Simulation of Constituent Transport in the Red River of the North Basin

Reclamation the Bureau of the Bureau Scientific Investigations Report 2006–5296 U.S. Department of the Interior U.S. Geological Survey Prepared in cooperation with cooperation in Prepared of the in the Red River of Constituent Transport Simulation Unsteady- and Minnesota, During North Dakota North Basin, 2003-04 1977 and Flow Conditions,

Nustad and Bales–Simulation of Constituent Transport in the Red River of the North Basin, North Dakota and Minnesota, During Unsteady-Flow Conditions, 1977 and 2003-04–Scientific Investigations Report 2006–5296 Simulation of Constituent Transport in the Red River of the North Basin, North Dakota and Minnesota, During Unsteady-Flow Conditions, 1977 and 2003-04

By Rochelle A. Nustad and Jerad D. Bales

Prepared in cooperation with the Bureau of Reclamation

Scientific Investigations Report 2006–5296

U.S. Department of the Interior U.S. Geological Survey U.S. Department of the Interior DIRK KEMPTHORNE, Secretary

U.S. Geological Survey Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2006

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Contents

Abstract...... 1 Introduction ...... 2 Purpose and Scope ...... 2 Study Area...... 2 Acknowledgments...... 5 Methods ...... 5 Simulation of Constituent Transport...... 8 Model Implementation ...... 8 Computational Grid ...... 8 Boundary Conditions ...... 8 Streamflow ...... 8 Water Quality ...... 13 Model Calibration and Testing ...... 13 Streamflow...... 13 Water Quality...... 19 Model Testing ...... 31 Model Application...... 33 Effects of Water-Supply Alternatives on Total Dissolved Solids, Sulfate, Chloride, Sodium, and Total Phosphorus...... 37 Model Limitations ...... 52 Summary...... 54 References...... 58

Figures

1. Map showing locations of sites used in study...... 3 2. Diagram showing schematic of Red River model ...... 9 3. Graphs showing measured and simulated streamflows for selected Red River model calibration points, 2003 and 2004 calibration periods...... 20 4. Graphs showing measured and simulated total dissolved solids concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods...... 27 5. Graphs showing measured and simulated dissolved sulfate concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods...... 28 6. Graphs showing measured and simulated dissolved chloride concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods...... 29 7. Graphs showing measured and simulated dissolved sodium concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods ...... 30 8. Graphs showing measured and simulated total phosphorus concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods ...... 32 9. Graph showing simulated total dissolved solids concentrations for the Red River of the North at Fargo, North Dakota, for three sets of boundary conditions ...... 33 iv

Figures, Continued

10. Graphs showing simulated annual concentration distribution of daily mean concentrations for the Red River of the North at river mile 536.3 immediately downstream from the Wahpeton Industrial return flow, 1976-77 simulation period ...... 38 11. Graphs showing simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Fargo, North Dakota, 1976-77 simulation period ...... 40 12. Graphs showing simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Grand Forks, North Dakota, 1976-77 simulation period...... 42 13. Graphs showing simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Emerson, Manitoba, 1976-77 simulation period ...... 44 14. Graphs showing simulated annual concentration distribution of daily mean concentrations for the Sheyenne River below Baldhill Dam, North Dakota, 1976-77 simulation period...... 46 15. Graphs showing simulated annual concentration distribution of daily mean concentrations for the Red River of the North at West Fargo, North Dakota, 1976-77 simulation period...... 48

Tables

1. Description of water-supply alternatives for Red River Valley Water-Supply Project ...... 4 2. Data-collection network...... 6 3. Streamflow summaries for selected sites for 2003 and 2004 calibration periods and for 1976-77 simulation period ...... 7 4. Boundary condition and flow/water-quality calibration points for Red River model ...... 10 5. Water-quality boundary conditions for 2003 and 2004 calibration periods...... 14 6. Variables used to estimate ungaged local inflows and Manning’s n...... 17 7. Differences between measured and simulated streamflows for Red River model calibration points for 2003 and 2004 calibration periods...... 21 8. Estimated constituent concentrations for ungaged local inflows for 2003 and 2004 calibration periods...... 22 9. Ranges of historical measured constituent concentrations for tributaries within selected Red River model reaches...... 24 10. Median historical measured concentrations for tributaries within selected Red River model reaches...... 25 11. Percentage of total simulated constituent load contributed by estimated ungaged local inflows for 2003 and 2004 calibration periods...... 34 12. Change in median constituent concentrations as a result of additional streamflow required to maintain model stability...... 37 13. Annual constituent loads for the Red River of the North at Emerson, Manitoba, for water-supply alternatives ...... 52 14. Maximum, minimum, and average estimated annual constituent loads for the Red River of the North at Emerson, Manitoba, for 1978-2001 ...... 53 v

Conversion Factors, Abbreviations, and Datum

Multiply By To obtain Length foot (ft) 0.3048 meter (m) mile (mi) 1.609 kilometer (km)

Area square mile (mi2) 259.0 hectare (ha) square mile (mi2) 2.590 square kilometer (km2)

Volume acre-foot (acre-ft) 1,233 cubic meter (m3)

Flow rate cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s) million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

Mass ton, short (2,000 lb) 0.9072 megagram (Mg) ton, long (2,240 lb) 1.016 megagram (Mg)

Hydraulic gradient foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Transmissivity foot squared per second (ft2/s) 0.0929 meter squared per second (m2/s)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows: °F = (1.8 x °C) + 32 Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows: °C = (°F - 32) / 1.8 Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 (NGVD 29). Horizontal coordinate information is referenced to the North American Datum of 1927 (NAD 27). Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (µS/cm at 25°C). Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) or micrograms per liter (µg/L). vi Simulation of Constituent Transport in the Red River of the North Basin, North Dakota and Minnesota, During Unsteady-Flow Conditions, 1977 and 2003-04

By Rochelle A. Nustad and Jerad D. Bales

Abstract centrations 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 calibra- The Bureau of Reclamation identified eight water-supply tion period and -24 percent for the 2004 calibration period. The alternatives for the Red River Valley Water Supply Project. Of Red River model demonstrates sensitivity to changes in bound- those alternatives, six were considered for this study. Those six ary conditions so a reasonable assumption is that the model can alternatives include a no-action alternative, two in-basin alter- be used to compare relative effects of the various water-supply natives, and three interbasin alternatives. To address concerns alternatives. of stakeholders and to provide information for an environmen- The calibrated Red River model was used to simulate the tal impact statement, the U.S. Geological Survey, in coopera- effects of the six water-supply alternatives by using measured tion with the Bureau of Reclamation, developed and applied a streamflows for September 1, 1976, through August 31, 1977, water-quality model to simulate the transport of total dissolved when streamflows throughout the Red River Basin were rela- solids, sulfate, chloride, sodium, and total phosphorus during tively low. Streamflows for the Red River at Fargo, North unsteady-flow conditions and to simulate the effects of the Dakota, were less than 17.9 cubic feet per second on 159 days water-supply alternatives on water quality in the Red River and of that 12-month period, and monthly average streamflows for the Sheyenne River. The physical domain of the model, herein- the Red River at Grand Forks, North Dakota, and the Red River after referred to as the Red River model, includes the Red River at Emerson, Manitoba, were less than 30 percent of the respec- from Wahpeton, North Dakota, to Emerson, Manitoba, and the tive long-term average monthly streamflows for 11 of the 12 Sheyenne River from below Baldhill Dam, North Dakota, to the months during September 1976 through August 1977. confluence with the Red River. Water-quality boundary conditions were generated using a Boundary conditions were specified for May 15 through stochastic approach in which probability distributions derived October 31, 2003, and January 15 through June 30, 2004. from all available historical data on instream concentrations Measured streamflow data were available for August 1 through were used to produce daily concentrations at model boundaries. October 31, 2003, and April 1 through June 30, 2004, but Return flow concentrations were estimated from source concen- water-quality data were available only for September 15 trations and current (2006) wastewater-treatment technology. through 16, 2003, and May 10 through 13, 2004. The water- Because no historical information on ungaged local inflow con- quality boundary conditions were assumed to be time invariant stituent concentrations is available to estimate those boundary for the entire calibration period and to be equal to the measured conditions, time-invariant concentrations for the low-flow 2003 value. calibration period were used as the ungaged local inflow bound- The average difference between the measured and simu- ary conditions. The effects of the water-supply alternatives on lated streamflows was less than 4 percent for both calibration water quality in the Red River and the Sheyenne River were periods, and most differences were less than 2 percent. The evaluated by comparing the effects of five of the alternatives average differences are considered to be acceptable because the relative to the No-Action Alternative. differences are less than 5 percent, or the same as the error that Alternatives that involve the transfer of water from within would be expected in a typical streamflow measurement. Sim- the Red River Basin tended to have total dissolved solids, sul- ulated total dissolved solids, sulfate, chloride, and sodium con- fate, sodium, and total phosphorus concentrations that were centrations generally were less than measured concentrations about the same or less than those for the No-Action Alternative. for both calibration periods. The average absolute differences In contrast, alternatives that involve the transfer of water from generally were less than 25 percent. Total phosphorus was sim- the Missouri River tended to have higher sulfate and sodium ulated as a nonconservative constituent by assuming that con- concentrations than those for the No-Action Alternative. 2 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Introduction study. Total dissolved solids, sulfate, chloride, and sodium are conservative constituents and were selected because they affect the usability of water for municipal and industrial purposes. Population growth along with possible future droughts in Total phosphorus is a nonconservative constituent and was the Red River of the North (Red River) Basin (fig. 1) in North selected because of its potential effect on instream eutrophica- Dakota, Minnesota, and South Dakota will create an increasing tion. Representatives at the meeting agreed that transport of the need for reliable water supplies. Therefore, the Dakota Water selected constituents would be simulated for a 12-month period Resources Act passed by the U.S. Congress on December 15, of unsteady and extremely low flows, such as those during 2000, authorized the Secretary of the Interior to conduct a com- which the water-supply alternatives would be operated. The prehensive study of the future water needs in the basin in North low-flow conditions that occurred during the 1930s drought Dakota and of possible options to meet those water needs. As represent the low-flow conditions in which representatives of part of the comprehensive study, the Bureau of Reclamation the agencies were interested, but few streamflow and water- identified eight water-supply alternatives, including a No- quality data are available for that period. Therefore, after an Action Alternative, for the Red River Valley Water Supply extensive hydrologic analysis by the Bureau of Reclamation, Project (RRVWSP) (U.S. Department of the Interior, Bureau of September 1976 through August 1977 was selected as the sim- Reclamation, 2005). The possible effects of those alternatives ulation period for this study. That period was selected because on water quality in the Red River and the Sheyenne River it was a 365-day period during which extremely low stream- caused concern among many stakeholders. Also, the Dakota flows occurred at several USGS gaging stations and for which Water Resources Act mandates that the Bureau of Reclamation a sufficient amount of streamflow data was available for model prepare an environmental impact statement (EIS) that describes application. the specific environmental effects of each alternative. There- The model developed during this study will, hereinafter, fore, to address the concerns of the stakeholders and to provide be referred to as the Red River model. The model was devel- information for the EIS, the U.S. Geological Survey (USGS), in oped using the RIV1 modeling system (U.S. Army Corps of cooperation with the Bureau of Reclamation, developed a Engineers, 2006) and was calibrated and tested using data col- water-quality model for part of the Red River and the Sheyenne lected during 2003 and 2004. River to simulate the transport of total dissolved solids, sulfate, and chloride during steady-flow conditions (Nustad and Bales, 2005). Purpose and Scope Since the model to simulate the transport of total dissolved solids, sulfate, and chloride during steady-flow conditions was The purpose of this report is to describe the simulation of developed, concerns have been expressed about the transport of constituent transport in the Red River and the Sheyenne River those constituents and additional constituents during different during unsteady-flow conditions and to document the effects of flow conditions. Therefore, to address those concerns and to six proposed water-supply alternatives on water quality in the provide further information for the EIS, the USGS, in coopera- rivers. Development and calibration of the Red River model tion with the Bureau of Reclamation, conducted a study to also are documented. develop and apply a water-quality model for the Red River from The Red River model was used to simulate the transport Wahpeton, N. Dak., to Emerson, Manitoba, and the Sheyenne of total dissolved solids, sulfate, chloride, sodium, and total River from Baldhill Dam, N. Dak., to the confluence with the phosphorus during unsteady-flow conditions. Data for August Red River to simulate the transport of total dissolved solids, sul- through October 2003 and April through June 2004 were used fate, chloride, sodium, and total phosphorus during unsteady- to develop, calibrate, and test the model. The physical model flow conditions. In addition, the effects of six water-supply domain includes the Red River from Wahpeton, N. Dak., to alternatives (table 1) on water quality in the rivers were simu- Emerson, Manitoba, and the Sheyenne River from below lated using streamflow conditions that approximated those that Baldhill Dam, N. Dak., to the confluence with the Red River existed in 1976-77. Although the Bureau of Reclamation iden- (fig. 1). The model was used to simulate flow and constituent tified eight alternatives as part of the comprehensive study of transport for each of the six water-supply alternatives operating water needs in the Red River Basin, two of the alternatives were during conditions that approximated those that existed during removed from consideration for this study. Of the six alterna- September 1976 through October 1977. Inputs from Lake tives considered, three include the interbasin transfer of water. Ashtabula to the Sheyenne River were estimated for the water- supply alternatives by using a simple mixing model for the lake. To determine the flow conditions and constituents to be simulated by the model for this study, representatives from the Bureau of Reclamation met with representatives from the U.S. Study Area Environmental Protection Agency, the USGS, the States of Minnesota and North Dakota, Environment Canada, and other The study area includes the Red River from Wahpeton, agencies. During the meeting, which was held in January 2006, N. Dak., to Emerson, Manitoba, the Sheyenne River from total dissolved solids, sulfate, chloride, sodium, and total phos- below Baldhill Dam, N. Dak., to the confluence with the Red phorus were selected as the constituents to be included in the River, and selected tributaries to the Red River. The Red River Introduction 3

MANITOBA 49° 99° 32 Emerson 35 97° Pembina R. 49° Neche Roseau Pembina 34 33 Two N. Br. Tongue R. Hallock R. Lake Bronson River 3Red 1 30 S. Br. DEVILS 29 Drayton R. 27 28 Grafton R. R. R. LAKE Park S Tamarac Oakwood nake 95° 26 Middle . R Forest Fordville Big Woods Thief Upper BASIN River RiverOslo Red

Devils R. SHEYENNE Turtle 25 24 Warren Lake Lake River Maddock 23 Manvel Stump Turtle River 22 East Grand Lake Lower Peterson Coulee State Park Forks Lake Grand Red Warwick Arvilla Forks Harvey Beaver 21 Lake Sheyenne 20 Red of Fisher GooseThompson

99° Cr. Climax RIVER Sand R. 19 Hill R. 95° Cooperstown Baldhill 17 Shelly Hillsboro 16 18 Marsh R. Halstad River River Base f rom U. S. Geological Survey Cr. Hendrum Elm 15 Rice 1:2,000,000, 1972 Wild

Lake Rush Perley Ashtabula Brooktree the Maple EXPLANATION 7 Baldhill Park 13 Dam R. 47° West Fargo 6 14 River Valley 47° Red River of the North 12 11 MOORHEAD Buffalo City Mapleton Dilworth Basin boundary River FARGO BASIN 5 River 10 4 River Horace River Subbasin boundaries Hickson 2 Kindred 2 9 ican Site and number Pel North 8 Abercrombie Lisbon Tail 3 1 Breckenridge Rice Ot Wahpeton Sioux R. de Bois ter d Orwell Reservoir River Doran Orwell Dam Wil Rabbit R NORTH DAKOTA . MINNESOTA Mustinka R White Rock . R. White Rock Dam Mud L ake BAY Reservation Dam HUDSON 0 20 40 60 MILES Nelson SOUTH DAKOTA Lake Traverse aeWinnipegLake 97° 0 20 40 60 KILOMETERS

Winnipeg SASKATCHEWAN MANITOBA ONTARIO

CANADA Red

UNITED STATES River RED RIVER OF THE Of NORTH BASIN The

NORTH D AKOTA North MINNESOTA

SOUTH DAKO TA

INDEX MAP

Figure1. Locations of sites used in study. 4 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Table 1. Description of water-supply alternatives for Red River Valley Water Supply Project.

[Modified from U.S. Department of the Interior, Bureau of Reclamation, 2005]

Description of alternative

No-Action Alternative (NA). This alternative would use the current water supply in the Red River of the North Basin without the Red River Valley Water Supply Project.

In-basin alternatives

North Dakota In-Basin Alternative (NDIB). This alternative would supplement existing water supplies and would use the Red River of the North and other North Dakota water sources to meet future water demands. The main water-supply feature is a 48-cubic-feet-per-second pipeline that captures Red River of the North flows downstream from Grand Forks, North Dakota, and conveys flows back to Lake Ashtabula for storage and release down the Sheyenne River and the Red River of the North to meet municipal, rural, and industrial water demands. Two rural systems would be connected to cities by pipelines. The Grafton, North Dakota, water intake would be relocated farther north in the Red River of the North. The alternative also would include developing new ground-water sources in southeastern North Dakota; aquifer storage and recovery systems are proposed for Fargo, North Dakota; Moorhead, Minnesota; and West Fargo, North Dakota; and the city of Moorhead would continue to draw on Minnesota ground-water sources for some of its water demand.

Red River Basin Alternative (RRB). This alternative would supplement existing water supplies and would draw on a combination of the Red River of the North, other North Dakota water sources, and Minnesota ground-water resources to meet future water demands. Two rural systems would be connected to cities by pipelines. The main water-supply feature would be a series of well fields developed in Minnesota with an interconnecting conveyance pipeline serving the Fargo, North Dakota—Moorhead, Minnesota, metropolitan area. The alternative also would include developing new ground-water sources in southeastern North Dakota; aquifer storage and recovery systems are proposed for Fargo; Moorhead; and West Fargo, North Dakota; and the city of Moorhead would continue to draw on Minnesota ground- water sources for some of its water demand.

Interbasin alternatives

Garrison Diversion Unit Import to Sheyenne River Alternative (GDUIS). This alternative would supplement existing water supplies to meet future water needs with a combination of the Red River of the North, other North Dakota in-basin sources, and imported Missouri River water. The principal feature of this alternative would be a 122-cubic-feet-per-second pipeline from the McClusky Canal to Lake Ashtabula that would release treated Missouri River water into the Sheyenne River about 3 miles upstream from the reservoir. The biota treatment plant would be located adjacent to the McClusky Canal. The Grafton, North Dakota, water intake would be relocated farther north in the Red River of the North. The alternative would include a pipeline from Fargo, North Dakota, to the Wahpeton, North Dakota, area to serve industrial water demands in southeastern North Dakota.

