U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2006-5241

Prepared in cooperation with the 

Bureau of Reclamation, U.S. Department of the Interior

Continuous Water-Quality Monitoring and Regression 

Analysis to Estimate Constituent Concentrations and 

Loads in the Red River of the North, Fargo, North Dakota, 

2003-05
Continuous Water-Quality Monitoring 

and Regression Analysis to Estimate 

Constituent Concentrations and Loads in 

the Red River of the North, Fargo, North 

Dakota, 2003-05

By Karen R. Ryberg

Prepared in cooperation with the 

Bureau of Reclamation, U.S. Department of the Interior

Scientific Investigations Report 2006–5241

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

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

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Suggested citation:

Ryberg, K.R., 2006, Continuous water-quality monitoring and regression analysis to estimate constituent concentrations and loads in the Red River of the North, Fargo, North Dakota, 2003-05: U.S. Geological Survey Scientific Investigations Report 2006-5241, 35 p.
iii

Contents

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

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

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

Description of Study Area ...................................................................................................................2

Previous Studies ...................................................................................................................................2

Methods...........................................................................................................................................................2

Streamflow Measurements ................................................................................................................4

Continuous Water-Quality Monitoring...............................................................................................4

Manual Water-Quality Measurements, Sample Collection, and Analysis..................................4

Development of Regression Equations to Estimate Constituent Concentrations ......................7

Calculation of Measured and Estimated Constituent Loads .......................................................11

Results of Regression Analysis .................................................................................................................12

Alkalinity...............................................................................................................................................12

Dissolved Solids..................................................................................................................................13

Sulfate ..................................................................................................................................................13

Chloride.................................................................................................................................................13

Total Nitrite Plus Nitrate ....................................................................................................................17

Total Nitrogen ......................................................................................................................................17

Total Phosphorus ................................................................................................................................21

Suspended Sediment .........................................................................................................................21

Measured and Estimated Constituent Loads ..........................................................................................24

Summary........................................................................................................................................................24

References Cited..........................................................................................................................................26

Figures

1. Map showing location of the Fargo gaging station in the Red River of the 

North Basin, North Dakota..........................................................................................................3

2. Aerial photograph showing location of gaging station and locations of waterquality sampling sites on the Red River of the North in Fargo, North Dakota....................5

3–22. Graphs showing:

3. Streamflow for the Red River of the North at Fargo, North Dakota, 

January 1, 2003, to December 31, 2005 ............................................................................6

4. Turbidity for the Red River of the North at Fargo, North Dakota, January 1, 

2003, to December 31, 2005 ................................................................................................7

5. Specific conductance for the Red River of the North at Fargo, North Dakota, 

January 1, 2003, to December 31, 2005 ............................................................................8

6. Comparison of measured and estimated alkalinity concentrations in the 

Red River of the North at Fargo, North Dakota, 2003-05 .............................................14

7. Comparison of measured and estimated dissolved-solids concentrations 

in the Red River of the North at Fargo, North Dakota, 2003-05 ..................................15
iv

8. Comparison of measured and estimated sulfate concentrations in the 

Red River of the North at Fargo, North Dakota, 2003-05 .............................................16

9. Comparison of measured and estimated chloride concentrations in the Red River of the North at Fargo, North Dakota, 2003-05....................18

10. Comparison of measured and estimated total nitrite plus nitrate concentrations in the Red River of the North at Fargo, North Dakota, 2003-05....................19

11. Measured total nitrogen concentrations in the Red River of the North at 

Fargo, North Dakota, 2003-05...........................................................................................20

12. Comparison of measured and estimated total nitrogen concentrations in 

the Red River of the North at Fargo, North Dakota, 2003-05.......................................22

13. Comparison of measured and estimated total phosphorus concentrations 

in the Red River of the North at Fargo, North Dakota, 2003-05 ..................................23

14. Comparison of measured and estimated suspended-sediment concentrations in the Red River of the North at Fargo, North Dakota, 2003-05....................25

15. Comparison of measured and estimated alkalinity loads in the Red River of the 

North at Fargo, North Dakota, 2003-05...........................................................................28

16. Comparison of measured and estimated dissolved-solids loads in the Red 

River of the North at Fargo, North Dakota, 2003-05 .....................................................29

17. Comparison of measured and estimated sulfate loads in the Red River of 

the North at Fargo, North Dakota, 2003-05 ....................................................................30

18. Comparison of measured and estimated chloride loads in the Red River of 

the North at Fargo, North Dakota, 2003-05 ....................................................................31

19. Comparison of measured and estimated total nitrite plus nitrate loads in 

the Red River of the North at Fargo, North Dakota, 2003-05.......................................32

20. Comparison of measured and estimated total nitrogen loads in the Red 

River of the North at Fargo, North Dakota, 2003-05 .....................................................33

21. Comparison of measured and estimated total phosphorus loads in the 

Red River of the North at Fargo, North Dakota, 2003-05 .............................................34

22. Comparison of measured and estimated suspended-sediment loads in the 

Red River of the North at Fargo, North Dakota, 2003-05 .............................................35

Tables

1. Summary statistics for manually measured water-quality physical properties and 

constituents for the Red River of the North at Fargo, North Dakota, 2003-05 ....................9

2. Constituents estimated using regression equations for the Red River of the North 

at Fargo, North Dakota, 2003-05 .................................................................................................9

3. Possible surrogate physical properties, or explanatory variables, used to develop 

regression equations to estimate constituent concentrations in the Red River of 

the North at Fargo, North Dakota, 2003-05 .............................................................................10

4. Conversion factors used in calculation of measured and estimated loads .....................11

5. Regression equations for estimates of alkalinity, dissolved solids, chloride, sulfate, 

total nitrogen, total nitrite plus nitrate, total phosphorus, and suspended sediment 

in the Red River of the North at Fargo, North Dakota, 2003-05 ...........................................12
Conversion Factors, Abbreviations, and Datum

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

yard (yd) 0.9144 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Flow rate

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

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

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

°F=(1.8×°C)+32

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

°C=(°F-32)/1.8

A nanometer is one millionth of a millimeter.

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 

25°C).

Concentrations of chemical constituents in water are given in milligrams per liter (mg/L).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).
Continuous Water-Quality Monitoring and Regression 

Analysis to Estimate Constituent Concentrations and 

Loads in the Red River of the North, Fargo, North Dakota, 

2003-05

By Karen R. Ryberg

managers for comparison of current water-quality conditions 

to water-quality standards expressed as total maximum daily 

loads (TMDLs). TMDLs are a measure of the maximum 

amount of chemical constituents that a water body can receive 

and still meet established water-quality standards. The peak 

loads generally occurred in June and July when streamflow 

also peaked.

Introduction

The U.S. Geological Survey (USGS) gaging station 

(05054000) at Fargo, North Dakota, was established in June 

1901 to provide stage (gage-height) and streamflow values 

for the Red River of the North (Red River). The USGS began 

collecting water-quality samples at the gaging station in 1949. 

Since 1994, the gaging station has been equipped with a datacollection platform that uses satellite technology to transmit 

real-time stage and streamflow data 24 hours a day. In 1998, 

a continuous water-quality monitor began recording specific 

conductance (an indicator of dissolved chemical constituents 

in the water and the ability of water to conduct an electrical 

current) and water temperature. Continuous measurements of 

pH (a measure of hydrogen-ion activity), turbidity (an indicator of the amount of suspended sediment in the water), and 

dissolved oxygen concentration (an indicator of the balance 

between oxygen-consuming and oxygen-producing processes) 

began in October 2003. An acoustic doppler velocity meter 

(ADVM) was installed at the gaging station in 2004. The 

ADVM measures an instream index velocity that is related to 

mean channel velocity. Mean channel velocity, in conjunction 

with stage, allows for more accurate computation of real-time 

streamflows. For the study described in this report, the data 

collected at the USGS gaging station at Fargo during 2003-05 

were analyzed in cooperation with the Bureau of Reclamation, 

U.S. Department of the Interior, to determine whether streamflow and the continuously recorded physical properties could 

act as surrogates to estimate water-quality constituents that 

are important indicators of surface-water quality. The methods 

Abstract

This report presents the results of a study by the U.S. 

Geological Survey, done in cooperation with the Bureau of 

Reclamation, U.S. Department of the Interior, to estimate 

water-quality constituent concentrations in the Red River 

of the North at Fargo, North Dakota. Regression analysis of 

water-quality data collected in 2003-05 was used to estimate 

concentrations and loads for alkalinity, dissolved solids, 

sulfate, chloride, total nitrite plus nitrate, total nitrogen, 

total phosphorus, and suspended sediment. The explanatory 

variables examined for regression relation were continuously 

monitored physical properties of water—streamflow, specific 

conductance, pH, water temperature, turbidity, and dissolved 

oxygen. For the conditions observed in 2003-05, streamflow 

was a significant explanatory variable for all estimated constituents except dissolved solids. pH, water temperature, and 

dissolved oxygen were not statistically significant explanatory variables for any of the constituents in this study. Specific conductance was a significant explanatory variable for 

alkalinity, dissolved solids, sulfate, and chloride. Turbidity 

was a significant explanatory variable for total phosphorus and 

suspended sediment. For the nutrients, total nitrite plus nitrate, 

total nitrogen, and total phosphorus, cosine and sine functions 

of time also were used to explain the seasonality in constituent 

concentrations.

