U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2011–5172

Prepared in cooperation with the City of Tulsa, Oklahoma

Comparison of Load Estimation Techniques and Trend 

Analysis for Nitrogen, Phosphorus, and Suspended 

Sediment in the Eucha-Spavinaw Basin, Northwestern 

Arkansas and Northeastern Oklahoma, 2002–10
Cover Photograph. Beaty Creek near Jay, Oklahoma, by Waylon Z. Marler.
Comparison of Load Estimation Techniques 

and Trend Analysis for Nitrogen, Phosphorus, 

and Suspended Sediment in the EuchaSpavinaw Basin, Northwestern Arkansas 

and Northeastern Oklahoma, 2002–10

By Rachel A. Esralew, William J. Andrews, Monica L. Allen, and Carol J. Becker

Prepared in cooperation with the City of Tulsa, Oklahoma

Scientific Investigations Report 2011–5172

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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U.S. Government.

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:

Suggested citation:

Esralew, R.A., Andrews, W.J., Allen, M.L., and Becker, C.J., 2011, Comparison of load estimation techniques and trend 

analysis for nitrogen, phosphorus, and suspended sediment in the Eucha-Spavinaw basin, northwestern Arkansas and 

northeastern Oklahoma, 2002–10: U.S. Geological Survey Scientific Investigations Report 2011–5172, 60 p.
iii

Acknowledgments

The authors would like to thank the staff of the USGS Tulsa Field Office for measuring 

streamflow and collecting samples for this report. The authors also appreciate the assistance 

with statistical matters provided by David Lorenz of the USGS Minnesota Water Science 

Center. We appreciate the help of Jerrod Smith of the USGS Oklahoma Water Science, Gloria 

Ferrell of the USGS North Carolina Water Science Center, and Ray West and Roy Foster of the 

City of Tulsa in reviewing draft versions of this report.
iv

Contents

Acknowledgments .......................................................................................................................................iii

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

Introduction.....................................................................................................................................................2

Changes in Nitrogen, Phosphorus, and Suspended-Sediment Transport in the 

Eucha-Spavinaw Basin ..........................................................................................................4

Previous U.S. Geological Survey Reports.........................................................................................4

Purpose and Scope ..............................................................................................................................5

Description of the Study Area ............................................................................................................5

Streamflow in the Eucha-Spavinaw Basin.......................................................................................8

Methods of Analysis......................................................................................................................................8

Streamflow and Water-Quality Data Collection...............................................................................8

Quality Assurance.................................................................................................................................8

Streamflow Separation......................................................................................................................10

Development of Regression Equations to Estimate Concentrations and Loads ......................10

Comparison of Differences in Regression-Based Daily Load Estimates..........................11

Evaluation of Differences in Fit ...............................................................................................12

Methods of Analysis of Temporal Trends in Concentration.........................................................12

Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw 

Basin, 2002–10.................................................................................................................................13

Water-Quality Data Used to Develop Regression Equations ......................................................13

Nitrogen and Phosphorus Concentrations............................................................................13

Sediment Concentrations.........................................................................................................14

Estimated Loads and Yields of Nitrogen, Phosphorus, and Suspended 

Sediment, 2002–10.................................................................................................................14

Nitrogen Loads and Yields........................................................................................................14

Phosphorus Loads and Yields..................................................................................................16

Sediment Loads and Yields ......................................................................................................22

Estimated Mean Annual Nitrogen, Phosphorus, and Sediment Loads 

into Lake Eucha ...........................................................................................................24

Estimation of Instantaneous Concentrations from Water-Quality Samples, 

Streamflow, and Real-Time Continuous Water-Quality Data for 2005–10....................24

Nitrogen.......................................................................................................................................24

Phosphorus.................................................................................................................................27

Sediment......................................................................................................................................28

Comparison of Regression-Based 

Load Estimates.......................................................................................................................28

Nitrogen.......................................................................................................................................28

Phosphorus.................................................................................................................................35

Sediment......................................................................................................................................38

Evaluation of Temporal Trends in Nitrogen, Phosphorus, and Sediment 

Concentrations in the Eucha-Spavinaw Basin, 2002–10 .........................................................46

Summary........................................................................................................................................................56

References Cited..........................................................................................................................................57
v

Figures

1. Map of the Eucha-Spavinaw basin, Arkansas and Oklahoma, with 

locations of selected streamflow-gaging and lake-level stations in the 

basin and towns with wastewater-treatment plants that discharge into 

streams in the basin .....................................................................................................................3

2. Map showing land use in the basins draining to Spavinaw Creek near 

Colcord, and Beaty Creek near Jay, Oklahoma, in the Eucha-Spavinaw 

basin, Arkansas and Oklahoma..................................................................................................7

3. Boxplots of distributions of total nitrogen concentrations in water 

samples collected from different time periods at streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma......................................15

4. Boxplots of distributions of total phosphorus concentrations in water 

samples collected from different time periods at streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma......................................15

5. Boxplots of distributions of suspended-sediment concentrations in water 

samples collected from different time periods at streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma......................................16

6. Bar graphs of estimates of base-flow and runoff components of annual 

total nitrogen load and mean annual streamflow at water-quality 

monitoring stations in the Eucha-Spavinaw basin, Arkansas and 

Oklahoma, 2002–10 .....................................................................................................................20

7. Bar graphs of estimates of base-flow and runoff components of annual 

total phosphorus load and mean annual streamflow, at water-quality 

monitoring stations in the Eucha-Spavinaw basin, Arkansas and 

Oklahoma, 2002–10 .....................................................................................................................21

8. Bar graphs of estimates of base-flow and runoff components of 

suspended-sediment annual load and mean annual streamflow, at waterquality monitoring stations in the Eucha-Spavinaw basin, Arkansas and 

Oklahoma, 2002–10 .....................................................................................................................23

9. Graph of trends in error residuals of regression-estimated total phosphorus 

concentrations at Spavinaw Creek near Colcord, Oklahoma, streamflowgaging station, 2004–10..............................................................................................................27

10. Bar graphs of annual total nitrogen load estimated using two regression 

methods at Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near 

Jay, Okla., streamflow-gaging stations, 2005–10...................................................................31

11. Bar graphs of comparison of relative percent differences between annual 

total nitrogen load estimated from two regression methods for Spavinaw 

Creek near Colcord, Oklahoma, and Beaty Creek near Jay, Okla., 

streamflow-gaging stations, 2006–10......................................................................................32

12. Graphs of comparison of duration curves for estimated daily nitrogen loads 

at Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near Jay, 

Okla., using two regression methods ......................................................................................34

13. Graphs of comparison of measured and regression-estimated total nitrogen 

concentrations from (A) INSTC

 regressions that include physical waterquality constituents, streamflow, and seasonality as independent variables 

and (B) alternate INSTC regressions that include streamflow and seasonality 

as independent variables ..........................................................................................................35

14. Bar graphs of annual total phosphorus load estimated using two 

regression methods at Spavinaw Creek near Colcord, Oklahoma, and 

Beaty Creek near Jay, Okla., 2005–10......................................................................................36
vi

15. Bar graphs of comparison of relative percent differences between annual 

total phosphorus load estimated from two regression methods for 

Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near Jay, 

Oklahoma, 2006–10 .....................................................................................................................37

16. Graphs of comparison of duration curves for estimated daily phosphorus 

loads at Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near 

Jay, Okla., using two regression methods..............................................................................39

17. Graphs of comparison of measured and regression-estimated total 

phosphorus concentrations from (A) INST

C

 regressions based on physical 

water-quality constituents, streamflow, and seasonality as independent 

variables and (B) alternate INST

C

 regressions based on streamflow and 

seasonality as independent variables.....................................................................................40

18. Graphs of comparison of difference in daily mean streamflow to difference 

in estimated phosphorus load between two regression methods at 

Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near 

Jay, Okla. ......................................................................................................................................41

19. Bar graphs of suspended-sediment annual total load estimated using two 

regression methods, Spavinaw Creek near Colcord, and Beaty Creek near 

Jay, Oklahoma, 2005–10 ............................................................................................................42

20. Bar graphs of comparison of relative percent differences between 

suspended-sediment annual total load estimated from two regression 

methods for Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek 

near Jay, Okla., 2006–10.............................................................................................................43

21. Graphs of comparison of duration curves for estimated daily suspendedsediment loads at Spavinaw Creek near Colcord, Oklahoma, and Beaty 

Creek near Jay, Okla., streamflow-gaging stations using two 

regression methods ...................................................................................................................44

22. Graphs of comparison of measured and regression-estimated suspendedsediment concentrations from (A) INSTC

 regressions based on physical 

water-quality constituents, streamflow, and seasonality as independent 

variables and (B) alternate INST

C

 regressions based on streamflow and 

seasonality as independent variables.....................................................................................45

23. Graphs of total phosphorus concentrations and LOESS trend lines at 

Spavinaw Creek near Maysville, Arkansas, showing (A) total phosphorus 

concentrations with time, and (B) flow-adjusted total phosphorus 

concentrations (error residuals) from a LOESS regression ................................................

48

24. Graphs of total phosphorus concentrations and LOESS trend lines at 

Spavinaw Creek near Cherokee City, Arkansas, showing (A) total 

phosphorus concentrations with time, and (B) flow-adjusted total 

phosphorus concentrations (error residuals) from a LOESS regression..........................49

25. Graphs of total phosphorus concentrations and LOESS trend lines at 

Spavinaw Creek near Sycamore, Oklahoma, showing (A) total phosphorus 

concentrations with time, and (B) flow-adjusted total phosphorus 

concentrations (error residuals) from a LOESS regression ................................................50

26. Graphs of total phosphorus concentrations and LOESS trend lines at 

Spavinaw Creek near Colcord, Oklahoma, showing (A) total phosphorus 

concentrations with time, and (B) flow-adjusted total phosphorus 

concentrations (error residuals) from a LOESS regression ................................................51
vii

27. Graphs of total phosphorus concentrations and LOESS trend lines at 

Beaty Creek near Jay, Oklahoma, showing (A) total phosphorus 

concentrations with time, and (B) flow-adjusted total phosphorus 

concentrations (error residuals) from a LOESS regression ................................................52

28. Graphs of suspended-sediment concentrations and LOESS trend lines 

at Spavinaw Creek near Maysville, Arkansas, showing (A) suspendedsediment concentrations with time, and (B) flow-adjusted suspendedsediment concentrations (error residuals) from a LOESS regression...............................53

29. Graphs of suspended-sediment concentrations and LOESS trend lines 

at Spavinaw Creek near Sycamore, Oklahoma, showing (A) suspendedsediment concentrations with time, and (B) flow-adjusted suspendedsediment concentrations (error residuals) from a LOESS regression...............................54

30. Graphs of suspended-sediment concentrations and LOESS trend lines at 

Beaty Creek near Jay, Oklahoma, showing (A) suspended-sediment 

concentrations with time, and (B) flow-adjusted suspended-sediment 

concentrations (error residuals) from a LOESS regression ................................................55

Tables

1. Estimates of fertilizer application, population of cattle and calves, and 

number of broilers and other chickens sold for counties in the EuchaSpavinaw basin, Arkansas and Oklahoma, 2002 and 2007 ....................................................6

2. Station information and streamflow statistics for streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma........................................9

3. Regression equations for estimating daily mean loads (DMLs) of total 

nitrogen, total phosphorus, and sediment using streamflow, seasonality, 

and time at streamflow-gaging stations in the Eucha-Spavinaw basin, 

Arkansas and Oklahoma, 2002–10 ...........................................................................................17

4. Estimated mean annual total nitrogen, total phosphorus, and suspended 

sediment loads and yields using regression equations developed from 

concentrations in water-quality samples and streamflow, time, and 

seasonality, for water-quality monitoring stations in the Eucha-Spavinaw 

basin, Arkansas and Oklahoma, for the period 2002–10 ......................................................18

5. Summary of estimated mean annual total nitrogen, total phosphorus, and 

suspended-sediment loads to Lake Eucha, Oklahoma, 2002–10 ........................................25

6. Regression equations for estimating instantaneous concentrations (INSTC) 

of total nitrogen, total phosphorus, and suspended sediment using physical 

water-quality constituents, streamflow, and seasonality, at Spavinaw Creek 

near Colcord, Oklahoma and Beaty Creek near Jay, Okla., streamflowgaging stations, 2004–10............................................................................................................26

7. Alternate regression equations used for estimating instantaneous 

concentrations of total nitrogen, total phosphorus, and suspended sediment 

using streamflow and seasonality parameters for Spavinaw Creek near 

Colcord, Oklahoma, and Beaty Creek near Jay, Okla., streamflow-gaging 

stations, 2004–10.........................................................................................................................29
viii

8. Estimated mean annual total nitrogen, total phosphorus, and 

suspended-sediment loads and yields by using two different regression 

equations for streamflow-gaging stations in the Eucha-Spavinaw basin, 

Arkansas and Oklahoma, 2002–10 ...........................................................................................29

9. Wilcoxon signed-rank test results comparing daily loads estimated from 

two different regression methods at two streamflow-gaging stations in the 

Eucha-Spavinaw basin, 2004–10..............................................................................................33

10. Results of Kendall’s tau and Seasonal Kendall tests of time trends of 

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

suspended sediment in water samples collected at streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10......................47

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

mile (mi) 1.609 kilometer (km)

Area

acre 0.4047 hectare (ha)

acre 4,047 square meter (m2

)

acre 0.004047 square kilometer (km2

)

square foot (ft2

) 929.0 square centimeter (cm2)

square mile (mi2

) 259.0 hectare (ha)

square mile (mi2

) 2.590 square kilometer (km2) 

Volume

cubic foot (ft3

) 28.32 cubic decimeter (dm3) 

cubic foot (ft3

) 0.02832 cubic meter (m3) 

Flow rate

cubic foot per second (ft3

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

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3/s)

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

ton, short (2,000 lb) 0.9072 megagram (mg)

pound per year 0.4536 kilogram per year (kg/yr)

pound per year per square mile (lb/yr/mi2) kilogram per year per square mile 

(kg/yr/mi2)

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

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

or micrograms per liter (μg/L).
Comparison of Estimation Techniques and Trend 

Analysis of Nitrogen, Phosphorus, and Sediment in the 

Eucha-Spavinaw Basin, Northwestern Arkansas and 

Northeastern Oklahoma, 2002–10

By Rachel A. Esralew, William J. Andrews, Monica L. Allen, and Carol J. Becker

Abstract 

The City of Tulsa, Oklahoma, uses water from Lake 

Eucha and Spavinaw Lake in the Eucha-Spavinaw basin of 

northwestern Arkansas and northeastern Oklahoma for public 

water supply. Increases in algal biomass, which cause taste 

and odor problems in drinking water produced from the lakes, 

may be attributable to increases in nitrogen and phosphorus 

concentrations in the lakes and in streams discharging to the 

lakes. To evaluate transport of nitrogen, phosphorus, and 

suspended sediment in this basin, loads and temporal trends 

were evaluated for five streamflow-gaging stations in the 

Spavinaw and Beaty Creek basins.