Garrison Diversion Unit Import Pipeline Alternative (GDUIP). This alternative would supplement existing water supplies to meet future water needs by conveying water from the Missouri River via the McClusky Canal and a pipeline to the Red River Valley. The biota treatment plant would be located adjacent to the McClusky Canal. The principal feature of the alternative would be an 85-cubic-feet-per- second pipeline from the McClusky Canal to the Fargo, North Dakota, metropolitan area. The Grafton, North Dakota, river intake would be moved farther north in the Red River of the North. Two rural water systems would receive water from cities by pipelines. The alternative also would include developing new ground-water sources in southeastern North Dakota and expand use of the Buffalo aquifer as well as recharge of the Moorhead aquifer with an aquifer storage and recovery feature to serve the city of Moorhead, Minnesota.

Missouri River Import Pipeline to Red River Valley Alternative (MRIP). This alternative would supplement existing water supplies to meet future water needs by conveying treated water in a closed pipeline from the Missouri River south of Bismarck, North Dakota, directly to Fargo and Grand Forks, North Dakota. The principal features would be a 119-cubic-feet-per-second pipeline from the Missouri River at Bismarck to the Fargo area and a 21-cubic-feet-per-second pipeline to Grand Forks. The Missouri River water would be collected from a series of horizontal wells constructed in the sediments underlying the Missouri River. Two rural water systems would be served by pipelines from cities and the Grafton, North Dakota, river intake would be relocated farther north in the Red River of the North. The alternative would include a pipeline from Fargo to the Wahpeton, North Dakota, area to serve southeast industries. Methods 5

Basin is part of the Hudson Bay drainage system. Parts of North Acknowledgments Dakota, Minnesota, and South Dakota in the United States and parts of Saskatchewan and Manitoba in Canada are drained by A. Schlag and D. Goetzfried from the Bureau of Reclama- the Red River, and the North Dakota-Minnesota boundary is tion assisted throughout the study. M. Deutschman from Hous- formed by the river (fig. 1). The drainage area of the Red River ton Engineering supplied boundary condition data for the Sep- at Emerson is 40,200 mi2, including 3,800 mi2 of noncontribut- tember 1976 through August 1977 simulation period and also ing area. Downstream from Emerson, the Red River drains into provided valuable guidance throughout the study. K. Ryberg Lake Winnipeg, Manitoba. The streamflow-gaging station at and T. Banse from the USGS constructed the notched box plots Emerson is located 0.8 mi downstream from the international for constituent concentrations, and K. Vining from the USGS provided assistance with data preparation. A. Vecchia from the boundary. USGS supplied estimates of historical constituent loads for the The Red River is formed by the confluence of the Bois de Red River at Emerson, Manitoba. Sioux and Otter Tail Rivers at Wahpeton, N. Dak. (fig. 1), and flows northward 394 mi to the international boundary. The slope of the river, about 0.5 ft/mi, is extremely small. The river falls only about 200 ft over the reach between Wahpeton and Methods the international boundary. Between 1990 and 2000, the population in the United States part of the Red River Basin increased The Red River model was developed primarily from the 19 percent to 607,000 (Sether and others, 2004). About one- RIV1 modeling system. The RIV1 modeling system originally was released in 1991 by the U.S. Army Corps of Engineers, third of the population in the United States part of the basin Waterways Experiment Station, and was known as CE-QUAL- resides in Fargo, N. Dak., Grand Forks, N. Dak., and Moor- RIV1 (U.S. Army Corps of Engineers, 2006). Version 2.0 of the head, Minn. (Stoner and others, 1998). In 1990, total water use modeling system was released in 1995. The RIV1 modeling in the United States part of the basin was about 196 Mgal/d. system is a one-dimensional (cross-sectionally averaged), Most of the water was used for public supplies and irrigation. hydrodynamic, water-quality model that consists of two Slightly more than one-half of the water was obtained from parts—a hydrodynamic code (RIV1H) and a water-quality code ground-water sources, but the largest cities (Fargo, Grand (RIV1Q). RIV1H uses the widely accepted four-point, implicit, Forks, and Moorhead) obtained most of their water from the finite-difference, numerical scheme to solve the St. Venant flow Red River (Stoner and others, 1993). equations for flows, depths, velocities, water-surface eleva- The Sheyenne River, the largest tributary to the Red River, tions, and other hydraulic characteristics throughout a modeled has a drainage area of about 6,910 mi2 (not including the closed reach. RIV1Q can be used to simulate temporal and longitudinal Devils Lake Basin) and is about 500 mi long. The drainage area variations in each of 14 state variables—temperature, dissolved oxygen, two types of carbonaceous biochemical oxygen below Baldhill Dam is about 3,240 mi2. The Sheyenne River demand (CBOD), nitrogenous biochemical oxygen demand flows about 270 mi from Baldhill Dam to the confluence with (NBOD), nitrate plus nitrite nitrogen, ammonia nitrogen, the Red River and has an average slope of 1.0 to 1.5 ft/mi. Dur- organic nitrogen, organic phosphorus, dissolved phosphate, dis- ing the 1950s, zero streamflow was recorded along the Shey- solved iron, dissolved manganese, coliform bacteria, and enne River from above Harvey, N. Dak., to Lisbon, N. Dak. algae—and in conservative constituents. Numerical accuracy Flow in the lower reaches of the river is regulated partly by for the advection of sharp concentration gradients is preserved releases from Baldhill Dam, which was completed in 1949. in the code through the use of the explicit, two-point, fourth- Lake Ashtabula, which is formed by Baldhill Dam, has a capac- order accurate, Holly-Preissman scheme. The RIV1 modeling ity of 69,100 acre-ft between the invert of the outlet conduit and system was updated to run in a Windows environment in 2002 the normal pool elevation and a capacity of 157,500 acre-ft at and subsequently was called EPD-RIV1 (Martin and Wool, maximum pool elevation (U.S. Army Corps of Engineers, 2002). The EPD-RIV1 modeling system, which includes a pre- 2003). Lake Ashtabula is operated for flood control, municipal and post-processor to facilitate model application and data anal- water supply, recreation, and stream-pollution abatement. ysis, was used in this study. Ground water in the Red River Basin is primarily in sand The Red River model was calibrated and tested using streamflow and water-quality data for an extensive hydrologic and gravel aquifers near land surface or in buried glacial depos- network (fig. 1, table 2). Long-term records of streamflow are its throughout the basin. Ground water moves toward the Red available for most of the network sites. Streamflow summaries River through a regional system of bedrock and glacial-drift for selected sites for the calibration periods, August 1 through aquifers (Sether and others, 2004). Saline ground-water dis- October 31, 2003, and April 1 through June 30, 2004, and for charge from the bedrock aquifers is known to collect in wet- the simulation period for model applications, September 1, lands that drain into tributaries of the Red River (Strobel and 1976, through August 31, 1977, are given in table 3. The water- Haffield, 1995). The Turtle, Forest, and Park Rivers are the quality data were collected from September 15 through 16, major contributors of salinity to the Red River. 2003, when streamflows were low and steady and from May 10 6 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Table 2. Data-collection network.

[Q, continuous streamflow; QW, water-quality samples]

Site U.S. Geological Survey number Site name Data collected site number (figure 1)

1 05051500 Red River of the North at Wahpeton, North Dakota Q, QW 2 05051522 Red River of the North at Hickson, North Dakota Q, QW 3 05053000 Wild Rice River near Abercrombie, North Dakota Q, QW 4 05053800 Red River of the North above Fargo, North Dakota QW 5 05054000 Red River of the North at Fargo, North Dakota Q, QW

6 465602096472700 Red River of the North on Cass County Road 20 below Fargo, North Dakota QW 7 05058000 Sheyenne River below Baldhill Dam, North Dakota Q, QW 8 05058700 Sheyenne River at Lisbon, North Dakota Q, QW 9 05059000 Sheyenne River near Kindred, North Dakota Q, QW 10 05059300 Sheyenne River above Sheyenne River diversion near Horace, North Dakota Q, QW

11 05059500 Sheyenne River at West Fargo, North Dakota Q 12 05060100 Maple River below Mapleton, North Dakota Q, QW 13 470000096535300 Sheyenne River at Brooktree Park, North Dakota QW 14 05062000 Buffalo River near Dilworth, Minnesota Q, QW 15 05064000 Wild Rice River at Hendrum, Minnesota Q, QW

16 05064500 Red River of the North at Halstad, Minnesota Q, QW 17 05066500 Goose River at Hillsboro, North Dakota Q, QW 18 05067500 Marsh River near Shelly, Minnesota Q, QW 19 05069000 Sand Hill River at Climax, Minnesota Q, QW 20 05070000 Red River of the North near Thompson, North Dakota Q, QW

21 05080000 Red Lake River at Fisher, Minnesota Q, QW 22 05082500 Red River of the North at Grand Forks, North Dakota Q, QW 23 05082625 Turtle River at Turtle River State Park near Arvilla, North Dakota Q 24 480239097115000 Turtle River above Manvel, North Dakota QW 25 05084000 Forest River near Fordville, North Dakota Q

26 482118097090500 Forest River near confluence with Red River of the North, North Dakota QW 27 05090000 Park River at Grafton, North Dakota Q 28 482736097112800 Park River near Oakwood, North Dakota QW 29 05092000 Red River of the North at Drayton, North Dakota Q, QW 30 05094000 South Branch Two Rivers at Lake Bronson, Minnesota Q

31 05095000 Two Rivers at Hallock, Minnesota QW 32 05100000 Pembina River at Neche, North Dakota Q 33 485636097173800 Pembina River above Pembina, North Dakota QW 34 05102490 Red River of the North at Pembina, North Dakota Stage 35 05102500 Red River of the North at Emerson, Manitoba Q, QW Methods 7 /s) 3 -- (ft Average 1977

/s) 3 -- (ft Minimum August 31, August Simulation period Simulation 38 5.0 15 /s) September 1, 1976, September through 838479 5.0 18437 30 56 1.0 42 513388 1.7638 0 42 0 41 51 3 -- 1,9802,150 103,250 104 199 4,440 120 506 144 552 619 (ft Maximum /s) 257 710 807 3 1,285 1,299 1,327 1,327 1,173 4,251 9,340 (ft 13,061 18,740 Average

/s) 3 163 155 310 295 295 393 396 406 (ft 1,270 1,890 2,820 3,320 Minimum /s) 3 April 1 through June 30, April 1 through 2004 3,610 3,210 3,060 3,140 3,140 2,260 2,720 5,380 (ft 11,000 32,800 37,000 42,500 Maximum 57 62 99 /s) 3 105 105 220 254 239 523 821 942 Calibration periods Calibration 1,014 (ft Sheyenne River Average /s) 33 33 59 59 59 82 85 46 Red River of the North and tributaries Red River of the North 3 225 318 351 452 (ft Minimum 94 /s) 894 934 138 386 454 454 789 3 1,900 2,730 2,880 2,890 (ft August 1 August October 31, 2003 through Maximum

t North Dakota Fargo, Location North at Halstad, North at Streamflow summaries for selectedsites for 2003 2004 and calibration periods for 1976-77and simulation period.

North Dakota North Dakota Minnesota North Dakota North Dakota Manitoba North Dakota diversion near Horace, North Dakota North Dakota /s, cubic feet per second; --, no available /s, cubicdata] feet per second; --, no available 3 Red River of the North at Hickson, the North at of Red River Fargo, the North at of Red River the of Red River Forks, Grand the North at of Red River Drayton, the North at of Red River Emerson, the North at of Red River Dam, Baldhill below River Sheyenne at Lisbon, North Dakota Sheyenne River Dakota North Kindred, near Sheyenne River River Sheyenne above Sheyenne River Sheyenne River at Wes Red River of the North at Wahpeton, at the North of Red River Table 3. Table [ft 8 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 through 13, 2004, when streamflows were medium and The inflows and outflows for the 10 ungaged areas were unsteady (Nustad and Bales, 2005). The water-quality proper- represented as point inflows and outflows and, hereinafter, will ties and constituents for which water-quality samples were ana- be referred to collectively as ungaged local inflows (fig. 2, lyzed included total dissolved solids, sulfate, chloride, and table 4). Positive ungaged local inflows, which represent sodium, all of which are conservative, and total phosphorus. For inflows to the river from unmeasured surface-water and this study, the transport of total phosphorus was simulated by ground-water sources, were treated as tributaries. Negative assuming a first-order decay rate as a function of traveltime. ungaged local inflows, which represent outflows from the river Streamflow and water-quality boundary conditions are dis- from unmeasured surface-water and ground-water sinks, cussed in a later section of the report. unmonitored withdrawals, and evapotranspiration, were treated as withdrawals. Ungaged local inflows typically were added (or subtracted) in the middle of the reach bounded by respective Simulation of Constituent Transport USGS gaging stations. Return flows were included for Wahpeton, Fargo, Grand Forks, and West Fargo, N. Dak., and for Moorhead and East Implementation, calibration and testing, and application of Grand Forks, Minn., and withdrawals were included for Fargo, the one-dimensional, unsteady-flow, Red River model are Grand Forks, and Moorhead. The return flows for Fargo and described in this section. Data for implementation include the Moorhead were combined because those flows are in the same computational grid and boundary conditions. model segment, and the return flows for Grand Forks and East Grand Forks were combined for the same reason. The with- Model Implementation drawals for Fargo and Moorhead also were combined and represented as a single withdrawal. The Red River model was configured for implementation Channel-geometry data for the Red River and the Shey- to the study reaches by developing a computational grid that enne River were provided by the U.S. Army Corps of Engineers represents the physical domain of the study area. Boundary con- (Stuart Dobberpuhl and Aaron Buesing, written commun., ditions were specified for inflows and outflows of water and 2005). The data were used by the Corps in the one-dimensional, constituents to the river. The inflows and outflows included unsteady-flow, HEC-RAS model (Brunner, 2002), which was measured tributary flows, ungaged local inflows, return flows, used in a flood-insurance study. Channel cross-section profiles, and municipal withdrawals. thalweg elevations, and segment lengths were extracted from the HEC-RAS model and reformatted for the Red River model. The record for cross-section and invert elevation data for the Computational Grid Red River from Hickson, N. Dak., to Red River at Fargo, N. Dak., reach and the Sheyenne River from Kindred, N.Dak., The physical model domain includes the Red River from to the confluence with the Red River reach was less complete Wahpeton, N. Dak., to Emerson, Manitoba, and the Sheyenne than the record for other locations. Therefore, channel-geome- River from below Baldhill Dam, N. Dak., to the confluence try data for those reaches were interpolated from available with the Red River (fig. 2). The model domain is represented by information, such as cross sections at stream gage sites. a computational grid that includes two main branches. The 394- mi reach of the Red River from Wahpeton to Emerson is branch 1 in the Red River model and is represented by 99 seg- Boundary Conditions ments in the computational grid. Model segments in branch 1 range from 1.9 to 5.3 mi in length and average 4.0 mi in length. Boundary conditions were specified for May 15 through The 271-mi reach of the Sheyenne River from Baldhill Dam to October 31, 2003, and January 15 through June 30, 2004. The the confluence with the Red River is branch 2 in the model and first 2.5 months were used as an initialization period. The ini- is represented by 59 segments. Model segments in branch 2 tialization period was considered to be the period at the begin- range from 1.6 to 5.8 mi in length and average 4.5 mi in length. ning of a model simulation and was used to allow the effects of Inputs to the model included gaged inflows from the Shey- the estimated initial conditions to be transported out of the enne River and 12 tributaries to the Red River, inflows and out- model domain. Thus, simulated results after the initialization flows for 10 ungaged areas that were bounded by main-stem period should be unaffected by the initial conditions. USGS gaging stations, return flows from 6 point-source wastewater-treatment facilities, and withdrawals from 3 water-treat- Streamflow ment facilities (fig. 2, table 4). The tributaries for which gaged inflows were included are the Wild Rice River in North Dakota, A continuous time series of measured data was used to Buffalo River, Wild Rice River in Minnesota, Goose River, define streamflow boundary conditions for May 15 through Marsh River, Sand Hill River, Red Lake River, Turtle River, October 31, 2003, and January 15 through June 30, 2004. The Forest River, Park River, Two Rivers, Pembina River, and boundary conditions were specified for the upstream ends of Maple River. branches 1 and 2, and a stage boundary condition was specified Simulation of Constituent Transport 9

MANITOBA CANADA At Emerson UNITED STATES Pembina River NORTH DAKOTA MINNESOTA Two Rivers

EXPLANATION At Drayton U.S. Geological Survey stream gage Park River Tributary

Ungaged local inflow--Represented as point inflow Forest River

Return flow or withdrawals Turtle River Wastewater-treatment facility

Water-treatment facility GRAND FORKS-EAST GRAND FORKS WASTEWATER-TREATMENT FACILITY Miscellaneous site At Grand Forks GRAND FORKS WATER-TREATMENT FACILITY Red Lake River rnh1(e ie fteNorth) the of River (Red 1 Branch Near Thompson

Sand Hill River

Goose River Marsh River

At Halstad Branch 2 (Sheyenne River) RIVERWild Ric OFe River THE NORTH Brooktree Park Maple River WEST FARGO WASTEWATER-TREATMENT FACILITY Buffalo River Below Baldhill Dam At West Fargo FARGO-MOORHEAD WASTEWATER-TREATMENT FACILITY FARGO-MOORHEAD Above Sheyenne River At Fargo WATER-TREATMENT FACILITY diversion near Horace

S Wild HEYENNE Rice River

Near Kindred At Hickson

RIVER RED

WAHPETON WASTEWATER- At Lisbon TREATMENT FACILITY

At Wahpeton

Figure2. Schematic of Red River model. 10 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Table 4. Boundary condition and flow/water-quality calibration points for Red River model.