The regression equations were evaluated using common 

measures of variability, including R2, or the proportion of variability in the estimated constituent explained by the regression equation. R2

 values ranged from 0.703 for total nitrogen 

concentration to 0.990 for dissolved-solids concentration. The 

regression equations also were evaluated by calculating the 

median relative percentage difference (RPD) between measured constituent concentration and the constituent concentration estimated by the regression equations. Median RPDs 

ranged from 1.1 for dissolved solids to 35.2 for total nitrite 

plus nitrate.

Regression equations also were used to estimate daily 

constituent loads. Load estimates can be used by water-quality 
used in this study replicate those used in Kansas and may be 

replicated for other sites in North Dakota and the Nation to 

monitor water quality.

Estimation of water-quality constituents on the basis of 

surrogates provides several benefits. Although periodic Red 

River water samples are collected manually and analyzed, 

the delay associated with laboratory analysis does not permit 

immediate identification of undesirable levels of constituents. 

A relation between manually collected water-quality samples 

and real-time water-quality measurements allows immediate 

identification of potential water-quality problems. Examination of streamflow and physical properties of water that act as 

surrogates for constituents of interest also helps optimize visits 

for the collection of water-quality samples. For example, if 

turbidity is used as a surrogate for estimating suspended sediment, it is desirable to collect water-quality samples representative of the range of turbidity values possible for the Red 

River. In addition, the estimation of real-time water-quality 

information is useful in tracking changes in water quality as 

they occur. This information is important to North Dakota and 

Minnesota as well as Canada in assessing efforts to improve 

water quality in the upper Red River Basin. Availability of 

real-time information also could be used to assist the cities of 

Fargo, North Dakota, and Moorhead, Minnesota, in managing 

wastewater operations and in providing information that would 

allow citizens to assess the condition of the Red River relative to intended uses. Finally, real-time estimates of constituent concentrations that are based on surrogates monitored at 

the gaging station could more accurately estimate loads for 

comparison to total maximum daily loads (TMDLs). A TMDL 

is a calculation of the maximum amount of a constituent that a 

water body can receive and still meet water-quality standards. 

Section 303(d) of the 1972 Clean Water Act (U.S. Environmental Protection Agency, 2006) requires States to establish 

TMDLs.

Purpose and Scope

This report presents the results of regression analysis of 

water-quality constituents for the Red River at Fargo, North 

Dakota, using manually collected water-quality data and continuously recorded streamflow and water-quality data from the 

USGS gaging station (05054000) at Fargo for 2003-05. The 

report provides regression equations that can be used to estimate concentrations and loads for alkalinity, dissolved solids, 

sulfate, chloride, total nitrite plus nitrate, total nitrogen, total 

phosphorus, and suspended sediment.

Description of Study Area

The Red River (fig. 1) is formed by the confluence of 

the Bois de Sioux and Otter Tail Rivers at Wahpeton, North 

Dakota, and Breckenridge, Minnesota. The river then flows 

northward 394 mi to the international boundary and continues 

into Manitoba, Canada. The river from its confluence north to 

the international boundary separates North Dakota and Minnesota. The drainage area of the Red River at Fargo is about 

6,800 mi2, and the bed of the river slopes only about 200 ft 

over the reach between Wahpeton and the international boundary.

The Red River is a valuable resource and provides 

municipal and industrial water supplies, recreational opportunities, and wildlife habitat. The primary land use in the area 

is agriculture (Tornes, 2005). The July 1, 2003, population 

estimate for the city of Fargo was 91,048 and across the river 

the population estimate for Moorhead, Minnesota, was 32,849 

(U.S. Census Bureau, 2006). Cass County, the county in which 

Fargo is located, had an estimated population of 126,769 

in 2003 or 20 percent of North Dakota’s total population, 

633,400 (U.S. Census Bureau, 2006).

The Red River flows over lacustrine deposits of glacial 

Lake Agassiz through its entire length in North Dakota (Williams-Sether, 2004). Water quality in the Red River is affected 

by the lacustrine deposits, inflow from major tributaries in 

North Dakota and Minnesota, runoff from agricultural areas, 

ground-water discharge, industrial effluents, and wastewater 

discharges from cities along the river, including Fargo and 

Moorhead (Williams-Sether, 2004). Management strategies to 

control point- and nonpoint-source pollution from both agricultural and urban land uses are important issues in the Red 

River Basin, and the water quality of the Basin is an issue of 

international importance.

Previous Studies

Many aspects of water quality in the Red River Basin 

have been studied. A bibliography of USGS reports related to 

the Red River Basin is available online at http://nd.water.usgs.

gov/pubs/key/redriver.html. Notable among previous waterquality reports is Williams-Sether (2004), in which regression 

equations for estimating monthly mean concentrations of 

selected water-quality constituents were developed. WilliamsSether (2004) precedes continuous water-quality monitoring 

at the Fargo gaging station; therefore, the only continuously 

recorded variable available for regression analysis was streamflow. Regression analysis to estimate constituent concentrations and loads was used by Christensen and others (2000) 

for the Little Arkansas River in south-central Kansas and by 

Christensen (2001) for the Quivira National Wildlife Refuge, 

south-central Kansas.

Methods

This section describes how streamflow was measured, 

water-quality samples were collected and analyzed, and 

data were interpreted for this study. “Although technological 

advances in turbidity measurement have produced a variety of 

instrument types to meet one or more ... differing objectives, 

turbidity instruments of different designs commonly do not 

   Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 1. Location of the Fargo gaging station in the Red River of the North Basin, North Dakota.

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

0 20 40 60 MILES

0 20 40 60 KILOMETERS

Baldhill

Dam

Orwell Dam

EXPLANATION

 Basin boundary

 Gaging station and number 05054000

Grand

Forks

Oslo

Drayton

Pembina

Emerson

FARGO

MOORHEAD

Halstad

Thompson

Valley

City

Wahpeton

Breckenridge

Hickson

East Grand Forks

Index Map

RED RIVER

OF THE

NORTH BASIN

SASKATCHEWAN MANITOBA

CANADA

UNITED STATES

ONTARIO

Lake Traverse

Mud Lake White Rock Dam

Reservation Dam

SHEYENNE

RIVER

BASIN

DEVILS

 LAKE

 BASIN

Winnipeg

Nelson

R.

Red

River

of

the

North

Lake Winnipeg

HUDSON

BAY

NORTH DAKOTA

SOUTH DAKOTA

MINNESOTA

Upper Red

Lake

Devils

 Lake

Sheyenne

River

R.

River

Wild Rice

River River

River

Mustinka R.

Pelican

Tail

Otter

Orwell Reservoir

River

River

R.

R.

R.

R.

Tongue

Pembina

R.

River

R.

S. Br.

N. Br.

Roseau

R.

Two

River

R.

Middle

Thief

Red

Lake

Snake

Forest

Turtle

Park

Rice

Marsh River

R.

Sand Hill

Wild

Buffalo

R.

R.

R.

Elm

Goose

Maple

Rush

Bois de Sioux R.

Stump

 Lake

Lake

Ashtabula

Lower Red

Lake

05054000--Red of the

North at Fargo, N. Dak

RED

RIVER

OF

THE

NORTH

BASIN

Methods   
yield identical or equivalent results” (Wilde, variously dated); 

therefore special attention is given to the equipment used to 

continuously record turbidity and to manually measure turbidity.

Streamflow Measurements

Stage, or gage height, was measured to the nearest 0.01 

ft at the Fargo gaging station with a nonsubmersible, pressure 

transducer. The data were electronically recorded and transmitted by satellite to a downlink site and then to the USGS 

office in Bismarck, North Dakota.

Methods used to determine streamflow are described in 

Buchanan and Somers (1969). Streamflow measurements were 

made approximately 15 times per year (S. Robinson, USGS, 

oral commun., 2006). A stage-streamflow relation was developed on the basis of streamflow measurements and the stage 

of the stream at the time of measurement (Kennedy, 1984) 

and this relation was used to compute a continuous record of 

streamflow (Kennedy, 1983). Stage and streamflow values 

were stored in the USGS National Water Information System 

(NWIS) database in 1-hour increments.

