Simulation of a proposed emergency outlet from Devils Lake, North Dakota
From 1993 to 2001, Devils Lake rose more than 25 feet, flooding farmland, roads, and structures around the lake and causing more than $400 million in damages in the Devils Lake Basin. In July 2001, the level of Devils Lake was at 1,448.0 feet above sea level 1 , which was the highest lake level in more than 160 years. The lake could continue to rise to several feet above its natural spill elevation to the Sheyenne River (1,459 feet above sea level) in future years, causing extensive additional flooding in the basin and, in the event of an uncontrolled natural spill, downstream in the Red River of the North Basin as well. The outlet simulation model described in this report was developed to determine the potential effects of various outlet alternatives on the future lake levels and water quality of Devils Lake. Lake levels of Devils Lake are controlled largely by precipitation on the lake surface, evaporation from the lake surface, and surface inflow. For this study, a monthly water-balance model was developed to compute the change in total volume of Devils Lake, and a regression model was used to estimate monthly water-balance data on the basis of limited recorded data. Estimated coefficients for the regression model indicated fitted precipitation on the lake surface was greater than measured precipitation in most months, fitted evaporation from the lake surface was less than estimated evaporation in most months, and ungaged inflow was about 2 percent of gaged inflow in most months. Dissolved sulfate was considered to be the key water-quality constituent for evaluating the effects of a proposed outlet on downstream water quality. Because large differences in sulfate concentrations existed among the various bays of Devils Lake, monthly water-balance data were used to develop detailed water and sulfate mass-balance models to compute changes in sulfate load for each of six major storage compartments in response to precipitation, evaporation, inflow, and outflow from each compartment. The storage compartments--five for Devils Lake and one for Stump Lake--were connected by bridge openings, culverts, or natural channels that restricted mixing between compartments. A numerical algorithm was developed to calculate inflow and outflow from each compartment. Sulfate loads for the storage compartments first were calculated using the assumptions that no interaction occurred between the bottom sediments and the water column and no wind- or buoyancy-induced mixing occurred between compartments. However, because the fitted sulfate loads did not agree with the estimated sulfate loads, which were obtained from recorded sulfate concentrations, components were added to the sulfate mass-balance model to account for the flux of sulfate between bottom sediments and the lake and for mixing between storage compartments. Mixing between compartments can occur during periods of open water because of wind and during periods of ice cover because of water-density differences between compartments. Sulfate loads calculated using the sulfate mass-balance model with sediment interaction and mixing between compartments closely matched sulfate loads computed from historical concentrations. The water and sulfate mass-balance models were used to calculate potential future lake levels and sulfate concentrations for Devils Lake and Stump Lake given potential future values of monthly precipitation, evaporation, and inflow. Potential future inputs were generated using a scenario approach and a stochastic approach. In the scenario approach, historical values of precipitation, evaporation, and inflow were repeated in the future for a particular sequence of historical years. In the stochastic approach, a statistical time-series model was developed to randomly generate potential future inputs. The scenario approach was used to evaluate the effectiveness of various outlet alternatives, and the stochastic approach was used to evaluate the hydrologic and water-quality effects of the potential outlet alternatives that were selected on the basis of the scenario analysis. Given potential future lake levels and sulfate concentrations generated using either the scenario or stochastic approach and potential future ambient flows and sulfate concentrations for the Sheyenne River receiving waters, daily outlet discharges could be calculated for virtually any outlet alternative. For the scenario approach, future ambient flows and sulfate concentrations for the Sheyenne River were generated using the same sequence of years used for generating water-balance data for Devils Lake. For the stochastic approach, a procedure was developed for generating daily Sheyenne River flows and sulfate concentrations that were "in-phase" with the generated water-balance data for Devils Lake. Simulation results for the scenario approach indicated that neither of the West Bay outlet alternatives provided effective flood-damage reduction without exceeding downstream water-quality constraints. However, both Pelican Lake outlet alternatives provided significant flood-damage reduction with only minor downstream water-quality changes. The most effective alternative for controlling rising lake levels was a Pelican Lake outlet with a 480-cubic-foot-per-second pump capacity and a 250-milligram-per-liter downstream sulfate constraint. However, this plan is costly because of the high pump capacity and the requirement of a control structure on Highway 19 to control the level of Pelican Lake. A less costly, though less effective for flood-damage reduction, plan is a Pelican Lake outlet with a 300-cubic-foot-per-second pump capacity and a 250-milligram-per-liter downstream sulfate constraint. The plan is less costly because the pump capacity is smaller and because the control structure on Highway 19 is not required. The less costly Pelican Lake alternative with a 450-milligramper- liter downstream sulfate constraint rather than a 250-milligram-per-liter downstream sulfate constraint was identified by the U.S. Army Corps of Engineers as the preferred alternative for detailed design and engineering analysis. Simulation results for the stochastic approach indicated that the geologic history of lake-level fluctuations of Devils Lake for the past 2,500 years was consistent with a climatic history that consisted of two climate states--a wet state, similar to conditions during 1980-99, and a normal state, similar to conditions during 1950-78. The transition times between the wet and normal climatic periods occurred randomly. The average duration of the wet climatic periods was 20 years, and the average duration of the normal climatic periods was 120 years. The stochastic approach was used to generate 10,000 independent sequences of lake levels and sulfate concentrations for Devils Lake for water years 2001-50. Each trace began with the same starting conditions, and the duration of the current wet cycle was generated randomly for each trace. Each trace was generated for the baseline (natural) condition and for the Pelican Lake outlet with a 300-cubic-foot-per-second pump capacity and a 450-milligram-per-liter downstream sulfate constraint. The outlet significantly lowered the probabilities of future lake-level increases within the next 50 years and did not substantially increase the probabilities of reaching low lake levels or poor water-quality conditions during the same period.