Two approaches were used to develop regression 

equations for estimation of loads and yields of nitrogen, 

phosphorus, and sediment. The first approach used regression 

equations referred to as daily mean load (DML) regressions, 

developed from water-quality samples and daily mean 

streamflow data collected from 2002 through 2010 at five 

streamflow-gaging stations in the basin. This approach 

was updated to compare loading results with those used in 

previous investigations. The second approach used regression 

equations, referred to as instantaneous continuous (INSTC) 

regressions, developed from continuous measurements of 

physical water-quality constituents (specific conductance, 

temperature, and turbidity, and streamflow data) obtained from 

2004 through 2010 to estimate loads of nitrogen, phosphorus, 

and sediment at two of the streamflow-gaging stations, 

Spavinaw Creek near Colcord, Okla., and Beaty Creek near 

Jay, Okla. Daily, annual, and mean annual loads estimated 

from these two regression methods were compared for the 

period 2005–10.

Based on estimates obtained using DML regressions, 

mean annual loads of 1,640,000 pounds of nitrogen, 

99,900 pounds of phosphorus, and 116,000,000 pounds of 

sediment were transported into Lake Eucha from the 

Spavinaw and Beaty Creek basins. Estimated annual loads of 

nitrogen and phosphorus delivered to Lake Eucha from the 

Spavinaw and Beaty Creek basins during 2002–10 were 

2.5 to 7.8 percent less, respectively, than the loads of those 

constituents discharged to Lake Eucha from 2002–09, 

indicating that nitrogen and phosphorus loads in 2010 were 

less than loads typical for the period 2002–09.

Daily, annual, and mean annual load estimates varied 

substantially, depending on streamflow conditions and the 

independent variables used to develop regressions. Daily and 

annual loads estimated from INSTC regressions that included 

turbidity, streamflow, temperature, specific conductance, 

and seasonality fit better with the field data than loads 

estimated from DML regressions that included streamflow, 

seasonality, and time. Loads estimated from the INSTC

regression generally were greater than those estimated from 

the DML regression. Relative percent differences in the mean 

annual total nitrogen load estimated by the INSTC and DML

regressions were within 2 percent for Spavinaw Creek near 

Colcord, and Beaty Creek near Jay, Okla. The relative percent 

difference between the two types of regressions for estimates 

of mean annual total phosphorus loads at the two streamflowgaging stations was 27.7 for Spavinaw Creek near Colcord, 

Okla., and only -2.6 percent for Beaty Creek near Jay, 

Okla. The relative percent difference between mean annual 

suspended-sediment loads at the streamflow-gaging stations 

was -38.6 percent for Spavinaw Creek near Colcord, Okla., 

and -122.7 percent for Beaty Creek near Jay, Okla. The DML

regression may have substantially underestimated phosphorus 

load at the Spavinaw Creek near Colcord, Okla., streamflowgaging station in wet years and overestimated sediment load at 

both streamflow-gaging stations in wet years.

Temporal trends in flow-adjusted nitrate-nitrogen, 

nitrogen, phosphorus, and suspended-sediment concentrations 

were analyzed for the five streamflow-gaging stations for 

the period 2001–10. No significant trends were observed for 

nitrate plus nitrite-nitrogen or total nitrogen concentrations 

at any streamflow-gaging station. There were significant 

upward trends in phosphorus concentrations in water samples 

collected during base-flow conditions at the Spavinaw 

Creek near Maysville, Okla., streamflow-gaging station 

and during runoff conditions for the Beaty Creek near Jay, 
2 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Okla., streamflow-gaging station (3.5 to 4.2 percent per 

year). There were significant downward trends in phosphorus 

concentrations in base-flow and runoff samples collected at the 

Spavinaw Creek near Cherokee City, Sycamore, and Colcord, 

Okla., streamflow-gaging stations (-4.9 to -12.9 percent per 

year). There were significant downward trends in suspendedsediment concentration at the Spavinaw Creek near Maysville, 

and Sycamore, Okla., and the Beaty Creek near Jay, Okla., 

streamflow-gaging stations (-1.5 to -1.8 percent per year). 

No significant trends were detected in suspended-sediment 

concentration for the Spavinaw Creek near Cherokee City, and 

Colcord, Okla., streamflow-gaging stations. 

Possible causes for downward trends in phosphorus 

concentrations include decreases in phosphorus discharges 

from a wastewater-treatment plant upstream from the 

Spavinaw Creek near Cherokee City, Okla., streamflow-gaging 

station, and implementation of best management practices in 

the basin. Downward trends in sediment concentrations may 

be related to effects of best management practices in the basin.

Introduction

The City of Tulsa, Oklahoma, uses Lake Eucha and 

Spavinaw Lake in the Eucha-Spavinaw basin in northwestern 

Arkansas and northeastern Oklahoma for public water supply 

(fig. 1). Construction of Spavinaw Dam (U.S. Geological 

Survey (USGS) lake-level station at Spavinaw Lake, station 

identifier 07191300, fig. 1) on Spavinaw Creek began in 1922 

and was completed in 1924 (Oklahoma Water Resources 

Board, 2002). A series of 60-mile-long pipelines was 

constructed to transfer water from the base of the Spavinaw 

Dam to a drinking-water-treatment plant in Tulsa. In 1950, 

city officials decided to create an impoundment of Spavinaw 

Creek 4 miles upstream from Spavinaw Lake to serve as “an 

environmental and hydrologic barrier” for Spavinaw Lake 

to ensure a constant supply of clean water. This second dam 

came to be known as Eucha Dam (USGS lake-level station 

at Lake Eucha, station identifier 07191285, fig. 1) that was 

finished in 1954 to impound Lake Eucha (fig. 1) (City of Tulsa 

City Services, 2008a).

The Eucha-Spavinaw water-supply system continues to 

be used for public water supply as well as for recreation, fish 

and wildlife, agriculture, and aesthetics (City of Tulsa City 

Services, 2008b). On average, the Eucha-Spavinaw watersupply system provides 59 million gallons per day (Mgal/d) 

to the Tulsa metropolitan area. During peak demand, the 

system can produce a maximum of 100 Mgal/d (City of Tulsa 

City Services, 2008b). 

Taste and odor problems in drinking water have been 

reported by water customers to the City of Tulsa (COT) (City 

of Tulsa City Services, 2008c). The Tulsa Metropolitan Utility 

Authority (TMUA) spent millions of dollars from 1998–2005 

to eliminate taste and odor problems, likely attributable to 

the chemicals produced by blue-green algae, particularly 

geosmin, in drinking water from the Eucha-Spavinaw watersupply system (City of Tulsa City Services, 2008c; Oklahoma 

Water Resources Board, 2002). Increases in algal biomass 

in the lakes are believed to be the result of increases in 

nitrogen and phosphorus concentrations in tributaries of the 

lakes (City of Tulsa City Services, 2008c). Elevated nitrogen 

and phosphorus concentrations promote algae growth in 

streams (Sharpley, 1995; U.S. Geological Survey, 1999) 

and accelerate eutrophication (plant growth and dissolved 

oxygen depletion) in lakes (Daniel and others, 1998; U.S. 

Geological Survey, 1999). Reduction in suspended sediments 

also may increase algal growth by reducing water turbidity 

and increasing penetration of sunlight into water (Gloria 

Ferrell, U.S. Geological Survey, written commun., 2011). 

Studies of nitrogen and phosphorus loading in this basin began 

with a 1997 Oklahoma Conservation Commission report 

indicating increasing nitrogen and phosphorus concentrations 

in Spavinaw Creek, a main tributary to Lake Eucha (fig. 1), 

between 1975 and 1995 (Wagner and Woodruff, 1997). Lake 

Eucha and Spavinaw Lake were enriched in nitrogen and 

phosphorus (phosphorus was the limiting nutrient) and had 

high to excessive levels of algae in 2000 (Oklahoma Water 

Resources Board, 2002). 

Nitrogen and phosphorus can enter streams in discharges 

from wastewater-treatment plants (point sources) and in 

agricultural and urban runoff (nonpoint sources) (Oklahoma 

Water Resources Board, 2002). The main sources of elevated 

nitrogen and phosphorus concentrations in streams in 

the Eucha-Spavinaw basin are nonpoint sources (such as 

runoff from fertilized pastures) and point sources (primarily 

municipal wastewater discharge) (Tortorelli, 2006; 

Tortorelli, 2008; City of Tulsa, 2010). Storm and others (2002) 

reported that runoff from pastures to which animal manure or 

commercial fertilizer had been applied was a major source of 

nitrogen and phosphorus delivered to streams in this basin. 

One possible major contributor of nitrogen and 

phosphorus to the creeks discharging to Lake Eucha and 

Spavinaw Lake is the phosphorous-rich waste produced by 

commercial poultry operations in the basin. This waste is 

routinely spread onto fields as fertilizer and can be a source of 

nitrogen and phosphorous washed into streams as nonpointsource pollution, which ultimately reaches the water-supply 

lakes and promotes growth of unwanted algae (Storm and 

others, 2002). Another source of nitrogen and phosphorus is a 

municipal wastewater-treatment plant, operated by the City of 

Decatur, Arkansas (referred to in the remainder of this report 

as the “Decatur wastewater-treatment plant”), which releases 

municipal wastewater effluent, after secondary treatment, 

into Columbia Hollow, a tributary of Spavinaw Creek 

(U.S. Environmental Protection Agency and Oklahoma 

Department of Environmental Quality, 2009). Concentrations 

of nitrogen and phosphorus in streams receiving municipal 

wastewater can exceed those in streams draining agricultural 

areas (Petersen and others, 1998). 
Introduction 

3

Study area

OKLAHOMA ARKANSAS

Spavinaw Lake

07191300

Boundary of basin

ARKANSAS OKLAHOMA

Lake Eucha

Eucha

07191285

07191288 Jay

07191222

Colcord

071912213

Sycamore

07191220

Cherokee City

Maysville

07191179

07191160

Spavinaw

Eucha

Jay

Sycamore

Colcord

Decatur

Cherokee

City

Maysville

Gravette

Hiwasse

Base from U.S. Geological Survey digital data, 1:100,000, 1983, andU.S. Environmental Protection Agency enhanced River Reach File 3Albers Equal-Area Conic projection, North American Datum of 1983

07191288

071912213

0 50 5 10 KILOMETERS

10 MILES

U.S. Geological Survey streamflow- gaging station and number

U.S. Geological Survey lake-level station and number

U.S. Geological Survey streamflow- gaging station and water-quality monitoring station and number  (table 2)

EXPLANATION

95°00’ 94°45’ 94°15’ 94°30’

36°30’36°15’

SpavinawLake

LakeEucha

Creek

Beaty

Creek

Spavinaw

Tulsa

Columbia Hollow

07191285

Town with water-treatment plant that discharges into streams in  the Eucha-Spavinaw Basin

Figure 1. Eucha-Spavinaw basin, Arkansas and Oklahoma, with locations of selected streamflow-gaging and lake-level stations in the basin and towns with wastewatertreatment plants that discharge into streams in the basin.
4 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Nitrogen and phosphorus concentrations in streams 

vary throughout the year, in response to precipitation, 

streamflow, quantities and composition of wastewater 

effluent, and the timing of fertilizer and manure applications 

(U.S. Geological Survey, 1999). Nitrogen and phosphorus 

concentrations in streams generally are greater during runoff 

periods than during base-flow periods, especially in the 

spring and summer after fertilizer application. Sedimentbound and particulate forms of nitrogen (mostly organic) 

and phosphorus are likely to be delivered to the stream during 

high streamflow as a result of hillslope and channel bank 

erosion as well as resuspension of streambed sediments. 

Increases in concentrations of phosphorus and organic 

nitrogen are typically associated with increases in suspendedsediment concentrations. Increased nitrogen and phosphorus 

concentrations also were measured in streams during low 

flows, possibly because of minimal dilution of point sources, 

such as effluent from wastewater-treatment plants 

(U.S. Geological Survey, 1999).

Water-quality data collected at five USGS-operated 

streamflow-gaging stations (referred to in the remainder of this 

report as “stations”) in the basin were evaluated: (1) Spavinaw 

Creek near Maysville, Arkansas; (2) Spavinaw Creek near 

Cherokee City, Arkansas; (3) Spavinaw Creek near Sycamore, 

Okla.; (4) Spavinaw Creek near Colcord, Okla.; and (5) 

Beaty Creek near Jay, Okla. (fig. 1). For the remainder of this 

report, these stations are referred to as the Maysville station, 

Cherokee City station, Sycamore station, and Colcord station 

on Spavinaw Creek (or collectively as the “Spavinaw Creek 

stations”), and the Beaty Creek station, respectively.

Prior to July 2001, water-quality samples were collected 

in the Eucha-Spavinaw basin on a monthly schedule. Most 

of those water samples were collected during base-flow 

(non-runoff) conditions because runoff events are variable 

and infrequent. The lack of samples collected during runoff 

caused underestimation of true nitrogen and phosphorus 

concentrations, loads, and yields in the basin. From July 

2001 through 2010, the USGS, in cooperation with COT, has 

supplemented monthly collection of nitrogen and phosphorus 

samples with collection of nitrogen, phosphorus, and 

suspended-sediment samples during six runoff events per year 

to expand the range of streamflow over which water-quality 

data were collected.