Location Type of information Source of data

Red River of the North

Red River of the North at Wahpeton, North Dakota Upstream flow boundary Site 1, U.S. Geological Survey site number 05051500

Wahpeton, North Dakota, wastewater-treatment facility Return flow Leo Murr (Wahpeton Wastewater Treatment Facility, oral commun., 2006)

Red River of the North at Wahpeton, North Dakota, to Ungaged local inflow Estimated Red River of the North at Hickson, North Dakota

Red River of the North at Hickson, North Dakota Flow/water-quality Site 2, U.S. Geological Survey site number calibration point 05051522

Red River of the North at Hickson, North Dakota, to Ungaged local inflow Estimated Red River of the North at Fargo, North Dakota

Wild Rice River near Abercrombie, North Dakota Gaged tributary inflow Site 3, U.S. Geological Survey site number 05053000

Fargo, North Dakota, water-treatment facility and Withdrawal Ron Hendrickson (Fargo Water Treatment Moorhead, Minnesota, water-treatment facility Facility, written commun., 2006) and Troy Hall (Moorhead Water Treatment Facility, written commun., 2006)

Red River of the North at Fargo, North Dakota Flow/water-quality Site 5, U.S. Geological Survey site number calibration point 05054000

Fargo, North Dakota, wastewater-treatment facility Return flow Peter Bilstad (Fargo Wastewater Treatment and Moorhead, Minnesota, wastewater-treatment Facility, written commun., 2006) and facility Andy Bradshaw (Moorhead Wastewater Treatment Facility, written commun., 2006)

Buffalo River near Dilworth, Minnesota Gaged tributary inflow Site 14, U.S. Geological Survey site number 05062000

Red River of the North at Fargo, North Dakota, to Ungaged local inflow Estimated Red River of the North at Halstad, Minnesota

Wild Rice River at Hendrum, Minnesota Gaged tributary inflow Site 15, U.S. Geological Survey site number 05064000

Red River of the North at Halstad, Minnesota Flow/water-quality Site 16, U.S. Geological Survey site number calibration point 05064500

Goose River at Hillsboro, North Dakota Gaged tributary inflow Site 17, U.S. Geological Survey site number 05066500

Marsh River near Shelly, Minnesota Gaged tributary inflow Site 18, U.S. Geological Survey site number 05067500

Sand Hill River at Climax, Minnesota Gaged tributary inflow Site 19, U.S. Geological Survey site number 05069000

Red River of the North at Halstad, Minnesota, to Red Ungaged local inflow Estimated River of the North at Grand Forks, North Dakota Simulation of Constituent Transport 11

Table 4. Boundary condition and flow/water-quality calibration points for Red River model.—Continued

Location Type of information Source of data

Red River of the North—Continued

Red River of the North near Thompson, North Dakota Water-quality calibration Site 20, U.S. Geological Survey site number point 05070000

Red Lake River at Fisher, Minnesota Gaged tributary inflow Site 21, U.S. Geological Survey site number 05080000

Grand Forks, North Dakota, water-treatment facility Withdrawal Hazel Sletten (Grand Forks Water Treatment Facility, written commun., 2006)

Red River of the North at Grand Forks, North Dakota Flow/water-quality Site 22, U.S. Geological Survey site number calibration point 05082500

Grand Forks, North Dakota, wastewater-treatment Return flow Don Tucker (Grand Forks Wastewater facility and East Grand Forks, Minnesota, Treatment Facility, written commun., wastewater-treatment facility 2006) and Mark Kotrba (East Grand Forks Wastewater Treatment Facility, written commun., 2006)

Turtle River at Turtle River State Park near Arvilla, Gaged tributary inflow Sites 23 and 24, U.S. Geological Survey site North Dakota, and Turtle River above Manvel, North numbers 05082625 and 480239097115000 Dakota

Red River of the North at Grand Forks, North Dakota, Ungaged local inflow Estimated to Red River of the North at Drayton, North Dakota

Forest River near Fordville, North Dakota, and Forest Gaged tributary inflow Sites 25 and 26, U.S. Geological Survey site River near confluence with Red River of the North, numbers 05084000 and 482118097090500 North Dakota

Park River at Grafton, North Dakota, and Park River Gaged tributary inflow Sites 27 and 28, U.S. Geological Survey site near Oakwood, North Dakota numbers 05090000 and 482736097112800

Red River of the North at Drayton, North Dakota Flow/water-quality Site 29, U.S. Geological Survey site number calibration point 05092000

Red River of the North at Drayton, North Dakota, to Ungaged local inflow Estimated Red River of the North at Emerson, Manitoba

South Branch Two Rivers at Lake Bronson, Minnesota, Gaged tributary inflow Sites 30 and 31, U.S. Geological Survey site and Two Rivers at Hallock, Minnesota numbers 05094000 and 05095000

Pembina River at Neche, North Dakota, and Pembina Gaged tributary inflow Sites 32 and 33, U.S. Geological Survey site River above Pembina, North Dakota numbers 05100000 and 485636097173800

Red River of the North at Emerson, Manitoba Flow/water-quality Site 35, U.S. Geological Survey site number calibration point 05102500 Sheyenne River

Sheyenne River below Baldhill Dam, North Dakota Upstream flow boundary Site 7, U.S. Geological Survey site number 05058000

Sheyenne River below Baldhill Dam, North Dakota, Ungaged local inflow Estimated to Sheyenne River at Lisbon, North Dakota

Sheyenne River at Lisbon, North Dakota Flow/water-quality Site 8, U.S. Geological Survey site number calibration point 05058700 12 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Table 4. Boundary condition and flow/water-quality calibration points for Red River model.—Continued

Location Type of information Source of data

Sheyenne River—Continued

Sheyenne River at Lisbon, North Dakota, to Sheyenne Ungaged local inflow Estimated River near Kindred, North Dakota

Sheyenne River near Kindred, North Dakota Flow/water-quality Site 9, U.S. Geological Survey site number calibration point 05059000

Sheyenne River near Kindred, North Dakota, to Ungaged local inflow Estimated Sheyenne River above Sheyenne River diversion near Horace, North Dakota

Sheyenne River above Sheyenne River diversion Flow/water-quality Site 10, U.S. Geological Survey site number near Horace, North Dakota calibration point 05059300

Sheyenne River above Sheyenne River diversion Ungaged local inflow Estimated near Horace, North Dakota, to Sheyenne River at West Fargo, North Dakota

Sheyenne River at West Fargo, North Dakota Flow/water-quality Site 11, U.S. Geological Survey site number calibration point 05059500

West Fargo, North Dakota, wastewater-treatment Return flow Terry Rust (West Fargo Wastewater Treatment facility Facility, written commun., 2006)

Maple River below Mapleton, North Dakota Gaged tributary inflow Site 12, U.S. Geological Survey site number 05060100

Sheyenne River at Brooktree Park, North Dakota Water-quality calibration Site 13, U.S. Geological Survey site number point 470000096535300

for the downstream end of branch 1. The boundary condition calculation differed slightly by reach and was determined dur- for the downstream end of branch 2 was computed internally by ing calibration. Because ungaged local inflows can represent the model. both inflows and losses within a reach, both positive and nega- Hourly streamflow data for the Red River at Wahpeton, tive values were calculated. Positive flows were treated as trib- N. Dak., were used for the boundary condition for the upstream utaries, and negative flows were treated as withdrawals. end of branch 1, and hourly streamflow data for the Sheyenne Daily return flows for six major cities in the Red River River below Baldhill Dam, N. Dak., were used for the boundary Basin were obtained from the respective wastewater-treatment condition for the upstream end of branch 2. Because RIV1H facilities (table 4). Return flows were combined for Fargo, requires a water-depth time series for the boundary condition N. Dak., and Moorhead, Minn., and for Grand Forks, N. Dak., for the downstream end of branch 1, 15-minute measured stage and East Grand Forks, Minn., and then added, along with return data for the Red River at Pembina, N. Dak., were converted to flows for West Fargo, N. Dak., and Wahpeton, N. Dak., as point 15-minute depth data and used as that boundary condition. inflows in the model segment that best represented the actual High-frequency fluctuations in the data were smoothed using a location of the return flow. Daily withdrawals for three major 2-hour moving average centered in the 2-hour time window. cities that use the Red River for source water were obtained Gaged tributary inflows were specified using a daily time series from the respective water-treatment facilities (table 4). The of streamflows (Robinson and others, 2004, 2005) for the withdrawals were combined for Fargo and Moorhead and then downstream-most gaging location on each of the 12 tributaries were subtracted, along with the combined withdrawals for to the Red River (table 4). Grand Forks and East Grand Forks, from the model segment that best represented the actual location of the withdrawal. Ungaged local inflows were calculated using streamflows for the upstream and downstream gaging locations of a reach and inflows and outflows within the reach into which the ungaged local inflow was added (table 4). The actual method of Simulation of Constituent Transport 13

Water Quality RIV1H includes three parameters that affect aspects of the computational scheme in the model. The first parameter, Measured data for September 15 through 16, 2003, and THETA, controls weighting of the four-point, implicit, numer- May 10 through 13, 2004, were used to define water-quality ical method used to solve the governing differential equations boundary conditions. The data sets for those periods each con- in the model (Martin and Wool, 2002). The recommended range tain a single measurement for each location used in this study. for THETA is 0.55 to 0.75, and the optimal value for numerical Because no other water-quality data are available, the water- accuracy is 0.55 although a higher value can be used to enhance quality boundary conditions were assumed to be time invariant numerical stability. After initial testing, THETA was set at 0.75 for the entire calibration period and to be equal to the measured for the Red River model. The second parameter, BETA, is a value. momentum correction coefficient that generally is used when Time-invariant water-quality boundary conditions were structures affect flow in the river. The recommended value for specified for the upstream ends of branches 1 and 2 and for the BETA is 1.0, which was the value used for the Red River tributaries (table 5). Constituent concentrations for ungaged model, indicating no momentum correction. The third parame- local inflows were calculated in a manner similar to that used to ter, TOLER, is the tolerance factor. The differential equations calculate streamflow for the ungaged local inflows. The con- in RIV1H are solved iteratively, and the solution is assumed to centrations were based on constituent mass at the upstream and have converged when the difference between the current water- downstream gaging locations and on inflows and outflows of level calculation and the previous water-level calculation dif- mass within the reach into which the ungaged local inflows fers by less than TOLER. TOLER was set at 0.05 ft for the Red were added. As with streamflow, the actual method of calcula- River model. That value is a compromise between the best tion was determined during calibration and differed by reach. value for accuracy and the best value for computational time Constituent concentrations for daily return flows (unpublished (Martin and Wool, 2002). data on file in North Dakota Water Science Center, Grand As previously noted, channel-geometry data were Forks, N. Dak., field office) were measured concurrently with extracted from a HEC-RAS model developed by the U.S. Army instream sampling. The same constituent concentration was Corps of Engineers. These data were adjusted slightly during used for the return flows for both calibration periods. calibration of the Red River model to improve model perfor- mance. For example, when the Red River model is initialized, Model Calibration and Testing large instabilities in water level are generated throughout the model domain for the first few time steps. Therefore, channel The Red River model was calibrated by adjusting selected cross sections were arbitrarily extended upward and outward to boundary conditions, model parameters, and channel-geometry contain the instabilities. Streamflows are within the original data to obtain reasonable agreement between measured and cross sections after the instabilities dissipate, typically within 7 simulated streamflows and concentrations for 10 flow/water- days of the beginning of the simulation period. (As previously quality calibration points (table 4). This section describes the stated, a 2.5-month initialization period was used in the model calibration process, results, and limited model testing. to allow the effects of estimated initial conditions to be transported out of the model.) Bottom-geometry and bottom-slope data also were adjusted for selected locations. For example, dur- Streamflow ing low-flow conditions at cross sections that have a wide, relatively flat bottom, small changes in water level can result in The time step that can be used in the Red River model is large changes in wetted width and, thus, cause numerical oscil- limited by the Courant number. The Courant number, as lations. Therefore, the bottom-geometry data were adjusted to described by Chaudhry (1993), is as follows: avoid the numerical oscillations. The HEC-RAS channel slope for the entire Red River was increased 1 percent from 0.529 a∆t ft/mi to 0.537 ft/mi, and the bottom slope for the Sheyenne Cn = ------(1) ∆x River between Baldhill Dam and Lisbon, N. Dak., was increased 1 percent from 1.36 ft/mi to 1.37 ft/mi. Also, negative where slopes used in the HEC-RAS model for some model segments Cn is the Courant number between Fargo and Grand Forks, N. Dak., were removed to a is the wave velocity, avoid computational problems during the water-quality simula- ∆t is the time-step size, tions. and Initial simulations using measured hourly streamflow data ∆x is the spatial step size. for the Sheyenne River below Baldhill Dam, N. Dak., resulted in oscillations in the simulations for the downstream locations. The computational time step for the Red River model was set at Therefore, because abrupt changes in upstream boundary con- 300 seconds for all simulations. At this time step, Courant num- ditions, such as those that occur immediately downstream from bers always were less than 0.05, or much less than the maxi- a dam, can cause instabilities in the simulations from some mum allowable Courant number of 1.0. models, including RIV1H (Martin and Wool, 2002), the 14 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 2004 .15.06 .13 .45 .19 .24 .10.04 .29 .07 .46 .43 .07 .03 .58 .04 .01 .04 4.7 4.7 0.03 0.07 4.5 4.5 3.7 3.7 2003 Total phosphorus (milligrams per per (milligrams liter) 8.0 8.0 11 28 91 11 13 2004 180 190 210 230 120 190 12 18 16 28 10 11 180 640 880 230 170 190 100 2003 Dissolved sodium (milligrams per liter) (milligrams 5.0 8.0 12 49 33 37 11 11 2004 150 250 270 150 110 9.0 7.0 7.0 9.0 11 62 53 15 150 980 150 110 2003 1,300 Dissolved chloride (milligrams per liter) (milligrams 67 52 84 72 65 2004 460 400 350 950 580 380 110 460

32 78 52 83 46 41 460 540 680 950 740 380 470 2003 Dissolved sulfate (milligrams per liter) per (milligrams Red River of the North and tributaries Red River of the North 981 442 265 981 266 390 295 305 2004 1,300 1,210 1,120 1,940 1,210 981 407 334 458 326 258 262 2003 1,020 1,300 2,550 3,240 1,940 1,490 (milligrams per liter) (milligrams Total dissolved solids Total dissolved

facility return flow facility return wastewater-treatment kota, wastewater- kota, Dakota, wastewater- sboro, North Dakota Manvel, North Dakota onfluence with Red with onfluence Hendrum, Minnesota Hendrum, Location Water-quality conditions boundary 2003for and 2004 calibration periods.

facility and Minnesota, Moorhead, wastewater-treatment River of the North, Dakota North North Dakota flow return facility treatment North Dakota treatment facility and Grand Forks, East and facility treatment facility wastewater-treatment Minnesota, return flow Fargo, North Dakota, Fargo, River near Dilworth, Minnesota Buffalo at Wild Rice River at Hill Goose River near Marsh River Shelly, Minnesota Sand Hill River at Climax, Minnesota Minnesota Fisher, River at Red Lake Grand Forks, North Turtle River above Forest River near c Red River of the North at Wahpeton, at the North of Red River Da North Wahpeton, Abercrombie, near Wild Rice River Table 5. Table Simulation of Constituent Transport 15 .06.11 .14 .44 .26 .25 0.14 0.18 0.23 0.27 4.6 4.6 Total phosphorus (milligrams per per (milligrams liter) 8.0 33 39 91 350 580 23 51 31 120 580 Dissolved sodium 4,880 (milligrams per liter) (milligrams 9.0 17 12 31 480 570 45 21 19 66 570 7,660 Dissolved chloride (milligrams per liter) (milligrams 53 350 150 130 640 310 Sheyenne River 40 190 260 640 510 1,270 Dissolved sulfate (milligrams per liter) per (milligrams Red River of the North and tributaries—Continued and North of the River Red 347 737 279 382 2,280 1,480 713 379 555 2003 2004 2003 2004 2003 2004 2003 2004 2003 2004 2,280 1,110 14,400 (milligrams per liter) (milligrams Total dissolved solids Total dissolved

Pembina, North Dakota, wastewater- Dakota, kwood, North Dakota Location Water-quality boundary conditions 2003for and 2004 calibration periods.—Continued North Dakota flow return facility treatment Dakota Dakota Sheyenne River below Baldhill Dam, Baldhill below River Sheyenne West Fargo, North below Maple River Mapleton, North Park River near Oa Park Two Rivers at Hallock, Minnesota above Pembina River Table 5. Table 16 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 upstream boundary conditions for the Sheyenne River were 2) on which the ungaged local inflow was applied to the model. smoothed slightly by using a 12-hour moving average flow cen- In most cases, T in equation 2 was equal to L (table 6). T was tered in the 12-hour time window. not used for reaches that had no tributary inflow. Ungaged local inflows were estimated for the 10 reaches The variables A, L, and T in equation 2 were adjusted bounded by main-stem long-term gaging stations (fig. 2). Sev- during model calibration. The variables differed from reach to eral approaches were considered to estimate the ungaged local reach and varied with streamflow (table 6). The values for A, inflows but, in general, the approach was to calculate the differ- L, and T were determined using the 2003 data set and then ence between the daily average streamflow for the upstream tested using the 2004 data set. The calibrated values of A, L, location and the daily average streamflow for the downstream and T resulted in good agreement between the measured and location, accounting for gaged tributary inflows, return flows, simulated streamflows for both 2003 streamflows and 2004 and withdrawals within the reach. The difference was desig- streamflows that were about the same magnitude as the 2003 nated as the ungaged local inflow for the reach. The estimates streamflows (table 3). The values for A, L, and T then were (both timing and magnitude) of the ungaged local inflows to the determined using the 2004 data set (table 6). Red River and the Sheyenne River had a large effect on simu- The mean estimated ungaged local inflow for the 2003 cal- lated streamflows. ibration period was determined for each reach and then com- The approach used to estimate the ungaged local inflows pared to the average streamflow for the same period for the was complicated by the differences in reach length, by unsteady downstream end of the reach. For the Sheyenne River at Lisbon, flows, and by the location of the ungaged local inflows and the N. Dak., to Sheyenne River near Kindred, N. Dak., reach, gaged tributary inflows (or outflows) in relation to the down- ungaged local inflow was estimated to be about one-third of the stream end of the reach. To account for traveltime through the total streamflow in the reach. The estimated ungaged local reach, the difference between the upstream and downstream inflow for the Sheyenne River at Lisbon to Sheyenne River near streamflows was based on a lagged value of streamflow. For Kindred reach is not unusual given the effects of the Sheyenne example, if the traveltime through the reach was about L days, River Delta aquifer in the reach (G. Wiche, U.S. Geological the ungaged local inflow for day X was calculated using the fol- Survey, oral commun., 2006). Ungaged local inflows for all lowing mass-balance equation: other reaches accounted for - 4 to 6 percent of the total streamflow in the respective reach. Ungaged local inflows for the 2003

