U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2008–5007

Prepared in cooperation with the North Dakota Department of Health, 

the Minnesota Pollution Control Agency, and the cities of Fargo, North Dakota, 

and Moorhead, Minnesota

Calibration of a Water-Quality Model for Low-Flow 

Conditions on the Red River of the North at Fargo, 

North Dakota, and Moorhead, Minnesota, 2003
Cover photograph: Injecting dye at a site downstream from the Moorhead, Minnesota, wastewater-treatment plant outfall on the

Red River of the North, September 24, 2003.
Calibration of a Water-Quality Model for 

Low-Flow Conditions on the Red River 

of the North at Fargo, North Dakota, and 

Moorhead, Minnesota, 2003

By Robert F. Lundgren and Rochelle A. Nustad

Prepared in cooperation with the North Dakota Department of Health, 

Minnesota Pollution Control Agency, and cities of Fargo, North Dakota, and 

Moorhead, Minnesota

Scientific Investigations Report 2008–5007

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: 2008

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Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Lundgren, R.F., and Nustad, R.A., 2008, Calibration of a water-quality model for low-flow conditions on the Red River 

of the North at Fargo, North Dakota, and Moorhead, Minnesota, 2003: U.S. Geological Survey Scientific Investigations 

Report 2008–5007, 41 p.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................2

Study Reach...........................................................................................................................................2

Methods...........................................................................................................................................................6

Data-Collection Network.....................................................................................................................6

Channel-Geometry and Streamflow Data.........................................................................................6

Traveltime Data and Reaeration-Rate Coefficients.........................................................................8

Water Sample Collection and Analysis...........................................................................................16

Model Implementation................................................................................................................................24

Computational Grid.............................................................................................................................24

Streamflow and Water-Quality Boundary Conditions...................................................................24

Model Calibration and Testing...................................................................................................................24

Streamflow and Transport.................................................................................................................24

Water Quality.......................................................................................................................................29

Model Testing ......................................................................................................................................35

Summary........................................................................................................................................................36

References....................................................................................................................................................40

Figures

1–2. Maps showing:

1. Location of Red River of the North Basin ........................................................................3

2. Location of sites used in study..........................................................................................4

3. Graph showing daily mean streamflow at Red River of the North at Fargo, 

North Dakota, gaging station (05054000) for September 15 through 30, 2003.....................6

4–5. Photographs showing:

4. Injecting dye at a site downstream from the Moorhead, Minnesota, 

wastewater-treatment plant outfall on the Red River of the North, 

September 24, 2003............................................................................................................12

5. Self-Contained Underwater Fluorescence Apparatus (SCUFA)................................12

6–8. Graphs showing:

6. Dye concentration in relation to traveltime for sites 4, 5, 5.7, 6, 7, 9.5, 

and 10 on the Red River of the North..............................................................................13

7. Traveltime of dye cloud centroid in relation to streamflow at the 

Red River of the North at Fargo, North Dakota, gaging station (05054000)..............14

8. Reaeration-rate coefficient as a function of streamflow for the Red River 

of the North 30.8-mile reach from Fargo, North Dakota, to Georgetown, 

Minnesota, April and October 1990 and September 2003...........................................15

9. Photograph showing Moorhead, Minnesota, wastewater-treatment plant 

outfall during September 24 through 27, 2003, streamflows................................................23

10. Schematic of the Fargo Water-Quality Analysis Simulation Program model...................25
iv

11–12. Graphs showing:

11. Measured and simulated dye concentrations for Fargo Water-Quality 

Analysis Simulation Program model calibration sites 5.7, 7, and 10 for 

September 24 through 27, 2003........................................................................................28

12. Measured and simulated dye concentrations for Fargo Water-Quality 

Analysis Simulation Program model calibration sites 5, 6, and 9.5 for 

September 24 through 27, 2003........................................................................................28

13. Diagram showing state variable interactions for nutrient cycles and dissolved 

oxygen in U.S. Environmental Protection Agency’s Water Quality Simulation 

Program........................................................................................................................................30

14–18. Graphs showing:

14. Maximum, mean, and minimum measured dissolved-oxygen and 

ammonia concentrations for calibration (September 24 through 27, 

2003) data set and average simulated concentrations for Fargo 

Water-Quality Analysis Simulation Program model calibration sites.......................32

15. Maximum, mean, and minimum measured ultimate carbonaceous 

biochemical oxygen demand concentrations for calibration (September 24 

through 27, 2003) data set and average simulated concentrations for 

Fargo Water-Quality Analysis Simulation Program model calibration sites............33

16. Maximum, mean, and minimum measured nitrate and organic nitrogen 

concentrations for calibration (September 24 through 27, 2003) data set 

and average simulated concentrations for Fargo Water-Quality Analysis 

Simulation Program model calibration sites .................................................................34

17. Maximum, mean, and minimum measured dissolved-oxygen concentrations for August 29–30, 1989, and August 14–15, 1990, data sets and 

average simulated concentrations for Fargo Water-Quality Analysis 

Simulation Program model data set for sites 4, 5, 6, and 7 .........................................37

18. Maximum, mean, and minimum measured ammonia concentrations for 

August 29–30, 1989, and August 14–15, 1990, data sets, and average 

simulated concentrations for Fargo Water-Quality Analysis Simulation 

Program model data set for sites 4, 5, 6, and 7 .............................................................38

Tables

1. Description of sites used in 2003 study.....................................................................................7

2. Streamflow data for the Red River of the North, September 24 through 27, 2003 .............8

3. Traveltime data for the Red River of the North, September 24 through 27, 2003 .............10

4. Reaeration-rate coefficients for the Red River of the North, September 24 

through 27, 2003 ..........................................................................................................................11

5. Properties and constituents for which water samples were analyzed.............................17

6. Statistical summaries for selected field property values and constituent 

concentrations for the Red River of the North, September 24 through 27, 2003..............18

7. Comparison of wastewater-treatment plant effluent water-quality data at 

different sampling locations for Fargo, North Dakota and Moorhead, 

Minnesota ....................................................................................................................................22

8. Estimated hydraulic coefficients for power functions used in Fargo 

Water-Quality Analysis Simulation Program model..............................................................27
v

9. Calibrated hydraulic coefficients used in power function equations for the 

Fargo Water-Quality Analysis Simulation Program model ..................................................27

10. Goodness-of-fit statistics for calibration of transport..........................................................27

11. Model parameters used for Fargo Water-Quality Analysis Simulation 

Program model............................................................................................................................31

12. Percent change in dissolved oxygen concentration as a result of a 50-percent 

increase in selected model parameters .................................................................................35

13. Measured and simulated traveltimes for streamflows from the Wesolowski 

(1994) study and the 2003 study................................................................................................36

14. Selected water-quality constituent concentrations in effluent from the 

Moorhead and Fargo wastewater treatment plants before and after 

addition of tertiary treatment to convert ammonia to nitrate..............................................39

Conversion Factors and Datum

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Flow rate

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Mass

pound per day (lb/d) 0.4536 kilogram per day (kg/d)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Concentrations of chemical constituents are given in milligrams per liter (mg/L) or micrograms 

per liter (μg/L).
Calibration of a Water-Quality Model for Low-Flow 

Conditions on the Red River of the North at Fargo, 

North Dakota, and Moorhead, Minnesota, 2003

By Robert F. Lundgren and Rochelle A. Nustad

Abstract

A time-of-travel and reaeration-rate study was conducted 

by the U.S. Geological Survey, in cooperation with the North 

Dakota Department of Health, the Minnesota Pollution 

Control Agency, and the cities of Fargo, North Dakota, and 

Moorhead, Minnesota, to provide information to calibrate a 

water-quality model for streamflows of less than 150 cubic 

feet per second. Data collected from September 24 through 

27, 2003, were used to develop and calibrate the U.S. Environmental Protection Agency Water Quality Analysis Simulation 

Program model (hereinafter referred to as the Fargo WASP 

water-quality model) for a 19.2-mile reach of the Red River of 

the North.

The Fargo WASP water-quality model was calibrated for 

the transport of dye by fitting simulated time-concentration 

dye curves to measured time-concentration dye curves. Simulated peak concentrations were within 10 percent of measured 

concentrations. Simulated traveltimes of the dye cloud 

centroid were within 7 percent of measured traveltimes. The 

variances of the simulated dye concentrations were similar to 

the variances of the measured dye concentrations, indicating 

dispersion was reproduced reasonably well.

Average simulated dissolved-oxygen concentrations were 

within 6 percent of average measured concentrations. Average simulated ammonia concentrations were within the range 

of measured concentrations. Simulated dissolved-oxygen and 

ammonia concentrations were affected by the specification 

of a single nitrification rate in the Fargo WASP water-quality 

model.

Data sets from August 1989 and August 1990 were used 

to test traveltime and simulation of dissolved oxygen and 

ammonia. For streamflows that ranged from 60 to 407 cubic 

feet per second, simulated traveltimes were within 7 percent 

of measured traveltimes. Measured dissolved-oxygen concentrations were underpredicted by less than 15 percent for 

both data sets. Results for ammonia were poor; measured 

ammonia concentrations were underpredicted by as much 

as 70 percent for both data sets. Overall, application of the 

Fargo WASP water-quality model to the 1989 and 1990 

data sets resulted in poor agreement between measured and 

simulated concentrations. This likely is a result of changes 

in the waste-load composition for the Fargo and Moorhead 

wastewater-treatment plants as a result of improvements to 

the wastewater-treatment plants since 1990. The change in 

waste-load composition probably resulted in a change in 

decay rates and in dissolved oxygen no longer being substantially depressed downstream from the Moorhead and Fargo 

wastewater-treatment plants. The Fargo WASP water-quality 

model is valid for the current (2008) treatment processes at the 

wastewater-treatment plants.

Introduction

The Clean Water Act requires all States to develop and 

implement total maximum daily loads (TMDLs) for surface 

water where existing controls are not adequate to achieve 

instream water-quality standards (U.S. Environmental Protection Agency, Assessment and Watershed Protection Division, 

1991). In the early 1990s, the North Dakota Department of 

Health (NDDH) and Minnesota Pollution Control Agency 

(MPCA) determined that TMDLs for dissolved oxygen (DO) 

and ammonia needed to be developed for a 30.8-mi reach of 

the Red River of the North (hereinafter referred to as the Red 

River) that includes Fargo, N. Dak., and Moorhead, Minn. 

(fig. 1). The NDDH currently (2008) lists this reach of the 

Red River as impaired for DO and ammonia (North Dakota 

Department of Health, 2007), and the MPCA currently (2008) 

lists this reach as impaired for ammonia (Minnesota Pollution 

Control Agency, 2007). Actions that prompted the impaired 

listings were the planned expansion of the Fargo wastewatertreatment plant (WWTP; fig. 2), the beginning of year-round 

effluent discharges from the Fargo WWTP, and the likely 

need for stricter controls for the Moorhead WWTP (fig. 2) to 

reduce effluent ammonia concentrations (Wesolowski, 1996c). 

In June 1994, Red River TMDL work group members from 

Federal, State, and local agencies began developing TMDLs 

for DO and ammonia for the 30.8-mi reach. Since that time, 

both the Fargo and Moorhead WWTPs made improvements 

to their wastewater processes to reduce effluent ammonia 

concentrations.
2 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

In the 1990s, the U.S. Geological Survey calibrated 

and verified a water-quality model (QUAL2E) to simulate 

water quality in the Red River from just upstream from the 

Moorhead WWTP effluent discharge to downstream at the 

confluence of the Buffalo and Red Rivers near Georgetown, 

Minn. (Wesolowski, 1994, 1996a, 1996b, 1996c). Data used 

to calibrate this model were collected during 1989 and 1990 

at streamflows that ranged from 150 to 250 ft3/s. Because 

of uncertainties in the model for streamflows of less than 

150 ft3/s, Red River TMDL work group members noted that a 

time-of-travel and reaeration-rate study should be completed 

for streamflows that ranged from 20 to 100 ft3/s and that the 

water-quality model should be recalibrated for those flows. 

A model calibrated for low-flow conditions would enable the 

NDDH and the MPCA to conduct the necessary waste-load 

allocations for the two municipal WWTPs, to develop TMDLs 

for the 30.8-mi reach, and to evaluate the Fargo and Moorhead WWTPs current effluent quality and potential impact 

to the Red River. A proposal and work plan to conduct a 

water-quality modeling study during drought conditions when 

headwater streamflow ranged from about 20 to 100 ft3/s were 

prepared by Wesolowski (2000).

In 2003, the USGS, in cooperation with the NDDH, 

MPCA, and cities of Fargo and Moorhead, conducted a timeof-travel and reaeration-rate study during low-flow conditions 

to provide information to calibrate a water-quality model 

for streamflows of less than 150 ft3/s. Because of resource 

limitations, data collection was limited to a 19.2-mi reach of 

the Red River from just downstream from Dam A to about 

2 mi upstream from the confluence of the Sheyenne and Red 

Rivers (fig. 2). Traveltime, reaeration-rate, and water-quality 

data were collected from the 19.2-mi reach from September 

24 through 27, 2003. During that period, daily mean streamflow was about 60 ft3

/s at the USGS Red River of the North 

at Fargo gaging station (05054000; fig. 3). In the 19.2-mi 

reach, streamflow ranged from about 80 to 100 ft3/s because 

of additional discharge from the Fargo and Moorhead WWTP 

outfalls.

In January 2006, Red River TMDL work group members 

met to discuss TMDL goals for the NDDH and MPCA, to 

determine which water-quality model should be used with 

the September 24 through 27, 2003 data, and to review the 

September 2003 study data-collection activities and current 

and future modeling requirements. During the meeting, TMDL 

work group members made the decision to use the U.S. Environmental Protection Agency (USEPA) Water Quality Analysis Simulation Program (WASP) model because that model 

can be used for unsteady streamflows, is widely accepted by 

regulatory agencies, simulates concentrations for a variety 

of constituents, and is well documented and supported. The 

model developed during this study, which was conducted in 

cooperation with the NDDH, the MPCA, and the cities of 

Fargo and Moorhead, will, hereinafter, be referred to as the 

Fargo WASP water-quality model. The model was developed 

and calibrated using data collected from September 24 through 

27, 2003, and tested using data collected during 1989 and 

1990 as part of the Wesolowski (1994) study.