Changes in Nitrogen, Phosphorus, and 

Suspended-Sediment Transport in the 

Eucha-Spavinaw Basin

To decrease eutrophication in the Eucha-Spavinaw 

basin, quantities of nitrogen and phosphorus in runoff to 

surface water or seepage into groundwater need to be reduced. 

Since 1998, efforts to minimize eutrophication in the basin 

have included reducing land applications of poultry litter, 

implementing best management practices (BMPs) to reduce 

runoff of nitrogen, phosphorus, and sediment; and reduction 

of nitrogen and phosphorus concentrations in municipal 

wastewater effluent.

Land applications of poultry litter as fertilizer probably 

have decreased since 2004. In 2001, an estimated 1,500 tons 

of nitrogen and phosphorous-rich animal wastes were 

generated in this basin annually (Tulsa Metropolitan Utility 

Authority, 2001). A lawsuit filed by the COT against several 

poultry-producing companies in 2001 was settled out of court 

in 2003 and starting in 2004, substantial reductions in land 

application of poultry litter in the basin commenced (City of 

Tulsa, 2010). 

BMPs designed to improve water quality have been 

implemented in the Eucha-Spavinaw basin since 1998, 

including creation of conservation easements, protection 

of riparian buffers, streambank stabilization, exclusion 

of cattle from waterways, and reductions in poultry litter 

application (Oklahoma Conservation Commission, 2007; 

U.S. Environmental Protection Agency, 2007). BMPs were 

implemented in the Beaty Creek basin for the period 

1998–2003 and in the Spavinaw Creek basin from 2003–2008; 

landowners have continued to keep BMP measures in place 

(Oklahoma Conservation Commission, 2007; Oklahoma 

Conservation Commission, 2009). A paired-basin study in 

the Beaty Creek basin indicated that the upward trend of 

phosphorus loading to Beaty Creek decreased by 31 percent 

after BMPs were implemented (U.S. Environmental 

Protection Agency, 2007).

Point-source discharges of municipal wastewater 

also have been reduced in the basin. As a result of a 2003 

settlement, effluent discharge from the Decatur wastewatertreatment plant was required to meet a monthly average of 

1 milligram per liter (mg/L) of phosphorus, an 80-percent 

reduction compared to previous discharges (Oklahoma 

Department of Environmental Quality, 2007). Improvements 

to the wastewater-treatment plant were operational as of 

January 2006 (Oklahoma Department of Environmental 

Quality, 2007). Haggard and Stoner (2009) analyzed average 

monthly effluent total phosphorus concentrations before and 

after the 2006 plant upgrade and found significantly less and 

less variable concentrations of total phosphorus in wastewater 

discharge since the upgrade. 

Previous U.S. Geological Survey Reports

Several reports characterizing nitrogen and phosphorus 

in the Eucha-Spavinaw basin have been published, including 

Wagner and Woodruff (1997), Haggard (2000), Haggard 

and others (2001), Storm and others (2001, 2002), Tulsa 

Metropolitan Utility Authority (2001), Delaune and others 

(2006), Tortorelli (2006, 2008), Christensen and others (2008), 

Haggard and Stoner (2009), City of Tulsa (2010), and Esralew 

and Tortorelli (2010). Because this report is an update to 

several previously published USGS reports, only those reports 

are described in the remainder of this section.

The USGS, in cooperation with COT, investigated 

and summarized characteristics of total nitrogen and total 
Introduction 5

phosphorus concentrations and provided estimates of 

nitrogen and phosphorus loads, yields, and flow-weighted 

concentrations in the Eucha-Spavinaw basin from January 

2002 through December 2009 (Esralew and Tortorelli, 2010). 

That report is an update of previous reports in which total 

nitrogen and phosphorus concentrations, loads, and yields 

were summarized for the periods 2002–04 and 2002–06 

(Tortorelli, 2006, 2008). 

Tortorelli (2006, 2008) and Esralew and Tortorelli 

(2010) used the S-LOADEST program (Dave Lorenz, U.S. 

Geological Survey, written commun., 2006) to estimate loads 

and yields. The S-LOADEST program provides estimates 

of constituent load by the rating-curve method, which is a 

regression-based approach that incorporates bias-correction 

procedures (Cohn and others, 1989; Crawford, 1991). 

Regression equations were developed for each station using 

streamflow, time, and seasonality as principal independent 

variables. These regression equations were used to estimate 

daily mean loads for days when samples were not collected. 

Those estimated daily mean loads were summed to compute 

total loads for seasons and years. Nitrogen and phosphorus 

loads and yields were used to characterize annual and seasonal 

inputs from Beaty and Spavinaw Creeks to Lake Eucha. As 

new water-quality and streamflow data become available, 

regression equations to estimate loads can be revised to 

provide more accurate estimates (D. Mueller, U.S. Geological 

Survey, written commun., 2010).

To better estimate nitrogen and phosphorus instantaneous 

concentrations for times when samples were not collected, 

continuous water-quality monitors were installed in 2004 and 

2005 at the Colcord and Beaty Creek stations, respectively. 

Data from those monitors, which measure and record 

physical water-quality constituents (temperature, pH, specific 

conductance, dissolved oxygen, and turbidity) at 15-60 

minute intervals, were used to develop regression equations 

for estimation of nitrogen and phosphorus concentrations to 

physical water-quality constituents (Christensen and others, 

2008). For the study described in this report, regression 

equations are formulated for the Beaty Creek and Colcord 

stations to estimate constituent concentrations in real time. 

Regression equations developed in Christensen and others 

(2008) were valid only for 2004–07, a period that was drier 

than normal.

Previous USGS reports (Tortorelli, 2006 and 2008; 

Christensen and others, 2008; Esralew and Tortorelli, 2010) 

did not analyze suspended-sediment (referred to in the rest of 

this report as “sediment”) loads and yields. Characterization 

of sediment loads using regression methods is useful for 

understanding transport mechanisms of sediment and of 

sorbed nutrients such as phosphorus and organic nitrogen. 

Therefore, the USGS, in cooperation with the COT, used the 

periodic water-quality sample data collected at the five stations 

and continuous water-quality monitor data collected at two 

stations to provide the COT with an updated assessment of 

loading through 2010 that can be compared to loads estimated 

for 2002–09 in Esralew and Tortorelli (2010).

Significance of trends in nitrogen, phosphorus, and 

sediment concentrations was not analyzed in previous USGS 

reports because not enough data had been collected during 

runoff conditions. Changes in the land uses and nitrogen 

and phosphorus discharges in the basin may have caused 

significant trends in concentrations of nitrogen, phosphorus, 

and sediment since 2001. As of 2010, 9 years of runoff 

samples have been collected, sufficient for analyzing longterm trends in flow-adjusted (concentrations corrected 

for changes in streamflow) concentrations of nitrogen, 

phosphorus, and sediment. Such information can be used 

to evaluate the effectiveness of nitrogen- and phosphorusreduction measures in this basin. 

Purpose and Scope

The purpose of this report is to compare and analyze load 

estimates computed using two types of regression methods for 

Beaty Creek and Colcord stations for 2005–10 and to analyze 

trends in flow-adjusted nitrogen, phosphorus, and sediment 

concentrations with time for five stations in the basin from 

2002–10. In addition, this report summarizes concentrations 

of nitrogen and phosphorus nutrients at five stations in 

the Eucha-Spavinaw basin; updates nitrogen, phosphorus, 

and sediment loads and yields at selected sites in the basin 

using data from periodic runoff water-quality samples and 

continuous streamflow data from 2002–10; and updates 

regression equations used to estimate continuous nitrogen, 

phosphorus, and sediment concentrations using continuous 

measurements of physical water-quality constituents and 

streamflow and water-quality samples collected from 2004–10 

for the Beaty Creek and Colcord stations. 

Description of the Study Area

The Eucha-Spavinaw basin is a 389-square mile area 

in northwestern Arkansas (30 percent of the basin area) and 

northeastern Oklahoma (70 percent of the basin area) (fig. 1). 

Lake Eucha and Spavinaw Lake store water discharged from 

Spavinaw and Beaty Creeks to supply the Tulsa metropolitan 

area and other local water users (Oklahoma Water Resources 

Board, 2002). The basin is in the southwestern part of the 

Ozark Plateaus physiographic province (Fenneman, 1938) 

and is underlain by the cherty limestone of the Springfield 

Plateau aquifer (Adamski and others, 1995). Soils in the 

basin are mostly classified as silty loam or gravelly silty 

loam (Storm and others, 2002). The undulating karstic 

topography of the region is caused by extensive dissolution 

of carbonate bedrock. That dissolution facilitates infiltration 

of runoff to groundwater through subterranean conduits and 

rapid groundwater flow to streams (Tulsa Metropolitan 

Utility Authority, 2001). Losses of streamflow to 

groundwater, referred to as “losing conditions,” also are 

common in the basin (J. Wellman, U.S. Geological Survey, 

written commun., 2007).
6 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Land in the Eucha-Spavinaw basin is dominated by 

pasture, hay fields, and forest, with interspersed minor 

amounts of urban land (fig. 2). The Spavinaw Creek basin has 

more forested land (39 percent) than the Beaty Creek basin 

(31 percent) and less land used for pasture and hay production 

(54 percent) than the Beaty Creek basin (62 percent) (fig. 2). 

Nitrogen and phosphorus concentrations typically are greater 

in Ozark streams draining agricultural lands than in streams 

draining forested lands (Petersen and others, 1998).

Livestock production is the primary form of agriculture 

in the basin; the basin is densely populated with poultry/beef 

cattle operations. Poultry litter is used widely as a fertilizer 

source for pastures in the study area (DeLaune and others, 

2006, table 1). The significance of nitrogen and phosphorus 

related to agriculture in the basin is evident from the estimates 

of commercial fertilizer and manure applications for counties 

in the Eucha-Spavinaw basin (table 1). Commercial fertilizer 

and manure applied is likely to be greater in Benton County, 

Ark., than in Delaware County, Okla., based on livestock 

populations (fig. 2; U.S. Department of Agriculture, 2004 

and 2009). Poultry litter application rates are greater in the 

Spavinaw Creek basin than in Beaty Creek basin (Storm and 

others, 2002, p. 25). As of 2007, poultry operations in the 

basin had the capacity to produce more than 160 million birds 

annually (U.S. Department of Agriculture, 2009; table 1). 

From 2002-2007, the amount of land fertilized with manure in 

the two counties that contain the basin decreased from 84,100 

acres to 51,700 acres and land fertilized with commercial 

fertilizer decreased from 137,900 to 115,400 acres (U.S. 

Department of Agriculture, 2004 and 2009, table 1).

In 2009, human population in the basin was estimated to 

be 225,504 in Benton County, Ark., and 40,555 in Delaware 

County, Okla. (U.S. Census Bureau, 2009). Surface-water 

and groundwater use in 1995 were 41.1 Mgal/d and 8.8 

Mgal/d, respectively, in Benton County and 2.6 Mgal/d and 

1.9 Mgal/d, respectively, in Delaware County (Adamski and 

others, 1995). Most of this water is used for public supply 

and very little agricultural water use is reported for these 

two counties. 

The Decatur wastewater-treatment plant discharged 

about 1.3 Mgal/d of wastewater to Spavinaw Creek in 

1999 (Haggard and others, 2001; Storm and others, 2002; 

DeLaune and others, 2006). After improvements to the 

wastewater-treatment plant in 2006, the plant has a wasteload allocation permit of 2.2 Mgal/d and a discharge limit of 

1 mg/L total phosphorus and 10 mg/L ammonia as nitrogen 

(U.S. Environmental Protection Agency, 2007; Oklahoma 

Department of Environmental Quality, 2009). A smaller 

wastewater-treatment plant located in the Spavinaw Creek 

basin (Gravette, Ark.) has a waste-load allocation permit of 

0.56 Mgal/d, but nitrogen and phosphorus contributions 

to Lake Eucha from that plant are considered to be 

substantially less than those of the Decatur plant because of 

the intermittent nature of the discharge from the smaller plant 

(U.S. Environmental Protection Agency and Oklahoma 

Department of Environmental Quality, 2009).

Mean annual precipitation in the basin from 1971–2000 

was 48.9 inches (in.) (1971-2000), with September having the 

highest average monthly precipitation (5.55 in.) (Oklahoma 

Climatological Survey, 2009). Annual precipitation was used 

to determine differences in precipitation between years in the 

National Weather Service Climate Divisions, OK03-NE and 

AR01-NW, in the Eucha-Spavinaw basin (National Oceanic 

and Atmospheric Administration, 2011). From 2002–10, the 

wettest year was 2008 with 59.6 and 66.7 in. of precipitation 

in OK03-NE and AR01-NW, respectively; the driest year was 

2005 with 32.3 and 33.6 in. of precipitation in OK03-NE and 

AR01-NW, respectively (National Oceanic and Atmospheric 

Administration, 2011).

Table 1. Estimates of fertilizer application, population of cattle and calves, and number of broilers and other chickens sold for 

counties in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002 and 2007.