QXA+ = DSXL+ – ()USX + IXT+ – WX (2) calibration period were negative for two reaches [the Red River at Hickson, N. Dak., to Red River at Fargo, N. Dak., reach (- 4 where percent) and the Red River at Drayton, N. Dak., to Red River at Q is the ungaged local inflow, in cubic feet per Emerson, Manitoba, reach (- 1 percent)], indicating a slight loss second, for the reach; of flow in the reaches as a result of evaporation, unmonitored withdrawals, ground-water recharge, or errors in streamflow X is the date on which the ungaged local inflow measurements. For the 2004 calibration period, ungaged local was applied; inflows accounted for a slightly higher percentage (- 3 to 15 per- A is an adjustment to the date on which the ungaged cent) of the total streamflow in each reach than for the 2003 cal- local inflow was applied; ibration period except for the Sheyenne River at Lisbon to DS is the average daily streamflow, in cubic feet per Sheyenne River near Kindred reach. That reach had a loss of second, for the downstream end of the reach; flow during the 2004 calibration period. Estimated ungaged L is the lag, in days, applied to the downstream end local inflows accounted for more than 10 percent of the total of the reach; streamflow in only three reaches (the Red River at Wahpeton, US is the average daily streamflow, in cubic feet per N. Dak., to Red River at Hickson reach at 11 percent; the Red second, for the upstream end of the reach; River at Grand Forks, N. Dak., to Red River at Drayton reach at I is the mean daily gaged tributary inflow and the 15 percent, and the Red River at Drayton to Red River at Emer- return flow, in cubic feet per second; son reach at 14 percent). T is the lag between the occurrence of the gaged The roughness coefficient, Manning’s n , was adjusted for tributary inflow and day X; each model segment to complete the streamflow calibration. and RIV1H includes an option that allows n to vary with depth such W is the mean daily withdrawal, in cubic feet per that second. nN= 1 – []N2 (depth) (3) Because of the differences in reach length and reach traveltime, the lag time varied among the reaches (table 6). Also, because of the differences in streamflow within a reach, the lag where time varied with streamflow (table 6). Therefore, to account for N1 and N2 are variables that are adjusted during the differences at the point where the ungaged local inflow model calibration. entered the reach, adjustments were made to the date (A in eq. Simulation of Constituent Transport 17 2 N .0001 .0001 0 0 0.0001 0 1 .030 .030 .033 .035 .035 N 0.030 1 2 1 3 3 2 2 4 2 4 3 -- -- 4 2 3 4 5 2 3 (days) Lag between in equation 2) in equation , greater than or to; >, equal greater than] ungaged local ungaged tributary inflow T > ( and date on which date and inflow was applied inflow occurrence of gaged occurrence Calibration variables Calibration 4 3 3 2 3 2 2 1 4 2 3 2 (days) in equation 2)

downstream end of reach Lag applied to applied Lag L ( <, less than; --, gaged no in reach; tributary 2 1 0 1 1 1 1 0 2 1 1 0 (days) to date on in equation 2) Adjustment

local inflow local was applied A which ungaged which ( Red River of the North

. n L, , A apply 300 300 400 400 500 500

T 1,000 1,000 1,200 1,200 1,000 1,000

< > < > < > < > < > < > range to (cubic feet Main-stem which streamflow and and per second) variable that is adjusted variable during model calibration; 2, N

Location at Halstad, Minnesota, Variables usedVariables to estimate ungaged local inflows Manning’sand

variable that is adjusted during model calibration;variable Dakota, to Red River of the North at North the River of Dakota, to Red Hickson, North Dakota at North the of River Dakota, to Red Dakota Fargo, North at North the of River Dakota, to Red Halstad, Minnesota to Red River of the North Forks, at Grand North Dakota North the River of Red Dakota, to North Dakota at Drayton, North at North the of River Dakota, to Red Emerson, Manitoba 1, Red River of the North at Wahpeton, North Wahpeton, the North at of Red River North Hickson, the North at of Red River North Fargo, the North at of Red River the North of Red River Forks, Grand the North at of Red River Drayton, North the North at of Red River N Table 6. Table [ 18 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 2 N .0001 0 0 0 1 .031 .037 .035 N 0.034 1 ------(days) Lag between in equation 2) in equation , greater than or to; >, equal greater than] ungaged local ungaged tributary inflow T ( and date on which date and inflow was applied inflow occurrence of gaged occurrence Calibration variables Calibration 4 3 3 2 1 2 1 1 0 (days) gaged in reach; tributary > in equation 2)

downstream end of reach Lag applied to applied Lag L ( 2 2 1 1 0 0 0 0 0 (days) to date on in equation 2) Adjustment

local inflow local was applied A which ungaged which ( Sheyenne River .—Continued n L, , A apply 100 100 150 500 500 500 300 300

T < > < > < > < > value. range to T 150 to 500 150 (cubic feet Main-stem which streamflow and and per second) at is adjusted during model calibration; <, less than; --, no 2, N lity–0; Red Lake River at Fisher, Minnesota–1. Fisher, at River Red Lake lity–0;

ies within reach the had the same Location used Variables to estimate ungaged local inflows Manning’sand Dakota, to Sheyenne River at Lisbon, River at Dakota, to Sheyenne North Dakota North near to Sheyenne River Kindred, Dakota River Sheyenne above to Sheyenne River diversion near Horace, North Dakota diversion near Horace, North Dakota, at to Sheyenne River West Fargo, North Dakota Unless otherwise specified, all tributar all otherwise specified, Unless Minnesota–1. at Hendrum, River Rice Wild faci GrandNorth Forks, Dakota, water-treatment NorthGrafton, at Dakota–0. River Park Dakota–2; North Fordville, near River Forest Dakota–0. North at Neche, River Pembina Minnesota–0; Bronson, at Lake Rivers Two Branch South 1, 1 2 3 4 5 Sheyenne River at Lisbon, North Dakota, Sheyenne River Dakota, North Kindred, near Sheyenne River River Sheyenne above Sheyenne River Sheyenne River below Baldhill Dam, North Dam, Baldhill below River Sheyenne N Table 6. Table [ that is adjusted variable calibration;during model th variable Simulation of Constituent Transport 19

N2 was used to adjust n so that the highest n values were at ungaged local inflows were difficult to estimate and errors in the shallowest depths. For the Red River model, N1 ranged the estimates were higher for the 2004 calibration period than from 0.030 to 0.037, and N2 ranged from zero to 0.0001 for the 2003 calibration period. Further refinement of local (table 6). Using these values in RIV1H, Manning’s n was com- inflow estimates probably would improve predictions, but these puted to be between 0.028 and 0.037. Those values were the refinements are not justified by the relatively small streamflow same as those used by Wesolowski (1994) for the Red River. prediction errors or by the future intended application of the Simulated streamflows for selected Red River model cali- model. bration points were in reasonable agreement with measured streamflows for the 2003 (low-flow) and 2004 (medium-flow) calibration periods (fig. 3). The average difference between the Water Quality measured and simulated streamflows for all calibration points The locations used for the water-quality calibration were was less than 4 percent for both periods, and most average dif- the same as those used for the streamflow calibration except that ferences were less than 2 percent (table 7). In general, stream- the Red River near Thompson, N. Dak., was added and the flows for the 2003 calibration period were somewhat underpre- Sheyenne River at Brooktree Park, N. Dak., was used instead of dicted, and streamflows for the 2004 calibration period were the Sheyenne River at West Fargo, N. Dak. Constituent concen- slightly overpredicted. However, the average differences trations for the ungaged local inflows were estimated and two between the measured and simulated streamflows are consid- model variables were adjusted as part of the calibration process. ered to be acceptable because the differences are less than 5 per- The variables that were adjusted were the dispersion coefficient cent, or the same as the error that would be expected in a typical and the first-order decay coefficient for total phosphorus. Mea- streamflow measurement. sured and simulated constituent concentrations were compared The root mean square difference and the average absolute for the single sample date for each calibration period. difference between the measured and simulated streamflows Constituent concentrations for the ungaged local inflows were higher for the 2004 calibration period than for the 2003 were estimated using a modified version of equation 2 such that calibration period (table 7) because of the higher streamflows during 2004. To account for the differences between the streamflows for the two calibration periods, the root mean square dif- C (4) ference and the average absolute difference can be expressed as XA+ a percentage of the average streamflow for each calibration ()DS C – []()US C + ()I C – ()W C = ------XL+ DS X US XT+ I X W period. For example, the root mean square difference for the QXA+ Red River at Emerson, Manitoba, for the 2004 calibration period represents 15 percent of the average streamflow for that where location, and the average absolute difference represents 9.1 per- C is the estimated concentration, in milligrams per cent of the average streamflow. Average absolute differences, liter, for the reach; expressed as a percentage of the average streamflow for the C is the measured concentration, in milligrams per respective calibration period, ranged from 2.0 percent for the DS liter, for the downstream end of the reach; Red River at Hickson, N. Dak., to 6.3 percent for the Sheyenne River near Kindred, N. Dak., for the 2003 calibration period and CUS is the measured concentration, in milligrams per from 2.0 percent for the Red River at Hickson to 9.3 percent for liter, for the upstream end of the reach; the Red River at Drayton, N. Dak., for the 2004 calibration CI is the measured concentration, in milligrams per period. The mean of the average absolute differences for all 10 liter, for the gaged tributary inflows and return calibration points was 3.9 percent of the average streamflow for flows; the 2003 calibration period and 5.4 percent of the average and streamflow for the 2004 calibration period. CW is the measured concentration, in milligrams per Calibration results indicate differences between measured liter, for the location nearest to the location and simulated streamflows tended to be smaller for the of the withdrawal. upstream locations than for the downstream locations. The smaller differences for the upstream locations probably resulted Concentrations and corresponding streamflows for the single from the smaller accumulated error in ungaged local inflow sample dates in both 2003 and 2004 were used to estimate a estimates for the upstream locations relative to the accumulated single concentration for each constituent for ungaged local error for the downstream locations. Calibration results also indi- inflow within a reach. Constituent concentrations were esti- cate differences were larger for the 2004 calibration period than mated for both calibration periods (table 8). The values used for for the 2003 calibration period, again a probable result of errors A, L, and T (table 6) were the same as those used for the in the ungaged local inflow estimates. Streamflows were mod- streamflow calibration. Equation 4 was not applied if the calcu- erate during the 2004 calibration period, and the percentage of lated ungaged local inflow was negative. As previously noted, flow being contributed to the main-stem rivers from the tribu- negative ungaged local inflows were treated as withdrawals so taries was larger than during the 2003 calibration period. Thus, the calculation was unnecessary. If negative concentrations 20 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

100,000

Measured Simulated 10,000 At Grand Forks

At West Fargo

At Fargo

1,000

100 OND C E S

10 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 FEET PER

C AUGUST SEPTEMBER OCTOBER UBI

C 2003

100,000 TREAMFLOW, IN S

10,000

1,000

Measured

Simulated

100 At Grand Forks At West Fargo

At Fargo

10 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 APRIL MAY JUNE 2004

Figure 3. Measured and simulated streamflows for selected Red River model calibration points, 2003 and 2004 calibration periods. Simulation of Constituent Transport 21

Table 7. Differences between measured and simulated streamflows for Red River model calibration points for 2003 and 2004 calibration periods.

Root mean square Average absolute difference between Average difference difference between measured and between measured and measured and simulated simulated streamflows simulated streamflows Location streamflows (percent) (cubic feet (cubic feet per second) per second)

2003 2004 2003 2004 2003 2004

Red River of the North

Red River of the North at Hickson, North Dakota 0 0.1 8.9 37 5.2 16

Red River of the North at Fargo, North Dakota - .5 .7 11 105 6.7 47

Red River of the North at Halstad, Minnesota - .2 .7 23 206 16 140

Red River of the North at Grand Forks, North Dakota 1.4 0 51 686 35 393

Red River of the North at Drayton, North Dakota 1.4 - .4 47 2,050 35 1,220

Red River of the North at Emerson, Manitoba .3 - .1 43 2,820 33 1,710 Sheyenne River

Sheyenne River at Lisbon, North Dakota 0.8 0 7.0 149 2.7 79

Sheyenne River near Kindred, North Dakota 1.6 1.7 14 182 6.2 110

Sheyenne River above Sheyenne River diversion - .2 2.5 7.0 194 3.3 111 near Horace, North Dakota

Sheyenne River at West Fargo, North Dakota - .5 3.1 9.3 183 4.0 114

were determined from equation 4, the concentration was ies within the reaches. Therefore, the median historical mea- assumed to be zero. sured concentration for all tributaries within each of the two Ranges of historical measured constituent concentrations reaches was used as the estimated concentration for the ungaged for tributaries within selected Red River model reaches were local inflow (table 10). Sample sizes used to compute the medi- compiled from Rowland and Dressler (2002) (table 9) to place ans given in table 10 differ slightly from those used by Rowland the estimated constituent concentrations for ungaged local and Dressler (2002) because of additional years of data and inflows (table 8) into the context of historical measured constit- because changes have been made to the USGS water-quality uent concentrations for the Red River Basin. For the 2003 cali- database to accommodate new methodologies and procedures. bration period, the estimated concentrations generally were Not all reaches (for example, the Red River at Hickson, within the range of historical concentrations except for the Red N. Dak., to Red River at Fargo reach) had tributaries for which River at Fargo, N. Dak., to Red River at Halstad, Minn., and historical measured concentrations were available for compari- Red River at Drayton, N. Dak., to Red River at Emerson, Man- son to concentrations for the ungaged local inflows. Therefore, itoba, reaches. For the 2004 calibration period, the estimated for those reaches, the concentrations for the ungaged local concentrations also generally were within the range of historical inflows were compared to the historical range of concentrations concentrations. For the Red River at Fargo to Red River at Hal- in adjacent reaches; agreement between the values generally stad and Red River at Drayton to Red River at Emerson reaches, was acceptable. the estimated concentrations for the 2003 calibration period Few total phosphorus concentrations are available for the may be high because of sample collection bias. High concentra- USGS sites used by Rowland and Dressler (2002). However, tions for the Red River at Halstad and the Red River at Emerson ranges of historical measured total phosphorus concentrations caused the estimated concentrations for those reaches to be sub- for many locations in the Red River Basin in addition to those stantially higher than the historical concentrations for tributar- for USGS gaging stations are given by Tornes and Brigham 22 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 .13 .10 .73 .22 .12 2004 0.38 0.49 0 .10 .17 2003 Total phosphorus Total 0 1.57 0 0 0 0 (milligrams per liter) per (milligrams 0 53 78 17 31 32 53 150 2004 0 0 24 80 180 260 175 277 2003 Dissolved sodium (milligrams per liter) per (milligrams 0 76 16 78 20 17 17 43 2004

0 0 15 74 2003 110 210 185 371 Dissolved chloride Dissolved (milligrams per liter) per (milligrams 0 0 60 570 170 130 140 180 2004 0 0 Sheyenne River 470 110 210 130 749 262 2003 Red River of the North Dissolved sulfate (milligrams per per (milligrams liter) 0 400 452 526 513 365 235 2004 1,210 0 0 465 475 2003 1,702 1,326 1,047 1,165 (milligrams per liter) (milligrams Total dissolved solids Total dissolved

1 1 Location North at Halstad, North at Estimated constituent concentrations for localungaged inflows 2003 for and 2004 calibration periods.

Dakota, to Red River of the North at North the River of Dakota, to Red Halstad, Minnesota to Red River the North of Minnesota, North Dakota at Grand Forks, North the River of Red Dakota, to North Dakota at Drayton, North at North the of River Dakota, to Red Emerson, Manitoba Lisbon, River at Dakota, to Sheyenne North Dakota North near to Sheyenne River Kindred, Dakota Dakota, to Red River of the North at North the River of Dakota, to Red Hickson, North Dakota at North the River of Dakota, to Red Dakota Fargo, North Red River of the North at Fargo, North Fargo, at the North of Red River the of Red River Forks, Grand the North at of Red River Drayton, North the North at of Red River North Dam, Baldhill below River Sheyenne at Lisbon, North Dakota, Sheyenne River Red River of the North at Wahpeton, North Wahpeton, the North at of Red River North Hickson, the North at of Red River Table 8. Table Simulation of Constituent Transport 23 .81 0 .60 Total phosphorus Total 0 (milligrams per liter) per (milligrams 0 31 0 160 Dissolved sodium (milligrams per liter) per (milligrams 0 47 tions. 0 63 Dissolved chloride Dissolved (milligrams per liter) per (milligrams 0 320 cal inflow median concentra median cal inflow 0 180 Dissolved sulfate (milligrams per per (milligrams liter) Sheyenne River—Continued Sheyenne 0 500 used to represent ungaged lo 0 568 2003 2004 2003 2004 2003 2004 2003 2004 2003 2004 (milligrams per liter) (milligrams Total dissolved solids Total dissolved

aries within this reach were

Location Estimatedconstituent concentrations for ungaged local inflows 2003 for 2004 and calibration periods.—Continued Dakota to Sheyenne River above Sheyenne River Sheyenne above to Sheyenne River diversion near Horace, North Dakota diversion near Horace, North Dakota, at to Sheyenne River West Fargo, North Historical median concentrations for tribut 1 Sheyenne River near Kindred, North Dakota, North Kindred, near Sheyenne River River Sheyenne above Sheyenne River Table 8. Table

24 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

(mg/L) Range -- -- 0.18-0.21 0.01-0.41 0.09-0.39 Total

phosphorus Number of samples of Number

2 2

-- -- 35

(mg/L) Range 19-59 5.9-59 5.3-420 8.5-330 6.0-2,100

sodium

Dissolved Number of samples of Number

54 14 97

271 211 (mg/L)

Range 3.4-34 4.5-41 2.3-180 5.4-310 1.3-3,660

chloride Dissolved Number of samples of Number

54 48 97

217 211

(mg/L) Range 56-250 35-210 49-800 11-1,200 36-1,600

sulfate

Dissolved Number of samples of Number

51 14 97

233 211

(mg/L) Range 0-761 0-666 0-2,660 0-2,060 0-8,120

solids Number of samples of Number

Total dissolved Total 320 448 350 626 Period of record of Period

1962-99

1996-2001 1966-2001 1968-2001 1971-2001 which historical data are available are data historical which

1 4 4 1 Number of tributaries within reach for reach within tributaries of Number 3 1

North at Halstad, North at Location Ranges ofRanges measured historical constituent concentrations within for tributaries selected Red River model reaches.