Continuous Water-Quality Monitoring

Continuous monitoring of specific conductance and water 

temperature began at the Fargo gaging station in September 

1998 using a Campbell Scientific CR247 conductivity and 

temperature sensor. In October 2003, a YSI Environmental 

YSI 6820 SONDE continuously recording water-quality 

monitor was installed at the gaging station. This water-quality 

monitor measures specific conductance, pH, water temperature, turbidity, and dissolved oxygen concentration. Initially, 

the monitor was installed inside the Fargo water-treatment 

pumping plant. In November 2004, the water-quality monitor 

was relocated to an in-stream location near the water-treatment 

plant intake structure. Specific conductance, pH, and turbidity 

values obtained at both locations were similar; however, water 

temperature and dissolved oxygen values differed between the 

two locations.

A YSI 6920 SONDE was used as a backup water-quality 

monitor, and beginning in 2005, the two models were used 

alternately to allow them to be brought back to the USGS 

field office for cleaning. A comparison of models 6820 and 

6920 indicates that the two instruments are the same in terms 

of measurement range, resolution, and accuracy (YSI Environmental, 2001). The YSI 6920 model has an internal power 

supply, whereas the YSI 6820 does not. The sensors were 

calibrated according to methods presented in Wilde (variously 

dated).

Manual Water-Quality Measurements, Sample 

Collection, and Analysis

Water-quality samples were collected manually according to methods described in U.S. Geological Survey techniques manuals (variously dated). All samples were collected 

downstream (north) of the Red River at Fargo gaging station 

(05054000) (fig. 2) because it was difficult to access the river 

by boat at the gaging station. In 2003, samples were collected 

from the Main Avenue Bridge or the First Avenue Bridge. In 

2004 and 2005, samples were collected from the First Avenue 

Bridge during high flow and from the walking-path bridge, 

between the gaging station and the Main Avenue Bridge, 

during low flow. Waste water from the cities of Fargo and 

Moorhead is returned to the Red River downstream from the 

water-quality sampling locations. Water-quality samples were 

analyzed by the North Dakota Department of Health Laboratory using published methods (North Dakota Department 

of Health, 2003b) and quality assurance procedures (North 

Dakota Department of Health, 2003a). Sediment samples 

were analyzed by the USGS Iowa Sediment Laboratory using 

procedures described in Guy (1969) and Matthes and others 

(1992). During the collection of water-quality samples, physical properties of water were measured, including specific conductance, pH, temperature, turbidity, and dissolved oxygen. In 

2003, the physical properties also were measured at the gaging 

station. The comparison of the two sets of measurements 

verified that river conditions were similar at the water-quality 

sampling location and the gaging station.

Because hydrologic conditions within a watershed 

may affect variability of many chemical constituents, waterquality samples were collected manually throughout a range 

of streamflow conditions. Streamflow from January 1, 2003, 

to December 31, 2005, and the days and streamflow values 

for which water-quality samples were collected and physical 

properties were manually measured are shown in figure 3. It 

is important to note that water-quality samples for this study 

were not collected under ice conditions during the winter.

Efforts also were made to collect water-quality samples 

throughout a range of turbidity values because turbidity was 

anticipated to be an important surrogate variable for this study. 

Manually measured and continuously recorded turbidity data 

are shown in figure 4. The manually measured turbidity values 

and dates correspond with the collection of water-quality 

samples.

Turbidity was manually measured using two different 

instruments. In 2003, manual turbidity measurements were 

obtained using a Hach Environmental Hydrolab DataSonde 3. 

The DataSonde 3 method of determining turbidity was the 

USGS-approved method ISO 7027, the European 

 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 2. Aerial photograph showing location of gaging station and water-quality 

sampling sites on the Red River of the North in Fargo, North Dakota.

96°47'06"

46°52'28"

15"

02"

46°51'49"

48" 96°46'30"

TerraServer Image by U.S. Geological Survey taken September 1997

0 100 200 YARDS

0 100 200 METERS

WALKING PATH BRIDGE

LOWHEAD DAM

FIRST AVENUE BRIDGE

MAIN AVENUE BRIDGE

INTAKE STRUCTURE

USGS GAGING STATION

05054000 AT PUMPING PLANT

WATER-TREATMENT

PLANT

FARGO MOORHEAD

NORTH DAKOTA MINNESOTA Direction of flow

Methods   
100

10

1,000

10,000

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

STREAMFLOW, IN CUBIC FEET PER SECOND

 EXPLANATION

Continuous record of streamflow

Streamflow values obtained during manual water-quality sampling

Figure 3. Streamflow for the Red River of the North at Fargo, North Dakota, January 1, 2003, to December 31, 2005.

drinking-water protocol (International Organization for 

Standardization, 1999). In 2004 and 2005 the manual turbidity measurements were made by removing the YSI 6820 or 

YSI 6920 water-quality monitor (which also uses ISO method 

7027) from the gaging station, using it to make manual measurements, and then placing the monitor back in the gage.

Manual and continuously recorded turbidity measurements for 2003 and 2004 were stored in the USGS NWIS 

database under parameter code P61028 (turbidity, water, 

unfiltered, field, nephelometric turbidity units). Effective 

October 1, 2004, a change was made in USGS turbidity datareporting procedures. The new procedures were a result of 

USGS collaboration with public and private sector entities and 

established “a suite of reporting units for storing and reporting turbidity data that is based on instrument design” (U.S. 

Geological Survey, 2004). Manual and continuously recorded 

turbidity measurements made using these new procedures 

were stored under parameter code P63680 (turbidity, water, 

monochrome near infra-red LED light, 780-900 nm, detection 

angle 90 +/ -2.5 degrees, FNU). FNU is the acronym for the 

formazin nephelometric unit of measurement and, under the 

new procedures, is used with instruments that comply with 

ISO method 7027. Despite the differences in monitor, parameter code, and units of measurement, the turbidity measurements were made using the same method. Therefore, the 

manual and continuously recorded turbidity values for 2003 

and 2004 were changed in the USGS database to parameter 

code P63680, and all turbidity data were treated as equivalent. 

Turbidity units are referred to as FNU throughout the remainder of the report.

 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

 0

100

200

400

300

500

600

700

800

900

1,000

TURBIDITY, IN FORMAZIN NEPHELOMETRIC UNIT

 EXPLANATION

Continuous record of turbidity. Break in line indicates periods when

turbidity values were not available

Turbidity values obtained during manual water-quality sampling

Figure 4. Turbidity for the Red River of the North at Fargo, North Dakota, January 1, 2003, to December 31, 2005.

Manual and continuously recorded specific conductance 

data collected are shown in figure 5. The manual specific 

conductance values and dates correspond to the collection of 

water-quality samples, which were made over a broad range of 

specific conductance values.

Summary statistics of the manually measured physical 

properties and water-quality constituents are listed in table 1. 

The data are stored in the USGS NWIS database and are 

available online at http://nwis.waterdata.usgs.gov/nd/nwis/

qwdata?site_no=05054000.

Development of Regression Equations to 

Estimate Constituent Concentrations

The water-quality constituents selected for estimation are 

listed in table 2. The rationale and methodology for expressing water-quality constituent concentrations in terms of other 

surrogate constituents or physical properties in a regression 

equation are explained in Helsel and Hirsch (1995). Helsel 

and Hirsch (1995) also detail the computations for regression 

estimation and identify measures commonly used to evaluate 

regression equations, including mean square error, standard 

deviation, and R2. They explain the benefit of log transformation of variables, which was a technique used for some of the 

regression relations in this study.

Methods 
Figure 5. Specific conductance for the Red River of the North at Fargo, North Dakota, January 1, 2003, to December 31, 2005.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

200

400

600

800

1,000

1,200

SPECIFIC CONDUCTANCE, IN MICROSIEMENS PER CENTIMETER AT 25 DEGREES CELSIUS

 EXPLANATION

Continuous record of specific conductance. Break in line indicates periods when

specific-conductance values were not available

Specific-conductance values obtained during manual water-quality sampling

 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Table 1. Summary statistics for manually measured water-quality physical properties and constituents for the Red River of the North at 

Fargo, North Dakota, 2003-05.