[modified from U.S. Department of Agriculture (2004, and 2009)]

County

Percentage 

of county in 

drainage 

basin of 

Beaty Creek 

near Jay 

(station 

07191222)

Percentage 

of county in 

drainage basin 

of Spavinaw 

Creek near 

Colcord 

(station 

071912213)

Farmland 

(acres) Year

Acres 

treated 

with commercial 

fertilizer

Acres 

treated 

with 

manure

Total 

acres 

treated

Percent of 

county area 

(farms only) 

treated 

with 

fertilizer1

Population 

of cattle 

and calves

Number of 

broilers and 

other 

chickens 

sold

Delaware, 

Okla. 67.4 23.5 282,000 2002 53,200 21,300 74,500 26 74,700 37,100,000

2007 57,600 17,900 75,500 27 83,200 48,000,000

Benton, 

Ark. 32.6 76.5 313,000 2002 84,700 62,800 148,000 47 114,000 128,000,000

2007 57,800 33,800 91,600 29 94,600 117,000,000

1

Fertilizer application to land other than farms (for example, golf courses or residences) was not included.
Introduction 

7

Land use in the basin of Spavinaw

Creek near Colcord (071912213)

Land use in the basin of BeatyCreek near Jay (07191222)

Base from U.S. Geological Survey digital data, 1:100,000, 1983, and U.S. Geological Survey National Hydrography DatasetAlbers Equal-Area Conic projection, North American Datum of 1983

EXPLANATION

UrbanForestedPasture/HayRow CropsOther

Land-cover classes

Boundary of sampling basinU.S. Geological Survey streamflow- gaging station and number

Study area

OKLAHOMA ARKANSAS

Tulsa

Delaware County

Benton County

94°45’W 94°30’W

36°15’N

’

Jay (07191222) Maysville (07191160)

Cherokee City (07191179) Colcord (071912213) Sycamore (07191220)

Spavinaw Creek

Beaty Creek

OKLAHOMA ARKANSAS

Row Crops

0 percent

Other

2 percent Urban 4 percent

Forested

39 percent Pasture/Hay

62 percent

Row Crops

1 percent

Other

2 percent Urban 4 percent

Forested

31 percent Pasture/Hay

62 percent

Figure 2. Land use in the basins draining to Spavinaw Creek near Colcord, and Beaty Creek near Jay, Oklahoma, in the Eucha-Spavinaw basin, Arkansas and Oklahoma.
8 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Streamflow in the Eucha-Spavinaw Basin

The combined drainage areas of Spavinaw Creek near 

Colcord, Okla., and Beaty Creek near Jay, Okla., account for 

about 73 percent of the Eucha-Spavinaw basin. Several small 

tributaries, which are not routinely monitored or sampled, may 

be additional sources of nitrogen and phosphorus to 

Lake Eucha and Spavinaw Lake. Streamflow and waterquality data in this report are compared and analyzed in terms 

of calendar year. Annual mean daily streamflow at stations in 

the Eucha-Spavinaw basin was computed for calendar years 

2002–10. Streamflow was greater in 2004, 2008, and 2009 

than in other years (table 2). From 2002–10, there was no 

streamflow at the Beaty Creek station for 128 days during 

dry periods.

Methods of Analysis

Streamflow and Water-Quality Data Collection

Streamflow data, and nitrogen, phosphorus, and 

sediment concentration data, and continuously monitored 

real-time physical water-quality constituent data collected 

through 2010 were analyzed for this report. All streamflow 

and water-quality data in this report are available at 

http://water.usgs.gov/ok/nwis.

Stations were operated and streamflows were measured 

according to methods described in Rantz and others (1982). 

Prior to July 2001, only scheduled, monthly water-quality 

samples were collected at these stations by COT staff, 

including a few runoff samples. Starting in July 2001 at the 

Cherokee City, Colcord, and Beaty Creek stations and in 

December 2001 at the Maysville and Sycamore stations, an 

average of six runoff water-quality samples were collected 

annually at these stations by USGS staff. USGS staff collected 

most of the runoff samples at times of peak flows of each 

runoff event. COT staff collected water samples at a single 

point near the center of the stream. USGS staff collected water 

samples using equal-width increment techniques as described 

in Edwards and Glysson (1999).

Nitrogen and phosphorus concentrations in this report 

represent dissolved and particulate components in water 

because the samples were not filtered. The COT Water Quality 

Laboratory in Tulsa, Oklahoma, analyzed all water-quality 

samples using methods described by the U.S. Environmental 

Protection Agency (1983, 1993). U.S. Environmental 

Protection Agency (USEPA) method code 351.2 was used for 

analysis of total Kjeldahl nitrogen, USEPA method code 353.2 

was used for analysis of nitrate plus nitrite-nitrogen, USEPA 

method code 365.2 was used for analysis of total phosphorus 

(U.S. Environmental Protection Agency, 1983, 1993). Total 

nitrogen concentrations were calculated by adding total 

Kjeldahl nitrogen (measure of ammonia plus organic nitrogen) 

and nitrite plus nitrate-nitrogen analyses.

USGS staff installed real-time water-quality monitors 

at the Colcord station in November 2004 and at the Beaty 

Creek station in March 2005. The monitors recorded 

specific conductance, pH, water temperature, turbidity, and 

dissolved-oxygen concentration. The monitors were initially 

programmed to record data at hourly intervals at the Colcord 

station and at half-hour intervals at the Beaty Creek station. 

The monitor at the Colcord station has collected data readings 

at half-hour intervals since November 2007 and at 15-minute 

intervals since March 2010.

Each sensor on the water-quality monitor has a fixed 

range of operation. The ranges of operation of the specificconductance, pH, water-temperature, and dissolved-oxygen 

sensors did not exceed those ranges of operation from 

2002–10. However, the operational range for turbidity sensors 

(maximum readings of 1,200 formazin nephelometric units 

(FNU)) were exceeded during part of the study. At the Colcord 

station, turbidity values ranging from 1,240 to 1,650 FNU 

were recorded on June 9 and 19, 2008, and a value of 1,480 

FNU was recorded on June 12, 2007. At the Beaty Creek 

Station, turbidity readings exceeded 1,200 FNU on January 

8, 2008. Estimates of nitrogen and phosphorus concentrations 

from the regression equations described in this report are only 

valid for the range of sensor values measured from November 

2004 and March 2005 through September 2010 at the Colcord 

and Beaty Creek stations, respectively.

None of the phosphorus or nitrogen data were censored 

(reported as less than a reporting limit). One sediment 

sample collected at the Maysville station was censored. In 

S-LOADEST, model coefficients were calculated using the 

maximum likelihood method (MLE). When a data set includes 

censored data, implementation of MLE also is known as tobit 

regression (Helsel and Hirsch, 1992). For tobit regression, 

model residuals are assumed to be normally distributed with 

constant variance.

Quality Assurance

Quality assurance was achieved through following 

protocols and procedures described in U.S. Geological 

Survey (2006) for environmental samples and procedures 

described in Wagner and others (2006) for the water-quality 

monitors and collection of quality control (QC) samples. 

Field blanks and field replicates were collected by the USGS 

and COT personnel at rates of 3–20 percent of the number 

of environmental samples annually to document bias and 

variability in data from collection, processing, shipping, 

handling, and analyses of samples.

Five field blank samples were collected from the Beaty 

Creek station—two in 2006 and three in 2010. One blank 

sample was collected from the Sycamore station in 2007. 

Total phosphorus concentrations were 0.011 and 0.006 mg/L 

in the two field blank samples collected at the Beaty Creek 

station in 2006 and were nondetectable (less than 0.01 mg/L) 

in the three samples collected from the Beaty Creek station in 

2010. Total phosphorus concentration also was nondetectable 
Methods of Analysis 

9

Table 2. Station information and streamflow statistics for streamflow-gaging stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma.[NWIS, National Water Information System of the U.S. Geological Survey; WY, water year (October 1 through September 30); ddmmss, degrees, minutes, seconds; mi2, square mile; ft3/s, cubic foot per second; 

analysis period, January 1st, 2002 to December 31st, 2010]

 Station name 

(NWIS station 

number)

Period of 

streamflow 

record for 

station 

(WY)

 Latitude 

(ddmmss)

Longitude 

(ddmmss)

Drainage 

area (mi2)

Mean annual streamflow in water year (ft3/s) Annual 

mean 

streamflow 

for analysis 

period 

(ft3/s) 

Minimum 

daily mean, 

in ft3/s (date) 

Maximum 

daily mean, 

in ft3/s (date) 

Maximum 

instantaneous, 

in ft3/s (date) 2002 2003 2004 2005 2006 2007 2008 2009 2010

Spavinaw 

Creek near Maysville, Ark. (07191160)

2002-present 362152 943304 88.2 57.9 32.0 95.8 61.2 22.6 42.6 160 96.4 75.8 71.6 3.9 (08/04/2006) 4,150 (07/03/2004) 9,330 (07/03/2004)

Spavinaw 

Creek near Cherokee City, Ark. (07191179)

2002-present 362031 943515 104 68.7 36.4 118 79.0 27.3 58.7 187 108 87.0 85.6 6.7 (08/01/2006) 5,180 (07/03/2004) 12,100 (07/03/2004) 

Spavinaw 

Creek near Sycamore, Okla. (07191220)

1962-present 362005 943829 133 83.4 45.4 161 90.8 25.7 74.9 242 132 97.2 106 2.0 (08/18/2006) 6,300 (07/03/2004) 16,100 (07/03/2004) 

Spavinaw 

Creek near Colcord, Okla. (071912213)

2002-present 361921 944106 163 105 56.9 218 119.9 38.0 104.1 354 195 129 147 8.7 (07/29/2006) 8,720 (03/19/2008) 18,200 (03/19/2008) 

Beaty Creek 

near Jay, Okla. (07191222)

1998-present 362119 944634 59.2 20.8 14.9 80.4 36.9 10.0 48.0 151 63.1 35.3 51.2

Periodic

no flow

(2002, 2003,

2005, 2006)

6,300

(01/08/2008)

22,700

(01/08/2008) 
10 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

(less than 0.015 mg/L) in the blank sample collected at the 

Sycamore station. Nitrogen concentrations were nondetectable 

(less than 0.1 to less than 0.41 mg/L total Kjehldahl nitrogen 

and less than 0.06 to less than 0.2 mg/L nitrate plus nitrite) 

in the five blank samples collected at Beaty Creek. Total 

Kjehldahl nitrogen was nondetectable (less than 0.58 mg/L) 

but the nitrate plus nitrite-nitrogen concentration was 

0.22 mg/L for the blank sample collected at the Sycamore 

station. Blank samples indicate that minor contamination may 

have occurred during sample collection or sample processing 

and that small bias from potential contamination should be 

considered in evaluation of the nutrient data in this report. 

Suspended-sediment concentration was not analyzed in any 

of the blank samples. 

From January 2001 until December 2010, 117 sequential 

replicate samples were collected. Mean relative percent 

differences for nitrogen compounds, phosphorus, and sediment 

ranged from less than 1 percent to 14.5 percent, indicating 

good reproducibility of data. Relative percent differences 

between replicate samples were calculated using the equation: 

RPD = |(E-R)/((E+R)/2))|*100 percent (1)

where

E is the constituent value of the environmental 

sample and 

R is the constituent value of the 

replicate sample.

 Water-quality monitors were inspected, cleaned, and 

calibrated by USGS personnel at least monthly to maintain 

calibration. In the event of instrument malfunction or rapidly 

changing conditions, the monitors were cleaned and calibrated 

more frequently.

Streamflow Separation

Base-flow and runoff components of streamflow were 

separated because base-flow constituent concentrations are 

more indicative of point sources, and runoff concentrations are 

more indicative of nonpoint sources in the Eucha-Spavinaw 

basin. Daily mean streamflow was separated into base-flow 

and runoff components by using the hydrograph separation 

program Base-Flow Index (Institute of Hydrology, 1980a, 

1980b; Wahl and Wahl, 1995). From 2002–10, percentages of 

flow that were runoff ranged from 47 to 49 percent at stations 

on Spavinaw Creek and up to 67 percent at the Beaty Creek 

station, which are similar to values reported in table 3 of 

Esralew and Tortorelli (2010). Each day of the study period 

was designated to be base flow or runoff. Base-flow days are 

defined as days that base flow contributed greater than or equal 

to 70 percent of total flow; runoff days were defined as days 

that runoff contributed greater than 30 percent of total flow.

Development of Regression Equations to 

Estimate Concentrations and Loads

Esralew and Tortorelli (2010, p. 15-24) summarized 

nitrogen and phosphorus concentrations for the period 

2002–09, and an assumption was made that the results from 

that study did not change based on an additional year of data. 

Because sediment data were not previously analyzed, a brief 

analysis of characteristics of sediment concentrations, loads, 

and yields between stations is included in this report. The 

Kruskal-Wallis test (Helsel and Hirsch, 1992) was used to 

determine the statistical significance of differences in sediment 

concentrations among stations. Sediment analyses were not 

done for monthly samples collected by COT staff, therefore, 

only 18 base-flow sediment samples were collected by 

USGS staff. Linear regression was used to evaluate relations 

between nitrogen and phosphorus loads (dependent variables) 

and streamflow and time variables (independent variables). 

Methods for determination of loads using regressions based on 

flow, time, and seasonality used the S-LOADEST program 

(D. Lorenz, U.S. Geological Survey, written commun., 

2006) as described in Tortorelli (2006, 2008) and Esralew 

and Tortorelli (2010). In this report, the regression technique 

used to estimate daily mean load from streamflow, time, 

and seasonality is referred to as the DML regression. Load 

computations using DML regressions are compared with load 

computations from regressions used to estimate instantaneous 

concentration (INSTC) for the periods of 2005–10 at the 

Colcord station and 2006–10 at the Beaty Creek station.

To investigate whether the coefficients on the models 

and resulting load estimates changed substantially from those 

published in Esralew and Tortorelli (2010) with an additional 

year of data, models were rerun to estimate nitrogen and 

phosphorus load at all five stations using data from 2002–10. 

For all rerun models, the mean and median of all computed 

daily loads and mean annual total loads changed by no more 

than 2 percent. Because these differences were assumed to 

have negligible effect on the load computation for 2002–10 

and remain consistent with the previous publication, loads 

computed for this report used the same models published in 

Esralew and Tortorelli (2010).

Separate linear regression models were developed 

in S-LOADEST for estimation of sediment for the period 

2002–10 because loading of this constituent was not computed 

or analyzed for the Eucha-Spavinaw basin in previous 

publications. The “best” model for estimation of sediment load 

selected using S-LOADEST was selected for each station. 

Annual loads are computed by summing all daily 

mean loads for the year. The daily load values generated 

by S-LOADEST were separated into base-flow and runoff 

sample sets according to the number of base-flow days and the 

number of runoff days for the entire sampling period. Nitrogen 

and phosphorus yields for the study period at each station were 

calculated by dividing mean annual nitrogen and phosphorus 

loads by drainage area (table 2). 
Methods of Analysis 11

All of the estimates in this report have some uncertainty. 