Purpose and Scope

The purpose of this report is to document the development, calibration, and testing of the Fargo WASP water-quality 

model for low-flow conditions. Specific objectives of the study 

were to analyze the data collected during September 2003 

and provide estimates for stream velocities, traveltimes, and 

reaeration-rate coefficients and to calibrate the Fargo WASP 

water-quality model.

The Fargo WASP water-quality model was calibrated for 

streamflow, transport, DO, and ammonia during steady-state 

conditions. Data collected during low-flow conditions from 

September 24 through 27, 2003, were used to calibrate the 

model, while data collected during 1989 and 1990 (Wesolowski, 1994) were used to test the model. The data used to 

calibrate the model were collected within the 19.2-mi reach 

from just downstream from Dam A to about 2 mi upstream 

from the confluence of the Sheyenne and Red Rivers (fig. 2).

Study Reach

The study reach begins just downstream from Dam A 

(locally referred to as North Dam), which is located about 

0.1 mi downstream from the 12th Avenue North bridge in 

Fargo (fig. 2). From site 1 at about river mile 448.9, the study 

reach extends 19.2 mi downstream to site 10 at about river 

mile 429.7. Site 10 is about 2 mi upstream from the confluence of the Sheyenne and Red Rivers. About one-third of the 

land use in the study reach is urban-suburban and two-thirds is 

rural (Wesolowski, 1994).

The Wild Rice River enters the Red River in North 

Dakota upstream from the study reach at about river mile 470 

and is the only major tributary that affects water quality in 

the study reach (fig. 1). The USGS Red River of the North at 

Fargo gaging station (05054000) is located at river mile 453, 

about 4.1 mi upstream from the beginning of the study reach. 

The Sheyenne River enters the Red River downstream from 

the study reach at about river mile 428.

The river channel and the riverbanks along the study 

reach primarily consist of silts and clays, and the streamflow 

in the river is primarily controlled by the river channel. During 

low streamflows, such as those that existed from September 24 

through 27, 2003, the streamflow follows the natural channel. 

The meandering river channel, which gradually becomes wider 

and deeper in a downstream direction, is fairly uniform in 

shape. In some places within Fargo, the river has been rechanneled to permit high streamflows to bypass the meanders. The 

riverbanks, which are fairly stable, are lined with deciduous 

trees. Tree density varies and, in places, open areas exist. The 

open, treeless areas are covered with grass or crops.
Red

River

of

the

North

N O R T H D A K O T A M I N N E S O T A

M A N I T O B A

S O U T H D A K O T A

99° 97°

95°

95°

49°

47° 47°

49°

97°

99°

Base from U.S. Geological Survey

1:2,000,000, 1972

Baldhill

Dam

r

EXPLANATION

Red River of the North

Basin boundary

INDEX MAP

RED RIVER

OF THE

NORTH BASIN

SASKATCHEWAN MANITOBA

CANADA

UNITED STATES

ONTARIO

White Rock

Lake Traverse

Mud Lake

Winnipeg

Nelson

R

Red

River

North

Lake Winnipeg

HUDSON

BAY

NORTH DAKOTA

SOUTH DAKOTA

MINNESOTA

Grand

Forks

Oslo

Manvel

Arvilla

Fordville

Grafton

Pembina

Emerson

FARGO

MOORHEAD

Thompson

Lisbon

Valley

City

Harvey

Cooperstown

Hillsboro

Abercrombie

Wahpeton

Breckenridge

Kindred

East Grand Forks Warwick

Upper

Red

Lake Devils

Lake

Sheyenne

River

River

River

Wild Rice

River RiverRiver

Rabbit R

Mustinka R

Pelican

Tail

Otter

Orwell Reservoir

River

River

R

R

Tongue

Pembina

R

River River

South

Roseau

Two

River

Middle

Tamarac

Thief

Red

Lake

Snake

Forest

Turtle

Park

Rice

Marsh River

Sand Hill

River

Wild

Buffalo

R

River

R

Elm

Goose

Maple

Rush

xuoi Sedsi oB

Stump

Lake

Lake

Ashtabula

Beaver

Baldhill

Creek

Cr

Lower

Red

Lake

Peterson Coulee

0 20 40 60 MILES

0 20 40 60 KILOMETERS

STUDY REACH

River

River

River

River

River

Branch

Branch North

of the

R

Figure 1. Location of Red River of the North Basin.

Introduction 3
Base from U.S. Geological Survey

Georgetown, Minn.-N. Dak. 1:24,000, 1963

Fargo North, N. Dak.-Minn. 1:24,000, 1959

Photorevised 1971 and 1976, revised 1993

0 1/2 1 MILE

46°55'

46°52'30"

96°50' 96°47'30" 96°45' CASS CO. CLAY CO.

MINNESOTA

NORTH DAKOTA

NORTH

THE

OF

RIVER

RED

10 10

75

Site 6

Site 5

Site 4

 Site 1

 Site 2

DAM A

36 31

1 6

F A R G O M O O R H E A D

19th Ave. N

University Dr. N

Broadway N

10th St. N

32nd Ave. N

Hector

International

Airport

35th Ave. N

23rd Ave. N

94

29

7th Ave. N

12th Ave. N

35th Ave. N

81

81

81

University Dr. S

25th St. S

10th St. S

25th St. N

13th Ave. S 12th Ave. S

Main Ave.

Main Ave.

Center Ave.

1st Ave. N

Northern Pacific Ave.

15th St. N

29th Ave. N Longfellow Rd. N Maple St.

Woodcrest Dr. S

Woodcrest Dr. N

Willow Rd

Kandi Ln

Veterans

Hospital

Trollwood

Park

Cardinal Muench

Seminary

11th St. N14th St. N

11th St. S14th St. S

15th Ave. N

R. 49 W. R. 48 W.

T. 140 N.

T. 139 N.

Elm St.

14th Ave. N

Treefoil

Park

Red River of the North

at Fargo, North Dakota

(05054000)

75

20

31

1

96

22

3

Fargo

wastewater-treatment

plant outflow

Moorhead wastewater-treatment plant outflow

Site 5.8

Site 5.7

Figure 2. Location of sites used in study.

4 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
GEORGETOWN BRIDGE

Georgetown

RED

RIVER

OF

THE

NORTH

CLAY CO.

CASS CO.

MINNESOTA

NORTH DAKOTA

Buffalo

River

River

Sheyenne

36 31

1 6

36 31

1 6

R. 49 W. R. 48 W.

R. 49 W. R. 48 W.

T. 142 N.

T. 141 N.

T. 141 N.

T. 140 N.

47°05'

47°02'30"

47°

46°57'30"

96°50' 96°47'30"

96°45'

CLAY CO. DITCH NO. 28

Site 7

Site 9.5

Site 10

Base from U.S. Geological Survey

Georgetown, Minn.-N. Dak. 1:24,000, 1963

Fargo North, N. Dak.-Minn. 1:24,000, 1959

0 1/2 1 MILE

75

26

31

22

31

1 96

LEVEE

Figure 2. Location of sites used in study.—Continued

Introduction 5
105 104

116

169

143

159

190

149

89

63

51 48 46 48 52

61

0

20

40

60

80

100

120

140

160

180

200

9/15 9/16 9/17 9/18 9/19 9/20 9/21 9/22 9/23 9/24 9/25 9/26 9/27 9/28 9/29 9/30

DAILY MEAN STREAMFLOW, IN CUBIC FEET PER SECOND

DATE

Figure 3. Daily mean streamflow at Red River of the North at Fargo, North Dakota, gaging station (05054000) for 

September 15 through 30, 2003.

6 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

Methods

Input data required to develop the Fargo WASP 

water-quality model include channel-geometry data, streamflow data, traveltime data, reaeration-rate coefficients, and 

water-quality data. Methods used to collect or compile the 

data are summarized in this section. Field property values and 

constituent concentrations used for the study are on file at the 

USGS and NDDH offices in Bismarck, N. Dak.

Data-Collection Network

The data-collection network for the 2003 study consisted 

of 10 sites that were numbered in a downstream order (fig. 2 

and table 1). The 10 sites are located on the main stem of the 

Red River and no sites are located at USGS gaging stations. Of 

the 10 sites, 6 (sites 1, 4, 5, 5.7, 7, and 10) are located at intervals that were determined on the basis of site access points and 

2 (sites 6 and 9.5) are located at existing bridges. The remaining two sites (sites 2 and 5.8) represent point sources from the 

WWTPs. Of the 10 sites used in the 2003 study, 7 (sites 1, 2, 

4, 5, 6, 7, and 10) also were used in the Wesolowski (1994) 

study.

Channel-Geometry and Streamflow Data

The Fargo WASP water-quality model requires channelgeometry data to characterize the segments between sites. 

Streamflow was measured with a current-meter according to 

techniques outlined by Rantz and others (1982). Information 

from the streamflow measurements were used for model input. 

Streamflows measured at seven sites (sites 4, 5, 5.7, 6, 7, 9.5, 

and 10) in the study reach are given in table 2. The study reach 

slope and bottom roughness were available from the Wesolowski (1994) study. Discharge data included in the model for 

the two point-source WWTP outfall sites were obtained from 

the NDDH (Gary Bracht, North Dakota Department of Health, 

written commun., 2004) and the city of Moorhead (Bob 

Zimmerman, Moorhead Wastewater Treatment Facility, oral 

commun., 2004).
Table 1. Description of sites used in 2003 study.

[RM, river mile; WWTP, wastewater-treatment plant]

Site 

number 

(fig. 2)

U.S. Geological 

Survey 

site number

Site name and location Description

1 465327096461800 Red River of the North 0.1 mile below 12th Avenue North bridge at Fargo, North 

Dakota (RM448.9)—Beginning of study reach at about 0.1 mile downstream from 12th Avenue North bridge. Immediately downstream from Dam A. Enter Treefoil Park from Elm Street just south of intersection with 14th Avenue North. Dam A is southeast of park entrance.

Site for dye and gas injecti

optic water-quality samp

2 465328096461200 Red River of the North at WWTP outfall at Moorhead, Minnesota (RM448.89)—At 

Moorhead, Minnesota, wastewater-treatment plant outflow (buried pipe) on east bank downstream from Dam A.

Point-source site for synop

quality sampling 

4 465431096455000 Red River of the North 2.3 miles below 12th Avenue North bridge at Fargo, North 

Dakota (RM446.6)—At intersection of Woodcrest Drive and Elm Street (north of Veterans Hospital). From Elm Street, turn east on Woodcrest Drive South. Site is located near 204 Woodcrest Drive. Follow trail to river.

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen

5 465544096455300 Red River of the North 2 miles above North Broadway Street bridge at Fargo, North 

Dakota (RM443.7)—At intersection of Elm Street North and Kandi Lane. From Elm Street North, turn northeast on Golf Course Avenue and follow to river.

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen

5.7 465530096465900 Red River of the North 0.6 mile above North Broadway Street bridge at Fargo, 

North Dakota (RM440.9)—At intersection of Kandi Lane and Broadway Street North. From Broadway Street North, turn east on Kandi Lane and into west end of Trollwood Park parking lot.

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen

5.8 465537096470700 Red River of the North at WWTP outfall at Fargo, North Dakota (RM440.5)—At 

Fargo, North Dakota, outlet end of wastewater-treatment plant outflow. East of Broadway Street North.

Point-source site for synop

quality sampling 

6 465602096472900 Red River of the North at Cass Co. 20 bridge at Fargo, North Dakota (RM439.15—

At bridge on Cass County, North Dakota, Road No. 20.

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen

7 465721096481100 Red River of the North 1.5 miles below Cass Co. 20 bridge at Fargo, North Dakota 

(RM437.6)—Immediately upstream from discontinued Fargo, North Dakota, wastewater-treatment plant outflow. About 1.5 miles north of Cass County, North Dakota, Road No. 20.

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen

9.5 465836096491300 Red River of the North at Cass Co. 22 bridge below Fargo, North Dakota 

(RM433.42)—At bridge on Cass County, North Dakota, Road No. 22 (Clay County, Minnesota, Road No. 26).

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen

10 470022096501900 Red River of the North 3.7 miles above Cass Co. 22 bridge below Fargo, North Dakota (RM429.7)—End of study reach. East of Cass County, North Dakota, Road 

No. 31 and about 2 miles north of Cass County, North Dakota, Road No. 20.

Calibration site for dye, ga

synoptic water-quality sastreamflow measuremen
Table 2. Streamflow data for the Red River of the North, September 24 through 27, 2003.

[ft3/s, cubic feet per second; ft2, feet squared; ft/s, feet per second; ft, feet; --, no data]

Site number

(fig. 2) Sampling date Sampling time

Mean daily 

discharge 

(ft3/s)

Instantaneous 

streamflow 

(ft3/s)

Area 

(ft2)

Velocity 

(ft/s)

Width 

(ft)

1 -- -- -- -- -- -- --

2 -- -- 15.6 -- -- -- --

4 9/24/2003 1040 -- 84.3 138 0.61 82

5 9/24/2003 1625 -- 82.9 206 .40 70

5.7 9/24/2003 2000 -- 83.3 197 .42 95

5.8 -- -- 216.3 -- -- -- --

6 9/25/2003 1220 -- 95.4 152 .63 68

7 9/25/2003 1500 -- 100.8 255 .40 96

9.5 9/26/2003 1110 -- 99.8 213 .47 76

10 9/26/2003 1110 -- 85.9 131 .65 62

10 9/26/2003 1905 -- 84.3 132 .64 62

1

Mean daily discharge from the Moorhead, Minnesota, wastewater-treatment plant outfall for September 24 through 27, 2003.

2

Mean daily discharge from the Fargo, North Dakota, wastewater-treatment plant outfall for September 24 through 27, 2004.

8 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

Traveltime Data and Reaeration-Rate 

Coefficients

Traveltime measurements provide transport velocity 

values that integrate all of the physical variability within the 

reach between two points. Important factors in determining 

the effects of discharging treated wastewater to the Red River 

are the effect of the wastewater on the DO concentration in the 

river and the river’s capacity to reaerate. The major source of 

oxygen to the Red River is the atmosphere. Traveltime data 

for the study reach are given in table 3, and reaeration-rate 

coefficients are given in table 4. The traveltime measurements 

were made when streamflow ranged from about 80 to 100 ft3/s. 

Daily mean streamflow at the USGS Red River of the North at 

Fargo gaging station (05054000) for September 15 through 30, 

2003, is shown in figure 3.