[Streamflow in cubic feet per second, ft3/s; specific conductance in microsiemens per centimeter at 25 degrees Celsius, μS/cm at 25°C; pH in standard units; 

temperature in degrees Celsius, °C; turbidity in formazin nephelometric units, FNU; other physical properties and constituent concentrations in milligrams per 

liter, mg/L]

Physical property or 

constituent

Descriptive statistics Percent of samples in which values were less than or equal to 

those shown

Sample 

size Maximum Minimum Mean 0.95 0.75 (Median) 50 percent 0.25 0.05

Streamflow 31 9,010 165 2,190 7,170 2,720 1,230 812 193

Specific conductance 31 1,110 312 707 968 832 698 642 399

pH 31 8.50 7.30 8.00 8.35 8.20 8.00 7.80 7.53

Temperature, water 31 27.2 3.1 19.1 25.9 21.4 20.0 15.9 11.3

Turbidity 31 808.0 22.9 136.0 441.0 144.0 78.0 54.1 35.0

Dissolved oxygen 31 11.5 4.7 7.5 10.2 8.4 7.4 6.4 5.1

Alkalinity 13 239 127 192 238 228 209 162 127

Dissolved solids 13 610 264 430 591 497 439 370 266

Sulfate 13 271.0 91.1 167.0 260.0 190.0 167.0 113.0 93.7

Chloride 13 21.10 6.51 14.20 21.00 16.60 15.70 11.30 6.76

Nitrite plus nitrate 31 2.14 .02 .36 1.09 .41 .24 .06 .02

Nitrogen, total 31 3.26 .42 1.04 1.69 1.13 .95 .75 .57

Phosphorus, total 31 .70 .08 .28 .55 .40 .22 .16 .09

Suspended sediment 31 1,020.0 46.0 205.0 533.0 266.0 111.0 79.5 50.0

Table 2. Constituents estimated using regression equations for the Red River of the North at 

Fargo, North Dakota, 2003-05.

Constituent Unit of measurement U.S. Geological Survey 

parameter code

Alkalinity Milligrams per liter as calcium carbonate P90410

Dissolved solids Milligrams per liter P70301

Sulfate Milligrams per liter P00945

Chloride Milligrams per liter P00940

Total nitrite plus nitrate Milligrams per liter as nitrogen P00630

Total nitrogen Milligrams per liter P00600

Total phosphorus Milligrams per liter P00665

Suspended sediment Milligrams per liter P80154

Methods   
Standard deviation, s, is the positive square root of the 

mean square error (MSE), a common measure of variability 

in regression equations. Standard deviation is calculated as 

follows:

s MSE SSE

n p = = −

where

SSE is the error sum of squares defined in Helsel 

and Hirsch (1995),

n is the number of observations used to develop 

the regression equation,

and

	 p is the number of parameters estimated in the 

regression equation.

The standard deviation, like MSE, is an indicator of the variability of the probability distributions of the response, or 

explanatory, variable. However, the standard deviation is in 

the same units as the response variable, milligrams per liter 

(mg/L) for example, whereas MSE is in squared milligrams 

per liter (mg/L)2. Therefore, the standard deviation is easier to 

interpret in relation to the response variable.

R2, the multiple coefficient of determination, is calculated 

as follows:

R SSE

SSy

2 = −1

where

SSE is the error sum of squares,

and

SSy is the sums of squares y, or total sums of 

squares, defined in Helsel and Hirsch 

(1995).

R2 is a number, 0 through 1, that when multiplied by 100 is 

interpreted as the percentage of the variability in the response 

variable explained by the explanatory variables and the 

regression equation. Generally, the higher the R2, the better 

the regression equation. However, this does not guarantee 

the regression equation is useful (Neter and others, 1996). 

For example, if estimates require extrapolation outside the 

observed response variables, the regression equation may not 

provide accurate estimates. In relation to this study, a regression equation with a high R2

 does not imply that the equation 

will work well for estimating constituent concentrations and 

loads during the winter because winter constituent concentrations are outside the range of observed constituent concentrations.

As an indicator of the ability of the regression relations to 

estimate constituent concentrations, the measured concentrations were compared to the concentrations estimated by the 

regression relations by calculating relative percentage difference (RPDs) using the following equation:

RPD B A

A = X − 100 ,

where

B is the constituent concentration estimated 

from the regression equation,

and

A is the measured constituent concentration.

A is assumed to be correct and the RPD is the relative difference of B from A, expressed as a percentage.

The potential pool of surrogate physical properties, or 

explanatory variables, is listed in table 3. In addition to the 

properties in table 3, variables related to time were included in 

the pool of possible explanatory variables for nutrients in order 

to model the cyclical behavior of nutrients. These variables 

Table 3. Possible surrogate physical properties, or explanatory variables, used to develop regression 

equations to estimate constituent concentrations in the Red River of the North at Fargo, North Dakota, 2003-05.

Physical properties Unit of measurement U.S. Geological Survey 

parameter code

Streamflow Cubic feet per second P00060

Specific conductance Microsiemens per centimeter at 25 degrees Celsius P00095

pH Standard units P00400

Temperature, water Degrees Celsius P00010

Turbidity Nephelometric turbidity units

Formazin nephelometric unit

P61028

P63680

Dissolved oxygen Milligrams per liter P00300

10 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05

(1)

(2)

(3)
included t, t 2

, cos

2

365

 j t π



 



 , and sin

2

365

 j t π



 



 , where t is 

the Julian date, or the ordinal day of the year (92 for April 3, 

2005), j is an integer 1 through 3, cos is the cosine function, and sin is the sine function. An increase in j decreases 

the period of the cos and sin functions. Larger j values may 

be used to model behavior that has multiple cycles per year 

(Helsel and Hirsch, 1995). A model may include two or more 

cos/sin pairs with different periods. This may indicate two different seasonal processes that affect the response variable. In 

selection of a regression model, cos/sin terms were required to 

be used in pairs. For example, if 2

cos

365

 π t      was a statistically

 significant explanatory variable, the corresponding sin term, 

2 sin

365

  π t    , was included in the model. Including pairs of

cos/sin terms may result in models where one member of the 

pair is significant and the other is not. However, using only 

one member of the cos/sin pair forces an arbitrary phase shift 

rather than a phase shift determined by the data (Helsel and 

Hirsch, 1995).

To select the best model for estimating a particular constituent, stepwise regression (Insightful Corporation, 2001b), 

an automatic search procedure that sequentially adds terms to 

and deletes terms from the model, was performed to determine 

the best subset of explanatory variables. These variables were 

examined for scientific validity, and diagnostics were examined that in some cases resulted in logarithmic transformations 

of one or more of the explanatory variables or the response 

variable. In the case of transformation of one or more variables, stepwise regression was performed again to verify that 

the best subset of explanatory variables had been selected.

Calculation of Measured and Estimated 

Constituent Loads

Daily load is the total mass of a constituent that is transported past a gaging station in 1 day. Measured constituent 

loads were calculated by multiplying measured constituent 

concentrations by streamflow at the time the constituent concentrations were measured and multiplying by the conversion 

factor listed in table 4. Estimated mean daily constituent loads 

were calculated by multiplying the constituent concentrations 

estimated using the regression equations by daily streamflow 

and by a conversion factor (table 4).

Table 4. Conversion factors used in calculation of measured and 

estimated loads.

[ft3/s, cubic feet per second]

Multiply By By To obtain

milligrams per liter streamflow, in ft3/s 5.39 pounds per day

Methods 11
Results of Regression Analysis

Regression relations between constituents of concern and 

surrogate physical properties were examined, and a regression equation was developed for each constituent using one or 

more surrogate variables. The regression equations and each 

equation’s associated standard deviation, R2, and median RPD

are listed in table 5. A discussion of each constituent and the 

associated regression equations follows.

Table 5. Regression equations for estimates of alkalinity, dissolved solids, chloride, sulfate, total nitrogen, total nitrite plus nitrate, total 

phosphorus, and suspended sediment in the Red River of the North at Fargo, North Dakota, 2003-05.

[n, numbers of samples used to develop regression equation; R2, coefficient of multiple determination; median RPD, median relative percentage difference; 

SC, specific conductance; Q, streamflow; t, ordinal day of year; Turb, turbidity]

Constituent n Equation Standard 

deviation R 2 Median RPD

Alkalinity (Alk) 13 Alk = 0.165SC -54.3log10(Q) + 261 10.5 0.951 2.3

Dissolved solids (DS) 13 DS = 0.689SC -52.0 12.3 .990 1.1

Sulfate (SO4) 13 log10(SO4) = 0.128log10(Q) + 1.67log10(SC) -2.96 0.034 .963 5.8

Chloride (Cl) 13 Cl = -9.55log10(Q) + 0.011SC + 38.8 1.81 .895 10.7

Total nitrite plus nitrate 

(NO2 + NO3)

30 log10(NO2

+NO3) = 0.818log10(Q) + 1.69cos(2�t/365) 

-0.134sin(2�t/365) + 0.755cos(4�t/365) + 

0.016sin(4�t/365) -2.31

.309 .714 35.2

Total nitrogen (N) 30 N = 0.422log10(Q) + 0.699cos(2�t/365) -0.318sin(2�t/365) + 

0.400cos(4�t/365) -0.202sin(4�t/365) + 0.030

.188 .703 14.7

Total phosphorus (P) 30 P = 0.111log10(Q) + 0.353log10(Turb) + 0.056cos(2�t/365) 

-0.047sin(2�t/365) -0.734

.080 .771 17.2

Suspended sediment 

(SSC)

30 log10(SSC) = 0.213log10(Q) + 0.814log10(Turb) -0.092 .128 .873 19.3

Alkalinity

Alkalinity is an important characteristic of natural and 

polluted water and is the capacity of the solutes in the water to 

react with and neutralize acid, such as inflow from acid rain or 

wastewater (Hem, 1985). Several different compounds contribute to the alkalinity of water, mainly bicarbonates, carbonates, 

and hydroxides. If water is unable to neutralize acid inputs, the 

affected stream becomes more acidic (pH below 7.0 standard 

units). Acidification is generally harmful at pH below 5.0 and 

results in a reduction in the number of aquatic species present in the water body (Allan, 1995). Most rivers, in areas not 

affected by pollution, have a pH of 6.5 to 8.5 standard units, 

although some water bodies are naturally acidic even without 

the effects of acid rain or other human-related acid sources 

(Hem, 1985). For the water-quality samples used in this study, 

the mean pH was 8.0, the minimum was 7.3, and the maximum was 8.5 standard units. Although high alkalinity may 

result in drinking water with an unpleasant taste, it is not detrimental to humans (North Dakota Department of Health, 2006).