The uncertainty of the DML regressions need to be considered 

if the equations are to be used to estimate future loads. The 

coefficient of determination (R2

) and root mean square error 

(RMSE) give indications of the proportion of variability 

in a data set accounted for by a regression model and 

uncertainty (table 3). Uncertainty of daily load estimates 

also was determined from the S-LOADEST software using 

a 90-percent prediction interval (Helsel and Hirsch, 1992). 

Error computation methods used in this report are described in 

greater detail in Cohn and others (1989) and Gilroy and others 

(1990). Prediction intervals for annual loads were summed for 

the upper and lower 90-percent prediction intervals for each 

daily estimate. 

A method of estimating concentrations and loads 

of water-quality constituents in real time was applied in 

Christensen and others (2008) to estimate nitrogen and 

phosphorus in the Eucha-Spavinaw basin using data collected 

from 2004–07. In this report, those regressions were 

updated using data through 2010 using the same methods, 

and sediment regressions also were developed. Similar to 

the DML regression, nitrogen-, phosphorus-, and sedimentconcentration data from water-quality samples (dependent 

variables) and physical water-quality constituents collected 

from real-time water-quality monitors (independent variables) 

at Spavinaw Creek and Beaty Creeks were used to develop 

regression equations to estimate instantaneous concentrations 

of nitrogen, phosphorus, and sediment when sample 

data were not available. For the remainder of this report, 

regressions developed with this technique are referred to as 

INSTC regressions. Unlike DML regressions, time was not 

considered a variable in the INSTC regressions in Christensen 

and others (2008) so that these regressions could be used 

to estimate future concentrations in real time. However, if 

time is a significant variable in the INSTC regression for 

a given constituent, that significance may indicate a trend 

in constituent concentration with time and may bias future 

INSTC estimates. To be consistent with methods used in 

previous reports, time, in this report, was not included as 

an independent variable, but error residuals in the INSTC

regressions were checked for trends with time using Kendall’s 

tau trend test (Kendall, 1975). If significant trends in error 

residuals were detected, later subperiods were used in the 

regression to eliminate time as a significant variable so 

that future estimates using INSTC regressions were more 

representative of recent conditions. INSTC estimates can 

be used to compute daily loads, annual loads, and yields of 

nitrogen and phosphorus. Instantaneous concentration and 

instantaneous streamflow correspond to a single moment in 

time as opposed to an average or sum. Loads can be computed 

from the INSTC regression estimates of instantaneous 

concentration by computing instantaneous load for each 

estimate and summing these loads for each day and over the 

year.

Instantaneous concentration and load could not be 

estimated using the INSTC regression for all days because 

of missing water-quality-monitor records. For days in which 

instantaneous concentrations could not be measured or 

interpolated for all time intervals, daily load estimates and 

prediction intervals from the DML regression were substituted 

if: (a) less than one-half of instantaneous INSTC estimates 

were available for a day and streamflow and water-quality 

conditions were not substantially variable, or (b) more than 

one-half of instantaneous INSTC estimates were available but 

streamflow and water-quality conditions were substantially 

variable (for example, if monitor measurements were 

missing during a storm). Uncertainties of DML estimates 

also were determined from the S-LOADEST software using 

a 90-percent prediction interval (Helsel and Hirsch, 1992). 

Error computation methods used in this report are described 

in greater detail in Cohn and others (1989), and Gilroy 

and others (1990). The 90-percent prediction interval was 

computed for all estimates for this report for evaluation 

and discussion purposes and for comparison to ranges from 

the alternate equations regardless of whether streamflow or 

water-quality constituents used to compute the estimate were 

within the range of streamflow used to develop the regression. 

Therefore, annual load estimates and 90-percent prediction 

intervals presented in this report may contain substantial 

uncertainty because the total annual load and annual prediction 

interval computation contained some instantaneous or daily 

estimates that were extrapolated. The SEP contains the 

effects of random error in addition to the error because of 

the model calibration (parameter uncertainty) and increases 

substantially when independent variables for the estimate are 

outside the range of independent variables used to develop the 

regression. The SEP and the 90-percent prediction interval for 

estimated instantaneous concentrations were computed using 

S-LOADEST software. Uncertainty of streamflow data used 

to estimate daily load could not be quantified for this report 

because uncertainty information about daily streamflow data is 

not readily available or feasible to calculate. 

The uncertainty of the INSTC regressions needs to 

be considered if the equations are used to estimate future 

concentrations or nitrogen and phosphorus loads. The 

R2

, RMSE, standard error of prediction (SEP), prediction 

intervals, and Duan’s smearing bias-correction factor (Duan, 

1983) give indications of uncertainty. Similar to the DML

regressions, uncertainties of instantaneous load estimates were 

determined using a 90-percent prediction interval (Helsel and 

Hirsch, 1992) and were extrapolated for some estimates in 

which independent variables exceeded the variables used to 

develop the regressions. The SEP was used to compute the 

90-percent prediction interval for each concentration estimate 

from the INSTC regressions.

Comparison of Differences in Regression-Based 

Daily Load Estimates

Data used to develop the DML and INSTC regression 

equations were compared graphically rather than statistically 
12 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

because tests, such as the Mann-Whitney test, require that data 

be from independent populations (Helsel and Hirsch, 1992). 

Graphical comparisons of nitrogen, phosphorus, and sediment 

concentrations used to generate regressions were made for 

data collected from 2002–10 (used in the DML regression 

equations) and collected from 2004–10 and 2005–10 for the 

Colcord and Beaty Creek stations, respectively (used in the 

INSTC regression equations).

Estimates of annual loads at the Colcord and Beaty 

Creek stations obtained using the DML and INSTC regression 

methods were compared using bar graphs for the period 

2006–10 and load-duration curves for the period November 

2004 through December 2010 for the Colcord station and 

March 2005 through December 2010 for the Beaty Creek 

station. Load-duration curves were developed using in the 

Hydrostat program (C. Konrad, U.S. Geological Survey, 

written commun, 2007). Load-duration curves are graphical 

representations of the percentage of the time that daily load is 

equaled or exceeded during a specified period. Load-duration 

curves were developed for nitrogen, phosphorus, and sediment 

loads for each station and regression method to visually 

identify differences in daily load between the regression 

methods at different probabilities of exceedance. 

For this report, a negative relative percent difference 

indicates that loads from a DML regression were greater than 

loads from the INSTC regression. The two-sided Wilcoxon 

signed-rank test (Wilcoxon, 1945; referred to in this report as 

the “signed-rank test”) was used to determine if there were 

significant differences in daily mean loads computed using 

the two regression methods for data collected at the Colcord 

and Beaty Creek stations. Comparisons were made using 

daily loads from different flow conditions to see if differences 

varied with runoff or base-flow conditions. For this report, if 

the two-sided test for any given station, constituent load, and 

flow type was statistically significant at a p-value of 0.05, 

then a one-sided signed-rank test was done in which the null 

hypothesis was that the median difference between paired 

observations was greater than zero, indicating that daily loads 

estimated from the DML regression probably are greater than 

daily loads estimated from the INSTC regression. Differences 

in load were considered statistically greater for daily load 

estimated from the DML regression at a p-value of 0.05. 

Differences in load were considered statistically greater for 

daily loads computed from INSTC regressions at a p-value of 

0.95. To avoid bias for comparison of days when daily load 

estimates from the DML regression was substituted for daily 

load estimates from the INSTC regression, only days where 

daily load estimates from INSTC regressions could be made 

were used for the signed-rank test.

Evaluation of Differences in Fit 

Fit of the DML and INSTC regressions in this report 

cannot be directly compared using R2

 and RMSE because 

the DML regressions were used to estimate daily mean load, 

whereas, INSTC regressions were used to estimate constituent 

concentration converted to a daily load. A bias correction 

factor was applied for each daily load estimate developed from 

the DML regressions, referred to as the minimum variance 

unbiased estimate (MVUE) (Bradu and Mundlak, 1970). The 

smearing bias-correction factor (Duan, 1983) was used to 

correct underestimation resulting from retransformation of 

regression-estimated concentrations for the INSTC regressions 

because that method was used in previous investigations 

(Christensen and others, 2008). The benefit of Duan’s 

smearing coefficient is this coefficient is easily applied to all 

estimates, compared to the MVUE bias correction procedure 

used in development of the DML regression in S-LOADEST, 

which requires a different factor for each daily estimate and 

is computationally more complex than Duan’s smearing 

coefficient. A comparison of Duan’s smearing coefficient and 

the MVUE bias correction procedure was beyond the scope 

of this report. The R2

 and RMSE values of these regressions 

do not have identical units, and different regression methods 

and bias correction procedures were used, which also preclude 

direct comparisons. Although the fit from these regression 

methods could not be directly compared, comparison of the 

size of the prediction intervals can give an indication of the 

general reliability of these regression estimates under various 

streamflow and water-quality conditions. Graphs showing 

the 90-percent confidence intervals for both methods were 

developed for selected periods of daily measurements to show 

examples of comparative uncertainty between regression 

methods.

For this report, alternate regressions to estimate 

concentration using the independent variables of the DML

regressions were computed to compare accuracy between 

regression methods because the difference in variance could 

be more easily observed and compared between regressions 

without the notable influence of streamflow on loads. The 

purpose of comparisons between DML and INSTC regressions 

were to evaluate differences and potential biases from 

regression methods used in previous reports (Tortorelli, 2006; 

Tortorelli, 2008; Christensen and others 2008; Esralew and 

Tortorelli, 2010). Evaluation of regression methods that use 

physical water-quality constituent values and streamflow to 

estimate instantaneous load compared to loads computed 

from estimated instantaneous concentrations from INSTC

regressions presented in this report may be beneficial for 

future improvements to regression methods.

Methods of Analysis of Temporal Trends in 

Concentration

Trends in concentrations of nitrogen (nitrate plus nitritenitrogen and total nitrogen), phosphorus, and sediment with 

time were evaluated for data collected at the five stations from 

2002–10 to determine whether BMPs and wastewater effluent 

affected concentrations of those constituents in this basin. The 

S-Plus statistical program S-Estimate Trend (S-ESTREND) 

(Schertz and others, 1991) based on the Seasonal Kendall tau 
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 13

(Kendall, 1975) or Kendall-Thiel tests (Helsel and Hirsch, 

1992) was used for analysis of water-quality trends. The 

small number of suspended-sediment analyses during baseflow conditions was insufficient to determine temporal 

trends of suspended-sediment concentrations at base-flow 

conditions. Kendall’s tau test (Kendall and Gibbons, 1990) 

is a nonparametric statistical test used to indicate the 

likelihood of upward or downward trends in data with time 

and is effective for identifying trends in streamflow because 

high or low data outliers and skewness in the dataset do not 

affect the test (Helsel and Hirsch, 1992). The tau is an 

indicator of the relative number of data pairs with positive or 

negative differences: 

 t = ((P-M)/(n(n-1)/2) (2)

where

P is the number of increases, and 

M is the number of decreases between data pairs. 

The Kendall-Thiel test is similar to the Seasonal Kendall 

tau test but has no seasonal correction (Helsel and Hirsch, 

1992). A trend slope, which is a measure of the magnitude 

and direction of a trend, was computed using the Sen 

Slope Estimator (Sen, 1968; Helsel and Hirsch, 1992). The 

Seasonal Kendall tau test reduces the effects that season has 

on streamflow and concentration by limiting comparisons to 

data from the same seasons and adjusting for variations in 

streamflow. Seasonal Kendall tau tests also were performed 

on base-flow and runoff datasets to compare trends associated 

with different flow regimes. Trends based on flow regime 

may provide information regarding factors associated with 

the trend, for example, base-flow concentrations generally 

are more indicative of point sources (or groundwater quality), 

and runoff concentrations are more indicative of nonpoint 

sources. To compensate for variations in data density resulting 

from inconsistencies in sample collection during base flow 

and runoff, data were divided into four seasons: spring 

(March-May), summer (June-August), autumn (SeptemberNovember), and winter (December-February). Sediment trend 

analysis could only be applied to samples collected during 

runoff and seasons could not be analyzed because of limited 

data. The Seasonal Kendall or Kendall’s tau trend test also 

was applied to error residuals and time. Significant trends in 

flow-adjusted concentrations determined by p-values of the 

Seasonal Kendall tau test would indicate that factors other 

than variation of streamflow may have caused changes in 

concentration, such as application of BMPs or changes in 

nitrogen and phosphorus contribution from 

wastewater treatment.

The Seasonal Kendall tau test was used to test the 

significance of trends in water quality with time. Factors other 

than time can affect water quality. A statistically significant 

correlation between constituent concentration and streamflow 

may obscure underlying trends with time or other variables. 

Flow-adjustment techniques were used to remove the effects 

of streamflow variability on concentrations by computing a 

time series of flow-adjusted concentrations (Helsel and Hirsch, 

1992). Flow-adjusted concentrations are the error 

residuals from a regression between concentration and 

streamflow at the time of sample collection (Helsel and 

Hirsch, 1992, p. 331–335).

A LOESS regression (Cleveland and Devlin, 1988) 

was used to describe the relation between streamflow and 

constituent concentration. This method is robust because use 

of distance and residual-weighting functions with weighted 

least squares avoids use of complex data transformations, 

and the influence of outliers in fitting a smooth line to the 

data is minimized (Schertz and others, 1991, p. 24). Natural 

logarithm transformation of each annual streamflow parameter 

and annual precipitation were used to improve the fit of the 

LOESS regression (and are referred to as a “log-log LOESS” 

regressions). Log-log LOESS regressions were used if 

streamflow was significantly (p-value less than or equal to 

0.05) correlated to constituent concentration based on a partial 

t-test (Helsel and Hirsch, 1992) evaluating the correlation 

between streamflow at the time of sample collection and 

constituent concentration. If there was no statistically 

significant correlation between streamflow and constituent 

concentration, flow adjustment for that station, constituent, 

and flow type was not calculated.