For the Wesolowski (1994) study and the 2003 study, 

Rhodamine WT (RWT) 20-percent stock solution (a conservative fluorescent dye) and nonconservative propane gas 

(commercial grade) tracers were used to determine traveltime and to calculate reaeration-rate coefficients. The dye 

and gas injections were done simultaneously. Traveltime 

calculations require only fluorescent dye concentration data, 

but reaeration-rate calculations require fluorescent dye and 

propane gas concentration data. Methods described by Kilpatrick and Wilson (1989) were used to measure traveltimes. The 

modified-tracer technique developed by Kilpatrick and others 

(1989) was used to measure reaeration rates.

Dye concentrations were determined using a fluorometer, which is an instrument that measures fluorescence. 

Fluorescence readings, when compared to known dye concentrations (standards), can be used to determine dye concentrations in water. The fluorescence of a water sample needs to be 

measured using the same fluorometer used to determine the 

known dye concentrations and under the same environmental 

conditions (Wilson and others, 1986). Otherwise, comparison 

of the fluorescence readings and the dye concentrations will 

not be representative.

Before dye injection during the 2003 study, the fluorometer was calibrated to a set of known RWT concentrations, 

usually 10, 25, and 100 micrograms per liter (μg/L). The 

prepared concentrations in the samples used to calibrate the 

fluorometer were mixed using water from the Red River to 

account for the natural fluorescence effects that might occur in 

the river. For quality assurance, the calibration of the fluorometer was checked after each dye trace to ensure that it had not 

drifted during the dye trace.

The RWT dye was slug injected at about the center of 

the river on September 24, 2003 (table 3). The amount of dye 

injected into the river was predetermined using the methods 

described by Kilpatrick and Wilson (1989). The dye was 

injected in the upstream part of the study reach, about 30 ft 

downstream from site 1 or 10 ft downstream from site 2 

(fig. 4). During the 2003 study, this was the only section of the 

study reach that transitioned from a pool to a riffle.

At sites downstream from the dye injection, water 

samples were collected at predetermined intervals before and 

during the arrival of the dye cloud and until the dye concentration was less than 10 percent of the peak concentration passing 

the site. Streamflow measurements that were made at all 
Methods 9

centroid (fig. 7) on the basis of data collected on two dates 

in August 1989, and one in April and October 1990. This 

relation is intended to be used to estimate flow velocities in 

the study reach. Except for site 4, the traveltime of the dye 

cloud centroid for each of the sites in the 2003 study plotted 

close to the lines shown in figure 7, verifying the relations 

developed by Wesolowski (1994). The traveltime of the dye 

cloud centroid measured for site 4 is much faster than the 

traveltime measured in previous studies (fig. 7). There is some 

uncertainty regarding the traveltime data for site 4 (table 3). 

Traveltime was used to calculate mean streamflow transport 

velocities for each of the sites (table 3). The mean streamflow 

transport velocity of the dye cloud at the centroid of 1.35 ft/s 

for site 4 (table 3) is much greater than the mean measured 

velocity of 0.61 ft/s for site 4 from the streamflow measurement (table 2). For other sites, the mean streamflow transport 

velocity of the dye cloud at the centroid (table 3) and the 

mean measured velocity (table 2) are much closer. Also, the 

mean streamflow transport velocity for site 4 is much greater 

than the mean streamflow transport velocity for other sites 

(table 3). These differences may be an indication of different 

channel characteristics between site 1 and site 4 as compared 

to the channel characteristics downstream from site 4 or it 

may be an indication of sampling error. In addition, there 

is some uncertainty as to whether the dye was 100-percent 

laterally mixed before reaching site 4. The actual channel 

length between site 1 and site 4 is 2.3 mi. Using equations 

from Kilpatrick and Wilson (1989), the length necessary for 

the dye to be 95-percent laterally mixed is between 2.1 and 

2.5 mi, depending on how width is estimated. However, the 

channel length required to obtain 100-percent lateral mixing 

may be twice that required for 95-percent mixing (Kilpatrick 

and Wilson, 1989). When lateral mixing is still taking place, 

the tracer cloud typically moves faster than the mean stream 

velocity (Funkhouser and Barks, 2004). Thus, if the dye had 

been 100-percent laterally mixed, the traveltime would likely 

have been greater than the 2.3 hours estimated from the 2003 

study.

For the 2003 study, propane gas was injected at a constant 

rate into the river, at the same location as the dye injection, 

through small-pore diffusers. The gas is not readily absorbed 

into water, and only 20 to 50 percent of the amount that is 

injected is ultimately absorbed, the rest being lost to the atmosphere (Wesolowski, 2000). Absorption efficiency is related 

to water depth, and about 2 ft of depth is required for efficient 

absorption. For the 2003 study, the propane gas was injected 

at a constant rate until the gas arrived at the most downstream 

site. Because continuous injection was used, longitudinal 

dispersion was not a factor in decreased concentration; 

therefore, the concentration decreased only by desorption and 

dilution.

Propane gas samples were collected for this study from 

the study reach after the gas concentration reached a plateau. 

The gas plateau is reached when the dye concentration returns 

to background concentrations (Kilpatrick and others, 1989). 

For the 2003 study, background concentrations were defined 

dye-sampling sites were used to determine the location of the 

centroid of flow, and samples were collected at that location in 

the river.

Dye concentrations were measured at seven sites along 

the study reach. At sites 4, 5.7, 7, and 10, the fluorescence 

(dye concentration) of the water was measured continuously 

using a Self-Contained Underwater Fluorescence Apparatus 

(SCUFA) submersible fluorometer (fig. 5; Turner Designs, 

Inc., 2002a). These sites were selected because of availability and setup time of the SCUFA. A SCUFA measures the 

fluorescence of the water once per second and is capable of 

measuring RWT concentrations as small as 0.04 micrograms 

per liter (μg/L; Turner Designs, Inc., 2002a). For this study, 

the fluorescence readings obtained every second were averaged over 1-minute intervals and the 1-minute averages were 

stored for later analysis.

At sites 5, 6, and 9.5, the dye concentrations were 

measured in discrete water samples using a Turner Designs 

model 10 fluorometer. Samples were collected and later 

analyzed in the USGS laboratory in Bismarck, N. Dak. As 

with the SCUFA, the Turner Designs model 10 fluorometer 

was calibrated using standards mixed with river water to 

account for natural fluorescence effects. However, samples 

were not at ambient stream temperature when they were 

analyzed. Therefore, because fluorescence is affected by 

temperature, the dye concentrations for sites measured with 

the Turner Designs model 10 fluorometer were corrected to a 

temperature of 20°C (Turner Designs, Inc., 2002b).

Time-concentration curves are used to interpret traveltime 

and longitudinal dispersion (Kilpatrick and Wilson, 1989). 

For the 2003 study, time-concentration curves for seven sites 

(sites 4, 5, 5.7, 6, 7, 9.5, and 10) were prepared by plotting 

the measured dye concentration in relation to the elapsed 

traveltime after injection (fig. 6). A smooth curve was drawn 

through the plotted points. These curves represent the passage 

of the dye cloud at the sites. Traveltime and velocity are 

determined by comparing upstream and downstream curves. 

At sites 5, 6, and 9.5 where the fluorescence was measured in 

discrete samples, the leading and trailing edge of the timeconcentration curve were not captured. As a result, timeconcentration curves were more accurate for sites where the 

dye concentration was measured continuously using a SCUFA 

than for sites where dye concentrations were measured from 

discrete water samples.

The main features of time-concentration curves are 

the leading edge, peak, centroid, and trailing edge. The 

centroid is a point that represents the center of the area 

under the time-concentration curve. The main features of the 

time-concentration curves are described in terms of elapsed 

traveltime after dye injection. Data for these and other features 

of the curves are given in table 3. The leading edge, centroid, 

and trailing edge for the discrete sample locations were estimated.

Wesolowski (1994) developed a relation between 

measured streamflow at the Red River of the North at Fargo 

gaging station (05054000) and traveltime of the dye cloud 
Table 3. Traveltime data for the Red River of the North, September 24 through 27, 2003.

[ft3/s, cubic feet per second; μg/L, micrograms per liter; ft/s, feet per second]

Site 

number 

(fig. 2)

Distance 

downstream 

from dye 

injection 

(miles)

Instantaneous 

streamflow

(ft3/s)

Elapsed traveltime after dye injection 

(hours)

Time for 

dye cloud 

to pass 

site 

(hours)

Measured

peak 

dye 

concentration 

(μg/L)

Mean streamflow 

transport velocity 

of dye cloud 

(ft/s)

Leading 

edge Peak Centroid Trailing edge Peak Centroid

Slug injection of dye (2 liters) at 0916 hours on September 24, 2003, about 10 feet downstream from site 2; daily mean streamflow at Red 

River of the North at Fargo, N. Dak., gaging station (05054000) was 63 ft3/s 

1

4 2.3 84.3 1.88 2.32 2.50 4.58 2.7 27.3 1.46 1.35

2

5 5.2 82.9 312.00 14.23 315.00 319.00 7.0 6.9 .36 .34

1

5.7 8.0 83.3 20.77 23.88 24.33 30.17 9.4 5.3 .43 .44

2

6 9.8 95.4 323.50 28.48 330.00 336.00 12.5 4.0 .56 .45

1

7 11.8 100.8 30.23 35.37 36.02 41.77 11.5 3.2 .44 .50

2

9.5 15.48 99.8 338.00 45.73 348.00 360.00 22.0 3.0 .52 .45

1

10 19.2 85.9 50.48 56.63 58.47 74.00 23.5 2.2 .50 .52

1

A Self-Contained Underwater Fluorescence Apparatus (SCUFA) submersible fluorometer was used to continuously measure dye concentrations.

2

A Turner Designs model 10 fluorometer was used to manually measure dye concentrations in discrete samples.

3

Estimated.

10 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

as less than 10 percent of the peak concentration. Discrete gas 

samples were collected at seven sites within a 3-hour period 

at 30-minute intervals. To meet residence time requirements 

between sampling sites, gas samples were collected only at 

sites 4, 5, 5.7, 6, 7, 9.5, and 10. Residence time (unitless) is 

the ratio of upstream to downstream gas concentration and 

should be greater than 2.72 to ensure accurate computation of 

the reaeration-rate coefficient (Kilpatrick and others, 1989). 

The gas samples were analyzed for propane concentration at 

Severn Trent Laboratories in Denver, Colo. The average of the 

propane concentrations for each site was used to calculate the 

reaeration-rate coefficient for the site.

The rate of reaeration in a river usually is expressed as a 

reaeration-rate coefficient (Friedman and Blanc, 1991). Calculated reaeration-rate coefficients for the study reach, adjusted 

to a 20°C water temperature, ranged from 1.18 to 1.58 per 

day when streamflow ranged from 80 to 100 ft3/s (table 4) 

with an average of 1.4 per day. The reaeration-rate coefficient 

increased in the downstream direction. The residence time 

ranged from 1.89 to 6.89. The calculated average reaerationrate coefficient from site 4 to site 10 should be an accurate 

estimate of the reaeration-rate coefficient for the study reach 

because the residence time is greater than 2.72.

To estimate reaeration-rate coefficients when streamflows 

differ from measured streamflows, a graphical regression of 

streamflows and reaeration-rate coefficients was developed 

by Wesolowski (1994). The reaeration-rate coefficient of 

1.4 per day computed for the reach from site 4 to site 10, at 

an average streamflow of 85.1 ft3/s, for the 2003 study was 

added to the original regression and the regression equation 

was recomputed (fig. 8). From the regression, an R-squared 

value of 0.949 was determined, indicating that 95 percent of 

the variability in the reaeration coefficient can be explained 

by streamflow. The R-squared value is large despite the fact 

that the reaeration coefficients were computed on the basis 

of data from different sites. For example, the reaeration-rate 

coefficient from the 2003 data was computed from data for 

sites 4 and 10, whereas the reaeration-rate coefficient for the 

April 1990 data point was computed from data for sites 4 and 

7 (Wesolowski, 1994, table 7). The regression is valid for 

streamflows of 85 to 415 ft3/s.
Table 4. Reaeration-rate coefficients for the Red River of the North, September 24 through 27, 2003.

[Coefficients were determined by the steady-state method using a constant-rate injection of propane. ft3/s, cubic feet per second; °C, degrees Celsius; μg/L, micrograms per liter; 

Site number 

(fig. 2)

Distance 

downstream 

from propane 

injection 

(miles)

Instantaneous 

streamflow

(ft3/s)

Mean water temperature 

(°C)

Traveltime of dye 

cloud centroid 

(hours)

Mean

concentration of 

propane at 

50-percent 

streamflow lines 

(μg/L)

Reaeration-rate 

coefficient at 

measured water 

temperature 

(per day)1

Reaeratio

coeffic

adjuste

20°C w

temper

(per d

Monitoring continuous propane injection from 0800 hours on September 24, 2003

4 2.3 84.3 14.1 2.5 33.0 -- -- 5 5.2 82.9 12.4 -- 18.0 -- -- 

5.7 8.0 83.3 11.9 24.3 17.7 0.70 1.1

6 9.75 95.4 13.2 -- 12.7 -- -- 7 11.80 100.8 12.7 36.0 9.2 .95 1.5

9.5 15.48 99.8 12.2 -- 7.5 -- -- 

10 19.20 85.9 11.9 58.5 4.7 .89 1.5

4 to 10 -- 285.1 -- -- -- .83 1.4

1Calculations were made as discussed by Kilpatrick and others (1989).2Average of streamflows for sites 4 and 10. 
Figure 4. Injecting dye at a site downstream from the Moorhead, Minnesota, wastewatertreatment plant outfall on the Red River of the North, September 24, 2003.

Figure 5. Self-Contained Underwater Fluorescence Apparatus (SCUFA).

12 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
0

5

10

15

20

25

30

0 10 20 30 40 50 60 70

DYE CONCENTRATION, IN MICROGRAMS PER LITER

ELAPSED TRAVELTIME AFTER INJECTION, IN HOURS

Dye trace

Discrete dye samples

Site number

[Slug injection of dye 

(2 liters) at 0916 hours on 

September 24, 2003]

(10)

(10)

(9.5) (7)

(6) (5.7)

(5)

(4)

Figure 6. Dye concentration in relation to traveltime for sites 4, 5, 5.7, 6, 7, 9.5, and 10 on the Red River of the North.