Hem (1985) showed a positive linear relation between 

specific conductance and hardness, which is measured in milligrams per liter as calcium carbonate, as is alkalinity, for the 

Gila River in Arizona. Christensen and others (2000) showed 

a positive relation between specific conductance and alkalinity for the Little Arkansas River in Kansas. Streamflow also 

may have a relation to specific conductance and alkalinity as 

runoff can have a dilution effect on water-quality constituents 

(Christensen, 2000).

The surrogate variables chosen to estimate alkalinity of 

the Red River at Fargo were specific conductance and streamflow. Ranges for these explanatory variables were 447.0 to 

967.0 μS/cm for specific conductance and 560 to 9,010 ft3/s 

for streamflow. The multiple regression equation was:

Alk = 0.165SC-54.3log10(Q) + 261, (4)

12 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
where

Alk is the estimated alkalinity concentration, in 

milligrams per liter,

SC is specific conductance, in microsiemens per 

centimeter at 25°C,

and

log10(Q) is the base-10 logarithm of streamflow, in 

cubic feet per second.

The measured alkalinity concentration was compared to the 

estimated alkalinity concentration calculated by equation 4 

graphically and by calculating the RPD (fig. 6).

Dissolved Solids

Dissolved-solids, also called total dissolved solids, 

concentration is used to evaluate water quality and to compare water from one location to the next. Dissolved-solids 

concentration may be determined in two ways: (1) by the 

weight of the dry residue remaining after evaporation of the 

water samples, or (2) by summing the concentrations of other 

dissolved constituents if the concentrations of major ions are 

known (Hem, 1985). According to Hem, the computed value 

for dissolved solids, which was used in this Red River at 

Fargo, North Dakota, study, “may give a more useful indication of total dissolved-ion concentration than the residue left 

by evaporation.” High concentrations of dissolved solids may 

have an adverse effect on taste and make the water appear 

cloudy (North Dakota Department of Health, 2006).

Specific conductance “provides general indication of the 

content of dissolved matter for water that is not too saline or 

too dilute” (Hem, 1985). Streamflow also may affect dissolved 

solids, but the relation is not a simple one (Allan, 1995). For 

the Red River at Fargo, specific conductance was a significant explanatory variable for estimating dissolved solids; 

streamflow was not. Regression diagnostics, Cooks’ distance (Neter and others, 1996), and jackknife after bootstrap 

(Insightful Corporation, 2001b) indicated that the specific 

conductance value of the October 12, 2005, water-quality 

sample had a large effect on the estimation of the regression 

parameters. This sample changed the intercept term for the 

regression equation but had little effect on R2 or the median 

RPD. Therefore, the sample was retained for the estimation of 

the regression parameters. The range for specific conductance 

was 447.0 to 967.0 μS/cm. The multiple regression equation 

was:

DS = 0.689SC -52.0,

where

DS is the estimated dissolved-solids 

concentration, in milligrams per liter,

and

SC is specific conductance, in microsiemens per 

centimeter at 25°C.

The measured dissolved-solids concentrations were compared 

to the estimated dissolved-solids concentrations calculated by 

equation 5 graphically and by calculating the RPD (fig. 7).

Sulfate

Sulfate sources include the weathering of rocks, agricultural runoff, fuel combustion, municipal and industrial effluent, and precipitation (Hem, 1985; Allan, 1995). The presence of too much sulfate has three main undesirable effects 

in drinking water: (1) sulfate can have a laxative effect with 

excessive intake, (2) water with high sulfate concentrations 

can form hard scales in boilers, and (3) sulfate can negatively 

affect taste (North Dakota Department of Health, 2006).

Sulfate is negatively charged and increased sulfate concentrations increase specific conductance (Hem, 1985). For 

the Red River at Fargo, both streamflow and specific conductance were statistically significant explanatory variables for 

estimating sulfate. The range for streamflow values was 560 to 

9,010 ft3/s, and the range for specific conductance was 447.0 

to 967.0 μS/cm. The multiple regression equation was:

log10(SO4) = 0.128log10(Q) + 1.67log10(SC) -2.96,

where

log10(SO4 ) is the base-10 logarithm of estimated sulfate 

concentration, in milligrams per liter,

log10(Q) is the base-10 logarithm of streamflow, in 

cubic feet per second,

and

SC is specific conductance, in microsiemens per 

centimeter at 25°C.

The measured sulfate concentrations were compared to the 

estimated sulfate concentrations calculated by equation 6 

graphically and by calculating the RPD (fig. 8).

Chloride

Chloride is present in virtually all rocks and is present in the tissues of all plants and animals. In surface water, 

concentrations of chloride range from less than 1 to more than 

280,000 mg/L, the extreme value representative of the Dead 

Sea (Feth, 1981), and in most streams the concentration is less 

than that of sulfate (Hem, 1985). Chloride is generally conservative (unchanging) in water; therefore, its circulation in the 

hydrologic cycle is mostly through physical processes (Hem, 

1985). Chloride in streams may originate from the weathering 

of rocks, ground-water inflow, precipitation, and municipal 

and industrial effluent (Feth, 1981; Hem, 1985). The presence 

of too much chloride can have undesirable effects in drinking 

water; consumers may find the taste objectionable, and pipes 

in hot water systems may corrode (North Dakota Department 

of Health, 2006).

(5)

(6)

Results of Regression Analysis 13
MEASURED ALKALINITY CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED ALKALINITY CONCENTRATION, IN MILLIGRAMS PER LITER

0 50 100 150 200 250

0

50

100

150

200

250

RPD = 2.3

RPD = 2.3

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between

instantaneous measured alkalinity concentrations

and instantaneous estimated alkalinity concentrations

Figure 6. Comparison of measured and estimated alkalinity concentrations in the Red River of the North at Fargo, North Dakota, 

2003-05.

14  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 7. Comparison of measured and estimated dissolved-solids concentrations in the Red River of the North at Fargo, North 

Dakota, 2003-05.

MEASURED DISSOLVED-SOLIDS CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED DISSOLVED-SOLIDS CONCENTRATION, IN MILLIGRAMS PER LITER

0

0

100 200 300 400 500 600 700

100

200

300

400

500

600

700

RPD = 1.1

RPD = 1.1

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between

instantaneous measured dissolved-solids concentrations

and instantaneous estimated dissolved-solids concentrations

Results of Regression Analysis 15
Figure 8. Comparison of measured and estimated sulfate concentrations in the Red River of the North at Fargo, North Dakota, 

2003-05.

MEASURED SULFATE CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED SULFATE CONCENTRATION, IN MILLIGRAMS PER LITER

0

0

50 100 150 200 250 300

50

100

150

200

250

300

RPD = 5.8

RPD = 5.8

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between

instantaneous measured sulfate concentrations

and instantaneous estimated sulfate concentrations

16  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Chloride is a negatively charged ionic species that makes 

water conductive. Therefore, as chloride concentrations 

increase, the specific conductance increases. Chloride concentrations may be higher in the winter when a higher percentage 

of streamflow is from ground-water discharge, and sudden 

increases in chloride may indicate pollution in the stream 

(Hem, 1985). Feth (1981) found that western rivers in the 

United States generally have higher chloride concentrations in 

drought years.

For the Red River at Fargo, both streamflow and specific 

conductance were statistically significant explanatory variables for estimating chloride. The range for streamflow values 

was 560 to 9,010 ft3/s, and the range for specific conductance 

was 447 to 967 μS/cm. The multiple regression equation was:

Cl = -9.55log10(Q) + 0.011SC + 38.8,

where

Cl is the estimated chloride concentration, in 

milligrams per liter,

log10(Q) is the base-10 logarithm of streamflow, in 

cubic feet per second,

and

SC is specific conductance, in microsiemens per 

centimeter at 25°C.