Streamflows, Loads, and Instantaneous 

Concentrations in the Eucha-Spavinaw 

Basin, 2002–10

During 2002–10, the smallest mean annual streamflows at 

the five stations occurred in 2006 (table 2), although 2005 was 

the year with the least amount of precipitation from 2002–10. 

The maximum peak flows for this period occurred in 2004 

at the Maysville, Cherokee City, and Sycamore stations and 

in 2008 at the Colcord and Beaty Creek stations. Maximum 

daily mean streamflow was substantially less than maximum 

instantaneous streamflow at all stations.

Water-Quality Data Used to Develop Regression 

Equations

Data used to develop regressions were collected during 

varying climatic conditions that affected streamflow and water 

quality. Summaries of significant differences in nitrogen and 

phosphorus concentrations are from Esralew and Tortorelli 

(2010).

Nitrogen and Phosphorus Concentrations

Nitrogen concentrations generally increased with 

increasing streamflow, indicating substantial contribution of 
14 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

nitrogen from nonpoint sources. Nitrogen concentrations were 

significantly greater (p less than or equal to 0.05) in runoff 

samples than in base-flow samples collected at the Maysville, 

Cherokee City, Colcord, and Beaty Creek stations. 

Nitrogen concentrations in all samples from Spavinaw 

Creek significantly increased (p less than or equal to 0.05) 

downstream from the Maysville station to the Sycamore 

station and significantly decreased from the Sycamore station 

downstream to the Colcord station. Nitrogen concentrations 

in samples from Beaty Creek were significantly less than 

those in Spavinaw Creek (Esralew and Tortorelli, 2010). 

Nitrogen concentrations were significantly greater in samples 

collected during winter and spring than in summer or autumn 

at most stations, possibly because of lesser uptake of nitrogen 

and phosphorus by aquatic plants in winter, application of 

fertilizers in spring, and greater runoff in spring (Esralew and 

Tortorelli, 2010).

Phosphorus concentrations in samples collected at 

the Beaty Creek and Maysville stations were significantly 

less than those in samples collected at the other Spavinaw 

Creek stations and were smallest at the Maysville station 

(Esralew and Tortorelli, 2010). Except for the Cherokee 

City station, where water quality was affected by discharge 

from the Decatur wastewater-treatment plant, phosphorus 

concentrations were significantly greater (p less than or equal 

to 0.05) in runoff samples than in base-flow samples. The 

larger concentration of phosphorus associated with runoff 

indicates primarily nonpoint sources of phosphorus.

Phosphorus concentration in base-flow samples collected 

from Spavinaw Creek significantly increased (p-value less 

than or equal to 0.05) from the Maysville station to the 

Cherokee City station, perhaps because of effluent discharged 

from the Decatur wastewater-treatment plant between those 

stations. Phosphorus concentration significantly decreased 

downstream from the Cherokee City station to the Colcord 

station, perhaps caused by sorption into streambed sediments 

or aquatic plants. Phosphorus concentrations did not differ 

significantly by season except at the Maysville station, where 

spring and summer concentrations were greater than autumn 

and winter concentrations (Esralew and Tortorelli, 2010). 

Boxplots showing nitrogen and phosphorus 

concentrations from all samples used to develop the DML

regressions for the period 2002–10 for all five stations, and 

samples used to develop the INSTC regressions for the period 

2004–10 for the Colcord and Beaty Creek stations are shown 

in figures 3-4. Nitrogen and phosphorus concentrations used in 

the DML regressions were not substantially different than those 

concentrations used in the INSTC regressions for the Colcord 

or Beaty Creek stations.

Sediment Concentrations

Unlike nitrogen and phosphorus concentrations, 

suspended-sediment concentrations did not differ significantly 

by season or between stations (p-value less than or equal 

to 0.05) based on a Kruskal-Wallis test. Boxplots showing 

distributions of suspended-sediment concentrations used 

to develop the DML regression for the period 2002–10 for 

all five stations and the INSTC regression for the period 

2005–10 for the Colcord and Beaty Creek stations are shown 

in figure 5. Suspended-sediment concentrations used in the 

DML regressions were not substantially different than those 

concentrations used in the INSTC regressions for the Beaty 

Creek station.

Estimated Loads and Yields of Nitrogen, 

Phosphorus, and Suspended Sediment, 2002–10

The best-fit DML regressions were different for each 

constituent and station (table 3). Nitrogen and phosphorus 

equations were the same as those determined in Esralew and 

Tortorelli (2010). Consistency and details about the regression 

selection are described in more detail in that report. Seasonal 

variables were not statistically significant estimators of daily 

sediment load for any of the stations, and negative linear time 

(T) was a statistically significant estimator of daily sediment 

load at the Maysville, Sycamore, and Beaty Creek stations, 

indicating significant decreases in sediment concentration 

with time. 

Nitrogen and phosphorus DML regressions had higher R2

values, indicating better fits to the data than the sediment DML

regressions (table 3). Uncertainty in sediment DML regression 

models is associated with substantial variability in sampled 

sediment concentrations, even for replicates, and by a poorer 

correlation between sediment concentration and streamflow as 

compared to nitrogen and phosphorus concentrations.

Nitrogen Loads and Yields

Mean annual total nitrogen loads ranged from 354,000 

to 1,290,000 pounds per year (lbs/yr) as estimated from the 

DML regressions from 2002–10 (table 4). Nitrogen loads 

and yields were similar to those reported in Esralew and 

Tortorelli (2010), indicating that the 2010 annual load was not 

a substantial outlier compared to those for 2002–09. Estimated 

mean annual nitrogen total loads (the sum of base-flow and 

runoff loads) were substantially greater at Spavinaw Creek 

stations than at the Beaty Creek station. Annual total baseflow and runoff loads increased in Spavinaw Creek in a 

downstream direction from the Maysville station 

(table 4, fig. 6). 

The runoff component of the mean annual nitrogen load 

at the Spavinaw Creek stations ranged from 66 to 71 percent 

and increased with larger drainage areas (table 4). About 87 

percent of the mean annual nitrogen load for Beaty Creek was 

from runoff (table 4). The runoff components of nitrogen were 

about 1 to 2 percent less for 2002–10 than those reported in 

Esralew and Tortorelli (2010) for 2002–09.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 15

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x x

0

2

4

6

8

10

12

Total nitrogen, in milligrams per liter as nitrogen

(139)

75th percentile of flowweighted nitrogen

concentrations from

relatively undeveloped

basins of the United States

(Clark and others, 2000)

(140) (102) (155) (106) (144) (65)

Streamflow-gaging station and year range

Spavinaw

Creek near

Maysville, Ark.,

(07191160)

2002–10

Spavinaw

Creek near

Cherokee

City, Ark.,

(07191179)

2002–10

Spavinaw

Creek near

Sycamore,

Okla.,

(07191220)

2002–10

Spavinaw

Creek near

Colcord,

Okla.,

(071912213)

2002–10

Spavinaw

Creek near

Colcord,

Okla.,

(071912213)

2004–10

Beaty Creek

near Jay,

Okla.,

(07191222)

2002–10

Beaty Creek

near Jay,

Okla.,

(07191222)

2005–10

75th Percentile

Median

25th Percentile

Inter- quartile

Range

x

x

Data value greater

than 1.5 times the

interquartile range

Data value less than

1.5 times the

interquartile range

Outlier

Outlier

EXPLANATION

(96) Number of samples

x

x

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

x

x x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

x

x

x

x

x

x

x

x

xx

x

x

x

(133)

0.01

0.1

1.0

3.0

0.03

0.3

75th percentile flowweighted phosphorus

concentrations from

relatively undeveloped

basins of the United States

(Clark and others, 2000)

(136) (100) (151) (102) (144) (95)

Total phosphorus, in milligrams per liter as phosphorus

Streamflow-gaging station and year range

Spavinaw

Creek near

Maysville, Ark.,

(07191160)

Spavinaw

Creek near

Cherokee

City, Ark.,

(07191179)

Spavinaw

Creek near

Sycamore,

Okla.,

(07191220)

Spavinaw

Creek near

Colcord,

Okla.,

(071912213)

Spavinaw

Creek near

Colcord,

Okla.,

(071912213)

Beaty Creek

near Jay,

Okla.,

(07191222)

Beaty Creek

near Jay,

Okla.,

(07191222)

75th Percentile

Median

25th Percentile

Inter- quartile

Range

x

x

Data value greater

than 1.5 times the

interquartile range

Data value less than

1.5 times the

interquartile range

Outlier

Outlier

EXPLANATION

(95) Number of samples

2002–10

2002–10 2002–10 2002–10 2004–10

2002–10 2005–10

Figure 3. Distributions of total nitrogen concentrations in water samples collected from different time periods at streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma.

Figure 4. Distributions of total phosphorus concentrations in water samples collected from different time periods at streamflow-gaging 

stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma.
16 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

x

x

(46) (45) (42) (59) (40) (55) (36)

Spavinaw

Creek near

Maysville, Ark.,

(07191160)

Spavinaw

Creek near

Cherokee

City, Ark.,

(07191179)

Spavinaw

Creek near

Sycamore,

Okla.,

(07191220)

Spavinaw

Creek near

Colcord,

Okla.,

(071912213)

Spavinaw

Creek near

Colcord,

Okla.,

(071912213)

Beaty Creek

near Jay,

Okla.,

(07191222)

Beaty Creek

near Jay,

Okla.,

(07191222)

0.1

100

10

1,000

1.0

10,000

75th Percentile

Median

25th Percentile

Inter- quartile

Range

x

x

Data value greater

than 1.5 times the

interquartile range

Data value less than

1.5 times the

interquartile range

Outlier

Outlier

EXPLANATION

(36) Number of samples

Suspended sediment, in milligrams per liter

Streamflow-gaging station and year range

2002–10

2002–10 2002–10 2002–10 2004–10

2002–10 2005–10

Figure 5. Distributions of suspended-sediment concentrations in water samples collected from different time periods at streamflowgaging stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma.

Mean annual total nitrogen yields at the stations 

ranged from 5,980 to 7,890 pounds per year per square mile 

(lbs/yr/mi2) and generally increased in a downstream direction 

in the Spavinaw Creek basin (table 4). The base-flow yields 

were less at the Beaty Creek station than at the Maysville 

station. Beaty Creek mean annual runoff yields of nitrogen, 

however, were similar to most runoff yields in the Spavinaw 

Creek basin (table 4) and more than the runoff yield at the 

Maysville station. Possible explanations for the difference 

in base-flow yield between Beaty and Spavinaw Creeks may 

be a greater influence of groundwater on streamflow and 

greater nitrogen base-flow concentrations in Spavinaw Creek 

(downstream from the Maysville station) than in Beaty Creek 

(table 4), and, therefore, a greater percentage of nitrogen 

load delivered during base flow for Spavinaw Creek 

(table 4, Esralew and Tortorelli, 2010).

Phosphorus Loads and Yields

Mean annual total phosphorus loads ranged from 

25,000 to 66,900 lb/yr from 2002–10 as estimated from the 

DML regressions. Phosphorus loads and yields were slightly 

less than those reported in Esralew and Tortorelli (2010), 

indicating that the 2010 annual load was not substantially 

different than those for the period 2002–09 (fig. 7). 

Estimated mean annual total phosphorus, base-flow, 

and runoff loads were substantially greater for at least half 

of the Spavinaw Creek stations than the Beaty Creek station, 

primarily because of greater streamflow at the Spavinaw 

Creek stations (Esralew and Tortorelli, 2010). Annual total, 

base-flow, and runoff loads generally increased in Spavinaw 

Creek in a downstream direction from the Maysville station 

(table 4), with the exception of the Cherokee City station, 

at which phosphorus base-flow load was greater than at the 

Sycamore station.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 17

Table 3. Regression equations for estimating daily mean loads (DMLs) of total nitrogen, total phosphorus, and sediment using 

streamflow, seasonality, and time at streamflow-gaging stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10.

[ln, natural logarithm; DMLTN, total nitrogen daily mean load in pound per day; DMLTP, total phosphorus daily mean load in pound per day; DMLSed, 

suspended sediment daily load in pound per day; Q, mean daily streamflow in cubic foot per second; T, decimal time, time parameter in decimal years; 

sin, sine; cos, cosine; SS, seasonality parameter; R2, coefficient of determination, *from Esralew and Tortorelli, 2010]

Number of 

observations Daily mean load regression equation

Estimated 

residual 

variance 

(pounds 

per day)

Root mean 

square error 

(pounds per 

day)

R2

(percent)

Spavinaw Creek near Maysville, Ark. (07191160)

139* ln(DMLTN) = 8.09 + 1.13*(lnQ-4.93) - 0.018*(lnQ-4.93)2

 - 0.005*(T-2005.92) 

+ 0.002*(T-2005.92)2

 - 0.013*sin SS + 0.14*cos SS 0.048 0.219 98.3

133* ln(DMLTP) = 3.63 + 1.54*(lnQ-4.93) + 0.159*(lnQ-4.93)2

 + 0.023*(T-2005.93) 

- 0.089*sin SS - 0.135*cos SS 0.200 0.447 96.3

46 ln(DMLSed) = 9.79 + 2.02*(lnQ-3.28) - 0.263*(lnQ-3.28)2

 - 0.13*(T-2006.11) 0.775 0.880 93.5

Spavinaw Creek near Cherokee City, Ark. (07191179)

140* ln(DMLTN) = 8.44 + 1.08*(lnQ-5.18) - 0.015*(lnQ-5.18)2

 + 0.002*(T-2005.92) 

- 0.002*(T-2005.92)2

 + 0.002*sin SS + 0.176*cos SS 0.026 0.160 99.0

136* ln(DMLTP) = 4.80 + 1.22*(lnQ-5.18) + 0.146*(lnQ-5.18)2

 - 0.125*(T-2005.93) 

- 0.125*sin SS + 0.005*cos SS 0.126 0.355 96.0

45 ln(DMLSed) = 10.3 + 2.13*(lnQ-3.53) - 0.195*(lnQ-3.23)2 1.52 1.231 88.1

Spavinaw Creek near Sycamore, Okla. (07191220)