Methods 13
STREAMFLOW, IN CUBIC FEET PER SECOND

1

10

100

10 100 1,000

TRAVELTIME OF DYE CLOUD CENTROID, IN HOURS

SITE 4

SITE 5

SITE 6

SITE 7

SITE 9 (Site 9.5 during 2003 study)

SITE 10

Estimated line extension

Measured streamflow at Red River of the North gaging station—August 8, 1989

Measured streamflow at Red River of the North gaging station—August 17, 1989

Measured streamflow at Red River of the North gaging station—April 1990

Measured streamflow at site—October 1990

Measured streamflow at Red River of the North gaging station—September 24–27, 2003

Location of sites shown on figure 2

EXPLANATION

Figure 7. Traveltime of dye cloud centroid in relation to streamflow at the Red River of the North at Fargo, North Dakota, 

gaging station (05054000; modified from Wesolowski, 1994).

14 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
0.1

1

10

10 100 1000

REAERATION-RATE COEFFICIENT, IN PER DAY

STREAMFLOW, IN CUBIC FEET PER SECOND

MEASURED DATA

Estimated regression 

line extension. [The 

equation of the line is 

y  13.27x−0.50 and R

2  0.949. 

Modified from Wesolowski, 1994]

April 1990

October 1990

September 2003

Figure 8. Reaeration-rate coefficient as a function of streamflow for the Red River of the North 

30.8-mile reach from Fargo, North Dakota, to Georgetown, Minnesota, April and October 1990 and 

September 2003.

Methods 15
16 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

Water Sample Collection and Analysis

Water samples were collected during low, steady-state 

streamflow conditions from September 24 through 27, 

2003. The samples were collected at 10 sites that included 

1 upstream site used for the model boundary condition (site 1), 

2 point-source sites (sites 2 and 5.8), and 7 calibration sites 

(sites 4, 5, 5.7, 6, 7, 9.5, and 10; fig. 2 and table 1). Field properties were measured and samples were collected according to 

methods described by the U.S. Geological Survey (variously 

dated). The samples were analyzed by the NDDH Laboratory 

in Bismarck, N. Dak., for selected properties and constituents 

(table 5).

Field quality assurance and quality control for the study 

described in this report were addressed by using the same 

data-collection procedures that are used in the USGS National 

Stream Quality Accounting Network (NASQAN) program 

(Kelly and others, 2001). Results for blank and replicate 

samples collected during 2003 for the NASQAN program 

in North Dakota indicate that no sample contamination was 

introduced by field activities (data on file at the USGS North 

Dakota Water Science Center, Bismarck, North Dakota).

Field properties were measured and water samples were 

collected at each site for a 24-hour period in 3-hour intervals 

from September 24 through 27, 2003, except for chlorophyll 

samples, which were collected every 12 hours. Unfiltered 

samples were collected at the centroid of streamflow where 

tracer samples were collected. Water-quality sampling began 

at each site near the time of the dye concentration peak and 

continued until 10 percent of the peak concentration or a 

concentration of 0.1 μg/L was reached.

Statistical summaries of field property values and 

constituent concentrations for each of the sites are given in 

table 6 for September 24 through 27, 2003. DO ranged from 

7.3 milligrams per liter (mg/L) at site 2 to 10.1 mg/L at site 10. 

Ammonia concentrations ranged from less than 0.01 mg/L 

at four sites to 11.4 mg/L at the Moorhead WWTP outfall 

(site 2).

Samples were analyzed for the different forms of 

biochemical oxygen demand (BOD; table 5). BOD is a 

measure of the amount of oxygen consumed by decaying organic matter over a specified period of time and is 

commonly characterized by a two-step process (U.S. Environmental Protection Agency, 1995). Although both steps can 

occur simultaneously, the first step typically involves oxidation of carbonaceous organic matter by saprophytic organisms and is considered the carbonaceous phase of the BOD 

reaction. The second step, the nitrogenous phase of the BOD 

reaction, includes the conversion of organic nitrogen to ammonia by autotrophic organisms and the subsequent oxidation 

of ammonia. A standardized test that measures the amount 

of oxygen that has been consumed after incubation of the 

sample at 20°C for a specific length of time, usually 5 days, 

is used to determine BOD (U.S. Environmental Protection 

Agency, 1995). The BOD test, unless it is run with a nitrification inhibitor, measures the oxygen required to carry out both 

steps of the BOD reaction. This amount commonly is called 

total BOD (hereinafter referred to as BOD). If a nitrification inhibitor is used, the BOD test measures the oxidation 

of carbonaceous material only, and the results are reported 

as carbonaceous biochemical oxygen demand (CBOD). If 

independent tests are run for BOD and CBOD, NBOD can 

then be calculated by subtracting CBOD from BOD. For the 

BOD samples in this study, the NDDH laboratory used Standard Method 5210C (American Public Health Association, 

American Water Works Association, and Water Environment 

Federation, 1995). In this method BOD is determined, but in 

addition, NBOD is determined by analyzing the nitrite plus 

nitrate concentration within the BOD sample each time DO 

is measured. The nitrite plus nitrate concentrations are then 

corrected to compute the oxygen equivalency of the nitrification reaction (American Public Health Association, American 

Water Works Association, and Water Environment Federation, 

1995). These values of NBOD are then subtracted from BOD 

to determine CBOD. In some instances, the NBOD concentrations were greater than the BOD concentrations, and the 

resulting CBOD concentrations were negative. These negative 

CBOD concentrations were reported as zero by the NDDH 

Laboratory (James Quarnstrom, North Dakota Department of 

Health Laboratory, written commun., 2006). For the majority of the samples analyzed for this study, the BOD test was 

run for 5 days to determine 5-day oxygen demand (BOD5, 

NBOD5, and CBOD5; table 6). A 96-day test was also run for 

two samples from each site and results were reported after 

5 days and after 96 days. Hereinafter, results reported for 

96 days will be referred to as ultimate oxygen demand (BODu, 

NBODu, and CBODu).

 Field properties were measured and water samples 

were collected from the Red River immediately downstream 

from the outfall pipe to determine the water-quality of the 

discharge from the Moorhead WWTP (site 2). At site 2, the 

end of the outfall discharge pipe was partially submerged 

below the water surface (fig. 9). As a result, some mixing of 

wastewater effluent with Red River water may have occurred, 

which may have caused the water-quality data for site 2 to be 

nonrepresentative of pure wastewater effluent. To determine 

whether water-quality data at site 2 are representative of pure 

wastewater effluent, data from site 2 for September 24 through 

27, 2003, were compared with routine data collected by the 

Moorhead WWTP staff at the last sampling location inside the 

Moorhead WWTP (Andy Bradshaw, Moorhead Wastewater 

Treatment Facility, written commun., 2007; table 7). Average concentrations were consistent between the two sampling 

locations, which indicates water-quality data collected at site 2 

are representative of pure wastewater effluent.

Water samples from the Fargo WWTP (site 5.8) were 

collected from an open, rock-lined channel that flows from 

the treatment plant and then discharges into the Red River. At 

site 5.8, only one set of field properties (table 7) was measured 

because of safety concerns in accessing the site. The samples 

were collected before the effluent discharge entered the 

river, so the constituent concentrations should represent pure 
Table 5. Properties and constituents for which water samples were analyzed.

[Samples were analyzed by the North Dakota Department of Health Laboratory, Bismarck, North Dakota. --, no data; <, less than; mL, milliliter]

Property or constituent Parameter 

code

Measurement type

Minimum 

detection 

limit

Units

Streamflow 00060 Field -- Cubic feet per second

Specific conductance 00095 Field -- Microsiemens per centimeter at 25 degrees 

Celsius

pH 00400 Field -- Standard units

Temperature, water 00010 Field -- Degrees Celsius

Barometric pressure 00025 Field -- Millimeters of mercury

Dissolved oxygen 00300 Field -- Milligrams per liter

Biochemical oxygen demand (5th day and 1

ultimate) 

(

2

) Laboratory -- Milligrams per liter

Nitrogenous biochemical oxygen demand 

(5th day and 1ultimate)

(

2

) Calculated -- Milligrams per liter

Carbonaceous biochemical oxygen demand 

(5th day and 1ultimate)

(

2

) Calculated -- Milligrams per liter

Nitrite plus nitrate, unfiltered 00630 Laboratory <0.02 Milligrams per liter

Ammonia, unfiltered 00610 Laboratory <.010 Milligrams per liter

Nitrogen, ammonia plus organic (Kjeldahl), 

unfiltered

00625 Calculated <.001 Milligrams per liter

Nitrogen, total, unfiltered 00600 Laboratory <.015 Milligrams per liter

Phosphorus, unfiltered 00665 Laboratory <.004 Milligrams per liter

Chlorophyll a3 70951 Laboratory (

3

) Micrograms per liter

Chlorophyll b3 70952 Laboratory (

3

) Micrograms per liter

1

Results reported after 96 days were referred to as ultimate oxygen demand.

2

Parameter code not available.

3

The detection limit for chlorophyll a and b depends on the volume of water that is filtered through the media. For chlorophyll a, the limit, in micrograms per 

liter, is 1.5 for 2,000 mL of water, 2.0 for 1,000 mL of water, 6.0 for 500 mL of water, and 12.0 for 250 mL of water. For chlorophyll b, the limit, in micrograms 

per liter, is 0.5 for 2,000 mL of water, 1.0 for 1,000 mL of water, 2.0 for 500 mL of water, and 4.0 for 250 mL of water.

Methods 17

wastewater effluent. Comparison of water-quality data from 

site 5.8 and data collected at the last sampling location inside 

the Fargo WWTP indicated average concentrations generally 

are in close agreement except for BOD5 (table 7). The average BOD5

 concentration for samples collected from site 5.8 

was smaller than that for samples collected inside the Fargo 

WWTP and is most likely related to analysis error at low 

concentrations.
Specific 

conductance 

(μS/cm at 

25°C)

(00095)

pH 

(standard 

units)

(00400)

Temperature, 

water 

(°C)

(00010)

Dissolved 

oxygen 

(mg/L)

(00300)

BOD, 

5-day 

(mg/L)

(00319)

BOD 

ultimate1,2

mg/L

Nitrogenous 

BOD, 

5-day 

(mg/L)

(00321)

Nitrogenous 

BOD, 

ultimate1,2

(mg/L)

Carbonaceous 

BOD, 

5-day 

(mg/L)

(00320)

Carbonaceous 

BOD, 

ultimate1,2

(mg/L)

Nitrite plus 

nitrate, 

unfiltered 

(mg/L)

(00630)

Ammonia, 

unfiltered 

(mg/L)

(00610)

Ammonia 

plus organic 

nitrogen, 

water, 

unfiltered 

(mg/L)

(00625)

Nitrogen, 

total, 

unfiltered 

(mg/L)

(00600) 

Phosphorus, 

unfiltered 

(mg/L)

(00665)

Chlorophyll a

(μg/L)

(70951)

Chlorophyll b

(μg/L)

(70952)

Site 1; Red River 0.1 mile below 12th Ave N., Fargo, N. Dak. (RM448.90) Site 1; Red River 0.1 mile below 12th Ave N., Fargo, N. Dak. (RM448.90)

Number of values 9 9 9 9 9 2 9 2 9 2 9 9 9 9 9 2 2

Minimum 688 8.0 13.7 8.6 1.19 7.13 0.18 1.83 .95 5.22 .02 <.01 .47 .49 .18 15.3 1.99

Mean 724 8.2 14.4 9.0 1.45 -- .22 -- 1.23 -- .03 -- .53 .56 .24 -- --

Median 725 8.2 14.6 8.8 1.49 -- .20 -- 1.23 -- .03 -- .54 .56 .24 -- --

Maximum 750 8.3 14.8 9.8 1.65 7.32 .38 1.91 1.46 5.49 .05 <.01 .58 .61 .31 16.8 3.56

Site 2; Red River at WWTP outflow at Moorhead, Minn. Site 2; Red River at WWTP outflow at Moorhead, Minn.

Number of values 9 9 9 9 9 2 9 2 9 2 9 9 9 9 9 2 2

Minimum 1,160 7.0 14.5 7.3 6.44 62.2 7.22 49.4 -- 9.4 9.82 9.89 10.7 21.1 3.74 <6.00 <2.00

Mean 1,166 7.0 15.3 7.5 7.29 -- 9.62 -- -- -- 10.1 10.6 11.5 21.6 3.86 -- --

Median 1,170 7.0 15.3 7.5 7.26 -- 8.82 -- -- -- 10.1 10.5 11.3 21.4 3.85 -- --

Maximum 1,170 7.0 16.3 7.7 7.89 62.4 13.2 52.8 -- 13 10.4 11.4 12.2 22.2 4.02 E6.67 E2.22

Site 4; Red River 2.3 mile below 12th Ave. at Fargo, N. Dak. (RM446.60) Site 4; Red River 2.3 mile below 12th Ave. at Fargo, N. Dak. (RM446.60)

Number of values 9 9 9 9 9 2 9 2 9 2 9 9 9 9 9 2 2

Minimum 732 8.1 13.5 8.1 2.25 11.6 1.51 5.94 .36 5.57 .68 .20 .87 1.68 .41 13.1 2.19

Mean 754 8.1 14.1 8.6 2.66 -- 1.95 -- .71 -- .78 .4 1.11 1.89 .47 -- --

Median 758 8.1 14.0 8.6 2.71 -- 2.01 -- .70 -- .77 .35 1.12 1.89 .45 -- --

Maximum 769 8.2 15.0 9.3 2.94 11.7 2.29 6.03 1.01 6.86 .89 .54 1.29 2.18 .62 13.4 2.22

Site 5; Red River 2 mile above N. Broadway St. Bridge at Fargo, N. Dak. Site 5; Red River 2 mile above N. Broadway St. Bridge at Fargo, N. Dak.

Number of values 8 8 8 8 8 2 8 2 8 2 8 8 8 8 8 2 2

Minimum 751 8.1 11.7 8.2 2.24 9.76 1.37 4.8 .53 4.96 .75 .17 .86 1.61 .43 3.80 2.08

Mean 767 8.2 12.4 9.0 2.54 -- 1.62 -- .92 -- .88 .21 1.00 1.88 .4 -- --

Median 770 8.2 12.4 9 2.56 -- 1.60 -- 1.01 -- .90 .20 1.02 1.95 .44 -- --

Maximum 776 8.2 13.2 9.5 2.74 10.6 2.01 5.58 1.20 5.02 .96 .34 1.13 1.99 .46 16.0 5.05

Site 5.7; Red River 0.6 mile above N. Broadway St. Bridge at Fargo, N. Dak. Site 5.7; Red River 0.6 mile above N. Broadway St. Bridge at Fargo, N. Dak.