The measured chloride concentrations were compared to the 

estimated chloride concentrations calculated by equation 7 

graphically and by calculating the RPD (fig. 9).

Total Nitrite Plus Nitrate

Nitrite is seldom present in high concentrations and 

is generally an indicator of pollution from sewage or other 

organic waste (Hem, 1985). Nitrate is an important plant nutrient produced during nitrification. Nitrification is a two-step 

process in which bacteria convert ammonia to nitrite, and then 

a second kind of bacteria convert nitrite to nitrate (Chapra, 

1997).

Observed total nitrite plus nitrate was seasonal as was 

total nitrogen (fig. 10) and the same explanatory variables 

were used for nitrite plus nitrate as for total nitrogen. The 

range for streamflow values was 165 to 9,010 ft3/s. Regression 

diagnostics and the jackknife after bootstrap indicated that the 

June 6, 2005, total nitrite plus nitrate concentration had a large 

effect on the estimation of the regression parameters. This 

total nitrite plus nitrate measurement was very high compared 

to the other measured concentrations and was removed as an 

outlier (see discussion in “Total Nitrogen” section). The multiple regression equation was:





 

 log10(NO2

 + NO3) = 0.818 log10(Q) + 1.69cos 2� 

– 0.134sin 2� + 0.755cos 4�

365

t





 



 365

t

+ 0.016sin 4� – 2.31, 



 



 365

t

365

 t



 





where

log10(NO2+NO3) is the base-10 logarithm of the estimated

total nitrite plus nitrate concentration, in

milligrams per liter,

log10(Q) is the base-10 logarithm of streamflow, in

cubic feet per second,

and

t is the Julian date.

The measured total nitrite plus nitrate concentrations were 

compared to the estimated total nitrite plus nitrate concentrations calculated by equation 8 graphically and by calculating 

the RPD (fig. 10). Generally, measured total nitrite plus nitrate 

concentrations greater than 0.5 mg/L deviated more from the 

estimated concentrations than the measured concentrations 

less than 0.5 mg/L.

Total Nitrogen

Nitrogen is of vital importance in plant and animal nutrition and occurs in water as nitrite or nitrate anions, ammonia 

cations, and in other forms such as cyanide. Total nitrogen 

concentration is related to land use and sources of nitrogen 

include precipitation, soil leeching, agricultural runoff, and 

waste disposal (Allan, 1995). Nitrogen levels may fluctuate 

seasonally, with high concentrations occurring during high 

flow when there is drainage from cultivated fields or feedlots 

(Hem, 1985) and with an autumn increase due to the decomposition of leaves (Allan, 1995). Figure 11 shows that total 

nitrogen concentrations in the Red River at Fargo do appear to 

be seasonal with the peak occurring during high streamflow 

(fig. 3), followed by a decrease, and then an autumn increase 

that corresponds to an autumn increase in streamflow and may 

correspond with autumn-shed leaf decomposition.

For the Red River at Fargo, streamflow and cosine (cos) 

and sine (sin) terms were chosen as explanatory variables for 

estimating nitrogen. The range for streamflow values was 

165 to 9,010 ft3/s. Regression diagnostics and the jackknife 

after bootstrap indicated that the June 6, 2005, total nitrogen 

concentration of 2.73 mg/L (fig. 11) had a large effect on the 

estimation of the regression parameters. The field notes for 

June 6, 2005, indicated that the Red River at the water-quality 

(7)

Results of Regression Analysis 17

(8)
Figure 9. Comparison of measured and estimated chloride concentrations in the Red River of the North at Fargo, North Dakota, 

2003-05.

MEASURED CHLORIDE CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED CHLORIDE CONCENTRATION, IN MILLIGRAMS PER LITER

0 5 10 15 20 25

0

5

10

15

20

25

RPD = 10.7

RPD = 10.7

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between

instantaneous measured chloride concentrations

and instantaneous estimated chloride concentrations

18  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 10. Comparison of measured and estimated total nitrite plus nitrate concentrations in the Red River of the North at Fargo, 

North Dakota, 2003-05.

MEASURED TOTAL NITRITE PLUS NITRATE CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED TOTAL NITRITE PLUS NITRATE CONCENTRATION, IN MILLIGRAMS PER LITER

0 .5 1.0 1.5 2.0

0

.5

1.0

1.5

2.0

RPD = 35.2

RPD = 35.2

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between instantaneous

measured total nitrite plus nitrate concentrations and

instantaneous estimated total nitrite plus nitrate concentrations

Results of Regression Analysis 19
Figure 11. Measured total nitrogen concentrations in the Red River of the North at Fargo, North Dakota, 2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

TOTAL NITROGEN CONCENTRATION, IN MILLIGRAMS PER LITER

 0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Outlier

20 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
sampling site (the walking-path bridge) was “very turbid” with 

“lots of sediment suspended” (R. Nustad, USGS, unpub. data, 

2005). The total nitrogen observed under those conditions was 

very high compared to the other observations (fig. 11) and was 

removed as an outlier. The multiple regression equation was:





 

 N  = 0.422 log10(Q) + 0.699cos 2� – 0.318sin 2�

+ 0.400cos 4� – 0.202sin 4� + 0.30,

365

t 



 



 365

t





 



 365

t 



 



 365

t

where

N is the estimated total nitrogen concentration, 

in milligrams per liter,

log10(Q) is the base-10 logarithm of streamflow, in 

cubic feet per second,

and

t is the Julian date.

The measured nitrogen concentrations were compared to the 

estimated nitrogen concentrations calculated by equation 9 

graphically and by calculating the RPD (fig. 12).

Total Phosphorus

Phosphorus, like nitrogen, is an essential nutrient for 

plant growth. Increased phosphorus, or nitrogen, in a water 

body may be accompanied by an undesirable high rate of plant 

growth, such as algal blooms. Sources of phosphorus include 

soil erosion and domestic and industrial sewage effluent (Hem, 

1985). Like nitrogen, phosphorus may vary seasonally with 

streamflow and the growing season.

For the Red River at Fargo, streamflow, turbidity (an estimator of suspended sediment, which can transport constituents 

such as phosphorus), and cosine and sine terms were chosen as 

explanatory variables for estimating total phosphorus. Regression diagnostics and the jackknife after bootstrap indicated 

that the June 23, 2003, turbidity value (fig. 4) had a large 

effect on the estimation of the regression parameters. The field 

notes for June 23, 2003, indicated that it had rained the night 

before and while turbidity was measured it was raining and 

a small storm drain was discharging above the water-quality 

sampling site (First Avenue Bridge) (R. Nustad and C. Laveau, 

USGS, unpub. data, 2003). The measured turbidity value of 

808 FNU was very high in comparison to other turbidity values, and because of its effect on the regression relation, it was 

removed as an outlier. The range for streamflow values used to 

develop the regression equation was 165 to 9,010 ft3/s, and the 

range for turbidity values was 22.9 to 584 FNU. The multiple 

regression equation was:





 

 P  = 0.111 log10(Q) + 0.353log10(Turb) + 0.056cos 2�

– 0.047sin 2� – 0.734,

365

t





 



 365

t

where

P is the estimated total phosphorus 

concentration, in milligrams per liter,

log10(Q) is the base-10 logarithm of streamflow, in 

cubic feet per second,

log10(Turb) is the base-10 logarithm of turbidity, in 

FNUs,

and

t is the Julian date.

The measured total phosphorus concentrations were compared 

to the estimated total phosphorus concentrations calculated by 

equation 10 graphically and by calculating the RPD (fig. 13).

Suspended Sediment

The terms suspended-sediment concentration (SSC) and 

total suspended solids (TSS) are often used interchangeably. 

However, SSC and TSS represent different laboratory analytical methods used to quantify concentrations of suspended 

solids in surface water. The methods are described in Guy 

(1969) and Gray and others (2000). Gray and others (2000) 

evaluated 3,235 paired SSC and TSS values. They stated, “The 

method for determining TSS, which was originally designed 

for analyses of wastewater samples, is shown to be fundamentally unreliable for the analysis of natural-water samples. In 

contrast, the method for determining SSC produces relatively 

reliable results for samples of natural water, regardless of the 

amount or percentage of sand-size material in the samples. 

SSC and TSS data collected from natural waters are not comparable and should not be used interchangeably.” Therefore, 

SSC was used in this study.

SSC is an important indicator of water quality for several 

reasons. Suspended sediments may act as a transport for other 

constituents, including toxic substances, and some fish can 

be affected by sediment deposition on spawning beds. “An 

increased amount of fine sediments within the streambed 

reduces its permeability to water movement, affecting the 

delivery and removal of gases, nutrients and metabolites” for 

stream biota, and potentially restricting movement of biota 

(Allan, 1995).

