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Simulation of a Proposed Emergency Outlet from Devils Lake, North Dakota

Water-Resources Investigations Report 02-4042

2002

By Aldo V. Vecchia

Prepared in cooperation with the U.S. Army Corps of Engineers


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Abstract

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 level1, 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.

1In this report, "sea level" refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)--a geodetic datum derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called Sea Level Datum of 1929

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Contents

Abstract

Introduction

Methodology used to develop outlet simulation model

Monthly water-balance model for Devils Lake system

Precipitation, evaporation, and inflow data

Potential nonstationarity of precipitation, evaporation, and inflow

Estimation of monthly water-balance data for 1980-99

Detailed water and sulfate mass-balance models

Water mass-balance computation

Sulfate mass-balance computation

Sulfate mass-balance model with no sediment interaction and no mixing between lake boxes

Sulfate mass-balance model with sediment interaction

Sulfate mass-balance model with mixing between lake boxes

Outlet simulation model

Ambient streamflows and sulfate concentrations for the Sheyenne River

Outlet discharge

Simulation results for wet scenario

Simulation results based on stochastic analysis

Time-series model used to generate monthly water-balance data

Time-series model verification using long-term recorded data

Time-series model verification using geologic history of lake-level fluctuations

Conditional lake-level probability analysis

Stochastic outlet simulation analysis

Summary

References

Appendix A

Elevation/area/volume equations for lake boxes

Water mass-balance computations

Inflow to Stump Lake

Flows between lake boxes

Algorithm used to compute flows between lake boxes

Erosion of natural outlet from Stump Lake

Calculation of ambient Sheyenne River streamflow for outlet simulations

Appendix B

Table B1. Monthly water-balance data for Devils Lake for 1980-99

Table B2. Computed surface areas of Devils Lake for 1-foot increments

Table B3. Computed volumes of Devils Lake for 1-foot increments

 

FIGURES

 

1. Map showing locations of the Devils Lake Basin and the Red River of the North Basin

2. Map showing locations of gaging stations and water-quality sampling sites in the Devils Lake Basin and proposed outlet routes for West Bay and Pelican Lake

3. Graph showing recorded lake level for Devils Lake, 1867-2001

4. Bar charts showing estimated annual and quarterly precipitation totals for Devils Lake for 1950-99

5. Bar charts showing estimated annual and quarterly evaporation totals for Devils Lake for 1950-99

6. Bar charts showing gaged inflow to Devils Lake (inflow from Big Coulee and Channel A) for 1950-99

7. Graph showing estimated and fitted monthly changes in volume for Devils Lake for 1980-99 from regression model with constant coefficients

8. Graph showing residuals of estimated monthly changes in volume for Devils Lake for 1980-99 from regression model with constant coefficients

9. Graph showing estimated and fitted monthly changes in volume for Devils Lake for 1980-99 from regression model with monthly coefficients

10. Graph showing residuals of estimated monthly changes in volume for Devils Lake for 1980-99 from regression model with monthly coefficients

11. Graph showing time series of residuals of estimated monthly changes in volume for Devils Lake for 1980-99 from regression model with monthly coefficients

12. Graphs showing monthly water-balance data for Devils Lake for 1980-99

13. Graph showing recorded dissolved sulfate concentrations for Devils Lake and Stump Lake for 1988-2000

14. Diagram showing schematic of Devils Lake water and sulfate mass-balance models

15. Graphs showing monthly inflow and outflow for lake boxes for 1992-99

16. Graphs showing monthly precipitation and evaporation for lake boxes for 1992-99

17. Graphs showing monthly changes in volume for lake boxes for 1992-99

18. Graph showing recorded and fitted dissolved sulfate concentrations for Big Coulee for 1983-99 from regression model

19. Graph showing estimated monthly dissolved sulfate loads for Big Coulee for 1984-99

20. Graph showing recorded and fitted dissolved sulfate concentrations for Channel A for 1983-99 from regression model

21. Graph showing estimated monthly dissolved sulfate loads for Channel A for 1984-99

22. Graph showing recorded and fitted dissolved sulfate concentrations for Devils Lake and Stump Lake for 1988-99 from regression model with no sediment interaction and no mixing between lake boxes

23. Graph showing estimated and fitted dissolved sulfate loads for Devils Lake for 1988-99 from regression model with no sediment interaction and no mixing between lake boxes

24. Map showing locations of sediment cores taken from Devils Lake in July 1986 and September 1996

25. Graph showing average flow velocity based on wind-induced head differences for connections between lake boxes

26. Graph showing recorded and fitted dissolved sulfate concentrations for Devils Lake and Stump Lake for 1988-99 from regression model with sediment interaction and mixing between lake boxes

27. Graph showing estimated and fitted dissolved sulfate loads for Devils Lake for 1988-99 from regression model with sediment interaction and mixing between lake boxes

28. Graph showing estimated flux of sulfate from bottom sediments to lake boxes for Devils Lake and Stump Lake for 1988-99

29. Graphs showing estimated flux of sulfate between lake boxes for Devils Lake for 1988-99

30. Graph showing recorded and fitted dissolved sulfate concentrations for the Sheyenne River near Warwick for water years 1971-99 from regression model