Number of values 9 9 9 9 9 2 9 2 9 2 9 9 9 9 9 2 2

Minimum 750 8.1 11.3 8.8 2.16 9.05 1.23 3.66 .55 5.39 .78 .08 .77 1.55 .40 12.5 3.14

Mean 769 8.2 11.9 9.1 2.44 -- 1.53 -- .91 -- .92 .13 .90 1.82 .42 -- --

Median 771 8.2 12.1 9.1 2.43 -- 1.60 -- .90 -- .93 .14 .92 1.87 .43 -- --

Maximum 781 8.2 12.2 9.4 2.64 10.1 1.69 4.71 1.14 5.39 1.01 .17 .97 1.92 .44 16.0 4.14

Site 5.8; Red River at WWTP outflow at Fargo, N. Dak. Site 5.8; Red River at WWTP outflow at Fargo, N. Dak.

Number of values 1 1 1 1 9 2 9 2 9 1 9 9 8 9 9 0 0

Minimum 1,180 7.4 19.7 8.8 1.31 12.5 1.83 .46 1.34 12.7 19.6 <.01 .50 21.3 4.76 -- --

Mean -- -- -- -- 1.72 -- -- -- 1.75 -- 23.1 -- 1.11 24.1 4.84 -- --

Median -- -- -- -- 1.66 -- -- -- 1.71 -- 23.6 -- .80 24.8 4.84 -- --

Maximum 1,180 7.4 19.7 8.8 2.19 13.2 5.94 13.7 2.19 -- 25.4 <.01 2.10 25.3 4.94 -- --

Table 6. Statistical summaries for selected field property values and constituent concentrations for the Red River of the North, 

September 24 through 27, 2003.

[Site names and locations are given in table 1. Number in parentheses is parameter code. μS/cm, microsiemens per centimeter; °C, degrees Celsius; mg/L, 

milligrams per liter; BOD, biochemical oxygen demand; μg/L, micrograms per liter; <, less than; --, not calculated; WWTP, wastewater-treatment plant; 

E, estimated]

Table 6. Statistical summaries for selected field property values and constituent concentrations for the Red River of the North, 

September 24 through 27, 2003.—Continued

[Site names and locations are given in table 1. Number in parentheses is parameter code. μS/cm, microsiemens per centimeter; °C, degrees Celsius; mg/L, 

milligrams per liter; BOD, biochemical oxygen demand; μg/L, micrograms per liter; <, less than; --, not calculated; WWTP, wastewater-treatment plant; 

E, estimated]

18 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North Methods 19
Specific 

conductance 

(μS/cm at 

25°C)

(00095)

pH 

(standard 

units)

(00400)

Temperature, 

water 

(°C)

(00010)

Dissolved 

oxygen 

(mg/L)

(00300)

BOD, 

5-day 

(mg/L)

(00319)

BOD 

ultimate1,2

mg/L

Nitrogenous 

BOD, 

5-day 

(mg/L)

(00321)

Nitrogenous 

BOD, 

ultimate1,2

(mg/L)

Carbonaceous 

BOD, 

5-day 

(mg/L)

(00320)

Carbonaceous 

BOD, 

ultimate1,2

(mg/L)

Nitrite plus 

nitrate, 

unfiltered 

(mg/L)

(00630)

Ammonia, 

unfiltered 

(mg/L)

(00610)

Ammonia 

plus organic 

nitrogen, 

water, 

unfiltered 

(mg/L)

(00625)

Nitrogen, 

total, 

unfiltered 

(mg/L)

(00600) 

Phosphorus, 

unfiltered 

(mg/L)

(00665)

Chlorophyll a

(μg/L)

(70951)

Chlorophyll b

(μg/L)

(70952)

Site 6; Red River at Cass Co. 20 Bridge at Fargo, N. Dak. (RM439.15) Site 6; Red River at Cass Co. 20 Bridge at Fargo, N. Dak. (RM439.15

Number of values 9 9 9 9 9 2 8 2 9 2 9 9 9 9 9 2 2

Minimum 810 8.0 12.9 8.8 1.76 9.85 .18 4.52 .54 5.33 3.39 .06 .76 4.52 .95 9.90 2.17

Mean 848 8.1 13.2 9.2 2.01 -- .96 -- 1.15 -- 4.67 .10 .86 5.53 1.18 -- --

Median 860 8.1 13.0 9.2 2.06 -- 1.12 -- .88 -- 4.75 .10 .82 5.60 1.21 -- --

Maximum 867 8.1 14.1 9.9 2.15 10.4 1.33 4.62 1.96 5.78 5.57 .14 1.13 6.37 1.29 E10.0 E3.33

Site 7; Red River 1.5 mile below Cass Co. 20 at Fargo, N. Dak. (RM437.6) Site 7; Red River 1.5 mile below Cass Co. 20 at Fargo, N. Dak. (RM437.6)

Number of values 9 9 9 9 9 2 8 2 8 2 9 8 9 9 9 2 2

Minimum 815 8.0 12.3 8.5 1.79 10.1 .05 2.01 .65 6.26 3.34 .03 .51 4.09 .81 E10.0 E3.33

Mean 853 8.1 12.7 9.2 1.93 -- 1.47 -- 1.32 -- 4.47 .08 .94 5.40 1.08 -- --

Median 856 8.1 12.5 9.4 1.94 -- .80 -- 1.36 -- 4.72 .08 .87 5.63 1.15 -- --

Maximum 871 8.2 13.4 9.8 2.13 10.3 7.08 3.84 2.13 8.26 5.22 .14 1.56 6.46 1.22 13.8 3.68

Site 9.5; Red River at Cass Co. 22 Bridge below Fargo, N. Dak. Site 9.5; Red River at Cass Co. 22 Bridge below Fargo, N. Dak.

Number of values 9 9 9 9 9 2 7 2 9 2 9 9 9 9 9 2 2

Minimum 837 8.1 11.5 8.9 1.57 9.22 .18 3.47 .50 5.75 3.86 <.01 .46 4.45 .85 9.90 1.04

Mean 866 8.1 12.2 9.2 1.80 -- .86 -- 1.14 -- 4.41 .09 .82 5.22 1.06 -- --

Median 871 8.1 12.4 9.2 1.78 -- .87 -- .88 -- 4.52 .08 .83 5.53 1.11 -- --

Maximum 881 8.2 12.8 9.6 2.11 9.93 1.23 4.07 2.11 5.86 4.79 .15 1.12 5.77 1.17 14.2 4.87

Site 10; Red River 3.7 mile above Cass Co. 22 Bridge below Fargo, N. Dak. Site 10; Red River 3.7 mile above Cass Co. 22 Bridge below Fargo, N. Dak.

Number of values 9 9 9 9 9 2 9 2 9 2 9 8 9 9 9 2 2

Minimum 866 8.1 11.4 9.3 1.50 8.57 .14 3.75 .72 4.46 3.34 <.01 .92 4.26 .87 E9.68 E3.22

Mean 880 8.1 11.9 9.7 1.74 -- .45 -- 1.28 -- 4.30 .05 1.03 5.34 1.05 -- --

Median 884 8.1 11.8 9.5 1.69 -- .27 -- 1.35 -- 4.38 .04 1.02 5.41 1.09 -- --

Maximum 889 8.2 12.5 10.1 2.11 9.23 .96 4.11 1.97 5.48 4.96 .19 1.27 5.93 1.16 <12.0 <4.00

1

Results reported after 96 days were referred to as ultimate oxygen demand.

2

Parameter code not available.

Table 6. Statistical summaries for selected field property values and constituent concentrations for the Red River of the North, 

September 24 through 27, 2003.—Continued

[Site names and locations are given in table 1. Number in parentheses is parameter code. μS/cm, microsiemens per centimeter; °C, degrees Celsius; mg/L, 

milligrams per liter; BOD, biochemical oxygen demand; μg/L, micrograms per liter; <, less than; --, not calculated; WWTP, wastewater-treatment plant; 

E, estimated]

Table 6. Statistical summaries for selected field property values and constituent concentrations for the Red River of the North, 

September 24 through 27, 2003.—Continued

[Site names and locations are given in table 1. Number in parentheses is parameter code. μS/cm, microsiemens per centimeter; °C, degrees Celsius; mg/L, 

milligrams per liter; BOD, biochemical oxygen demand; μg/L, micrograms per liter; <, less than; --, not calculated; WWTP, wastewater-treatment plant; 

E, estimated]

20 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North Methods 21
Table 7. Comparison of wastewater-treatment plant effluent water-quality data at different sampling locations for Fargo, North Dakota 

and Moorhead, Minnesota.

[mg/L, milligrams per liter; °C, degrees Celsius; BOD, biochemical oxygen demand; WWTP, wastewater-treatment plant; --, not calculated; <, less than]

pH 

(standard units)

(00400)

Temperature, 

water 

(°C)

(00010)

Dissolved 

oxygen 

(mg/L)

(00300)

 BOD, 

5-day 

(mg/L)

(00319)

Carbonaceous 

BOD, 5-day 

(mg/L)

(00320)

Ammonia, 

unfiltered 

(mg/L)

(00610)

Phosphorus, 

unfiltered 

(mg/L)

(00665) 

Red River of the North at WWTP outflow at Moorhead, Minn. (site 2)1

Number of values 9 9 9 9 9 9 9

Minimum 7.0 14.5 7.3 6.44 -- 9.89 3.74

Mean 7.0 15.3 7.5 7.29 -- 10.6 3.86

Median 7.0 15.3 7.5 7.26 -- 10.5 3.85

Maximum 7.0 16.3 7.7 7.89 -- 11.4 4.02

Last sampling point inside Moorhead, Minn., WWTP2

Number of values 5 5 5 -- 3 3 1

Minimum 7.0 14.0 6.9 -- 3.6 8.70 4.18

Mean 7.4 15.6 7.6 -- 4.8 8.90 --

Median 7.7 16.0 7.6 -- 4.9 8.80 --

Maximum 7.7 17.0 8.2 -- 5.8 9.20 4.18

Red River of the North at WWTP outflow at Fargo, N. Dak. (site 5.8)1

Number of values 1 1 1 9 9 9 9

Minimum 7.4 19.7 8.8 1.31 1.34 <.01 4.76

Mean -- -- -- 1.72 1.75 -- 4.84

Median -- -- -- 1.66 1.71 -- 4.84

Maximum 7.4 19.7 8.8 2.19 2.19 <.01 4.94

Last sampling point inside Fargo, N. Dak., WWTP2

Number of values 5 5 2 3 -- 2 --

Minimum 7.5 19.7 8.6 3.10 -- <.10 --

Mean 7.5 20.4 -- 3.50 -- -- --

Median 7.5 20.8 -- 3.30 -- -- --

Maximum 7.6 20.9 8.6 4.10 -- .13 --

1

Based on data for samples collected during 2003 study, September 24 through 27, 2003. Samples were collected by the U.S. Geological Survey and analyzed 

by the North Dakota Department of Health, Bismarck, North Dakota.

2

Based on data for daily samples collected September 22 through 27, 2003. Samples were collected and analyzed by staff at the wastewater-treatment plant.

22 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
Figure 9. Moorhead, Minnesota, wastewater-treatment plant outfall during September 24 through 27, 2003, streamflows.

Methods 23
24 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

Model Implementation

The Fargo WASP water-quality model was developed 

using the USEPA WASP model, Version 7.3 (Ambrose and 

others, 1988; Wool and others, 2003; U.S. Environmental Protection Agency, 2005). WASP 7.3 is an enhanced 

Windows version of the WASP model and has features that 

include a preprocessor, a rapid data processor, and a graphical postprocessor that facilitate application of the model. The 

basic equation solved by the WASP 7.3 model is the onedimensional, advection-dispersion, mass-transport equation, 

which is numerically integrated in space and time for each 

water-quality constituent. For the purposes of this study, the 

WASP model was used in a steady-state mode.

Computational Grid

The physical domain of the Fargo WASP water-quality 

model includes the Red River main stem from just downstream 

from Dam A (site 1) to about 2 mi upstream from the confluence of the Sheyenne and Red Rivers (site 10, fig. 10). The 

model includes one main-branch and two point-source sites 

representing discharges from the Moorhead WWTP outfall 

(site 2) and the Fargo WWTP outfall (site 5.8). The 19.2-mi 

reach of the Red River is represented by 306 one-dimensional 

segments. Model segments were proportionally distributed 

among the sites so each segment was about 330 ft in length.

outfall (site 2) was 5.6 ft3/s and at the Fargo WWTP outfall 

(site 5.8) was 16.3 ft3/s.

As with streamflow boundary conditions, water-quality 

boundary conditions were specified for the most upstream site 

(site 1) and for each of the two point-source sites (sites 2 and 

5.8). Water-quality boundary conditions were specified for 

DO, CBODu, nitrate, ammonia, organic nitrogen, and chlorophyll a (a surrogate for phytoplankton). An average of the 

measured time series of concentrations was used to define the 

water-quality boundary conditions.

The following assumptions were made before specifying 

water-quality boundary conditions in the model:

•	 Nitrite plus nitrate concentrations were used to represent nitrate concentrations because samples were not 

analyzed for nitrite concentrations. Hereinafter, nitrite 

plus nitrate will be referred to as nitrate.

•	 If measured concentrations for selected constituents 

were less than the detection limit, half the detection 

limit was used as the water-quality boundary condition.

•	 Because of safety issues associated with measuring 

field properties at the Fargo WWTP outfall (site 5.8), 

the average DO concentration of 8.7 mg/L for samples 

collected at the last sampling location inside the 

Fargo WWTP (table 7) was used as the water-quality 

boundary condition for the Fargo WWTP outfall, and 

the average chlorophyll a concentration for samples 

collected at the Moorhead WWTP outfall (site 2) was 

used as the boundary condition for the Fargo WWTP 

outfall.

•	 Organic nitrogen concentrations were calculated by 

subtracting ammonia concentrations from Kjeldahl 

nitrogen concentrations (table 5).