North Dakota, to Red River of Dakota, to Red North Dakota North Fargo, the North at River of Red Dakota, to North Minnesota Halstad, the North at River to Red of Minnesota, the North at Grand Forks, North Dakota Forks, North Dakota, to Red River of the North at Drayton, North Dakota River of Red Dakota, to North Manitoba Emerson, the North at Does not include River. the Sheyenne 1 Red River of the North at Hickson, the North at of Red River Fargo, the North at of Red River the of Red River Grand the North at of Red River Drayton, the North at of Red River Table 9. Table [From2002; and Rowland data] --, Dressler, no available

Simulation of Constituent Transport 25

(mg/L) Median 18 43

sodium

Dissolved Number of samples of Number

28 76

(mg/L) Median

chloride Dissolved Number of samples of Number

77 14

144 4.6

(mg/L) Median 72 170

sulfate

Dissolved Number of samples of Number

34 77

(mg/L) Median 318 505

Total solids

dissolved Number of samples of Number 22 77 record Period of Period 1964-2004 1972-2006

kota; and Wild butaries within selectedwithin butariesreaches. River modelRed historical data are available historical Minnesota; near Elm River Kelso, North Da Rice River at Hendrum, Minnesota Dakota Tributaries within reach for which within reach Tributaries Pembina River at Neche, North Neche, at River Pembina Buffalo River near Dilworth,

Location Median historical measured concentrations for tri

North Dakota, to Red River of Dakota, to Red North Halstad, Minnesota the North at River of Red Dakota, to North Manitoba Emerson, the North at Red River of the North at Drayton, the North at of Red River Red River of the North at Fargo, at the North of Red River Table 10.Table [From2002] and Rowland Dressler, 26 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

(1994). Except for the Red River at Wahpeton, N. Dak., to Red Halstad, Minn., and the Red River at Emerson, Manitoba. The River at Hickson, N. Dak., and Red River at Grand Forks, measured and simulated sodium concentrations for the Red N. Dak., to Red River at Drayton, N. Dak., reaches, the esti- River at Emerson for the 2003 calibration period were in closer mated total phosphorous concentrations for the ungaged local agreement than the measured and simulated chloride concentra- inflows (table 8) generally were within the range of the histori- tions for that period. For the 2003 calibration period, the aver- cal measured total phosphorus concentrations given by Tornes age absolute difference for chloride, 11 mg/L, was about 27 per- and Brigham (1994). The high estimated total phosphorus con- cent of the average measured concentration, and the average centration for the Red River at Wahpeton to Red River at Hick- absolute difference for sodium, 12 mg/L, was about 16 percent son reach seems reasonable because two major industrial plants of the average measured concentration. For the 2004 calibration release wastewater into the reach. The high concentration for period, the average absolute difference for chloride, 4 mg/L, the Red River at Grand Forks to Red River at Drayton reach also was about 16 percent of the average measured concentration, is reasonable because that reach is greatly affected by ground and the average absolute difference for sodium, 6 mg/L, was water that may have relatively high phosphorus concentrations. about 14 percent of the average measured concentration. Model results were insensitive to changes in the dispersion Total dissolved solids, sulfate, chloride, and sodium were coefficient when the coefficient ranged from zero to 10,000 simulated as conservative constituents so the only parameters ft2/s. Further testing using time-varying boundary conditions (eq. 4) estimated in the calibration process were those associ- with strong concentration gradients is needed to determine if ated with ungaged local inflows. Total phosphorus is a noncon- simulations are insensitive to the dispersion coefficient for all servative constituent and undergoes complex interactions in the conditions. water column, in bed sediments, and in living organisms. There- Total dissolved solids concentrations generally were fore, to account for the loss of phosphorus from the system as a underpredicted for both calibration periods (fig. 4). The average result of algae and plant uptake and particulate phosphorus set- difference between the measured and simulated concentrations tling to the riverbed, and in the absence of any internal inputs, was - 9.9 percent for the 2003 calibration period and - 5.5 per- total phosphorus was simulated by assuming that phosphorus cent for the 2004 calibration period. The average absolute dif- concentrations change according to a first-order decay rate. In ferences, 10.1 and 7.2 percent for the 2003 and 2004 calibration RIV1Q, decay coefficients can be specified to vary seasonally periods, respectively, were higher than the average differences. and spatially by model branch and model segment. The decay Except for the Red River at Halstad, Minn., for the 2003 cali- coefficient for the Red River probably varies seasonally, but too bration period and the Sheyenne River at Lisbon, N. Dak., for few data were available to estimate a seasonally varying decay the 2004 calibration period, all differences were within 23 per- coefficient for phosphorus. Therefore, an iterative process was cent of the measured concentrations. The magnitude of the aver- used to estimate a first-order decay coefficient for each of the age absolute differences was less for the 2004 calibration period branches in the model. The decay coefficient was used for each than for the 2003 calibration period. The differences averaged model segment in a branch because a more spatially detailed about 58 mg/L for the 2003 calibration period and 34 mg/L for approach was not justified with the small amount of available the 2004 calibration period. data. Decay coefficients of 0.01 d-1 and 0.05 d-1 were deter- Sulfate concentrations also generally were underpredicted mined for branches 1 and 2, respectively. for both calibration periods (fig. 5). The patterns for the sulfate The effects of the decay coefficients on the loss of total concentrations (for example, poor agreement between the mea- phosphorus from branches 1 and 2 were determined by express- sured and simulated concentrations for the Red River at Hal- ing the percent loss of total phosphorus as a function of the first- stad, Minn., for the 2003 calibration period and the Sheyenne order decay coefficient ()k and traveltime ()T : River at Lisbon, N. Dak., for the 2004 calibration period) were similar to those for total dissolved solids because sulfate is a Loss= () 1 – e–()k ()T 100 (5) major component of dissolved solids in the Red River. The average absolute differences, 19 and 21 percent for the 2003 and 2004 calibration periods, respectively, were about double where the average absolute differences for total dissolved solids. The k is the first-order decay coefficient, magnitude of the average absolute differences for both calibra- and tion periods, however, was less than the magnitude for total dis- T is traveltime. solved solids. The differences for sulfate averaged about 32 mg/L for the 2003 calibration period and 31 mg/L for the 2004 Assuming a decay coefficient of 0.01 d-1 and a traveltime of 7 calibration period. to 14 days for branch 1, the loss of total phosphorus from the Chloride and sodium concentrations generally were under- system is between 7 and 13 percent. This implies that the loss of predicted for both calibration periods (figs. 6 and 7). The pat- total phosphorus probably is from physical processes within the terns for both constituents were similar, but the average differ- Red River, an implication that is consistent with current (2006) ences generally were smaller for the 2004 calibration period understanding of biological and physical processes in the river. than for the 2003 calibration period. The average differences for Particle sizes in the Red River generally are very fine and sedi- the 2003 calibration period were largest for the Red River at ment losses to bed sediment probably are small because the par- Simulation of Constituent Transport 27

900

2003 Measured 800 Simulated

700

600

500

400

300

200 PER LITER S 100 RAM G 0 900

2004 Measured 800 Simulated ENTRATION, IN MILLI

C 700 ON C

600

500

400

300

200

100

0 r k, a ed, r th at th at th at e th at th at th at r r r r r r ta r e, rth n o Kind heyennec ee Pa at Lisbon, S a r itoba r r r th Dakota n o f the No f the No f the Nonesota eNo f the Nor f the No nea H ookt o rth Dakota o o th rth Dakota o o rth Dak of the No akota r r r r r rth Dakota r r r r D above a e e e of e e n, Ma th Dakota r ta at B r ks, No o r nne o r akota r rs o th o D son, No go, No ive ton, No N r si th k r me heyenne Rive o r r Red Rivc Red Riv Red RivHalstad, Min Red Riv Red Rivray Red RiveE S N th Dak o Hi Fa ed R and Fo D ive r N R r heyenne Rive d o Thompson, No G S r N heyenne Rive S ive heyenne Rive R S

Figure4. Measured and simulated total dissolved solids concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods. 28 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

350

2003 Measured Simulated 300

250

200

150

100

PER LITER 50 S RAM G 0 350

2004 Measured Simulated 300 ENTRATION, IN MILLI C ON C 250

200

150

100

0 r k, a ed, r th at th at th at e th at th at th at r r r r r r ta r e, rth n o Kind heyennec ree Pa at Lisbon, r S ra itoba r o nesota rth Dakota n H ookt f the Noth Dakota f the No f the No eNoth Dakota f the Noth Dak nea r r o r o th Dakota o th r of the No o r of the No akota r a r r r r r r r D akota above e e of e n, Ma th D r ta at B r ks, No o r nne r akota r rs o th D son, No go, No ive ton, No N r sio th k r me heyenne Rive o r r Red Rivc Red Rive Red RivHalstad, Min Red Riv Red Riveray Red RiveE S N th Dako o Hi Fa ed R and Fo D ive r N R r heyenne Rive d o Thompson, No G S r N heyenne Rive S ive heyenne Rive R S

Figure5. Measured and simulated dissolved sulfate concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods. Simulation of Constituent Transport 29

100

2003 Measured 90 Simulated

20 PER LITER S 10 RAM G 0 100

2004 Measured 90 Simulated

ENTRATION, IN MILLI 80 C ON C 70

0 r k, a ed, r th at th at th at e th at th at th at r r r r r r ta r e, rth n o Kind heyennec ee Pa at Lisbon, S a r itoba r r r th Dakota n f the No f the Nonesota eNo f the Nor f the No nea Ho ookt o rth Dakota of the No o th rth Dakota o o rth Dak of the No akota r r r r r rth Dakota r r r r D above a e e e of e e n, Ma th Dakota r ta at B r ks, No o r nne o r e r rs o th o son, No go, No iv ton, No N r si th Dakota k r me heyenne Rive o r r Red Rivc Red Riv Red RivHalstad, Min Red Riv Red Rivray Red RiveE S N th Dak Hi Fa ed R and Fo D ive r No R r heyenne Rive d o Thompson, No G S r N heyenne Rive S ive heyenne Rive R S

Figure6. Measured and simulated dissolved chloride concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods. 30 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

160

2003 Measured

140 Simulated

120

100

40 PER LITER

S 20 RAM G 0 160

2004 Measured

140 Simulated ENTRATION, IN MILLI C

ON 120 C

100

ar at rk, e red, rth at rth at rth at rth at rth rth at th n o e, r kota Kind heyennec ree Pa a at Lisbon, r S ra D itoba r o nesota rth Dakota n H ookt f the Noth Dakota f the No f the No eNoth Dakota f the No th nea r r o r o th Dakota o th r o of ther N of the No akota r a r r r r r r r D akota above e e e of e e n, Ma th D r ta at B r ks, No o r nne o r akota r rs o th o D son, No go, No ive ton, No N r si th k r me heyenne Rive o r r Red Rivc Red Riv Red RivHalstad, Min Red Riv Red Rivray Red RiveE S N th Dak o Hi Fa ed R and Fo D ive r N R heyenne Rive d o Thompson, No Gr S r N heyenne Rive S ive heyenne Rive R S

Figure7. Measured and simulated dissolved sodium concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods. Simulation of Constituent Transport 31 ticles become resuspended. In more than half of the suspended Houston Engineering, written commun., 2006). This estimated sediment samples for the Red River at Emerson, Manitoba, 98 time series of total dissolved solids concentrations then was percent of the sediment was finer than sand (Tornes and used as an unsteady upstream boundary condition for one sim- Brigham, 1994). Also, the Red River is turbid and phytoplank- ulation. In a second simulation, this same time series of total ton growth is light-limited (Heiskary and Markus, 2003) so dissolved solids was used for the Red River at Wahpeton and phosphorus loss to algae and aquatic plants probably is small. for all inflows between the Red River at Wahpeton and the Red For the Sheyenne River, a decay coefficient of 0.05 d-1 and a River at Fargo (the Red River at Wahpeton, the Wahpeton traveltime of 4 to 7 days resulted in a loss of total phosphorus wastewater-treatment facility, the Wild Rice River in North from the system of between 18 and 30 percent. The Sheyenne Dakota, the Fargo-Moorhead water-treatment facility, and the River is shallower and, therefore, not as light-limited as the Red two ungaged local inflows between Wahpeton and Fargo). Sim- River. As a result, the amount of phosphorus lost to plant and ulation results indicate total dissolved solids concentrations are algae uptake probably is greater than that for the Red River. sensitive to assumed boundary conditions (fig. 9). The change However, the loss still is considered to be small and, as for the from time-invariant boundary conditions used for model cali- Red River, probably is related to resuspension of fine particles bration to unsteady upstream boundary conditions had a large on which phosphorus is adsorbed. For the Sheyenne River at effect on the magnitude of the simulated concentrations for the Lisbon, N. Dak., in 18 of 25 suspended sediment samples col- Red River at Fargo although the temporal distribution of total lected from 1977 to 1995, 98 percent of the sediment was finer dissolved solids was similar for both sets of boundary condi- than sand. tions (fig. 9). Unsteady boundary conditions for the gaged trib- Total phosphorus concentrations generally were underpre- utary inflows and the ungaged local inflows not only affected dicted for both calibration periods (fig. 8). The average differ- the magnitude of the simulated concentrations for the Red River ence between the measured and simulated concentrations was at Fargo but also the relative temporal distribution. For exam- 6.2 percent for the 2003 calibration period and - 24 percent for ple, the simulation using time-invariant boundary conditions the 2004 calibration period. The average absolute differences, and the simulation using unsteady upstream boundary condi- 23 and 29 percent for the 2003 and 2004 calibration periods, tions showed relatively large increases in concentration begin- respectively, were higher than the average differences. The ning about September 18, 2003, but the simulation using all magnitude of the average absolute difference was less for the unsteady boundary conditions showed only a small increase in 2003 calibration period than for the 2004 calibration period. concentration at that time. The differences averaged about 0.034 mg/L for the 2003 cali- Constituent concentrations for the ungaged local inflows bration period and 0.082 mg/L for the 2004 calibration period. also were not known because of the small amount of water- quality data. Therefore, the concentrations were calculated using a simplified mass-balance approach (eq. 4). Simulations Model Testing of chemical constituent concentrations during unsteady-flow conditions are highly dependent on accurate estimates of the Model testing was conducted to determine the effects of magnitude and timing of chemical loads contributed by the small amount of water-quality data on model calibration. ungaged local inflows. The method used to estimate the concen- Because few water-quality data are available for the gaging trations for the ungaged local inflows resulted in good agree- locations used for the calibration, water-quality boundary con- ment between measured and simulated streamflows, but, unlike ditions were not known. Therefore, to calibrate the model, time- for the water-quality boundary conditions, continuous records invariant boundary conditions of measured and estimated con- of streamflow were available to develop the estimates. stituent concentrations (tables 5, 8, and 10) were used for the The percentages of the total simulated constituent loads unsteady-flow simulations. The effects of the assumed bound- contributed by estimated ungaged local inflows are given in ary conditions on simulated concentrations was demonstrated table 11 for the 2003 and 2004 calibration periods. Generally, by comparing results from the calibrated model to results simu- the reaches for which the percentages were the highest were the lated using (1) unsteady total dissolved solids upstream bound- upstream reaches—the Red River at Wahpeton, N. Dak., to Red ary conditions for the Red River at Wahpeton, N. Dak., and River at Hickson, N. Dak., reach and the Red River at Hickson steady total dissolved solids boundary conditions for tributaries to Red River at Fargo, N. Dak., reach. The drainage area and ungaged local inflows and (2) unsteady total dissolved sol- between Wahpeton and Hickson increases less than 5 percent (a ids boundary conditions for the Red River at Wahpeton and relatively small increase), but no gaged tributaries are located unsteady total dissolved solids boundary conditions for tributar- within the reach. The drainage area between Hickson and Fargo ies and ungaged local inflows. increases 37 percent, but the Wild Rice River, a major gaged The upstream boundary condition for the Red River at tributary, is located within that reach. Other than for the Red Wahpeton, N. Dak., was estimated from measured daily mean River at Wahpeton to Red River at Hickson and Red River at specific-conductance values for the Red River at Fargo, N. Dak. Hickson to Red River at Fargo reaches, which were highly The values were converted to total dissolved solids concentra- affected by the assumed boundary conditions for the Red River tions by using a conversion factor of 0.65, which is an average at Wahpeton, estimated ungaged local inflows generally con- conversion factor for the Red River Basin (M. Deutschman, tributed less than about 35 percent of the total conservative- 32 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

0.6

2003 Measured Simulated 0.5

0.4

0.3

0.2

0.1 PER LITER S RAM G

0 0.6

2004 Measured Simulated 0.5 ENTRATION, IN MILLI C ON C

0.4

0.3

0.2

0.1

0 r k, a ed, r th at th at th at e th at th at th at r r r r r r ta r e, rth n o Kind heyennec ree Pa at Lisbon, r S ra itoba r o nesota rth Dakota n H ookt f the Noth Dakota f the No f the No eNoth Dakota f the No f the Noth Dak nea r r o r o th Dakota o th r o o r of the No akota r a r r r r r r r D akota above e e e of e e n, Ma th D r ta at B r ks, No o r nne o r akota e r rs o th son, No go, No iv ton, No N r sio th D k r me heyenne Rive o r r Red Rivc Red Riv Red RivHalstad, Min Red Riv Red Rivray Red RiveE S N th Dak o Hi Fa ed R and Fo D ive r N R r heyenne Rive d o Thompson, No G S r N heyenne Rive S ive heyenne Rive R S

Figure8. Measured and simulated total phosphorus concentrations for selected Red River model calibration points for 2003 and 2004 calibration periods. Simulation of Constituent Transport 33

900

800

700

600

500

400

300 CONCENTRATION, IN MILLIGRAMS PER LITER 200 Time-invariant total dissolved solids boundary conditions for model calibration Unsteady total dissolved solids upstream boundary conditions 100 Unsteady total dissolved solids boundary conditions for all inputs

0 5 10 15 20 25 30 5 10 15 20 25 30 5 10 15 20 25 30 AUGUST SEPTEMBER OCTOBER 2003

Figure 9. Simulated total dissolved solids concentrations for the Red River of the North at Fargo, North Dakota, for three sets of boundary conditions.

constituent load in a reach. Ungaged local inflows also contrib- Model Application uted a smaller part of the total constituent load during the 2004 calibration period, when streamflows in the river were high, The calibrated Red River model was used to simulate the than during the 2003 calibration period. relative effects of six water-supply alternatives identified by the Model testing indicated that improved point-by-point Bureau of Reclamation (table 1) on water quality in the Red agreement between measured and simulated concentrations can River and the Sheyenne River. Boundary conditions were spec- be obtained by adjusting boundary conditions for rivers, tribu- ified for April 1, 1976, through August 31, 1977. However, taries, and ungaged flows. Such a model, however, would be because April 1 through August 31, 1976, was used as an ini- considered “overtuned” and would be applicable only to the tialization period, simulation results for the alternatives were very specific conditions for which the model was calibrated compared for September 1, 1976, through August 31, 1977. (Bales and others, 2001). The Red River model provided good Streamflows throughout the Red River Basin during September simulations of streamflow throughout the model domain. 1976 through August 1977 were relatively low (table 3). Based Therefore, a reasonable assumption is that simulations made on the period of record, 1942-94, for the Red River at Fargo, using more realistic and complete boundary condition informa- N. Dak., the minimum mean streamflow for a 7-consecutive- tion than used for this study would provide better results than day period can be expected to be equal to or less than 17.9 ft3/s those obtained during the study. Also, the Red River model an average of once every 10 years. This statistic often is referred demonstrates a sensitivity to changes in boundary conditions so to as the 7Q10 streamflow. Streamflows for the Red River at a reasonable assumption is that the model can be used to com- Fargo were less than the 7Q10 streamflow on 159 days during pare relative effects of various water-supply alternatives. September 1976 through August 1977. Monthly average streamflows for the Red River at Grand Forks, N. Dak., and the Red River at Emerson, Manitoba, were less than 30 percent of the respective long-term average monthly streamflows for those 34 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 6 9 0 11 11 33 15 11 2004 (percent) 0 0 0 0 0 35 25 100 2003 Total phosphorus Total 4 7 7 0 18 18 34 16

2004 iods. (percent) 9 3 0 0 3.2 12 74 62 2003 Dissolved sodium 6 7 6 0 28 20 33 14 2004 (percent) 2 0 0 1 35 24 70 73 2003 Dissolved chloride Dissolved 3 0 4 9 7 0 17 18 2004 (percent) Sheyenne River 6 0 0 8 15 18 36 50 2003 Red River of the North Dissolved sulfate 7 7 0 2 4 15 18 10 2004 (percent) 5 0 0 5 12 25 27 36 2003 Total dissolved solids Total dissolved