31. Graph showing recorded dissolved sulfate concentrations for the Sheyenne River near Warwick for water years 1971-99 and percentiles of generated concentrations

32. Graphs showing results for wet scenario baseline (without-outlet) condition simulation with and without erosion of natural outlet

33. Graphs showing results for water years 2001-50 for wet scenario West Bay outlet 450-milligramper-liter sulfate constraint simulation

34. Graphs showing results for water years 2001-50 for wet scenario West Bay outlet 480-cubic-footper-second pump capacity simulation

35. Graph showing average annual dissolved sulfate concentrations for Devils Lake for water years 2001-50 for wet scenario baseline condition

36. Graph showing average annual dissolved sulfate concentrations for Devils Lake for water years 2001-50 for wet scenario West Bay outlet 480-cubic-foot-per-second pump capacity simulation with 450-milligram-per-liter sulfate constraint

37. Graphs showing results for water years 2001-50 for wet scenario modified West Bay outlet 480-cubic-foot-per-second pump capacity simulation

38. Graph showing average annual dissolved sulfate concentrations for Devils Lake for water years 2001-50 for wet scenario modified West Bay outlet 480-cubic-foot-per-second pump capacity simulation with 350-milligram-per-liter sulfate constraint

39. Graphs showing results for water years 2001-50 for wet scenario modified Pelican Lake outlet 480-cubic-foot-per-second pump capacity simulation

40. Graph showing average annual dissolved sulfate concentrations for Devils Lake for water years 2001-50 for wet scenario modified Pelican Lake outlet 480-cubic-foot-per-second pump capacity simulation with 250-milligram-per-liter sulfate constraint

41. Graphs showing recorded and fitted values of transformed evaporation, precipitation, and gaged inflow for 1980-99

42. Graphs showing normal probability plots of residuals for transformed evaporation, precipitation, and gaged inflow for 1980-99

43. Graphs showing recorded and fitted values of transformed evaporation, precipitation, and gaged inflow for 1950-78

44. Graphs showing normal probability plots of residuals for transformed evaporation, precipitation, and gaged inflow for 1950-78

45. Graph showing generated 20-year average annual evaporation and precipitation for Devils Lake for wet climate (1980-99) and normal climate (1950-78)

46. Graph showing generated 20-year average annual gaged inflow for Devils Lake for wet climate (1980-99) and normal climate (1950-78)

47. Graph showing generated annual maximum lake levels of Devils Lake for wet climate (1980-99) and normal climate (1950-78)

48. Graph showing generated 20-year average annual evaporation and precipitation for Devils Lake for mixed wet and normal climates

49. Graph showing generated 20-year average annual gaged inflow for Devils Lake for mixed wet and normal climates

50. Graph showing generated annual maximum lake levels of Devils Lake for mixed wet and normal climates

51. Graph showing percentiles of generated lake levels of Devils Lake for water years 2001-50 for baseline condition

52. Graph showing upper envelope curves for the level of Devils Lake for water years 2001-50 for baseline condition and for 300-cubic-foot-per-second Pelican Lake outlet

53. Graph showing average reductions in peak lake levels of Devils Lake for 300-cubic-foot-persecond Pelican Lake outlet

54. Graph showing lower envelope curves for the level of Devils Lake for water years 2001-50 for baseline condition and for 300-cubic-foot-per-second Pelican Lake outlet

55. Graph showing upper envelope curves for dissolved sulfate concentrations for Main Bay for water years 2001-50 for baseline condition and for 300-cubic-foot-per-second Pelican Lake outlet

 

TABLES

 

1. Results of statistical hypothesis tests to determine if Devils Lake precipitation was higher during 1975-99 than during 1950-74

2. Estimated coefficients for regression model used to compute monthly changes in volume for Devils Lake for 1980-99

3. Sulfate concentrations for pore-water samples collected from Devils Lake in July 1986 and September 1996

4. Properties of connections between lake boxes.

5. Estimated average flow velocities based on wind-induced head differences for connections between lake boxes

6. Parameter estimates obtained from nonlinear regression model used to compute in-lake sulfate concentrations

7. Starting values for outlet simulation model for October 1, 2000

8. Alternatives selected to illustrate outlet simulation model

9. Constraints for outlet operation

10. Fitted time-series model used to generate monthly water mass-balance model inputs based on monthly precipitation, evaporation, and inflow values for 1980-99

11. Modifications to fitted time-series model used to generate monthly water mass-balance model inputs based on monthly precipitation, evaporation, and inflow values for 1950-78

12. Statistics of recorded and generated annual (October through September) evaporation, precipitation, and inflow data for 1980-99

13. Statistics of recorded and generated annual (October through September) evaporation, precipitation, and inflow data for 1950-78

14. Average ratios of monthly water-balance inputs to winter water-balance inputs for water years 1980-99

15. Average ratios of monthly inflow from Big Coulee and monthly inflow from Channel A to gaged inflow for water years 1980-99

16. Frequency of extreme lake levels computed from generated 5,000-year sequences of annual maximum lake levels of Devils Lake

17. Probability distribution of year in which current Devils Lake wet cycle will end based on Markov model

18. Constraints for stochastic simulation

 

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