Model Calibration and Testing

The Fargo WASP water-quality model was calibrated for 

streamflow, transport, DO, and ammonia using data collected 

from September 24 through 27, 2003. Model testing was 

performed using available data from the 1989 and 1990 data 

sets collected during the Wesolowski (1994) study.

Streamflow and Transport

The Fargo WASP water-quality model was calibrated 

for streamflow and transport during steady-state conditions 

throughout the study reach. In the USEPA WASP model, 

streamflow can be simulated using a kinematic wave formulation (Wool and others, 2003). The kinematic wave formulation, which is based on Manning’s equation, assumes onedimensional flow and uses channel slope, width, initial depth, 

flow, and roughness to calculate water movement (Wool and 

Streamflow and Water-Quality Boundary 

Conditions

Streamflow and water-quality boundary conditions were 

specified for September 17 through September 27, 2003. The 

first 7 days were used as an initialization period. That number 

of days represents about twice the traveltime through the study 

reach. Thus, simulated results subsequent to the 7-day initialization period should be unaffected by initial conditions.

Streamflow boundary conditions were specified for the 

most upstream (main-branch) site (site 1) and for each of the 

two point-source sites (sites 2 and 5.8; the WWTP outfalls). A 

single streamflow value was specified for each of the boundary conditions and held constant because streamflow was 

assumed to be steady. An upstream streamflow boundary 

condition of 73 ft3/s was determined by taking an average of 

the instantaneous streamflow measured at site 4 on September 24, 2003 (table 2), with the daily mean streamflow at the 

Red River of the North at Fargo gaging station (05054000; 

fig. 3) on September 24, 2003. Daily mean discharges from 

the Moorhead and Fargo WWTPs were obtained from the 

respective facilities. Discharge from the WWTP outfalls was 

added as a point inflow in the model segment that represented 

the actual location of the WWTP outfall. The mean discharge 

for September 24 through 27, 2003, at the Moorhead WWTP 
37–82

2–36

83–127

128–133

134–155

156–179

180–246

247–306

446.6

443.7

440.9

440.5

439.15

437.6

433.42

429.7

1

2

4

5

9.5

7

6

5.7

10

MOORHEAD, MINNESOTA, WASTEWATER-TREATMENT PLANT OUTFALL (POINT-SOURCE SITE)

END OF STUDY REACH

 EXPLANATION

 SITE NUMBER

 WASTEWATER-TREATMENT

 PLANT OUTFLOW

 TRIBUTARY

1

5.8 FARGO, NORTH DAKOTA, WASTEWATER-TREATMENT PLANT OUTFALL (POINT-SOURCE SITE)

STUDY REACH

RIVER

MILE

MODEL SEGMENT

NUMBERS

UPSTREAM SITE (BEGINNING OF STUDY REACH)

448.89

448.9

SHEYENNE RIVER

1

Figure 10. Schematic of the Fargo Water-Quality Analysis Simulation Program model.

Model Calibration and Testing 25
26 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

others, 2003). In the kinematic wave formulation, the default 

is a rectangular channel shape unless the hydraulic coefficients 

for velocity and depth are specified. Initially, the kinematic 

wave formulation was used to simulate streamflow in the 

Fargo WASP water-quality model, but the assumption of a 

rectangular channel shape resulted in simulated velocities and 

depths that were not in close agreement with measured velocities and depths. Therefore, to better simulate velocities and 

depths with the Fargo WASP water-quality model, hydraulic 

coefficients were specified. Accurate velocities are important 

in calibration of the model for transport because of the effects 

of velocity on traveltime. Accurate depths are important in 

calibration of the model for DO because of the effects of depth 

on reaeration.

In the USEPA WASP model, power functions are used, 

after hydraulic coefficients are specified, to relate velocity, 

depth, and channel width to streamflow. The power functions 

are described by

V = aQb, (1)

D = cQd, (2)

B = eQf, (3)

where

V is the average velocity, in feet per second;

Q is streamflow, in cubic feet per second;

D is the average depth, in feet;

B is the average width, in feet; and

a, b, c, d, e, and f are empirical hydraulic coefficients.

When the power functions are used to simulate streamflow, the USEPA WASP model only requires specification 

of the hydraulic coefficients for velocity (eq. 1) and depth 

(eq. 2) because the coefficients for width (eq. 3) are implicitly 

determined by continuity (Wool and others, 2003). Brown 

and Barnwell (1987) indicated exponents b and d should be 

estimated and then multipliers a and c should be calibrated to 

measured streamflow, velocity, and depth. For this study, average literature values of 0.43 and 0.45 were used for exponents 

b and d, respectively (Wool and others, 2003). Multipliers a

and c then were calculated from 2003 measured streamflow, 

velocity, and depth for each site (table 8).

After the power functions were specified for the Fargo 

WASP water-quality model, the model was calibrated 

for transport. Because of uncertainty associated with the 

traveltime and velocity determined from the dye study 

for site 4, calibration for transport was started at site 5. 

Thus, all sites downstream from site 5 were used in the 

calibration. Calibration was achieved by fitting simulated 

time-concentration dye curves to measured time-concentration 

dye curves through the adjustment of velocity and longitudinal dispersion coefficients. Velocity was adjusted by varying 

the segments to which the power functions were applied until 

the best fit between measured and simulated traveltimes was 

achieved. Initially, the power function for a given site was 

applied midway between the sites immediately upstream 

and downstream from the given site. The segments to which 

a given power function was applied then were adjusted to 

achieve the best fit between the measured and simulated 

traveltimes (table 9). The longitudinal dispersion coefficients 

computed by Wesolowski (1994) for the same reach of the 

Red River as used in this study were between 10 and 100 ft2/s. 

For the Fargo WASP water-quality model, longitudinal dispersion coefficients were determined from calibration and were 

within the typical range of those computed by Wesolowski 

(1994). Longitudinal dispersion coefficients for the Fargo 

WASP water-quality model were determined to be 10 ft2/s 

for segments 1–59 (sites 1 to 4), 22 ft2/s for segments 60–157 

(sites 5 to 6), and 55 ft2/s for segments 158–306 (sites 7 to 10).

After the Fargo WASP water-quality model was calibrated for transport, goodness-of-fit statistics were computed 

for selected features of the time-concentration dye curves. 

Goodness-of-fit statistics were computed only for sites 

where a SCUFA was used to measure dye concentration (namely, sites 5.7, 7, and 10, table 10). The simulated 

time-concentration dye curves for the SCUFA sites were in 

reasonable agreement with the measured time-concentration 

dye curves (fig. 11). The simulated peak concentrations for 

sites 5.7, 7, and 10 were within 10 percent of the measured 

concentrations (fig. 11 and table 10). Dye concentrations 

measured with the SCUFA and Turner Designs model 10 

fluorometers generally are accurate to within 5 percent of the 

calibration standard (Thomas Brumett, Turner Designs, Inc., 

written commun., 2007). The peak concentrations for sites 5.7, 

7, and 10 were closest to a calibration standard of 10 μg/L, so 

measured dye concentrations should be accurate to within plus 

or minus 0.5 μg/L. On the basis of the accuracy of the SCUFA, 

differences between the measured and simulated peak concentrations for sites 5.7, 7, and 10 were within the measurement 

error of the fluorometer. The simulated traveltimes of the dye 

cloud centroids for sites 5.7, 7, and 10 were within 7 percent 

of the measured traveltimes (table 10). The variances of the 

simulated dye concentrations were similar to the variances of 

the measured dye concentrations (table 10), indicating dispersion was reproduced reasonably well. For sites 5, 6, and 9.5, 

the overall timing of the simulated dye cloud was reasonable 

as compared with that of the measured dye clouds (fig. 12). 

Also, for sites 5, 6, and 9.5, the peak concentrations were all 

within 0.5 μg/L, or the measurement error of the fluorometer.
Table 8. Estimated hydraulic coefficients for power functions used in Fargo Water-Quality Analysis Simulation Program model.

[a and b, velocity multiplier and exponent used in the power function, V = aQb; c and d, depth multiplier and exponent used in the power function, D = cQd]

Site number 

(fig. 2)

Q1

(cubic feet 

per second)

V2

(feet per 

second)

a4 b3 D5

(feet) c7 d 6

4 84.3 0.61 0.0906 0.43 2.19 0.2976 0.45

5 82.9 .40 .0599 .43 2.19 .2997 .45

5.7 83.3 .37 .0552 .43 2.26 .3093 .45

6 95.4 .63 .0887 .43 2.14 .2751 .45

7 100.8 .39 .0537 .43 2.48 .3115 .45

9.5 99.8 .47 .0649 .43 2.72 .3429 .45

10 85.9 .65 .0958 .43 2.49 .3363 .45

1

Measured streamflow on September 24, 25, or 26, 2003.

2

Average measured velocity between September 24 and 26, 2003.

3

An average literature value (Brown and Barnwell, 1987).

4

Given Q, V, and b, the power function was used to solve for a.

5

Average measured depth on September 24, 25, or 26, 2003.

6

An average literature value (Brown and Barnwell, 1987).

7

Given Q, V, and d, the power function was used to solve for c.

Table 9. Calibrated hydraulic coefficients for power functions used in Fargo Water-Quality Analysis Simulation Program model.

[a and b, velocity multiplier and exponent used in the power function, V = aQb; c and d, depth multiplier and exponent used in the power function, D = cQd]

Segments where power 

function was applied a b c d

1–59 0.0906 0.43 0.2976 0.45

60–83 .0599 .43 .2997 .45

84–133 .0552 .43 .3093 .45

134–213 .0537 .43 .3115 .45

214–247 .0649 .43 .3429 .45

248–306 .0958 .43 .3363 .45

Table 10. Goodness-of-fit statistics for calibration of transport.

[μg/L, micrograms per liter. Percent difference is simulated minus measured divided by measured]

Site number 

(fig. 2)

Peak concentration

 (μg/L)

Traveltime of dye cloud centrorid 

(hours)

Variance of dye cloud concentration 

(μg2

/L2)

Measured Simulated Percent 

difference Measured Simulated Percent difference Measured Simulated

5.7 5.32 4.82 –9.4 24.33 23.63 –2.9 2.67 3.23

7 3.23 3.20 –.9 36.02 33.50 –7.0 .60 .77

10 2.20 2.14 –2.7 58.47 59.70 2.1 .51 .45

Model Calibration and Testing 27
0

2

4

6

8

10

09/24/03 09/25/03 09/25/03 09/26/03 09/26/03 09/27/03 09/27/03 09/28/03

DYE CONCENTRATION, IN MICROGRAMS PER LITER

Site 7 measured

Site 10 measured

ELAPSED TRAVELTIME AFTER INJECTION

Site 5.7 measured

Site 5.7 simulated

Site 7 simulated

Site 10 simulated

DYE CONCENTRATION, IN MICROGRAMS PER LITER

Site 5 measured

Site 6 measured

Site 5 simulated

Site 6 simulated

Site 9.5 simulated

Site 9.5 measured

0

2

4

6

8

10

9/24/03

0:00

9/24/03

12:00

9/25/03

0:00

9/25/03

12:00

9/26/03

0:00

9/26/03

12:00

9/27/03

0:00

9/27/03

12:00

ELAPSED TRAVELTIME AFTER INJECTION

Figure 11. Measured and simulated dye concentrations for Fargo Water-Quality Analysis Simulation Program model calibration 

sites 5.7, 7, and 10 for September 24 through 27, 2003. At these sites, the dye concentration of the water was measured 

continuously using a Self-Contained Underwater Fluorescence Apparatus (SCUFA) submersible fluorometer.

Figure 12. Measured and simulated dye concentrations for Fargo Water-Quality Analysis Simulation Program model calibration 

sites 5, 6, and 9.5 for September 24 through 27, 2003. At these sites, the dye concentration of the water was measured discretely 

using a Turner Designs model 10 fluorometer.

28 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
Model Calibration and Testing 29

Water Quality

Several state variables and kinetic interactions are used in 

the USEPA WASP model to simulate DO and nutrient cycles 

(fig. 13). Although the phosphorus cycle can be simulated, 

only DO and the nitrogen cycle were simulated for the Fargo 

WASP water-quality model. State variables are defined here as 

those variables for which concentrations were simulated over 

time. State variables used in the Fargo WASP water-quality 

model included DO, CBOD, nitrate, ammonia, and organic 

nitrogen. Ultimate CBOD was used to represent CBOD in the 

Fargo WASP water-quality model. Several kinetic interactions 

affecting the state variables and model parameters describing the kinetic interactions were included in the Fargo WASP 

water-quality model (table 11). The Fargo WASP water-quality 

model was calibrated for DO and ammonia by specifying 

model parameters and adjusting selected model parameters to 

achieve the best fit between measured and simulated concentrations at sites 4, 5, 5.7, 6, 7, 9.5 and 10.

A combination of measured values, literature values, 

and calibrated values was used for the model parameters 

(table 11). The reaeration-rate coefficient and sediment 

oxygen demand describe kinetic interactions involving reaeration by atmospheric oxygen and DO consumption (fig. 13 and 

table 11). The calculated average reaeration-rate coefficient 

of 1.4 per day was used in the Fargo WASP water-quality 

model (table 4). For sediment oxygen demand, an average 

value was used from the Wesolowski (1994) study because 

sediment oxygen demand was not measured during the 2003 

study (table 11). The BOD decay-rate constant describes the 

kinetic interaction between CBODu and DO, and was determined through calibration (table 11). Biochemical oxygen 

demand decay-rate constants can be determined graphically, 

but the graphical method did not work for this study because 

too few data were available. Instead, the BOD decay rate was 

determined through calibration and was varied spatially to 

account for different decay rates downstream from the two 

different WWTPs. A BOD decay-rate constant of 0.09 per 

day was used downstream from the Moorhead WWTP, and 

a decay-rate constant of 0.25 per day was used downstream 

from the Fargo WWTP. Settling of CBODu is a kinetic interaction that can be simulated (fig. 13), but it was not simulated 

in the Fargo WASP water-quality model because measured 

CBOD settling rates were not available. Ultimate CBOD 

settling is most likely negligible because CBOD5 and total 

suspended solids concentrations are typically low from both of 

the WWTPs (table 7; Bob Zimmerman, Moorhead Wastewater Treatment Facility, written commun., 2007; Peter Bilstad, 

Fargo Wastewater Treatment Plant, written commun., 2007). 