Location North at Halstad, North at Percentage ofPercentage total simulated constituent load by contributed estimated local ungaged inflows for 2003 and 2004 calibration per

Dakota, to Red River of the North at North the River of Dakota, to Red Halstad, Minnesota to Red River the North of Minnesota, North Dakota at Grand Forks, North the River of Red Dakota, to North Dakota at Drayton, North at North the of River Dakota, to Red Emerson, Manitoba Lisbon, River at Dakota, to Sheyenne North Dakota North near to Sheyenne River Kindred, Dakota Dakota, to Red River of the North at North the River of Dakota, to Red Hickson, North Dakota at North the River of Dakota, to Red Dakota Fargo, North Red River of the North at Fargo, North Fargo, at the North of Red River the of Red River Forks, Grand the North at of Red River Drayton, North the North at of Red River North Dam, Baldhill below River Sheyenne at Lisbon, North Dakota, Sheyenne River Red River of the North at Wahpeton, North Wahpeton, the North at of Red River North Hickson, the North at of Red River Table 11.Table Simulation of Constituent Transport 35 0 19 (percent) 0 20 Total phosphorus Total 0 5 riods.—Continued (percent) 0 7 Dissolved sodium 0 18 (percent) 0 9.9 Dissolved chloride Dissolved 0 12 (percent) 0 3 Dissolved sulfate Sheyenne River—Continued Sheyenne 0 7 (percent) 0 4 2003 2004 2003 2004 2003 2004 2003 2004 2003 2004 Total dissolved solids Total dissolved

Location of Percentage total simulated constituent load by contributed estimated local ungaged inflows for 2003 and 2004 calibration pe Dakota to Sheyenne River above Sheyenne River Sheyenne above to Sheyenne River diversion near Horace, North Dakota diversion near Horace, North Dakota, at to Sheyenne River West Fargo, North Sheyenne River near Kindred, North Dakota, North Kindred, near Sheyenne River River Sheyenne above Sheyenne River Table 11.Table 36 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 locations for 11 of the 12 months between September 1976 and flows were disaggregated into daily streamflows by using 1976- August 1977. 77 historical daily tributary streamflows. StateMod also pro- Several minor modifications were made to the model grid duces a monthly streamflow gain and loss value for each reach. to accommodate the water-supply alternatives. Return flows That value, rather than the value estimated from equation 4, was and withdrawals for Fargo, West Fargo, and Grand Forks, used to represent ungaged local inflows because all other N. Dak., and Moorhead, Minn., were represented in the model streamflow boundary conditions for the model were generated as well as return flows and withdrawals for Wahpeton Industrial by StateMod. StateMod-generated monthly ungaged local use. Wahpeton Industrial is used herein as a generic term that inflows were disaggregated into daily inflows by using 1976-77 represents existing industries and potential future industries in historical daily inflows for the tributary nearest to the ungaged the Wahpeton, N. Dak., area. Also, point-source withdrawals local inflow input location. were added immediately upstream from the return flows for To offset operational limitations, StateMod simulations Wahpeton and West Fargo to account for withdrawals from the included the assumption that the monthly water-supply demand Red River at river mile 545 for Wahpeton Industrial use and for a municipality was equal to the peak daily demand that from the Sheyenne River at river mile 28.1 for West Fargo. occurred each day of the month. This assumption resulted in Withdrawals for Wahpeton and West Fargo were not included frequent periods of zero daily flow during the model application in the model because ground water is the current (2006) water- period for the Red River at Fargo, N. Dak., and periods of rela- supply source for those cities. Another withdrawal was added tively low flow (less than 5 ft3/s) for the Sheyenne River at West immediately upstream from the Grand Forks return flow at river Fargo, N. Dak., for some of the water-supply alternatives. mile 290.8 to account for the North Dakota In-Basin Alternative These occurrences are mathematically acceptable within an (table 1). Finally, Fargo and Moorhead return flows were sepa- accounting software like StateMod, but the algorithms within rated for the alternative simulations. the RIV1 modeling system would not allow for multiple Streamflow boundary conditions for the water-supply instances of zero flow. Therefore, to maintain numerical stabil- alternative simulations were provided by the Bureau of Recla- ity in the Red River model, a minimal amount of streamflow mation (A. Schlag, Bureau of Reclamation, written commun., was added upstream from the withdrawals on the Red River and 2006). The streamflows were generated by the Bureau of Rec- the Sheyenne River. Through a trial-and-error process, between lamation using the surface-water model StateMod. StateMod is 1 and 20 ft3/s of streamflow was added to the Red River and a monthly and daily water allocation and accounting model that between 5 and 15 ft3/s of streamflow was added to the Sheyenne is used for comparative analysis of various historical and future River. These additional streamflow amounts were considered water policies for a river basin (State of Colorado, 2004). State- by project partners to be reasonable to offset the operational Mod was used to superimpose projected 2050 water demands assumptions made for StateMod. The same volume of water on naturalized flows in the Red River Basin. The resulting flows was added for each of the alternative simulations. Limited sen- and water-source volumes for each community then were used sitivity analysis was conducted using the Red River Basin to develop upstream streamflow boundary conditions and return Alternative to determine the effects of the additional streamflow boundary conditions for the included communities. Those flows on simulated constituent concentrations because no addi- results were used in the Red River model with September 1976 tional flows were required for that alternative to maintain model through August 1977 streamflows to simulate the effects of the stability for branch 2. Therefore, two simulations—one without alternatives on water quality in the Red River and the Sheyenne additional streamflow and one with additional stream- River, flow—could be compared. Median concentrations for the Red StateMod-generated monthly streamflows were disaggre- River at Emerson, Manitoba, were reduced by 0.2 percent or gated into daily streamflows for the Red River model. Daily less for all constituents because of the additional streamflow patterns for 2006 withdrawals for Moorhead, Minn., were used (table 12). For the Sheyenne River at West Fargo, which is to disaggregate 2050 monthly withdrawals for Fargo and West immediately downstream from where additional streamflows Fargo, N. Dak., and Moorhead, and daily patterns for 2006 were input, median concentrations were reduced in relation to withdrawals for Grand Forks, N. Dak., were used to disaggre- those for the base condition by about 1 to 5 percent for all con- gate 2050 monthly withdrawals for Grand Forks. Thus, for stituents. example, if 3 percent of the October 2006 monthly total with- Historical water-quality data for the 1976-77 simulation drawal for Moorhead occurred on October 1, the assumption period were not available. Therefore, stochastically generated was made that 3 percent of the 2050 monthly total withdrawal constituent concentrations for the upstream boundary condi- for the water-quality alternative simulations occurred on Octo- tions, the tributaries, and the return flows for all water-supply ber 1. Upstream streamflow boundary conditions for the Red alternatives were provided by Houston Engineering (M. Deut- River at Wahpeton, N. Dak., and the Sheyenne River below schman, Houston Engineering, written commun., 2006) under Baldhill Dam, N. Dak., were synchronized with downstream contract to the Bureau of Reclamation. Probability distributions withdrawals by disaggregating the StateMod-generated were fit to the measured concentrations for locations for which monthly streamflows for those locations into daily streamflows a sufficient amount of data was available. Data were grouped based on 2006 daily withdrawals for Moorhead and West Fargo, for locations that had a small amount of available data; grouping respectively. StateMod-generated monthly tributary stream- was based on geographic location. The probability distributions Simulation of Constituent Transport 37

Table 12. Change in median constituent concentrations as a result of additional streamflow required to maintain model stability.

Total Dissolved Dissolved Dissolved Total dissolved Location sulfate chloride sodium phosphorus solids (percent) (percent) (percent) (percent) (percent)

Red River at Emerson, Manitoba - 0.2 - 0.1 0 0 0

Sheyenne River at West Fargo, North Dakota - 1.3 - 4.4 - 5.3 - 3.1 - 1.0

were stochastically sampled using a Monte Carlo approach, and Effects of Water-Supply Alternatives on Total Dissolved the probability distribution of 3 years of stochastically gener- Solids, Sulfate, Chloride, Sodium, and Total Phosphorus ated daily concentrations was compared to the measured probability distribution. In all but one case, the statistics of the mea- The effects of the water-supply alternatives on water sured and stochastically generated distributions were similar, quality in the Red River and the Sheyenne River during low- indicating the stochastic approach provided a reasonable flow conditions that approximated those that existed in 1976-77 approximation to the measured concentrations. The stochastic were evaluated by comparing the effects of five of the alterna- approach was used to generate water-quality boundary condi- tives relative to the No-Action Alternative. Results of the water- tions for the Red River at Wahpeton, N. Dak., and for all tribu- supply alternative simulations for selected locations are pre- tary inflows. The approach also was used for the boundary con- sented using notched box plots that summarize statistical infor- ditions for the Sheyenne River below Baldhill Dam, N. Dak. mation for the simulated annual concentration distribution for (branch 2), for four of the water-supply alternatives. Because each of five constituents. water is imported into Lake Ashtabula for the North Dakota In- Each notched box plot (see, for example, fig. 10) shows Basin Alternative and for the Garrison Diversion Unit Import to several statistics for the simulated annual concentration distribution for a particular water-supply alternative and a particular Sheyenne River Alternative, stochastically generated historical location. The box plots include the median, 25th and 75th per- water-quality conditions for the Sheyenne River below Baldhill centiles, maximum and minimum values, and outliers for the Dam would not necessarily represent the conditions that result simulated daily mean concentration for the 1976-77 simulation from those two alternatives. Boundary conditions for the Shey- period. The notches in each box plot represent the 95-percent enne River below Baldhill Dam for the two interbasin alterna- confidence interval for the simulated annual median concentra- tives were estimated by using a simple mixing model for Lake tion. If the notches for a selected alternative overlap the notches Ashtabula in which imported constituent loads were conserva- for the No-Action Alternative at the same location for a given tively mixed with Lake Ashtabula water to estimate concentra- constituent, then the selected alternative probably will have no tions for below the dam (M. Deutschman, Houston Engineer- effect relative to the No-Action Alternative on the annual ing, written commun., 2006). median concentration for that constituent for that location. Con- Return flow concentrations were estimated from source versely, if the notches for a selected alternative do not overlap concentrations and current (2006) wastewater-treatment tech- the notches for the No-Action Alternative, then the selected nology (M. Deutschman, Houston Engineering, written com- alternative probably will result in a change in the annual median mun., 2006). A factor that accounted for the combined effects concentration relative to the annual median concentration for of water and wastewater treatment on the source water was the No-Action Alternative. Simulation results are given for the Red River at river mile 536.3, which is immediately down applied to the different source-water qualities for each alterna- - stream from the Wahpeton Industrial return flow (fig. 10), and tive to compute a time series of volume-weighted average con- for the Red River at Fargo, N. Dak. (fig. 11), the Red River at centrations for each return flow location (M. Deutschman, Grand Forks, N. Dak. (fig. 12), the Red River at Emerson, Man- Houston Engineering, written commun., 2006). Because no his- itoba (fig. 13), the Sheyenne River below Baldhill Dam, torical information on ungaged local inflow concentrations is N. Dak. (fig. 14), and the Red River at West Fargo, N. Dak. available to estimate those boundary conditions, time-invariant (fig. 15). It is important to remember that (1) results are pre- concentrations estimated for the low-flow 2003 calibration sented for extremely low flow conditions, (2) changes in annual period (table 8) were used as the ungaged local inflow boundary median concentrations likely will be less for higher flow condi- conditions. Streamflows added to maintain model stability, as tions, and (3) results are reported relative to the No-Action previously described, were assumed to have constituent con- Alternative rather than as actual expected annual median concentrations of zero. centrations. 38 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

2,000 600 800

500

1,500 600

PER LITER 400 S PER LITER PER LITER S S RAM G RAM RAM G G

, IN MILLI 1,000 300 400 S OLID S ULFATE, IN MILLI HLORIDE, IN MILLI S C OLVED

SS 200 OLVED OLVED SS SS DI 500 DI 200 TOTAL DI

100

0 0 0 S S S NA I IP NA IB NA NDIB RRB DU DU ND RRB DUI DUIP NDIB RRB DUI DUIP G G MRIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Outlier--Values greater than 75th percentile plus Outlier 1.5 times interquartile range or less than 25th Largest value not considered an percentile minus 1.5 times interquartile range outlier; maximum if no outliers exist

Percentile--Percentage of analyses equal to or 75th percentile less than individual values Upper limit 95-percent confidence interval for median Interquartile range--Upper quartile, or Median 75th percentile, minus lower quartile, Lower limit 95-percent confidence interval for median or 25th percentile 25th percentile 95-percentconfidence interval for median--An estimated range of values, calculated from Smallest value not considered an sample data, that probably includes the outlier; minimum if no outliers exist unknown population median. The width of the Outlier confidence interval indicates the degree of uncertainty in the estimated population median. No-Action Alternative (NA) The confidence coefficient, 0.95, indicates that, North Dakota In-Basin Alternative (NDIB) if sampling is repeated, 95 percent of the Red River Basin Alternative (RRB) confidence intervals will contain the actual Garrison Diversion Unit ImporttoSheyenne River Alternative (GDUIS) population median Garrison Diversion Unit Import Pipeline Alternative (GDUIP) Missouri River Import to Red River Valley Alternative (MRIP)

Figure 10. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at river mile 536.3 immediately downstream from the Wahpeton Industrial return flow, 1976-77 simulation period. Simulation of Constituent Transport 39

50 8

6 PER LITER PER LITER S S 30 RAM RAM G G

4 , IN MILLI S

ODIUM, IN MILLI 20 PHORU S S OLVED SS DI TOTAL PHO 2

0 0 S S NA I IP NA NDIB RRB DU DU NDIB RRB DUI DUIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

1,400 400 400

1,200

300 300 1,000 PER LITER S PER LITER PER LITER S S RAM G RAM RAM G

800 G

, IN MILLI 200 200 S OLID

S 600 ULFATE, IN MILLI HLORIDE, IN MILLI S C OLVED SS OLVED OLVED

400 SS SS DI 100 DI 100 TOTAL DI

200

0 0 0 S S S NA IB I IP NA IB NA ND RRB DU DU ND RRB DUI DUIP NDIB RRB DUI DUIP G G MRIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 11. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Fargo, North Dakota, 1976-77 simulation period. Simulation of Constituent Transport 41

100 3

2.5 80

2 PER LITER PER LITER S S 60 RAM RAM G G

1.5 , IN MILLI S

ODIUM, IN MILLI 40 PHORU S S

1 OLVED SS DI TOTAL PHO

20 0.5

0 0 S S NA IB I IP NA ND RRB DU DU NDIB RRB DUI DUIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 11. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Fargo, North Dakota, 1976-77 simulation period--Continued. 42 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

1,200 400 50

1,000 40

300

PER LITER 800 S PER LITER PER LITER S S RAM

G 30 RAM RAM G G

, IN MILLI 600 200 S OLID S

ULFATE, IN MILLI 20 HLORIDE, IN MILLI S C OLVED

SS 400 OLVED OLVED SS SS DI 100 DI TOTAL DI

10 200

0 0 0 S S S NA I IP NA NA NDIB RRB DU DU NDIB RRB DUI DUIP NDIB RRB DUI DUIP G G MRIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 12. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Grand Forks, North Dakota, 1976-77 simulation period. Simulation of Constituent Transport 43

100 2

1.5 PER LITER PER LITER S S 60 RAM RAM G G

1 , IN MILLI S

ODIUM, IN MILLI 40 PHORU S S OLVED SS DI TOTAL PHO 0.5

0 0 S S NA I IP NA NDIB RRB DU DU NDIB RRB DUI DUIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 12. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Grand Forks, North Dakota, 1976-77 simulation period--Continued. 44 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

1,000 800 200

800

600 150 PER LITER S PER LITER PER LITER S S RAM

G 600 RAM RAM G G

, IN MILLI 400 100 S OLID S

400 ULFATE, IN MILLI HLORIDE, IN MILLI S C OLVED SS OLVED OLVED SS SS DI 200 DI 50 TOTAL DI

200

0 0 0 S S S NA IB I IP NA IB NA ND RRB DU DU ND RRB DUI DUIP NDIB RRB DUI DUIP G G MRIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure13. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Emerson, Manitoba, 1976-77 simulation period. Simulation of Constituent Transport 45

140 10

120

100 PER LITER PER LITER S S 6 RAM RAM

80 G G , IN MILLI S 60

ODIUM, IN MILLI 4 PHORU S S OLVED

SS 40 DI TOTAL PHO

0 0 S S NA IB I IP NA ND RRB DU DU NDIB RRB DUI DUIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure13. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at Emerson, Manitoba, 1976-77 simulation period--Continued. 46 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

2,000 400 40

1,500 300 30 PER LITER S PER LITER PER LITER S S RAM G RAM RAM G G

, IN MILLI 1,000 200 20 S OLID S ULFATE, IN MILLI HLORIDE, IN MILLI S C OLVED SS OLVED OLVED SS SS DI 500 100 DI 10 TOTAL DI

0 0 0 S S S NA I IP NA IB NA NDIB RRB DU DU ND RRB DUI DUIP NDIB RRB DUI DUIP G G MRIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 14. Simulated annual concentration distribution of daily mean concentrations for the Sheyenne River below Baldhill Dam, North Dakota, 1976-77 simulation period. Simulation of Constituent Transport 47

200 2

150 1.5 PER LITER PER LITER S S RAM RAM G G

100 1 , IN MILLI S ODIUM, IN MILLI PHORU S S OLVED SS DI 50 TOTAL PHO 0.5

0 0 S S NA IB I IP NA ND RRB DU DU NDIB RRB DUI DUIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 14. Simulated annual concentration distribution of daily mean concentrations for the Sheyenne River below Baldhill Dam, North Dakota, 1976-77 simulation period--Continued. 48 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

1,000 400 100

800 80

300 PER LITER S PER LITER PER LITER S S RAM

G 600 60 RAM RAM G G

, IN MILLI 200 S OLID S

400 ULFATE, IN MILLI 40 HLORIDE, IN MILLI S C OLVED SS OLVED OLVED SS SS DI 100 DI TOTAL DI

200 20

0 0 0 S S S NA IB I IP NA IB NA ND RRB DU DU ND RRB DUI DUIP NDIB RRB DUI DUIP G G MRIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 15. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at West Fargo, North Dakota, 1976-77 simulation period. Simulation of Constituent Transport 49