102* ln(DMLTN) = 8.78 + 1.07*(lnQ-5.41) + 0.003*(lnQ-5.41)2

 - 0.003*(T-2005.92)2

+ 0.012*sin SS + .169*cos SS 0.021 0.144 99.1

100* ln(DMLTP) = 4.91 + 1.30*(lnQ-5.41) + 0.123*(lnQ-5.41)2

 - 0.084*(T-2005.92) 

- 0.014*sin SS - 0.044*cos SS 0.101 0.318 97.1

42 ln(DMLSed) = 10.2 + 1.99*(lnQ-3.39) - 0.237*(lnQ-3.39)2

 - 0.139*(T-2006.09) 0.946 0.973 91.2

Spavinaw Creek near Colcord, Okla. (071912213)

152* ln(DMLTN) = 8.66 + 1.10*(lnQ-5.50) - 0.010*(lnQ-5.50)2

 - 0.006*(T-2005.97) 

- 0.001*(T-2005.97)2

 + 0.025*sin SS + 0.176*cos SS 0.029 0.171 99.0

148* ln(DMLTP) = 5.06 + 1.37*(lnQ-5.50) + 0.093*(lnQ-5.50)2

 - 0.061*(T-2005.97) 

- 0.062*sin SS - 0.081*cos SS 0.169 0.411 96.0

59 ln(DMLSed) = 11.2 + 1.9*(lnQ-3.54) - 0.074*(lnQ-3.54)2 1.25 1.117 87.5

Beaty Creek near Jay, Okla. (07191222)

146* ln(DMLTN) = 5.51 + 1.14*(lnQ-2.80) - 0.001*(lnQ-2.80)2

 + 0.014*(T-2005.99) 

+ 0.013*(T-2005.99)2

 + 0.124*sin SS - 0.124*cos SS 0.076 0.276 98.9

144* ln(DMLTP) = 1.31 + 1.30*(lnQ-2.80) + 0.059*(lnQ-2.80)2

 + 0.018*(T-2005.99) 

- 0.178*sin SS - 0.075*cos SS 0.149 0.386 98.4

55 ln(DMLSed) = 9.19 + 1.94*(lnQ-3.26) + 0.206*(lnQ-3.26)2

 - 0.205*(T-2006.29) 1.00 1.000 89.6
18 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Table 4. Estimated mean annual total nitrogen, total phosphorus, and suspended sediment loads and yields using regression 

equations developed from concentrations in water-quality samples and streamflow, time, and seasonality, for water-quality 

monitoring stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, for the period 2002–10.

[mi2, square mile; lb/yr, pound per year; lb/yr/mi2, pound per year per square mile; N, nitrogen; Differences between total load and the sum of the base-flow 

load plus runoff loads are caused by rounding.]

Station name

Total nitrogen

Mean annual loads and yields

Mean 

daily 

load1

(lb/d as N)

Total load1

(lb/yr as N)

Total yield1

(lb/yr/mi2

 as N)

Base-flow 

load1

(lb/yr as N)

Base-flow 

yield1

(lb/yr/mi2

 as N)

Runoff load2

(lb/yr as N)

Runoff yield2

(lb/yr/mi2

 as N)

Load 

delivered 

during 

runoff 

(percent)

Spavinaw Creek near 

Maysville, Ark. 

(07191160)

1,660 607,000 6,880 204,000 2,320 402,000 4,560 66

Spavinaw Creek near 

Cherokee City, Ark. 

(07191179)

2,190 800,000 7,690 272,000 2,620 528,000 5,080 66

Spavinaw Creek near 

Sycamore, Okla. 

(07191220)

2,800 1,020,000 7,680 310,000 2,330 712,000 5,340 70

Spavinaw Creek near 

Colcord, Okla. 

(071912213)

3,520 1,290,000 7,890 375,000 2,300 911,000 5,590 71

Beaty Creek near Jay, 

Okla. (07191222) 969 354,000 5,980 46,800 790 307,000 5,290 87

Total phosphorus

Mean annual loads and yields

Station name

Mean 

daily 

load1

(lb/d as P)

Total load1

(lb/yr as P)

Total yield1

(lb/yr/mi2

 as P)

Base-flow 

load1

(lb/yr as P)

Base-flow 

yield1

(lb/yr/mi2

 as P)

Runoff load2

(lb/yr as P)

Runoff yield2

(lb/yr/mi2

 as P)

Load 

delivered 

during 

runoff 

(percent)

Spavinaw Creek near 

Maysville, Ark. 

(07191160)

69 25,000 284 2,080 24 22,600 260 92

Spavinaw Creek near 

Cherokee City, Ark. 

(07191179)

96 35,200 339 7,900 76 27,300 263 78

Spavinaw Creek near 

Sycamore, Okla. 

(07191220)

115 41,900 315 7,180 54 34,700 261 83

Spavinaw Creek near 

Colcord, Okla. 

(071912213)

183 66,900 410 9,030 55 57,900 355 87

Beaty Creek near Jay, 

Okla. (07191222) 91 33,000 558 962 16 32,100 542 97
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 19

Suspended sediment

Mean annual loads and yields

Station name

Mean 

daily load1

(lb/d)

Total load1

(lb/yr)

Total yield1

(lb/yr/mi2

 )

Base-flow 

load1

(lb/yr as N)

Base-flow 

yield1

(lb/yr/mi2

)

Runoff load2

(lb/yr)

Runoff yield2

(lb/yr/mi2

)

Load 

delivered 

during 

runoff 

(percent)

Spavinaw Creek near 

Maysville, Ark. 

(07191160)

62,300 22,700,000 258,000 440,000 4,990 22,300,000 253,000 98

Spavinaw Creek near 

Cherokee City, Ark. 

(07191179)

126,000 46,000,000 442,000 684,000 6,580 45,300,000 436,000 99

Spavinaw Creek near 

Sycamore, Okla. 

(07191220)

112,000 41,000,000 309,000 718,000 5,400 40,300,000 303,000 98

Spavinaw Creek near 

Colcord, Okla. 

(071912213)

139,000 50,600,000 310,000 1,790,000 11,000 48,800,000 300,000 96

Beaty Creek near Jay, 

Okla. (07191222) 178,000 65,000,000 1,100,000 148,000 2,500 64,900,000 1,100,000 100

1

Means of the base-flow loads were calculated from base-flow days data only.

2

Means of the runoff loads were calculated from runoff days data only.

Table 4. Estimated mean annual total nitrogen, total phosphorus, and suspended sediment loads and yields using regression 

equations developed from concentrations in water-quality samples and streamflow, time, and seasonality, for water-quality 

monitoring stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, for the period 2002–10.—Continued

[mi2, square mile; lb/yr, pound per year; lb/yr/mi2, pound per year per square mile; N, nitrogen; Differences between total load and the sum of the base-flow 

load plus runoff loads are caused by rounding.]
20 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10 2002 2003 2004 2005 2006 2007 2008 2009 2010

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

Spavinaw Creek near Cherokee City, Ark. (07191179)

Spavinaw Creek near Sycamore, Okla. (07191220) Spavinaw Creek near Colcord, 

Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

Total nitrogen annual load from runoff

Total nitrogen annual load from base flow

Mean annual streamflow

Total annual loads less than 1,000 pounds are not

depicted on this figure

Spavinaw Creek near Maysville, Ark. (07191160)

Total annual nitrogen load, in pounds per year

Annual mean streamflow, in cubic feet per second

EXPLANATION

3,500,000

3,000,000

2,500,000

2,000,000

1,500,000

1,000,000

500,000

0

3,500,000

3,000,000

2,500,000

2,000,000

1,500,000

1,000,000

500,000

0

3,500,000

3,000,000

2,500,000

2,000,000

1,500,000

1,000,000

500,000

0

2002

2003

2004

2005

2006

2007

2008

2009

2010

Figure 6. Estimates of base-flow and runoff components of annual total nitrogen load and mean annual streamflow at water-quality 

monitoring stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 21

2002

2003

2004

2005

2006

2007

2008

2009

2010

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

Spavinaw Creek near Cherokee City, Ark. (07191179)

Spavinaw Creek near Sycamore, Okla. (07191220) Spavinaw Creek near Colcord, Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

Total phosphorus annual load from runoff

Total phosphorus annual load from base flow

Mean annual streamflow

Total annual loads less than 1,000 pounds are not

depicted on this figure

Spavinaw Creek near Maysville, Ark. (07191160)

Total phosphorus load, in pounds per year

Annual mean streamflow, in cubic feet per second

EXPLANATION

275,000,000

250,000,000

200,000,000

150,000,000

100,000,000

50,000,000

0

275,000,000

250,000,000

200,000,000

150,000,000

100,000,000

50,000,000

0

275,000,000

250,000,000

200,000,000

150,000,000

100,000,000

50,000,000

0

2002

2003

2004

2005

2006

2007

2008

2009

2010

Figure 7. Estimates of base-flow and runoff components of annual total phosphorus load and mean annual streamflow, at waterquality monitoring stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10.
22 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

The runoff component of the mean annual total 

phosphorus load for the Spavinaw Creek stations ranged from 

78 to 92 percent and generally increased in a downstream 

direction from the Cherokee City station to the Colcord station 

(table 4). About 97 percent of the annual phosphorus load at 

the Beaty Creek station was derived from runoff (table 4). The 

runoff components of phosphorus were only about 1 percent 

less in 2002–10 than those in 2002–09 (table 4, Esralew and 

Tortorelli, 2010). 

Mean annual total phosphorus yields ranged from 284 

to 558 lbs/yr/mi2

 (table 4). Mean annual total phosphorus 

yields in Spavinaw Creek generally increased in a downstream 

direction with the exception of the Cherokee City station, 

which is the first station downstream from the outfall of the 

Decatur wastewater-treatment plant, having greater total and 

base-flow yields than at the downstream Sycamore station. 

The mean total and runoff phosphorus yields for Beaty Creek, 

however, were greater than any of the Spavinaw Creek 

stations, perhaps because of less forested riparian areas in the 

Beaty Creek basin (fig. 2).

Phosphorus loading to streams is increased more in runoff 

conditions than nitrogen loading in this basin (Esralew and 

Tortorelli, 2010). Association of phosphorus with sediment 

may contribute to the greater transport of phosphorus during 

runoff conditions. A substantial source of nitrogen loading 

may be from nitrate delivered to the stream in groundwater 

seepage (Esralew and Tortorelli, 2010), explaining the greater 

proportion of base-flow transport for nitrogen. The greater 

total and runoff phosphorus yields in Beaty Creek compared 

to Spavinaw Creek may be caused by a greater contribution of 

nonpoint sources of phosphorus in Beaty Creek or by a greater 

percentage of streamflow from runoff, the main component 

of phosphorus transport, in Beaty Creek. Variability of baseflow phosphorus loads and yields among Spavinaw Creek 

stations, especially at the Cherokee City station, may have 

been caused by inflow of wastewater effluent from the Decatur 

wastewater-treatment plant between the Maysville station and 

Cherokee City station, with decreasing yields downstream 

from the Cherokee City station being caused by addition by 

groundwater seepage (Esralew and Tortorelli, 2010). 

Sediment Loads and Yields

Mean annual total sediment loads from 2002–10 

estimated from DML regressions ranged from 22,700,000 

to 65,000,000 lbs/yr. Estimated mean annual total sediment 

load and the runoff component of total load generally were 

similar at the three downstream Spavinaw Creek stations 

(table 4) and were smallest at the Maysville station. The 

Beaty Creek station had the largest mean annual sediment 

load (65,000,000 lbs/yr) and the largest annual sediment 

load (360,000,000 lbs/yr) in 2008 (fig. 8). For the Spavinaw 

Creek stations, the Colcord City station had the greatest mean 

annual sediment load (50,600,000 lbs/yr), with the greatest 

annual load of sediment also being at the Colcord station in 

2008 (275,000,000 lbs/yr, fig. 8). The years 2004 and 2008, 

which had the greatest streamflow (table 2), also had the 

greatest sediment load (fig. 8). For example, 77 percent of the 

sediment load for the period 2002–10 at the Colcord station 

and 91 percent of the sediment load at the Beaty Creek station 

occurred during 2004 and 2008.

The greater mean annual total and runoff sediment load 

estimates obtained for the Cherokee City station than at the 

Sycamore station indicate that sediment deposition occurred 

between these stations, which may have been facilitated by 

decreases or irregular changes in flow downstream causing 

changes in sediment transport capacity between these stations. 

Losses of streamflow to groundwater were observed, with 

streamflow being less at the Sycamore station than at the 

Cherokee City station during 25 percent of the study period, 

20 percent of which were runoff days. Base-flow sediment 

loads were relatively small (less than 5 percent of the total 

load) at the five stations. The runoff component of the mean 

annual sediment load for Beaty Creek was 100 percent, with 

the runoff component of the mean annual sediment load at 

the Spavinaw Creek stations ranging from 96 to 99 percent 

(table 4). Runoff and total loads increased with larger drainage 

areas for Spavinaw Creek but were greater at the Beaty Creek 

station than any of the Spavinaw Creek stations. 

Mean annual total sediment yields ranged from 258,000 

to 1,100,000 lbs/yr/mi2

. Mean annual total and runoff sediment 

yields for the Spavinaw Creek stations were greatest at the 

Cherokee City station, similar between the Sycamore and 

Colcord stations, and smallest at the Maysville station (table 

4). Mean annual total and runoff sediment yields at the Beaty 

Creek station were about 2 to 4 times greater than yields at 

the Spavinaw Creek stations (table 4). The greater sediment 

yield at the Cherokee City station than at the Maysville station 

and the decreasing sediment yield between the Cherokee 

City station and the downstream station at Sycamore indicate 

that substantial sediment inputs, derived from land or 

streambank erosion or resuspension of streambed sediments, 

occur between the Maysville and the Cherokee City stations. 