Nitrification is the kinetic interaction between ammonia 

and dissolved oxygen whereby ammonia, in the presence of 

oxygen and nitrifying bacteria, is converted through a two-step 

process to nitrate. During the nitrification process, oxygen 

is consumed at a rate that is described by the nitrification 

rate constant (table 11). The nitrification rate constant can be 

determined graphically, but too few data were available in this 

study. Organic nitrogen is converted into ammonia through the 

process of mineralization (bacterial decomposition). Mineralization was simulated in the Fargo WASP water-quality 

model and is described by the dissolved organic nitrogen 

mineralization rate constant (table 11). An average value of 

0.02 per day from Wesolowski (1994) was used in the model. 

Phytoplankton was not simulated as a state variable; however, 

model parameters relating to phytoplankton were specified 

in order to simulate photosynthetic production of oxygen 

and respiratory consumption of oxygen by phytoplankton 

(table 11). A combination of literature and calibrated values 

was used for model parameters related to phytoplankton. 

Many of the model parameters have a temperature coefficient 

associated with them (table 11), which is used to calculate the 

effect of temperature on the model parameter. Temperature can 

be simulated as a state variable in the USEPA WASP model, 

but for the Fargo WASP water-quality model, a mean water 

temperature was computed for each site on the main stem 

of the river and held constant. The mean water temperature 

for a given site (table 6) then was applied to the segment of 

the study reach that contained the given site and to segments 

midway between the site immediately upstream from the given 

site and the site immediately downstream from the given site.

After the model parameters were specified and calibrated, 

mean measured concentrations were compared with mean 

simulated concentrations. Simulated results for DO, ammonia, 

CBODu, nitrate, and organic nitrogen for sites 4, 5, 5.7, 6, 7, 

9.5, and 10 are presented, along with measured concentrations for site 1 for reference (figs. 14, 15, and 16). The effect 

of the WWTPs on constituent concentrations is visible in the 

longitudinal profile of measured and simulated concentrations. 

Changes in measured constituent concentrations generally 

occurs downstream from the WWTPs, which can result in a 

corresponding change in model parameters. In the USEPA 

WASP model, selected model parameters can be varied 

spatially. As a result, prediction of constituent concentrations 

tended to be grouped into two reaches—one downstream from 

the Moorhead WWTP (site 2) and another downstream from 

the Fargo WWTP (site 5.8).

For sites downstream from the Moorhead WWTP, DO 

concentrations were slightly underpredicted; for sites downstream from the Fargo WWTP, DO concentrations were 

slightly overpredicted (fig. 14). The difference between 

average simulated DO concentrations and average measured 

concentrations for sites 5.7 and 6 were less than 2 percent. 

Overall, the average simulated concentrations for all calibration sites were within 6 percent of the average measured 

concentrations.

Accurate simulation of DO is dependent upon many 

kinetic interactions. Concurrent with calibration, model 

parameters that describe the major kinetic interactions 

affecting DO were increased by 50 percent to determine the 

sensitivity of DO to these model parameters. The prediction of 

DO appears to be most sensitive to the reaeration-rate coefficient (table 12). For all model parameters, with the exception of the nitrification rate constant, a 50-percent increase 
NO3 = nitrate nitrogen

NH3 = ammonia nitrogen

ON = organic nitrogen

PHYT = phytoplankton

CBOD = carbonaceous biological 

 oxygen demand, ultimate

OPO4 = orthophosphate

OP = organic phosphorus

DO = dissolved oxygen

CO2 = carbon dioxide

O2

 = oxygen

EXPLANATION

Figure 13. State variable interactions for nutrient cycles and 

dissolved oxygen in U.S. Environmental Protection Agency’s Water 

Quality Simulation Program (WASP; from Wool and others, 2003).

30 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

resulted in a consistent change in DO for all sites. With 

a 50-percent increase in the nitrification rate constant, 

DO decreased at site 5, but increased slightly at sites 7 

and 10 (table 12). This is likely related to the disparate 

contributions of ammonia from the WWTPs. During 

the 2003 study, the average ammonia load (streamflow 

multiplied by concentration and an appropriate conversion factor) from the Moorhead WWTP was 323 pounds 

per day and the average ammonia load from the Fargo 

WWTP was 0.45 pound per day. This large difference 

in loads results in an increase in ammonia concentrations just downstream from the Moorhead WWTP, but 

further downstream concentrations steadily decrease. 

Concentrations continue to decrease downstream from the 

Fargo WWTP because the ammonia load from Fargo is 

small. With a 50-percent increase in the nitrification rate 

constant, more ammonia is nitrified downstream from the 

Moorhead WWTP, which results in lower concentrations 

of ammonia downstream from the Fargo WWTP. Thus, at 

the end of the reach, less ammonia is available for nitrification which results in less oxygen being consumed. The 

disparate contributions of ammonia from the WWTPs 

also affect the prediction of the DO concentrations. The 

nitrification rate constant cannot be varied spatially (or 

temporally) in the USEPA WASP model (Wool and 

others, 2003). The nitrification rate constant of 2.5 per 

day is generally accurate for sites downstream from the 

Moorhead WWTP, but is too high for sites downstream 

from the Fargo WWTP. The high nitrification rate downstream from the Fargo WWTP causes too much ammonia 

to be oxidized at sites 6 and 7, which causes very low 

concentrations of ammonia at sites 9.5 and 10. Therefore, 

with low ammonia concentrations at sites 9.5 and 10 and 

a high nitrification rate, little nitrification occurs, which 

causes less oxygen to be consumed and DO to be overpredicted at the end of the study reach.

Ammonia concentrations were slightly overpredicted for sites downstream from the Moorhead WWTP, 

whereas, for sites downstream from the Fargo WWTP, 

ammonia concentrations were increasingly underpredicted (fig. 14). The pattern of overprediction at the 

beginning of the study reach and underprediction at the 

downstream end of the reach resulted from using a single 

nitrification rate constant of 2.5 per day for the entire 

stream reach throughout the simulation. Because the 

nitrification rate constant cannot be varied spatially or 

temporally in the USEPA WASP model, a nitrification 

rate constant that resulted in some overprediction and 

some underprediction of concentrations was unavoidable. 

Overall, the average simulated ammonia concentrations 

are within the range of measured concentrations (fig. 14).

For all sites, simulated CBODu concentrations were 

within 15 percent of the measured concentrations or the 

amount of laboratory error associated with the BOD test 

(American Public Health Association, American Water 

Works Association, and Water Environment Federation, 

1995; fig. 15). The average measured CBODu concentration 

increases between sites 6 and 7; however, the Fargo WASP 

water-quality model does not simulate this increase. There is no 

known point source between sites 6 and site 7 (Andy Bradshaw, 

Moorhead Wastewater Treatment Facility, oral commun., 2007).

 Nitrate concentrations were overpredicted by an average 

of 20 percent for all calibration sites (fig. 16). Several factors 

may have contributed to the overprediction of nitrates: nitrite 

plus nitrate concentrations were used for boundary conditions 

instead of nitrate concentrations; nitrification was overpredicted 

for the end of the reach; denitrification was not simulated; 

and the interaction between phytoplankton and nitrate was not 

simulated. There is some error associated with the laboratory 

test for nitrates, but it is not large enough to account for the 

overprediction of nitrates. Organic nitrogen concentrations were 
Table 11. Model parameters used for Fargo Water-Quality Analysis Simulation Program model.

[mv, measured value; lv, literature value; --, comparable value not available; cv, calibrated value]

Model parameter Type

Value used in Fargo 

Water-Quality Analysis 

Simulation Program model

Calibrated value used in 

Wesolowski (1994) study

Parameters related to dissolved oxygen

Reaeration-rate coefficient at 20 degrees Celsius (per day) mv 1.4 1.7, 1.4

Reaeration rate-temperature coefficient (dimensionless) lv 1.03 (default1) 1.024

Oxygen to carbon stoichiometric ratio (dimensionless) lv 2.67 (default1) --

Sediment oxygen demand (grams of oxygen per square 

foot per day)

lv 0.1 0.1

Sediment oxygen demand temperature coefficient 

(dimensionless)

lv 1.06 1.06

Parameters related to carbonaceous biochemical oxygen demand

Biochemical oxygen demand decay rate constant at 

20 degrees Celsius (per day)

cv 0.09, 0.25 0.05

Biochemical oxygen demand decay rate temperature 

coefficient (dimensionless)

lv 1.047 1.047

Parameters related to ammonia

Nitrification rate constant at 20 degrees Celsius (per day) cv 2.5 --

Nitrification rate temperature coefficient lv 1.047 --

Half saturation constant for nitrification oxygen limit 

(milligrams of oxygen per liter)

cv 1 --

Parameters related to organic nitrogen 

Dissolved organic nitrogen mineralization rate constant at 

20 degrees Celsius (per day)

lv 0.02 Varied by reach

Dissolved organic nitrogen mineralization temperature 

coefficient (dimensionless)

lv 1.047 1.047

Parameters related to phytoplankton

Phytoplankton maximum growth rate constant at 

20 degrees Celsius (per day)

cv 1 1.6

Phytoplankton growth rate temperature coefficient 

(dimensionless)

lv 1.047 1.047

Phytoplankton carbon to chlorophyll ratio 

(dimensionless)

cv 15 --

Phytoplankton endogenous respiration rate constant 

(per day)

lv 0.06 0.06

Phytoplankton respiration rate temperature coefficient 

(dimensionless)

lv 1.047 1.047

1

From U.S. Environmental Protection Agency Water-Quality Analysis Simulation Program model documentation (Wool and others, 2003).

Model Calibration and Testing 31

consistently underpredicted (fig. 16). The concentrations were 

underpredicted by an average of 21 percent for all calibration 

sites. Organic nitrogen concentrations may have been underpredicted because the interaction between phytoplankton and 

organic nitrogen was not simulated.
RIVER MILE

Profile of simulated concentrations

MEASURED DISSOLVED OXYGEN OR AMMONIA

(7) Site number

Maximum concentration

Average concentration

Minimum concentration

EXPLANATION

0

2

4

6

8

10

12

DISSOLVED OXYGEN, IN MILLIGRA

MS PER LITER

River Mile 448.8,

Moorhead, Minnesota,

wastewater-treatment

plant (Site 2)

River Mile 440.5,

Fargo, North Dakota,

wastewater-treatment

plant (Site 5.8)

(1)

(4) (5) (5.7)

(6) (7) (9.5) (10)

0

0.1

0.2

0.3

0.4

0.5

0.6

450 448 446 444 442 440 438 436 434 432 430 428

A

M

MONIA, IN MILLIGRA

MS PER LITER

River Mile 448.8,

Moorhead, Minnesota,

wastewater-treatment

plant (Site 2)

River Mile 440.5,

Fargo, North Dakota,

wastewater-treatment

plant (Site 5.8)

(4)

(5)

(6) (7)

(1)

(5.7)

(9.5)

(10)

Figure 14. Maximum, mean, and minimum measured dissolved-oxygen and ammonia concentrations for calibration 

(September 24 through 27, 2003) data set and average simulated concentrations for Fargo Water-Quality Analysis 

Simulation Program model calibration sites.

32 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
RIVER MILE

Profile of simulated

concentrations

(7) Site number

Maximum concentration

Average concentration

Minimum concentration

EXPLANATION

0

1

2

3

4

5

6

7

8

9

10

450 448 446 444 442 440 438 436 434 432 430 428

ULTIM

ATE CARBONACEOUS BIOCHEMICAL OXYGEN DEM

AND,

IN MILLIGRA

MS PER LITER

River Mile 440.5,

Fargo, North Dakota,

wastewater-treatment

plant (Site 5.8)

River Mile 448.8,

Moorhead, Minnesota,

wastewater-treatment

plant (Site 2)

(1) (5.7)

(9.5)

(10)

(4)

(5)

(6)

(7)

Figure 15. Maximum, mean, and minimum measured ultimate carbonaceous biochemical oxygen demand concentrations 

for calibration (September 24 through 27, 2003) data set and average simulated concentrations for Fargo Water-Quality 

Analysis Simulation Program model calibration sites.

Model Calibration and Testing 33
NITRATE1 , IN MILLIGRA

MS PER LITER

RIVER MILE

Profile of simulated concentrations

MEASURED NITRATE OR ORGANIC NITROGEN

(7) Site number

Maximum concentration

Average concentration

Minimum concentration

EXPLANATION

0

1

2

3

4

5

6

River Mile 440.5,

Fargo, North Dakota,

wastewater-treatment

plant (Site 5.8)

River Mile 448.8,

Moorhead, Minnesota, 

wastewater-treatment 

plant (Site 2)

(1)

(5.7)

(9.5) (10)

(4)

(5)

(6)

(7)

0

0.4

0.8

1.2

1.6

2

450 448 446 444 442 440 438 436 434 432 430 428

ORGANIC NITROGEN, IN MILLIGRA

MS PER LITER

River Mile 448.8,

Moorhead, Minnesota,

wastewater-treatment

plant (Site 2) 

River Mile 440.5,

Fargo, North Dakota,

wastewater-treatment

plant (Site 5.8)

(1)

(5.7)

(9.5)

(10)

(4) (5)

(6)

(7)

1 Nitrite plus nitrate concentrations were used for boundary 

conditions, but were simulated as nitrate concentrations in 

the Fargo Water-Quality Analysis Simulation Program model.

Figure 16. Maximum, mean, and minimum measured nitrate and organic nitrogen concentrations for calibration 

(September 24 through 27, 2003) data set and average simulated concentrations for Fargo Water-Quality Analysis 

Simulation Program model calibration sites.

34 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
Table 12. Percent change in dissolved-oxygen concentration as a result of a 50-percent increase in selected model parameters.

Model parameter Percent change in dissolved-oxygen concentration

Site 5 Site 7 Site 10

Reaeration-rate coefficient at 20 degrees Celsius (dimensionless) 6.2 4.7 3.0

Nitrification rate constant at 20 degrees Celsius (per day) –2.0 .8 .7

Ultimate biochemical oxygen demand decay rate constant at 

20 degrees Celsius (per day)

–.9 –2.0 –2.2

Phytoplankton maximum growth rate constant at 20 degrees Celsius (per day) 1.7 1.9 2.1

Phytoplankton endogenous respiration rate at 20 degrees Celsius (per day) –.1 –.1 –.1

Sediment oxygen demand (grams of oxygen per square foot per day) –.3 –.3 –.3

Model Calibration and Testing 35

Model Testing

The performance of the Fargo WASP water-quality model 

was tested by using August 1989 and August 1990 streamflows and water-quality data from the Wesolowski (1994) 

study for boundary conditions and comparing simulated 

results to the measured data. During the time of data collection 

by Wesolowski, the Fargo WWTP outfall was located at site 8 

(fig. 2 from Wesolowski, 1994). In 1995, the Fargo WWTP 

outfall was relocated further upstream to site 5.8 (fig. 2). 