SSC increases with streamflow, unless the supply of sediment is depleted (Allan, 1995). SSC is also related to turbidity 

because turbidity includes suspended material. Turbidity is a 

field measurement that is an indicator of “suspended and 

Results of Regression Analysis 21

(9)

(10)
Figure 12. Comparison of measured and estimated total nitrogen concentrations in the Red River of the North at Fargo, North 

Dakota, 2003-05.

MEASURED TOTAL NITROGEN CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED TOTAL NITROGEN CONCENTRATION, IN MILLIGRAMS PER LITER

0 .5 1.0 1.5 2.0 2.5

0

.5

1.0

1.5

2.0

2.5

RPD = 14.7

RPD = 14.7

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between

instantaneous measured total nitrogen concentrations

and instantaneous estimated total nitrogen concentrations

22 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 13. Comparison of measured and estimated total phosphorus concentrations in the Red River of the North at Fargo, North 

Dakota, 2003-05.

MEASURED TOTAL PHOSPHORUS CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED TOTAL PHOSPHORUS CONCENTRATION, IN MILLIGRAMS PER LITER

0 0.2 0.4 0.6 0.8 1.0

0

0.2

0.4

0.6

0.8

1.0

RPD = 17.2

RPD = 17.2

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between instantaneous

measured total phosphorus concentrations and instantaneous

estimated total phosphorus concentrations

Results of Regression Analysis 23
dissolved matter, such as clay, silt, finely divided organic 

matter, plankton and other microscopic organisms, organic 

acids, and dyes” (Wilde, variously dated). For the Red River at 

Fargo, both streamflow and turbidity were statistically significant explanatory variables for estimating SSC.

As was the case with total phosphorus, regression 

diagnostics and jackknife after bootstrap indicated that the 

June 23, 2003, turbidity value (fig. 4) had a large effect on the 

estimation of the regression parameters. This turbidity value of 

808 FNU was very high in comparison to other turbidity values, and because of its extreme effect on the regression relation, it was removed as an outlier. The range for streamflow 

values was 165 to 9,010 ft3/s, and the range for turbidity values 

was 22.9 to 584 FNU. The multiple regression equation was:

log10(SSC) = 0.213log10(Q) + 0.814log10(Turb) -0.092,

where

log10(SSC) is the base-10 logarithm of estimated 

suspended-sediment concentration, in 

milligrams per liter,

log10(Q) is the base-10 logarithm of streamflow, in 

cubic feet per second,

and

log10(Turb) is the base-10 logarithm of turbidity, in FNUs.

The measured suspended-sediment concentrations were 

compared to the estimated suspended-sediment concentrations 

calculated by equation 11 graphically and by calculating the 

RPD (fig. 14).

Measured and Estimated Constituent 

Loads

Because the explanatory variables used in the regression equations (table 5) are related to time or are continuously 

monitored properties, the regression equations developed in 

this study may be used to estimate daily concentration loads in 

the Red River at Fargo. Measured daily load was computed for 

each constituent, and the daily load was estimated using the 

regression equations. Comparisons of measured and estimated 

daily loads are shown for each constituent in figures 15-22. No 

water-quality samples were collected under ice conditions, and 

the regression equations may not be appropriate for ice conditions. Therefore, loads were not estimated from November 1 

to March 31. Breaks in the lines representing estimated daily 

loads indicate ice conditions or time periods in which one or 

more of the continuously monitored physical property values 

was unavailable.

The peak loads generally occurred in June and July when 

streamflow also peaked (fig. 3). In 2004, high streamflow 

occurred in autumn (September and October). These high 

flows caused an increase in estimated loads in September 

and October 2004, especially for the nutrients (figs. 19-21). 

The estimated total nitrite plus nitrate nutrient loads were not 

graphed after October 24 (fig. 19) because the high streamflow 

in fall 2004 produced an extreme increase in the fall 2004 

load that was not supported by measured concentrations during that time. Further water-quality sampling may result in a 

refined regression equation that better estimates loads under 

such conditions or further analysis may indicate that a separate 

regression equation is needed for fall and winter estimation.

Summary

The U.S. Geological Survey gaging station at Fargo, 

North Dakota, was established in June 1901 to provide stage 

and streamflow values for the Red River. The USGS began 

collecting water-quality samples at the gaging station in 1949. 

During more recent years, 2004 to the present (2006), the gaging station has provided real-time stage and streamflow data, 

instream velocity, and water-quality data (the physical properties of specific conductance, pH, water temperature, turbidity, 

and dissolved oxygen concentration).

As shown in a previous study, physical properties measured by water-quality monitors may be used as surrogates 

for concentrations of important water-quality constituents. 

Because the surrogate physical properties used in this study 

are continuously recorded, the regression equations may be 

used to track changes in water quality as they occur. Potential 

benefits include providing the cities of Fargo, North Dakota, 

and Moorhead, Minnesota, with real-time information for 

the management of wastewater and providing the public with 

water-quality information that may affect their use of the Red 

River.

A regression analysis was performed on the streamflow 

and water-quality data collected in 2003 through 2005 from 

the Red River at Fargo, North Dakota, to determine the relation between physical properties of water and water-quality 

constituent concentrations. The explanatory variables considered in the regression analysis were streamflow, specific 

conductance, pH, water temperature, turbidity, and dissolved 

oxygen concentration. The response variables were alkalinity, dissolved solids, sulfate, chloride, total nitrite plus nitrate, 

total nitrogen, total phosphorus, and suspended sediment. For 

total nitrite plus nitrate, total nitrogen, and total phosphorus, 

cosine and sine functions of time also were used to explain the 

seasonality in concentration.

Streamflow, or the volume of water passing a particular 

point per unit time, is a fundamental measurement of streams. 

For the conditions observed in 2003-05, the base-10 logarithm 

of streamflow was a statistically significant estimator of all of 

the constituents in this study except dissolved solids. Specific 

conductance, or water’s ability to conduct an electric current, 

was a statistically significant estimator of alkalinity, dissolved 

solids, sulfate, and chloride. Turbidity, caused by the presence of suspended and dissolved matter in water, includes 

suspended sediment, which may act as a transport mechanism 

(11)

24  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 14. Comparison of measured and estimated suspended-sediment concentrations in the Red River of the North at Fargo, 

North Dakota, 2003-05.

MEASURED SUSPENDED-SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER

ESTIMATED SUSPENDED-SEDIMENT CONCENTRATION, IN MILLIGRAMS PER LITER

0

0

200 400 600 800 1,000 1,200

200

400

600

800

1,000

1,200

RPD = 19.3

RPD = 19.3

 EXPLANATION

Estimated concentration

Measured concentration

Median relative percentage difference between instantaneous

measured suspended-sediment concentrations and

instantaneous estimated suspended-sediment concentrations

Summary 25
for water-quality constituents. Turbidity was a statistically 

significant explanatory variable for total phosphorus and 

suspended sediment. pH, water temperature, and dissolved 

oxygen were not statistically significant explanatory variables 

for any constituent concentrations in this study.

As an indicator of the ability of the regression equations 

to explain the variability in the constituent concentrations, 

R2, the coefficient of multiple determination, was reported 

for each equation. R2 was 0.951 for alkalinity, 0.990 for dissolved solids, 0.963 for sulfate, 0.895 for chloride, 0.714 for 

total nitrite plus nitrate, 0.703 for total nitrogen, 0.771 for 

total phosphorus, and 0.873 for suspended sediment. Also, 

the median relative percentage difference (median RPD) was 

calculated for each equation. The median RPD compares the 

measured concentrations to the concentrations estimated by 

the regression equations and smaller median RPDs are 

desirable. The median RPD was 2.3 for alkalinity, 1.1 for 

dissolved solids, 5.8 for sulfate, 10.7 for chloride, 35.2 for 

total nitrite plus nitrate, 14.7 for total nitrogen, 17.2 for total 

phosphorus, and 19.3 for suspended sediment.

The regression equations presented in this report are 

site specific and apply only to the Red River at Fargo, North 

Dakota. An additional constraint is that the equations were 

developed with water-quality samples collected only during 

the months of March through October. The regression equations may not apply to the quality of water under ice. Future 

sampling may result in the refinement of these equations or in 

the development of different regression equations for spring/

summer and fall/winter for some constituents.

In addition to constituent concentrations, constituent 

loads also were estimated using the regression equations. 

These load estimates provide a visual summary of the 

seasonality of constituent loads and make a continuous record 

available for comparison to water-quality standards expressed 

as TMDLs. The peak loads generally occurred in June and 

July when streamflow also peaked. The increasing population 

of the Fargo, North Dakota, region, increasing public interest 

in TMDLs, and the international interest in water quality of 

the Red River make this study of regional and international 

importance because it shows how constituent loads may be 

calculated with surrogate variables continuously recorded at 

the Fargo gaging station. The methods used in this study replicate those used in Kansas and may be replicated for other sites 

in North Dakota and the Nation to monitor water quality.