140 0.4

120

0.3 100 PER LITER PER LITER S S RAM RAM

80 G G

0.2 , IN MILLI S 60 ODIUM, IN MILLI PHORU S S OLVED

SS 40 DI TOTAL PHO 0.1

0 0 S S NA IB I IP NA ND RRB DU DU NDIB RRB DUI DUIP G G MRIP G G MRIP ALTERNATIVE

EXPLANATION

Figure 15. Simulated annual concentration distribution of daily mean concentrations for the Red River of the North at West Fargo, North Dakota, 1976-77 simulation period--Continued. 50 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Simulated annual median concentrations for the Red River median total dissolved solids, sulfate, sodium, and total phos- at river mile 536.3 are noticeably greater for the action alterna- phorus concentrations for the Red River Basin Alternative are tives than for the No-Action Alternative for all simulated con- either not statistically different from or are less than those for stituents (fig. 10). This is because of the combination of smaller the No-Action Alternative. Constituent loads from Fargo and return flows and lower return flow concentrations for Wahpeton Moorhead return flows are, again, the reason for this result. For Industrial with the No-Action Alternative than with the action example, the combined sulfate load from Fargo and Moorhead alternatives. In StateMod, the No-Action Alternative was the for the Red River Basin Alternative is 28 percent less than that only alternative allowed to have water shortages, and, for the for the No-Action Alternative. Simulated annual median total No-Action Alternative, an approximate 75-percent shortage dissolved solids, sulfate, and total phosphorus concentrations occurred in the water supply for Wahpeton Industrial for the North Dakota In-Basin Alternative are less than those for (D. Goetzfried, Bureau of Reclamation, oral commun., 2006). the No-Action Alternative. This is, again, the result of consid- This water shortage corresponds to the smaller return flows for erably smaller loads from return flows for Fargo and Moorhead Wahpeton Industrial with the No-Action Alternative and the for the North Dakota In-Basin Alternative than for the No- Red River model. The action alternatives had a larger native- Action Alternative. water-to-return-flow ratio than the No-Action Alternative. In Generally, the three interbasin alternatives resulted in an addition, average return flow concentrations for Wahpeton increase in simulated annual median total dissolved solids, sul- Industrial for the No-Action Alternative were lower than those fate, and sodium concentrations for the Red River at Emerson, for the action alternatives because source waters used to com- Manitoba, relative to those for the No-Action Alternative pute return flow concentrations did not contain any ground (fig. 13). In contrast, the North Dakota In-Basin Alternative and water that had elevated constituent concentrations. the Red River Basin Alternative either had no effect on the sim- Simulated annual median concentrations for the Red River ulated annual median total dissolved solids, sulfate, and sodium at Fargo, N. Dak., are statistically greater for the action alterna- concentrations or caused a reduction in the concentrations rela- tives than for the No-Action Alternative for all constituents tive to those for the No-Action Alternative. Of the action alter- except sodium (fig. 11). The higher annual median concentra- natives, two had a slight effect on annual median chloride con- tions for the action alternatives are a result of the return flow centrations relative to the No-Action Alternative. The assumptions previously discussed for the No-Action Alterna- interquartile ranges for chloride and the annual median chloride tive. Simulated annual median sodium concentrations for the concentrations for all alternatives are similar. This similarity North Dakota In-Basin Alternative and the Red River Basin probably is a result of water contributed from the Forest and Alternative are not statistically different from that for the No- Park Rivers to the Red River between Grand Forks, N. Dak., Action Alternative. The relatively high sodium concentrations and Emerson. Water in the Forest and Park Rivers is poor in contributed from ungaged local inflows to the Red River at quality, primarily as a result of ground-water discharge, and Fargo resulted in median concentrations that are similar for all those tributaries contribute large chloride loads to the Red River alternatives. within the Red River at Grand Forks to Red River at Emerson Return flows for Fargo, N. Dak., and Moorhead, Minn., reach. For example, about half of the chloride load in the reach and for several tributaries, including the Sheyenne River and between Grand Forks and Emerson is attributed to the Forest Red Lake River, enter the Red River between Fargo and Grand and Park Rivers. Simulated annual median total phosphorus Forks, N. Dak. In general, the interquartile ranges for the Red concentrations for all action alternatives are significantly less River at Grand Forks are small and maximum concentrations than that for the No-Action Alternative. Simulated total phos- are low relative to those for other sites (fig. 12) largely because phorus concentrations are controlled largely by return flow con- of the inflow of relatively good quality water from the Red Lake centrations from Grand Forks. The simulated total phosphorus River. Relative differences between simulated concentrations load for the return flow for Grand Forks for the No-Action for the No-Action Alternative and the action alternatives for the Alternative was between 140 and 240 percent greater than the Red River at Grand Forks are affected by return flows for Fargo loads for the action alternatives. The source water at Grand and Moorhead. Simulated annual median total dissolved solids, Forks for the No-Action Alternative was assumed to be domi- sulfate, chloride, and sodium concentrations for the Garrison nated by return flows for Fargo, N. Dak., and Moorhead, Minn., Diversion Unit Import to Sheyenne River Alternative, Garrison thus causing a compounding effect on concentrations for the Diversion Unit Import Pipeline Alternative, and Missouri River return flow for Grand Forks. The action alternatives had addi- Import to Red River Valley Alternative are statistically greater tional source water that diluted the return flows for Fargo and than the corresponding annual median concentrations for the Moorhead. No-Action Alternative. These differences are the result of the Simulated concentrations for the Sheyenne River below upstream return flows for Wahpeton Industrial for the No- Baldhill Dam, N. Dak., represent the effects of mixing of Action Alternative and the large constituent loads from return upstream boundary conditions for branch 2 with the concentra- flows for Fargo and Moorhead. For example, the combined tions for one model segment downstream from the dam. As pre- sodium load from return flows for Fargo and Moorhead for the viously noted, the same time series of stochastically generated Garrison Diversion Unit Import Pipeline Alternative is nearly boundary conditions for the Sheyenne River below Baldhill triple that for the No-Action Alternative. Simulated annual Dam was used for the No-Action Alternative, the Red River Simulation of Constituent Transport 51

Basin Alternative, the Garrison Diversion Unit Import Pipeline streamflows for each alternative (table 13). Except for total Alternative, and the Missouri River Import to Red River Valley phosphorus, simulated loads for the Garrison Diversion Unit Alternative, but a different set of boundary conditions, which Import to Sheyenne River Alternative were about 20 to 40 per- takes into account inputs from Lake Ashtabula, was used for the cent greater than those for the No-Action Alternative. This dif- North Dakota In-Basin Alternative and the Garrison Diversion ference resulted, in part, from the minimum instream flow for Unit Import to Sheyenne River Alternative. Therefore, all sim- aquatic life that was incorporated into the Garrison Diversion ulated annual median constituent concentrations for the Red Unit Import to Sheyenne River Alternative. The minimum River Basin Alternative, the Garrison Diversion Unit Import instream flow resulted in streamflows that were about 14 per- Pipeline Alternative, and the Missouri River Import to Red cent higher for the Garrison Diversion Unit Import to Sheyenne River Valley Alternative are the same as those for the No- River Alternative than those for the No-Action Alternative. In Action Alternative (fig. 14). The North Dakota In-Basin Alter- general, the simulated annual loads for total dissolved solids, native had no statistically significant effect on simulated annual sulfate, and sodium were higher for alternatives that include median sodium concentrations but resulted in a statistically sig- interbasin transfer of water than for the No-Action Alternative. nificant increase in simulated annual median total dissolved sol- For the North Dakota In-Basin Alternative, loads for all constit- ids, chloride, and total phosphorus concentrations relative to uents were either less than or about the same as those for the No- those for the No-Action Alternative. Simulated annual median Action Alternative. This corresponds, in part, to the lower sulfate concentrations are lower for the North Dakota In-Basin streamflows for that alternative in relation to those for the No- Alternative than for the No-Action Alternative. The Garrison Action Alternative. Diversion Unit Import to Sheyenne River Alternative either had Annual constituent loads for the Red River at Emerson, no effect on or caused a decrease in simulated annual median Manitoba, were estimated using LOADEST and available his- total dissolved solids, chloride, and total phosphorus concentra- torical data (Runkel and others, 2004) for comparison with the tions relative to those for the No-Action Alternative. Simulated September 1976 through August 1997 simulated loads. Water- annual median sulfate and sodium concentrations are greater for quality data for the Red River at Emerson were unavailable the Garrison Diversion Unit Import to Sheyenne River Alterna- before 1978, so the annual loads (by water year) were estimated tive than for the No-Action Alternative. for 1978-2001. Those loads were used for comparison with sim- Boundary conditions within the Sheyenne River below ulated September 1976 through August 1977 loads for the six Baldhill Dam, N. Dak., to Sheyenne River at West Fargo, water-supply alternatives. N. Dak., reach were the same for all alternatives. As a result, the Between 1978 and 2000, the largest estimated annual load Red River Basin Alternative, the Garrison Diversion Unit for all constituents occurred in 1997 when annual runoff for the Import Pipeline Alternative, and the Missouri River Import to Red River at Emerson, Manitoba, was 9,285,000 acre-ft Red River Valley Alternative had no statistically significant (table 14). Annual runoff for the Red River at Emerson during effect on simulated annual median total dissolved solids, sul- water year 1997 was the highest on record. The smallest esti- fate, chloride, and sodium concentrations relative to those for mated annual load for sulfate and sodium occurred in 1981 the No-Action Alternative for the Sheyenne River at West when annual runoff for the Red River at Emerson was 875,900 Fargo (fig. 15). In contrast, those alternatives caused a decrease acre-ft, and the smallest estimated annual load for total dis- in simulated annual median total phosphorus concentrations rel- solved solids, chloride, and total phosphorus occurred in 1990 ative to those for the No-Action Alternative. This decrease is a when annual runoff for the Red River at Emerson was 727,000 result of less streamflow in the Sheyenne River for those alter- acre-ft. The annual runoffs for 1981 and 1990 were each almost natives than for the No-Action Alternative. The smaller double the annual runoff of 436,700 acre-ft for 1977. The long- amounts of streamflow resulted in a longer traveltime and, thus, term mean annual runoff for the Red River at Emerson is more time for phosphorus decay. The North Dakota In-Basin 2,897,000 acre-ft, and the lowest annual runoff between 1912 Alternative either had no statistically significant effect on or and 2005 occurred in 1934. A comparison of estimated loads for caused a decrease in simulated annual median sulfate, chloride, 1981 and 1990 and simulated loads for 1976-77 indicates the and sodium concentrations relative to those for the No-Action simulated loads for the water-supply alternatives generally are Alternative. Simulated annual median total dissolved solids and within the range of historical loads and, thus, seem reasonable. total phosphorus concentrations are statistically higher for the Total phosphorus loads for the alternatives are noticeably North Dakota In-Basin Alternative than for the No-Action higher than the upper limit 95-percent confidence interval for Alternative. The Garrison Diversion Unit Import to Sheyenne 1990, but total phosphorus loads are well below the average River Alternative either had no effect on or caused a decrease in estimated annual load for 1978-2001. simulated annual median total dissolved solids, chloride, and Simulated results for the six water-supply alternatives are total phosphorus concentrations relative to those for the No- affected by return flow concentrations. This is illustrated by the Action Alternative. Simulated annual median sulfate and total phosphorus loads and concentrations for the No-Action sodium concentrations for that alternative increased relative to Alternative relative to those for the action alternatives for the those for the No-Action Alternative. Red River at Emerson, Manitoba (table 13, fig. 13). Total phos- Annual constituent loads for the Red River at Emerson, phorus loads are much greater for the No-Action Alternative Manitoba, were estimated from simulated concentrations and relative to those for the action alternatives as a result of the 52 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Table 13. Annual constituent loads for the Red River of the North at Emerson, Manitoba, for water-supply alternatives.

[Simulated annual runoff for 1976-77 was 471,600 acre-feet for the No-Action Alternative, 457,100 acre-feet for the North Dakota In-Basin Alternative, 475,600 acre-feet for the Red River Basin Alternative, 535,600 acre-feet for the Garrison Diversion Unit Import to Sheyenne River Alternative, 515,000 acre-feet for the Garrison Diversion Unit Import Pipeline Alternative, and 527,200 acre-feet for the Missouri River Import Pipeline to Red River Valley Alternative]

Annual load1 (tons)

Garrison Missouri Diversion Garrison Constituent River Import North Dakota Red River Unit Diversion No-Action Pipeline to In-Basin Basin Import to Unit Import Alternative Red River Alternative Alternative Sheyenne Pipeline Valley River Alternative Alternative Alternative

Total dissolved solids 291,000 278,000 290,000 351,000 335,000 328,000

Dissolved sulfate 108,000 84,600 93,800 149,000 150,000 133,000

Dissolved chloride 28,500 29,500 28,700 33,400 32,300 28,900

Dissolved sodium 32,800 31,700 31,000 47,000 46,000 40,100

Total phosphorus 1,110 744 856 740 640 741

1Simulated concentrations and streamflows from the Red River model were used to estimate annual constituent loads.

assumption that, for the No-Action Alternative, source water to sodium concentration for the Missouri River at Bismarck is 59 Grand Forks, N. Dak., is dominated by return flows for Fargo, mg/L, and the historical median for the Red River at Fargo is 14 N. Dak., and Moorhead, Minn. Thus, the native-water-to- mg/L (M. Deutschman, Houston Engineering, written com- return-flow ratio was smaller for the action alternatives than for mun., 2006). the No-Action Alternative, causing return flows for Grand Forks to have elevated total phosphorus concentrations. Effects of the water-supply alternatives on water quality in the Red River and Sheyenne River can be grouped by the source of the Model Limitations water transfer. For instance, alternatives that involve the transfer of water from within the Red River Basin (the North Dakota Although the Red River model includes several limitations In-Basin Alternative and the Red River Basin Alternative) and assumptions, the model provides insight into the effects tended to have total dissolved solids, sulfate, sodium, and total of the water-supply alternatives on water quality in the Red phosphorus loads and concentrations that were about the same River and the Sheyenne River. Stochastically generated con- or less than those for the No-Action Alternative (table 13, centrations for upstream and tributary boundary conditions figs. 10 through 15). In contrast, alternatives that involve the were used in the Red River model because a time series of his- transfer of water from the Missouri River Basin (the Garrison torical data was unavailable and because too few historical data Diversion Unit Import to Sheyenne River Alternative, the Gar- were available to develop water-quality boundary conditions rison Diversion Unit Import Pipeline Alternative, and the Mis- deterministically through flow-concentration relations. The use souri River Import to Red River Valley Alternative) tended to of stochastically generated concentrations introduced certain have higher sulfate and sodium loads and concentrations than limitations relative to interpretation of the results. The time those for the No-Action Alternative (table 13, figs. 10 through series of simulated concentrations for the modeled alternatives 15). These tendencies seem reasonable because the Missouri was not used in the analysis of the effects of the various water- River tends to have higher sulfate and sodium concentrations supply alternatives, and conclusions could not be made about than the Red River. The historical median sulfate concentration the seasonal effects of the various alternatives on concentra- of 172 mg/L for the Missouri River at Bismarck, N. Dak., is tions. As a result, the simulated annual median concentrations much larger than the historical median sulfate concentration of for each alternative were compared to determine if a selected 61 mg/L for the Red River at Fargo (M. Deutschman, Houston alternative was expected to result in a change relative to the No- Engineering, written commun., 2006). The historical median Action Alternative.

Model Limitations 53

confidence interval confidence

Upper limit 95-percent limit Upper

confidence interval confidence Lower limit 95-percent limit Lower (tons)

Average annual load annual Average 2001. load Annual 1,740 1,540 1,940 570,000144,000 544,000152,000 138,000 597,000 147,000 150,000 157,000

2,170,000 2,120,000 2,210,000 confidence interval confidence

312 Upper limit 95-percent limit Upper

69,800 57,000

544,000 122,000 confidence interval confidence

224 Lower limit 95-percent limit Lower ter year 1997] year ter (tons) 97,800 54,000 47,500 494,000

Minimum annual Minimum annual load Annual load Annual 192

60,200 51,200

486,000 109,000

confidence interval confidence

Upper limit 95-percent limit Upper

confidence interval confidence Lower limit 95-percent limit Lower (tons)

Maximum annual load Maximum Annual load Annual 6,330 3,510 10,500 276,000 211,000327,000 266,000 354,000 398,000

1,570,000 1,210,000 2,000,000 5,070,000 4,490,000 5,720,000 Year in which minimum occurred minimum which in Year

1981 1990 1981 1990 1990 Year in which maximum occurred maximum which in Year 1997 1997 1997 1997 1997 Maximum, minimum, and estimated average annual constituent loads for the River of the Red Emerson, North at Manitoba, for 1978-

Constituent Dissolved sulfate Dissolved chloride Dissolved sodium Total phosphorus Total dissolved Total dissolved solids Table 14.Table wa for acre-feet 9,285,000 and 1981, year water for acre-feet 875,900 year 1990, water for acre-feet 727,000 was runoff [Annual 54 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04