Therefore, testing could be performed using the August 

1989 and August 1990 data sets for the study reach up to and 

including site 7 as long as boundary conditions were not specified for the relocated Fargo WWTP outfall site (site 5.8).

Traveltimes were tested using streamflows that ranged 

from 60 to 407 ft3/s. Comparisons were made between the 

measured traveltime of the dye cloud centroid for site 7 

and the simulated traveltime of the dye cloud centroid. 

Streamflows for the upstream boundary (site 1) and Moorhead WWTP outfall (site 2) were specified. Results for the 

August 1989 and August 1990 data sets were good; differences between the measured and simulated traveltimes were 

less than 7 percent (table 13). Dispersion coefficients were 

unchanged during model testing.

Model performance for the simulation of DO and ammonia was tested by specifying measured water-quality boundary conditions from August 1989 and August 1990 for the 

upstream boundary (site 1) and the Moorhead WWTP outfall 

(site 2). Other than reaeration rates, the 2003 calibrated model 

parameters (tables 9 and 10) were unchanged. Reaeration rates 

for the 1989 and 1990 data sets were determined using the 

equation given in figure 8. Reaeration rates for a streamflow 

of 140 ft3/s in 1989 and a streamflow of 200 ft3/s in 1990 were 

determined to be 1.07 and 0.91 per day, respectively. Results 

for DO and ammonia for sites 4, 5, 6, and 7 are shown in 

figures 17 and 18. Measured DO concentrations were underpredicted by less than 15 percent for both data sets (fig. 17). 

The simulated DO concentrations were within or close to 

the range of measured DO concentrations for the August 

1989 period, but were considerably less than the measured 

DO concentrations for the August 1990 period. Results for 

ammonia were poor; measured ammonia concentrations were 

underpredicted by as much as 70 percent for both data sets 

(fig. 18).

Overall, application of the Fargo WASP water-quality 

model to the August 1989 and August 1990 data sets resulted 

in poor agreement between the measured and simulated 

concentrations. This likely is a result of changes in the 

composition of the waste load for the Moorhead WWTP. Both 

Fargo and Moorhead made improvements to their WWTPs 

after 1990. The Moorhead WWTP added a tertiary treatment process in the spring of 2003 that uses a Biofilm Carrier 

System to convert ammonia to nitrate (Andy Bradshaw, Moorhead Wastewater Treatment Facility, written commun., 2007). 

In 1995, the Fargo WWTP started to continuously discharge 

wastewater and added a tertiary treatment process that uses 

trickling filters to convert ammonia to nitrate (Peter Bilstad, 

Fargo Wastewater Treatment Plant, written commun., 2007). 

For the Moorhead WWTP, the average ammonia concentration for the 2003 study was about 30 to 40 percent less than 

the average concentration for the 1989 and 1990 data sets, and 

the average CBODu concentration was about 46 to 70 percent 

less than the averages for the August 1989 and August 1990 

data sets (table 14). For the Fargo WWTP, average ammonia 

concentrations have been reduced to less than the detection 

limit of 0.01 mg/L, and the average CBODu concentration 

for the 2003 study was about 60 to 70 percent less than the 

averages for 1989 and 1990 (table 14). The change in wasteload composition for the two WWTPs resulted in two main 

differences between the Wesolowski (1994) study and the 

2003 study. These differences are (1) rate constants have 

changed and (2) DO is no longer being substantially depressed 

downstream from the Moorhead and Fargo WWTPs (fig. 14). 

The Fargo WASP water-quality model is valid for current 

(after 2003) treatment processes at the Fargo and Moorhead 

WWTPs.
Table 13. Measured and simulated traveltimes for streamflows from the Wesolowski (1994) study and the 2003 study.

[ft3/s, cubic feet per second; --, no data]

Site number 

(fig. 2) Date of dye injection Streamflow1(ft3/s)

Traveltime of dye cloud centroid 

(hours)

Percent difference between 

measured and simulated 

Measured Simulated traveltimes

7 8/8/1989 195 22.6 21.8 –3.5

7 8/17/1989 60 38.9 36.4 –6.4

7 4/25/1990 407 16.1 16.1 0

7 10/19/1990 160 25.3 23.9 –5.6

7 9/24/2003 73 36.0 33.6 –6.7

1

A flow of 6 cubic feet per second was used for the Minnesota wastewater-treatment plant outfall for both the 1989 and 1990 data sets.

2

From Fargo Water-Quality Analysis Simulation Program model.

36 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

Summary

In 2003, the U.S. Geological Survey, in cooperation 

with the North Dakota Department of Health, the Minnesota 

Pollution Control Agency, and the cities of Fargo, North 

Dakota, and Moorhead, Minnesota, conducted a time-of-travel 

and reaeration-rate study to provide information to calibrate 

a water-quality model for low-flow conditions (streamflows 

of less than 150 cubic feet per second). Data collected from 

September 24 through 27, 2003, were used to develop and 

calibrate the U.S. Environmental Protection Agency Water 

Quality Analysis Simulation Program model (hereinafter 

referred to as the Fargo WASP water-quality model) for a 

19.2-mile reach of the Red River of the North (hereinafter 

referred to as the Red River).

The data-collection network consisted of 10 sites, including the Fargo and Moorhead wastewater-treatment plant 

outfall sites. Streamflow measurements provided channelgeometry data for the model, and dye and propane gas tracers 

were used to determine traveltime and to calculate reaerationrate coefficients. The calculated reaeration-rate coefficients 

ranged from 1.18 to 1.58 per day. The calculated reaerationrate coefficient for an average streamflow of 85.1 cubic feet 

per second from site 4 to site 10 was 1.4 per day. On the basis 

of residence time, the calculated reaeration-rate coefficient 

from site 4 to site 10 is the most accurate estimate of the 

reaeration-rate coefficient for the study reach.

In the Fargo WASP water-quality model, the 19.2-mile 

reach of the Red River is represented by 306 one-dimensional, 

330-ft segments. The Moorhead and Fargo wastewatertreatment plants are represented as point sources. Streamflow and water-quality boundary conditions were specified 

for September 17 through September 27, 2003. The first 

7 days were used as an initialization period. Streamflow 

and water-quality boundary conditions were specified for 

the most upstream site and for each of the two point-source 

wastewater-treatment plant outfalls. A single streamflow 

value was specified for each of the boundary conditions 

and held constant because streamflow was assumed to be 

steady. Water-quality boundary conditions were specified for 

dissolved oxygen, ultimate carbonaceous biochemical oxygen 

demand, nitrate, ammonia, nitrogen, and chlorophyll a (phytoplankton). An average of the measured time series of concentrations was used to define water-quality boundary conditions.

Power functions, which relate velocity, depth, and channel width to streamflow, were used to simulate streamflow 

in the Fargo WASP water-quality model. For each site, two 

power functions were defined: one for velocity and one for 

depth. A combination of literature values and measured values 

was used for the hydraulic coefficients in the power equations.

The Fargo WASP water-quality model was calibrated 

for the transport of dye by fitting simulated time-concentration 

dye curves to measured time-concentration dye curves through 

the adjustment of velocity and longitudinal dispersion coefficients. Velocity was adjusted by varying the segments to which 

the power functions were applied until the best fit between 

measured and simulated traveltimes was achieved. Longitudinal dispersion coefficients were determined from calibration 

and ranged from 10 to 55 feet squared per second. Simulated 

time-concentration dye curves were in reasonable agreement 

with measured time-concentration dye curves. Simulated peak 

concentrations for sites 5.7, 7, and 10 were within 10 percent 

of the measured concentrations. Simulated traveltimes of 

the dye cloud centroid for sites 5.7, 7, and 10 were within 

7 percent of the measured traveltimes. The variances of the 

simulated dye concentrations were similar to the variances of 

the measured dye concentrations, indicating dispersion was 

reproduced reasonably well.

The Fargo WASP water-quality model was calibrated for 

dissolved oxygen and ammonia by specifying model parameters and adjusting selected model parameters to achieve the 

best fit between measured and simulated concentrations. A 

combination of measured values, literature values, and calibrated values was used for model parameters.
RIVER MILE

Profile of simulated

concentrations

(7) Site number

Maximum concentration

Average concentration

Minimum concentration

EXPLANATION

DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

4

6

8

10

12

14

(4)

(5)

(6) (7)

4

6

8

10

12

14

448 447 446 445 444 443 442 441 440 439 438

(4)

(5)

(6) (7)

August 29-30, 1989, data set

August 14-15, 1990, data set

Figure 17. Maximum, mean, and minimum measured dissolved-oxygen concentrations for August 29–30, 1989, and 

August 14–15, 1990, data sets and average simulated concentrations for Fargo Water-Quality Analysis Simulation 

Program model data set for sites 4, 5, 6, and 7.

Summary 37
Profile of simulated

concentrations

(7) Site number

Maximum concentration

Average concentration

Minimum concentration

EXPLANATION

A

M

MONIA, IN MILLIGRAMS PER LITER

0

0.1

0.2

0.3

0.4

0.5

0.6

(4) (5)

(6)

(7)

August 29–30, 1989, data set

448 447 446 445 444 443 442 441 440 439 438

RIVER MILE

0

0.1

0.2

0.3

0.4

0.5

0.6

(4)

(5)

(6)

(7)

August 14–15, 1990, data set

Figure 18. Maximum, mean, and minimum measured ammonia concentrations for August 29–30, 1989, and August 14–15, 

1990, data sets, and average simulated concentrations for Fargo Water-Quality Analysis Simulation Program model data set 

for sites 4, 5, 6, and 7.

38 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North
Table 14. Selected water-quality constituent concentrations in effluent from the Moorhead and Fargo wastewater-treatment plants 

before and after addition of tertiary treatment to convert ammonia to nitrate (as measured during USGS studies).

[BOD, biochemical oxygen demand; mg/L, milligrams per liter; WWTP, wastewater-treatment plant]

Month and year in which 

data were collected

Ultimate carbonaceous 

BOD 

(mg/L)

Ammonia, unfiltered

(mg/L)

Nitrite plus nitrate, 

unfiltered

(mg/L)

Ammonia plus organic 

nitrogen, unfiltered 

(mg/L)

Moorhead WWTP1

August 1989 21 15.8 0.60 22

August 1990 36.5 17.7 1.03 20

September 2003 11.2 10.6 10.1 11.5

Fargo WWTP2

August 1989 29 9.81 0.23 14.9

August 1990 48 4.45 1.13 11.7

September 2003 12.7 <.01 23.1 1.1

1

Moorhead WWTP added tertiary treatment in 2003.

2

Fargo WWTP added tertiary treamtent in 1995.

Summary 39

Measured constituent concentrations and model parameters were affected by discharge from the wastewater-treatment 

plants. As a result, prediction of constituent concentrations 

tended to be grouped into two reaches—one downstream from 

the Moorhead wastewater-treatment plant and another downstream from the Fargo wastewater-treatment plant.

Dissolved oxygen concentrations were slightly underpredicted for sites downstream from the Moorhead 

wastewater-treatment plant and slightly overpredicted for 

sites downstream from the Fargo wastewater-treatment plant. 

Average simulated dissolved oxygen concentrations for all 

calibration sites were within 6 percent or less of the average 

measured concentrations. The combination of low ammonia 

concentrations and a high nitrification rate caused dissolved 

oxygen to be overpredicted at the downstream end of the study 

reach.

Ammonia concentrations were slightly overpredicted 

for sites downstream from the Moorhead WWTP, whereas 

for sites downstream from the Fargo WWTP, ammonia 

concentrations were increasingly underpredicted. The pattern 

of overprediction at the beginning of the study reach and 

underprediction at the downstream end of the reach resulted 

from using a single nitrification rate constant for the entire 

stream reach throughout the simulation. The average simulated 

ammonia concentrations are within the range of measured 

concentrations.

Simulated ultimate carbonaceous biochemical oxygen 

demand concentrations were within 15 percent of the 

measured concentrations, or the amount of laboratory error 

associated with the biochemical oxygen demand test. Nitrate 

concentrations were overpredicted by an average of 20 percent 

and may have been caused by several different factors. 

Organic nitrogen concentrations were consistently underpredicted, possibly because the interaction between phytoplankton and organic nitrogen was not simulated.

Data sets from August 1989 and August 1990 were used 

to test the performance of the Fargo WASP water-quality 

model. For streamflows that ranged from 60 to 407 cubic feet 

per second, differences between the measured and simulated 

traveltimes were less than 7 percent. Measured dissolvedoxygen concentrations were underpredicted by less than 

15 percent for both data sets. Measured ammonia concentrations were underpredicted by as much as 70 percent for both 

data sets.

Overall, application of the Fargo WASP water-quality 

model to the August 1989 and August 1990 data sets resulted 

in poor agreement between the measured and simulated 

concentrations. This likely is a result of changes in the 

composition of the waste load for the Moorhead wastewatertreatment plant. Tertiary treatment at both wastewatertreatment plants has substantially reduced ammonia concentrations in the plants’ effluent. The change in waste-load 

composition for the two wastewater-treatment plants probably 

resulted in two main differences between the 1994 study and 

the 2003 study. These differences are (1) rate constants have 

changed and (2) dissolved oxygen is no longer being substantially depressed downstream from the wastewater-treatment 

plants. The Fargo WASP water-quality model is valid for 

current (after 2003) treatment processes at the Fargo and 

Moorhead wastewater-treatment plants.
40 Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North

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Publishing support provided by:

Helena Publishing Service Center

For more information concerning this publication, contact:

Director, USGS North Dakota Water Science Center

821 E. Interstate Ave.

Bismarck, ND 58503

(406) 457–5900

Or visit the North Dakota Water Science Center Web site at:

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Lundgren and Nustad—Calibration of a Water-Quality Model for Low-Flow Conditions on the Red River of the North—Scientific Investigations Report 2008–5007