References Cited

Allan, J.D., 1995, Stream ecology—structure and function of 

running waters: London, Chapman & Hall, 388 p.

Buchanan, T.J., and Somers, W.P., 1969, Discharge measurements at gaging stations: U.S. Geological Survey Techniques of Water-Resources Investigations, book 3, chap. A8, 

65 p., accessed June 2, 2006, at http://pubs.usgs.gov/twri/

twri3a8/

Chapra, S.C., 1997, Surface water-quality modeling: New 

York, McGraw-Hill, 844 p.

Christensen, V.G., 2001, Characterization of surface-water 

quality based on real-time monitoring and regression 

analysis, Quivira National Wildlife Refuge, south-central 

Kansas, December 1998 through June 2001: U.S. Geological Survey Water-Resources Investigations Report 01-4248, 

28 p., accessed March 2, 2006, at http://pubs.water.usgs.

gov/wri014248

Christensen, V.G., Jian, Xiaodong, and Ziegler, A.C., 2000, 

Regression analysis and real-time water-quality monitoring 

to estimate constituent concentrations, loads, and yields in 

the Little Arkansas River, south-central Kansas, 1995-99: 

U.S. Geological Survey Water-Resources Investigations 

Report 00-4126, 36 p., accessed March 2, 2006, at http://

pubs.water.usgs.gov/wri004126

Feth, J.H., 1981, Chloride in natural continental water—a 

review: U.S. Geological Survey Water-Supply Paper 2176, 

30 p., accessed June 9, 2006, at http://pubs.er.usgs.gov/

usgspubs/wsp/wsp2176

Gray, J.R., Glysson, G.D., Turcios, L.M., and Schwarz, G.E., 

2000, Comparability of suspended-sediment concentration 

and total suspended solids data: U.S. Geological Survey 

Water-Resources Investigations Report 00-4191, 14 p., 

accessed June 2, 2006, at http://pubs.er.usgs.gov/usgspubs/

wri/wri004191

Guy, H.P., 1969, Laboratory theory and methods for sediment 

analysis: U.S. Geological Survey Techniques of WaterResources Investigations, book 5, chap. C1, 58 p., accessed 

June 2, 2006, at http://pubs.usgs.gov/twri/twri5c1/

26  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Helsel, D.R., and Hirsch, R.M., 1995, Statistical methods in 

water resources: New York, Elsevier Science B.V., 529 p.

Hem, J.D., 1985, Study and interpretation of the chemical 

characteristics of natural water, (3rd ed.): U.S. Geological 

Survey Water-Supply Paper 2254, 264 p., accessed March 7, 

2006, at http://pubs.er.usgs.gov/usgspubs/wsp/wsp2254

Insightful Corporation, 2001a, Resampling techniques—bootstrap and jackknife, in S-PLUS 6 for Windows guide 

to statistics, volume 2: Seattle, Insightful Corporation, 

p. 537-562.

Insightful Corporation, 2001b, S-Plus 6 for Windows user’s 

guide: Seattle, Insightful Corporation, 688 p.

International Organization for Standardization, 1999, Water 

quality—Determination of turbidity: Geneva, Switzerland, 

International Organization for Standardization, ISO 7027, 

10 p.

Kennedy, E.J., 1983, Computation of continuous records 

of streamflow: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 3, chap. A13, 53 p., 

accessed June 2, 2006, at http://pubs.usgs.gov/twri/twri3-

a13/

Kennedy, E.J., 1984, Discharge ratings at gaging stations: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 3, chap. A10, 59 p., accessed June 2, 

2006, at http://pubs.usgs.gov/twri/twri3-a10/

Matthes, W.J., Sholar, C.J., and George, J.R., 1992, Qualityassurance plan for analysis of fluvial sediment: U.S. Geological Survey Open-File Report 91-467, 31 p., accessed 

June 2, 2006, at http://pubs.er.usgs.gov/usgspubs/ofr/

ofr91467

Neter, John, Kutner, M.H., Nachtsheim, C.J., and Wasserman, 

William, 1996, Applied linear statistical models, (4th ed.): 

Boston, WCB/McGraw-Hill, 1408 p.

North Dakota Department of Health, 2003a, North Dakota 

Department of Health Chemistry Division quality assurance 

plan: Bismarck, North Dakota, North Dakota Department of 

Health, [variously paged].

North Dakota Department of Health, 2003b, North Dakota 

Department of Health environmental methods manual: Bismarck, North Dakota, North Dakota Department of Health, 

[variously paged].

North Dakota Department of Health, 2006, How minerals 

affect water supplies: Miscellaneous publication, about 3 p., 

accessed June 9, 2006, at http://www.health.state.nd.us/WQ/

GW/pubs/mineral.htm

Tornes, L.H., 2005, Water quality of streams in the Red River 

of the North Basin, Minnesota, North Dakota, and South 

Dakota, 1970-2001: U.S. Geological Survey Scientific 

Investigations Report 2005-5095, 81 p., accessed July 19, 

2006, at http://pubs.water.usgs.gov/sir20055095/

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accessed August 28, 2006, at http://quickfacts.census.

gov/qfd/states/

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act section 303: accessed July 19, 2006, at http://www.epa.

gov/waterscience/standards/303.htm

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book 9, chaps. A1-A9, [variously paged], accessed June 2, 

2006, at http://pubs.water.usgs.gov/twri9A

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implements new turbidity data-reporting procedures: 

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TurbidityInfoSheet.pdf

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selected gaging stations in the Red River of the North Basin, 

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References Cited 27
Figure 15. Comparison of measured and estimated alkalinity loads in the Red River of the North at Fargo, North Dakota, 2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

ALKALINITY LOAD, IN POUNDS PER DAY

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

7,000,000

8,000,000

EXPLANATION

 Estimated Load

 Measured Load

28  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 16. Comparison of measured and estimated dissolved-solids loads in the Red River of the North at Fargo, North Dakota, 

2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

 DISSOLVED-SOLIDS LOAD, IN POUNDS PER DAY

0

2,000,000

6,000,000

4,000,000

8,000,000

10,000,000

12,000,000

14,000,000

16,000,000

18,000,000

EXPLANATION

 Estimated Load

 Measured Load

References Cited 29
Figure 17. Comparison of measured and estimated sulfate loads in the Red River of the North at Fargo, North Dakota, 2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

SULFATE LOAD, IN POUNDS PER DAY

0

1,000,000

2,000,000

3,000,000

4,000,000

5,000,000

6,000,000

7,000,000

8,000,000

EXPLANATION

 Estimated Load

 Measured Load

30 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 18. Comparison of measured and estimated chloride loads in the Red River of the North at Fargo, North Dakota, 2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

 CHLORIDE LOAD, IN POUNDS PER DAY

0

50,000

150,000

100,000

200,000

250,000

300,000

350,000

400,000

450,000

EXPLANATION

 Estimated Load

 Measured Load

References Cited 31
Figure 19. Comparison of measured and estimated total nitrite plus nitrate loads in the Red River of the North at Fargo, North 

Dakota, 2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

TOTAL NITRITE PLUS NITRATE LOAD, IN POUNDS PER DAY

0

10,000

20,000

30,000

40,000

50,000

60,000

EXPLANATION

 Estimated Load

 Measured Load

32 Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 20. Comparison of measured and estimated total nitrogen loads in the Red River of the North at Fargo, North Dakota, 

2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

TOTAL NITROGEN LOAD, IN POUNDS PER DAY

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

EXPLANATION

 Estimated Load

 Measured Load

References Cited 33
Figure 21. Comparison of measured and estimated total phosphorus loads in the Red River of the North at Fargo, North Dakota, 

2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

TOTAL PHOSPHORUS LOAD, IN POUNDS PER DAY

0

10,000

5,000

15,000

20,000

25,000

EXPLANATION

 Estimated Load

 Measured Load

34  Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05
Figure 22. Comparison of measured and estimated suspended-sediment loads in the Red River of the North at Fargo, North Dakota, 

2003-05.

2003

J F M A M J J A S O N D J F M A M J J A S O N D J F M A M J J A S O N D

2004 2005

SUSPENDED-SEDIMENT LOAD, IN POUNDS PER DAY

0

5,000,000

20,000,000

25,000,000

15,000,000

10,000,000

30,000,000

35,000,000

EXPLANATION

 Estimated Load

 Measured Load

References Cited 35
For more information concerning the 

research in this report, contact:

Director, U.S. Geological Survey

North Dakota Water Science Center

821 East Interstate Avenue

Bismarck, North Dakota 58503

(701) 250-7400

http://nd.water.usgs.gov/
Ryberg—Continuous Water-Quality Monitoring and Regression Analysis, Red River of the North, 2003-05—Scientific Investigations Report 2006-5241

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