Total phosphorus concentrations for the ungaged local Summary inflows were estimated in the same manner as the concentrations for the conservative constituents (eq. 4). Because equation 4 does not take into account first-order decay, total phosphorus Population growth along with possible future droughts in concentrations for the ungaged local inflows were slightly the Red River of the North (Red River) Basin in North Dakota, underestimated. To account for first-order decay, equation 4 Minnesota, and South Dakota will create an increasing need for could have been modified to the following equation: reliable water supplies. Therefore, the Dakota Water Resources Act of 2000 authorized a comprehensive study of future water needs in the basin in North Dakota and of possible options to C (6) meet those water needs. As part of the comprehensive study, the Bureau of Reclamation identified eight water-supply alternatives, including a No-Action Alternative, for the Red River Val- DS C – ()US C e–kL + I C e–kL()– T – W C = ------XL+ DS X US XT+ I X ------W- ley Water Supply Project. Of those eight alternatives, two were –kL()– A QXA+ e removed from consideration for this study. Of the remaining six alternatives, three include the interbasin transfer of water. where To address concerns of stakeholders and to provide infor- k is the first-order decay coefficient as in equation 5. mation for an environmental impact statement, the U.S. Geo- logical Survey, in cooperation with the Bureau of Reclamation, Equation 6 accounts for the decay of total phosphorus according developed and applied a water-quality model to simulate the to the various lag times. The available time for the upstream transport of total dissolved solids, sulfate, chloride, sodium, and input to decay before reaching the downstream point is L days. total phosphorus during unsteady-flow conditions and to simu- Similarly, the available times for known tributary inputs and late the effects of the six water-supply alternatives on water ungaged inputs to decay before reaching the downstream point quality in the Red River and the Sheyenne River. The model, are LT– and LA– , respectively. If all lag times are zero or if hereinafter referred to as the Red River model, was developed no decay occurred, k = 0; then, e0 is equal to 1.0 and using the RIV1 modeling system, which is a one-dimensional equation 6 reverts to equation 4. A difficulty in using equation 6 (cross-sectionally averaged), hydrodynamic, water-quality is that an iterative process would be required because the cali- model originally released in 1991 by the U.S. Army Corps of brated value of k must be known before the concentrations for Engineers, Waterways Experiment Station, as CE-QUAL- the ungaged local inflows are estimated. Also, equation 6 RIV1. The RIV1 modeling system was updated to run in a Win- noticeably increases the estimated concentrations only if the lag dows environment in 2002 and subsequently was called EPD- times are substantial in relation to the reactive time scale of the RIV1. The EPD-RIV1 modeling system, which includes a pre- nonconservative constituent. For total phosphorus in these sim- and post-processor to facilitate model application and data anal- ulations, a reasonable reactive time scale can be approximated ysis, was used in this study. by its first-order half-life. If, for example, a decay coefficient of The physical domain of the Red River model includes the 0.2 d-1 was applied, the first-order half-life would be 3.5 days. Red River from Wahpeton, North Dakota, to Emerson, Mani- This reactive time scale is substantial in comparison to a typical toba, and the Sheyenne River from below Baldhill Dam, North lag time ()LA– of 2 days (table 6). In equation 6, if a decay Dakota, to the confluence with the Red River. Inputs to the coefficient of 0.2 d-1 and a lag time of 2 days are used, the model included gaged inflows from the Sheyenne River and 12 e–kL()– A in the denominator alone would cause the concentra- tributaries to the Red River, ungaged local inflows for 10 tions for the ungaged local inflows to be underestimated by ungaged areas, return flows from 6 point-source wastewater- 50 percent. However, for the Red River model, where decay treatment facilities, and withdrawals from 3 water-treatment coefficients of 0.01 d-1 and 0.05 d-1 were applied, the first-order facilities. half-life of phosphorus was 69 and 14 days, respectively. Those Boundary conditions were specified for May 15 through values are not substantial relative to the typical lag time of October 31, 2003, and January 15 through June 30, 2004. The 2 days. As a result, for decay coefficients of 0.01 d-1 and first 2.5 months were used as an initialization period. Data –kL()– A 0.05 d-1 and a lag time of 2 days in equation 6, e in the obtained from long-term records of streamflow for 27 stream denominator causes the concentrations for the ungaged local gage sites were used as boundary conditions for model calibra- inflows to be slightly underestimated at 2 and 10 percent, tion and testing. Water-quality data for model calibration and respectively. These percentages are considered to be within the testing were collected at selected stream gage sites as well as at acceptable error for a measured sample. six ungaged sites during September 2003 when streamflows Many of the Red River model limitations that have been were low and steady and May 2004 when streamflows were discussed could be eliminated by a consistent long-term water- medium and unsteady. Measured streamflow data were avail- quality data set that could be used to provide known boundary able for August 1 through October 31, 2003, and April 1 conditions for the model. This data set could allow for more through June 30, 2004 (the calibration periods), but water-qual- constituents to be simulated and could allow for more realistic ity data were available only for September 15 through 16, 2003, simulation of the transport of nonconservative constituents. and May 10 through 13, 2004. The water-quality boundary con- Summary 55 ditions were assumed to be time invariant for the entire calibra- average absolute difference for chloride, 11 mg/L, was about tion period and to be equal to the measured value. 27 percent of the average measured concentration, and the aver- The Red River model was calibrated by adjusting selected age absolute difference for sodium, 12 mg/L, was about boundary conditions, model parameters, and channel-geometry 16 percent of the average measured concentration. For the 2004 data to obtain reasonable agreement between measured and calibration period, the average absolute difference for chloride, simulated streamflows and concentrations. Streamflow was cal- 4 mg/L, was about 16 percent of the average measured concen- ibrated by adjusting model parameters, channel geometry, esti- tration, and the average absolute difference for sodium, 6 mg/L, mates of ungaged local inflows, and Manning’s n to obtain rea- was about 14 percent of the average measured concentration. sonable agreement between measured and simulated values. Total phosphorus was simulated as a nonconservative constitu- The estimates (both timing and magnitude) of the ungaged local ent by assuming that concentrations change according to a first- inflows to the Red River and the Sheyenne River had a large order decay rate. In RIV1Q, decay coefficients can be specified effect on simulated streamflows. Simulated streamflows for to vary seasonally and spatially by model branch and model selected model calibration points were in reasonable agreement segment. However, because too few data were available to jus- with measured streamflows for the 2003 (low-flow) and 2004 tify varying the decay coefficient seasonally or by model seg- (medium-flow) calibration periods. The average difference ment, decay coefficients were varied by branch. Decay coeffi- between the measured and simulated streamflows was less than cients of 0.01 d-1and 0.05 d-1were determined for branch 1 4 percent for both periods, and most differences were less than (Red River) and branch 2 (Sheyenne River), respectively. The 2 percent. In general, streamflows for the 2003 calibration smaller decay coefficient for the Red River resulted in a smaller period were somewhat underpredicted, and streamflows for the loss of total phosphorus than that for the Sheyenne River. The 2004 calibration period were slightly overpredicted. However, larger loss of total phosphorus for the Sheyenne River than for the average differences between the measured and simulated the Red River is supported by known physical and biological streamflows are considered to be acceptable because the differ- processes in the rivers. Total phosphorus concentrations gener- ences are less than 5 percent, or the same as the error that would ally were underpredicted for both calibration periods. The aver- be expected in a typical streamflow measurement. Further age difference between the measured and simulated concentra- refinement of local inflow estimates probably would improve tions was 6.2 percent for the 2003 calibration period and -24 predictions, but these refinements are not justified by the rela- percent for the 2004 calibration period. tively small streamflow prediction errors or by the future Model testing was conducted to determine the effects of intended application of the model. the small amount of water-quality data on model calibration. For the water-quality calibration, constituent concentra- Because few water-quality data are available for the gaging tions for the ungaged local inflows were estimated and two locations used for the calibration, water-quality boundary con- model variables, the dispersion coefficient and a first-order ditions were not known. Therefore, time-invariant boundary decay coefficient for total phosphorus, were adjusted. The con- conditions were used for the unsteady-flow simulations. The stituent concentrations for the ungaged local inflows were esti- change from time-invariant boundary conditions to unsteady mated using a modified version of the equation used to calculate upstream boundary conditions had a large effect on the magni- ungaged local inflow. The estimated concentrations for the tude of simulated total dissolved solids concentrations for the ungaged local inflows then were compared to ranges of histori- Red River at Fargo, North Dakota, although the temporal distri- cal measured constituent concentrations. Except for two bution of total dissolved solids was similar for both sets of reaches, the estimated concentrations for the 2003 calibration boundary conditions. Also because of the small amount of period generally were within the range of historical concentra- water-quality data, constituent concentrations for the ungaged tions for the tributaries within each reach. For the two excep- local inflows were not known. Therefore, the concentrations tions, the median historical measured concentration was used as were calculated using a simplified mass-balance approach. the estimated concentration for the ungaged local inflow. For Simulations of chemical constituent concentrations during the 2004 calibration period, the estimated concentrations also unsteady flow conditions are highly dependent on accurate esti- generally were within the range of historical concentrations. mates of the magnitude and timing of chemical loads. The Total dissolved solids concentrations generally were method used to estimate the concentrations for the ungaged underpredicted for both calibration periods. The average differ- local inflows resulted in good agreement between measured and ence between the measured and simulated concentrations was simulated streamflows, but, unlike for the water-quality bound- - 9.9 percent for the 2003 calibration period and - 5.5 percent for ary conditions, continuous records of streamflow were avail- the 2004 calibration period. Sulfate concentrations also gener- able to develop the estimates. ally were underpredicted for both calibration periods. The aver- Model testing indicated that improved point-by-point age absolute differences, 19 and 21 percent for the 2003 and agreement between measured and simulated concentrations can 2004 calibration periods, respectively, were about double the be obtained by adjusting boundary conditions for rivers, tribu- average absolute percent differences for total dissolved solids. taries, and ungaged flows. Such a model, however, would be Chloride and sodium concentrations generally were underpre- considered “overtuned” and would be applicable only to the dicted for both calibration periods, and the patterns for both very specific conditions for which the model was calibrated. constituents were similar. For the 2003 calibration period, the The Red River model provided good simulations of streamflow 56 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 throughout the model domain. Therefore, a reasonable assump- centrations for model boundaries. Return flow concentrations tion is that simulations made using more realistic and complete were estimated from source concentrations and current (2006) boundary condition information than used for this study would wastewater-treatment technology. Because no historical infor- provide better results than those obtained during the study. mation on ungaged local inflow concentrations is available to Also, the Red River model demonstrates sensitivity to changes estimate those boundary conditions, time-invariant concentra- in boundary conditions so a reasonable assumption is that the tions for the low-flow 2003 calibration period were used as the model can be used to compare relative effects of various water- ungaged local inflow boundary conditions. supply alternatives. The effects of the water-supply alternatives on water qual- The calibrated Red River model was used to simulate the ity in the Red River and the Sheyenne River were evaluated by relative effects of the six water-supply alternatives identified by comparing the effects of five of the alternatives relative to the the Bureau of Reclamation on water quality in the Red River No-Action Alternative. Simulated annual median concentra- and the Sheyenne River. Boundary conditions were specified tions for the Red River at river mile 536.3, downstream from for April 1, 1976, through August 31, 1977. However, because Wahpeton, North Dakota, are noticeably greater for the action April 1 through August 31, 1976, was used as an initialization alternatives than for the No-Action Alternative for all simulated period, simulation results for the alternatives were compared for constituents. This results from the combination of smaller September 1, 1976, through August 31, 1977. Streamflows return flows and lower return flow concentrations for Wahpeton throughout the Red River Basin during September 1976 Industrial with the No-Action Alternative than with the action through August 1977 were relatively low. Streamflows for the alternatives. Simulated annual median concentrations for the Red River at Fargo, North Dakota, were less than 17.9 cubic Red River at Fargo, North Dakota, are statistically greater for feet per second on 159 days of that 12-month period. Monthly the action alternatives than for the No-Action Alternative for all average streamflows for the Red River at Grand Forks, North constituents except sodium. The relatively high sodium concen- Dakota, and the Red River at Emerson, Manitoba, were less trations contributed from ungaged local inflows to the Red than 30 percent of the respective long-term average monthly River at Fargo resulted in median concentrations that are similar streamflows for 11 of the 12 months between September 1976 for all alternatives. and August 1977. Return flows for Fargo, North Dakota, and Moorhead, Streamflow boundary conditions for the water-supply Minnesota, and inflow from the Red Lake River affect simu- alternative simulations were provided by the Bureau of Recla- lated concentrations for the Red River at Grand Forks, North mation. The streamflows were generated by the Bureau of Rec- Dakota. In general, the interquartile ranges for the Red River at lamation using the surface-water model StateMod. StateMod Grand Forks are small and maximum concentrations are low was used to superimpose projected 2050 water demands on nat- relative to those for other sites largely because of the inflow of uralized flows in the Red River Basin. The resulting flows and relatively good quality water from the Red Lake River. For the water-source volumes then were used to develop upstream Red River at Grand Forks, simulated annual median total dis- streamflow boundary conditions and return flow boundary con- solved solids, sulfate, chloride, and sodium concentrations for ditions and those results were used in the Red River model with the Garrison Diversion Unit Import to Sheyenne River, Garri- September 1976 through August 1977 streamflows to simulate son Diversion Unit Import Pipeline, and Missouri River Import the effects of the alternatives on water quality in the Red River to Red River Valley Alternatives are greater than the corre- and the Sheyenne River. StateMod-generated monthly stream- sponding annual median concentrations for the No-Action flows were disaggregated into daily streamflows for the Red Alternative. For the Red River Basin Alternative, simulated River model by using daily patterns for 2006 withdrawals and annual median total dissolved solids, sulfate, sodium, and total streamflow. Monthly streamflow gains and losses produced by phosphorus concentrations are either not statistically different StateMod for each reach were used to represent ungaged local from or are less than those for the No-Action Alternative. For inflows. Because StateMod-generated streamflows were some- the North Dakota In-Basin Alternative, simulated annual times equal to zero, a minimal amount of streamflow was added median total dissolved solids, sulfate, and total phosphorus con- upstream from the withdrawals on the Red River and the Shey- centrations are less than those for the No-Action Alternative. enne River to maintain numerical stability of the model. Lim- The differences between the action alternatives and the No- ited sensitivity analysis indicated the additional water caused Action Alternative are largely the result of return flows for concentrations immediately downstream from where the addi- Fargo and Moorhead. tional streamflows were input to be reduced by about 1 to For the Red River at Emerson, Manitoba, the three interba- 5 percent. sin alternatives resulted in an increase in simulated annual Constituent concentrations for upstream boundary condi- median total dissolved solids, sulfate, and sodium concentrations, tributaries, and return flows for all water-supply alterna- tions relative to those for the No-Action Alternative. In contrast, tives were provided by an engineering consulting firm under the North Dakota In-Basin and Red River Basin Alternatives contract to the Bureau of Reclamation. Water-quality boundary either had no effect on the simulated annual median total dis- conditions were generated using a stochastic approach in which solved solids, sulfate, and sodium concentrations or caused a probability distributions derived from all available historical reduction in the concentrations relative to those for the No- data on instream concentrations were used to produce daily con- Action Alternative. The interquartile ranges for chloride and the Summary 57 annual median chloride concentrations for all alternatives are Alternative in relation to those for the No-Action Alternative, similar, probably as a result of poor quality water from tributar- loads for all constituents were either less than or about the same ies between Grand Forks, North Dakota, and Emerson. Because as those for the No-Action Alternative. of assumptions about the return flow concentrations for Grand Annual constituent loads for the Red River at Emerson, Forks, simulated annual median total phosphorus concentra- Manitoba, were estimated for 1978-2001 using LOADEST and tions for the Red River at Emerson for all action alternatives are available historical data. Estimated constituent loads for 1981 significantly less than that for the No-Action Alternative. and 1990, years with little annual runoff, were compared to sim- For the Sheyenne River below Baldhill Dam, North ulated loads for 1976-77 for the six water-supply alternatives. Dakota, simulated annual median constituent concentrations for The comparison indicates the simulated loads generally are the Red River Basin, Garrison Diversion Unit Import Pipeline, within the range of historical loads, and, thus, seem reasonable. and Missouri River Import to Red River Valley Alternatives are Total phosphorus loads for the alternatives are noticeably the same as those for the No-Action Alternative because those higher than the upper limit 95-percent confidence interval for alternatives have no effect on Lake Ashtabula water quality. 1990, but total phosphorus loads are well below the average The North Dakota In-Basin Alternative resulted in a statistically estimated annual load for 1978-2001. significant increase in simulated annual median total dissolved Simulated results for the six water-supply alternatives are solids, chloride, and total phosphorus concentrations relative to affected by return flow concentrations. This is illustrated by the those for the No-Action Alternative. The Garrison Diversion total phosphorus loads and concentrations for the No-Action Unit Import to Sheyenne River Alternative either had no effect Alternative relative to those for the action alternatives for the on or caused a decrease in simulated annual median total dis- Red River at Emerson, Manitoba. Effects of the water-supply solved solids, chloride, and total phosphorus concentrations rel- alternatives on water quality in the Red River and the Sheyenne ative to those for the No-Action Alternative. River can be grouped by the source of water transfer. Alterna- Because boundary conditions within the Sheyenne River tives that involve the transfer of water from within the Red below Baldhill Dam, North Dakota, to Sheyenne River at West River Basin (the North Dakota In-Basin and Re River Basin Fargo, North Dakota, reach were the same for all alternatives, Alternatives) tended to have total dissolved solids, sulfate, simulated annual median total dissolved solids, sulfate, chlo- sodium, and total phosphorus concentrations that were about ride. and sodium concentrations for the Sheyenne River at West the same or less than those for the No-Action Alternative. In Fargo for the Red River Basin, Garrison Diversion Unit Import contrast, consistent with median sulfate and sodium loads and Pipeline, and Missouri River Import to Red River Valley Alter- concentrations in the Missouri River, alternatives that involve natives are not statistically different from those for the No- the transfer of water from the Missouri River Basin (the Garri- Action Alternative. In contrast, because of longer traveltime, son Diversion Unit Import to Sheyenne River, Garrison Diver- those alternatives caused a decrease in simulated annual median sion Unit Import Pipeline, and Missouri River Import to Red total phosphorus concentrations. The North Dakota In-Basin River Valley Alternatives) tended to have higher sulfate and Alternative either had no statistically significant effect on or sodium loads and concentrations than those for the No-Action caused a decrease in simulated annual median sulfate, chloride, Alternative. and sodium concentrations relative to those for the No-Action The Red River model includes several limitations and Alternative, and simulated annual median total dissolved solids assumptions; however, the model provides insight into the and total phosphorus concentrations for the North Dakota In- effects of the water-supply alternatives on water quality in the Basin Alternative are statistically higher than those for the No- Red River and the Sheyenne River. Because of few historical Action Alternative. The Garrison Diversion Unit Import to data, stochastically generated concentrations were used in the Sheyenne River Alternative either had no effect on or caused a Red River model for boundary conditions. The use of stochas- decrease in simulated annual median total dissolved solids, tically generated concentrations limited interpretation of the chloride, and total phosphorus concentrations relative to those results. The time-series of simulated concentrations for the for the No-Action Alternative. Simulated annual median sulfate modeled alternatives was not used in the analysis of the effects and sodium concentrations for that alternative increased relative of the various water-supply alternatives, and conclusions could to those for the No-Action Alternative. not be made about the seasonal effects of the various alterna- Except for total phosphorus, simulated constituent loads tives on concentrations. As a result, the simulated annual for the Red River at Emerson, Manitoba, for the Garrison Diver- median concentrations for each alternative were compared to sion Unit Import to Sheyenne River Alternative were about 20 determine if a selected alternative was expected to result in a to 40 percent greater than those for the No-Action Alternative. change relative to the No-Action Alternative. Total phosphorus This difference resulted, in part, from the minimum instream concentrations for the ungaged local inflows were estimated in flow for aquatic life that was incorporated into the Garrison the same manner as the concentrations for the conservative con- Diversion Unit Import to Sheyenne River Alternative. In gen- stituents. As a result, total phosphorus concentrations for the eral, the simulated annual loads for total dissolved solids, sul- ungaged local inflows were slightly underestimated at 2 and 10 fate, and sodium were higher for alternatives that include inter- percent. However, those percentages are considered to be basin transfer of water than for the No-Action Alternative. within the acceptable error for a measured sample. A long-term Because of lower streamflows for the North Dakota In-Basin water-quality data set could eliminate many of the Red River 58 Simulation of Constituent Transport in the Red River of the North Basin, 1977 and 2003-04 model limitations and could allow for more constituents to be Runkel, R.L., Crawford, C.G., and Cohn, T.A., 2004, Load simulated and for more realistic simulation of the transport of Estimator (LOADEST)—A FORTRAN program for nonconservative constituents. estimating constituent loads in streams and rivers: Techniques of Water Resources Investigations of the U.S. Geological Survey, book 4, chap. A5, 69 p. 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