River model was used to simulate the effects of the six water-supply alternatives by using measured streamflows for September 1, 1976, through August 31, 1977, when streamflows throughout the Red River Basin were relatively low. Streamflows for the Red River at Fargo, North Dakota, were less than 17.9 cubic feet per second on 159 days of that 12-month period, and monthly average streamflows for the Red River at Grand Forks, North Dakota, and the Red River at Emerson, Manitoba, were less than 30 percent of the respective long-term average monthly streamflows for 11 of the 12 months during September 1976 through August 1977. Water-quality boundary conditions were generated using a stochastic approach in which probability distributions derived from all available historical data on instream concentrations were used to produce daily concentrations at model boundaries. Return flow concentrations were estimated from source concentrations and current (2006) wastewater-treatment technology. Because no historical information on ungaged local inflow constituent concentrations is available to estimate those boundary conditions, time-invariant concentrations for the low-flow 2003 calibration period were used as the ungaged local inflow boundary conditions. The effects of the water-supply alternatives on water quality in the Red River and