Decrease in sediment yield between the Cherokee City and 

Sycamore stations may be caused by sediment deposition 

between those stations. Increases in sediment yield with 

increasing drainage basin size, as between the Maysville 

and Cherokee City stations, may be caused by dominance 

of bank erosion or changes in land use, whereas uniform or 

decreasing sediment yield with drainage area, as was observed 

between the Sycamore and Colcord stations, may be caused 

by dominance of hillslope erosion (Birkinshaw and Bathurst, 

2006). Similar to phosphorus, the greater total and runoff 

sediment yields in Beaty Creek compared to Spavinaw Creek 

may be caused by a greater contribution of nonpoint sediment 

sources in the Beaty Creek basin, which has less forested 

riparian areas, or by a greater percentage of streamflow from 

runoff, the main source of sediment transport, for Beaty Creek.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 23

2002

2003

2004

2005

2006

2007

2008

2009

2010

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

0

50

100

150

200

250

300

350

400

Spavinaw Creek near Cherokee City, Ark. (07191179)

Spavinaw Creek near Sycamore, Okla. (07191220) Spavinaw Creek near Colcord, Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

Total suspended-sediment annual load

Mean annual streamflow

Total annual loads less than 100,000 pounds are not

depicted on this figure

Spavinaw Creek near Maysville, Ark. (07191160)

Suspended-sediment load, in pounds per year

Mean annual streamflow, in cubic feet per second

EXPLANATION

400,000,000

350,000,000

300,000,000

250,000,000

200,000,000

150,000,000

100,000,000

50,000,000

0

400,000,000

350,000,000

300,000,000

250,000,000

200,000,000

150,000,000

100,000,000

50,000,000

0

400,000,000

350,000,000

300,000,000

250,000,000

200,000,000

150,000,000

100,000,000

50,000,000

0

2002

2003

2004

2005

2006

2007

2008

2009

2010

Figure 8. Estimates of base-flow and runoff components of suspended-sediment annual load and mean annual streamflow, at waterquality monitoring stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10.
24 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Estimated Mean Annual Nitrogen, Phosphorus, 

and Sediment Loads into Lake Eucha 

Much of the mean annual nitrogen and phosphorus loads 

entering Lake Eucha can be estimated by adding the loads at 

the Beaty Creek station and the Colcord station on Spavinaw 

Creek. Nitrogen and phosphorus loads at these stations do 

not represent the entire loads of those constituents into Lake 

Eucha, but the drainage area upstream from these stations 

accounts for about 62 percent of the Lake Eucha drainage 

basin. Spavinaw Creek and Beaty Creek contributed a mean 

annual total nitrogen load of about 1,640,000 lbs/yr, with 74 

percent of the annual total nitrogen load being transported 

to Lake Eucha during runoff conditions (table 5). Spavinaw 

Creek contributed a majority of the mean annual nitrogen load 

of the two creeks (78 percent).

Spavinaw Creek near Colcord and Beaty Creek 

contributed a mean annual total phosphorus load of 100,000 

lbs/yr, 90 percent of which was transported to Lake Eucha 

during runoff conditions (table 5). The majority of the 

phosphorus (67 percent) was derived from the Spavinaw 

Creek basin. Spavinaw Creek and Beaty Creek contributed 

a combined mean annual total sediment load of about 

116,000,000 lbs/yr with 98 percent of the annual total 

phosphorus load being transported to Lake Eucha during 

runoff conditions (table 5). About 56 percent of the estimated 

total sediment load was from the drainage area of the Beaty 

Creek station.

Mean annual total nitrogen loads from 2002–10 were 2.5 

percent less and mean annual total phosphorus loads were 7.8 

percent less than those reported for 2002–09 (table 5, Esralew 

and Tortorelli, 2010). These decreases indicated that nitrogen 

and phosphorus loads in 2010 were below average compared 

to loads from 2002–09. However, percent contributions of 

nitrogen and phosphorus load from both creeks and during 

base-flow and runoff conditions were within 1 percent of those 

reported in Esralew and Tortorelli (2010).

Estimation of Instantaneous Concentrations 

from Water-Quality Samples, Streamflow, 

and Real-Time Continuous Water-Quality 

Data for 2005–10

Instantaneous concentration regression equations used 

for load computations are listed in table 6. Regressions using 

base-10 and natural logarithm transformations are presented 

for comparison with previously reported DML regressions of 

Esralew and Tortorelli (2010), which used natural logarithms, 

and previously reported INSTC regression equations 

developed by Christensen and others (2008), which used 

base-10 logarithmic transformations. Both equations produce 

equivalent estimates and have the same RMSE, R2, and bias 

correction factors. 

Nitrogen

Turbidity, streamflow, and seasonality were used in 

INSTC regressions to estimate nitrogen concentration at the 

Colcord station (table 6). Turbidity was positively associated 

with nitrogen, which may be related to particulate organic 

nitrogen that coincides with transport of sediment. The 

streamflow terms were quadratic with a negative square term 

(Q – Q2), indicating a nonlinear increase of nitrogen with 

streamflow, and that at higher streamflows, such as near or 

after the peak of a storm event, dilution may cause the rate 

of increase in concentrations, with respect to streamflow, 

to decline relative to the start of a storm event. Nitrogen 

concentrations varied with season, generally being greater 

in winter and spring than in summer and fall (Esralew and 

Tortorelli, 2010).

Temperature, specific conductance, turbidity, and 

streamflow were used in the INSTC regression to estimate 

nitrogen concentration at the Beaty Creek station (table 

6). Those variables, except temperature, were positively 

correlated with nitrogen concentration. Positive turbidity and 

streamflow terms indicate sources of nitrogen from runoff. 

A positive correlation between nitrogen concentration and 

specific conductance, which tends to decrease with increasing 

streamflow, may serve a similar function to the quadratic 

streamflow term used in the regression equation for the 

Colcord station. The negative correlation with temperature 

likely reflects elevated nitrogen concentrations observed in 

winter and spring compared to summer and fall (Esralew and 

Tortorelli, 2010), which may be because of greater seasonal 

application and runoff of animal wastes and other fertilizers.

The addition of seasonality and temperature as variables, 

use of quadratic terms, and availability of additional data 

contribute to the differences between the current and previous 

INSTC regression equations (Christensen and others, 2008). 

The previous INSTC regression equations developed by 

Christensen and others (2008) to estimate nitrogen at both 

stations differ from those developed for this report. For 

example, the nitrogen INSTC regression for the Colcord 

station from Christensen and others (2008) included specific 

conductance and turbidity, which were negatively correlated 

to nitrogen concentration and the regression for the Beaty 

Creek station included streamflow. Christensen and others 

(2008) reported substantial seasonality in regression error 

residuals, which may have been reduced after use of seasonal 

terms in the new INSTC regressions. The new INSTC

regression developed for the Colcord station for this report 

had better fit to the field data compared to the nitrogen 

regression in Christensen and others (2008), as indicated by 

an increase in the R2 from 0.708 in that report to 0.777 in this 

report. The new INSTC regression developed for the Beaty 

Creek station for this report also had improved fit compared 

to the nitrogen regression in Christensen and others (2008) as 

indicated by an increase in the R2 from 0.602 in the that report 

to 0.647 in this report. 
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 25

Table 5. Summary of estimated mean annual total nitrogen, total phosphorus, and suspended-sediment loads to Lake Eucha, Oklahoma, 2002–10.[lb/yr, pound per year; N, nitrogen; P, phosphorus; Sed, sediment] 

Site Lake Eucha

Spavinaw 

Creek near 

Colcord, 

Okla.

Beaty Creek 

near Jay, 

Okla. Lake Eucha

Spavinaw 

Creek near 

Colcord, 

Okla.

Beaty 

Creek near 

Jay, Okla. Lake Eucha

Spavinaw 

Creek near 

Colcord, 

Okla.

Beaty Creek 

near Jay, 

Okla.

Flow type

Mean annual 

nitrogen load1

Component 

of mean 

annual 

nitrogen 

load

Component 

of mean 

annual 

nitrogen 

load

Mean annual 

phosphorus load

Component 

of mean 

annual 

phosphorus 

load

Component 

of mean 

annual 

phosphorus 

load

Mean annual 

sediment load

Component 

of mean 

annual 

sediment 

load

Component 

of mean 

annual 

sediment 

load

(lb/yr as N) (percent) (percent) (percent) (lb/yr as P) (percent) (percent) (percent)

(lb/yr as 

Sed) (percent) (percent) (percent)

Base Flow2 422,000 26 89 11 9,980 10 90 10 1,940,000 2 92 8

Runoff3 1,220,000 74 75 25 90,000 90 64 36 114,000,000 98 43 57Total4 1,640,000 100 78 22 100,000 100 67 33 116,000,000 100 44 56

1 Loads to Lake Eucha were calculated by adding loads from Spavinaw Creek near Colcord, Okla., to loads from Beaty Creek near Jay, Okla. These two locations accounted for 62 percent of the drainage 

area that inflows to Lake Eucha.

2 Means of the base-flow loads were calculated from base-flow day data only by S-LOADEST and are statistics of all data from 2002–10.3 Means of the runoff loads are calculated from runoff day data only by S-LOADEST and are statistics of all data from 2002–10.4 Differences between total load and the sum of the base-flow load plus runoff loads are caused by rounding.
26 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10 Table 6. Regression equations for estimating instantaneous concentrations of total nitrogen, total phosphorus, and suspended sediment using physical water-quality constituents, streamflow, and seasonality, at Spavinaw Creek near Colcord, Oklahoma and Beaty Creek near Jay, Okla., streamflow-gaging stations, 2004–10. [INSTC, estimated instantaneous concentration; log10, base-10 logarithm; TN, total nitrogen concentration in milligrams per liter; FNU, turbidity in formazin nephelometric units; Q, streamflow in cubic feet per second; sin, sine; cos, cosine; SS, seasonality parameter; R2, coefficient of determination; RMSE, root mean square error; ln, natural logarithm; TP, total phosphorus concentration in milligrams per liter; DEGC, temperature in degrees celcius; Sed, suspended sediment concentration in milligrams per liter; SC, specific conductance in microsiemens per centimeter at 25 degrees Celsius] Number of observations Transfor- mation1 Instantaneous concentration regression equation2 RMSE3 R2 Bias- correction factor4 Data range Spavinaw Creek near Colcord, Okla. (071912213) 106 Log10 log10(INSTCTN) = 0.0003*FNU + 0.3374 + 0.1226*log10Q - 0.0412*(log10Q-1.9)2 + 0.0072*sinSS + 0.1004*cosSS 0.057 0.777 1.01 TN 2.08-9.62 Ln ln(INSTCTN) = .8467 + 0.1074*lnQ - 0.0179*(lnQ-4.8)2 + 0.0006*FNU + 0.0166*sinSS + 0.2313*cosSS Q 11-9,620 FNU 0.2 -1,480 102 no transform- ation used INSTCTP = 0.0709 + 0.0009*FNU + 0.0001*Q 0.060 0.948 1.00 TP 0.04-1.6 FNU 0.2 -1,480 Q 12-9,620 40 Log10 log10(INSTCSed) = .6098 + 0.8222*log10FNU 0.332 0.830 1.34 Sed 1-1,810 Ln ln(INSTCSed) = 1.404 + 0.8222*lnFNU FNU 0.6-1,480 Beaty Creek near Jay, Okla. (07191222) 111 Log10 log10(INSTCTN) = -2.064 - 0.0134*DEGC + 0.9810*log10SC + 0.0007*FNU + 0.1799*log10Q 0.113 0.647 1.03 TN 0.67-7.27 Ln ln(INSTCTN) = -4.7535 - 0.0309*DEGC + 0.9810*lnSC + 0.0017*FNU + 0.1799lnQ Q 0.04-3,040 FNU 0.1-446 SC 120-339 TEMP 6.1-25.5 127 Log10 log10(INSTCTP) = -1.340 + .1861*log10FNU + 0.0903*(log10FNU-.204)2 + 0.0946*log10Q 0.170 0.791 1.10 TP 0.021-1.1 Ln ln(INSTCTP) = -3.102+ 0.1861*lnFNU + 0.0393*(lnFNU-0.470)2 + 0.0946*lnQ FNU 0.1-446 Q 0-3,040

37 Log10 log10(INSTCSed) = 0.7232 + 0.4508*log10FNU + 0.1344*(log10FNU-0.204)2 0.385 0.757 1.07 Sed 0.5-664

Ln ln(ISNTCSed) = 1.665 + 0.4508*lnFNU + 0.0584*(lnFNU-0.470)2 FNU 0.1-446

1 Regressions using base-10 logarithm and natural logarithm transformations are presented for comparison with previously reported DML surrogate regressions of Esralew and Tortorelli (2010), which 

used natural logarithms and previously reported INSTC regression equations developed by Christensen and others (2008), which used base-10 logarithmic transformations, and LOADEST equations (table 7), respectively. Estimates and errors are equivalent for both equations.

2 The seasonality parameter is computed as 2*pi*decimal date, which is the time parameter in decimal time.3 In base-10 logarithmic units. Units can be converted to natural log by multiplying by 2.3024.4 From Duan (1983).
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 27

-0 .2

-0 .1

0.0

0.1

0.

0.3

2

Spavinaw Creek near Colcord, Okla. (071912213)

2005 2006 2007 2008 2009 2010

LOESS trend line

Total phosphorus concentration residuals from INSTc1

regression, in natural log of milligrams per liter as phosphorus

-0.3

October 2007

Year

1

INSTC regression, regression used to estimate constituent concentrations where physical 

water-quality constituents, streamflow, and seasonality are independent variables

Figure 9. Trends in error residuals of regression-estimated total phosphorus concentrations at Spavinaw Creek near Colcord, 

Oklahoma, streamflow-gaging station, 2004–10.

Phosphorus

Turbidity and streamflow were used as independent 

variables for the INSTC regression equation developed to 

estimate phosphorus concentrations at the Colcord station 

(table 6). Turbidity and streamflow were positively correlated 

with phosphorus, indicating increases in sediment-sorbed 

phosphorus during runoff. Error residuals from the INSTC

regression had a slight negative correlation with time, 

when data from 2004 through 2010 were used, indicating 

a downward trend in phosphorus concentration. Plots of 

error residuals (fig. 9) also indicated decreases in estimated 

phosphorus concentrations from October 2004 through 

October 2007. An INSTC regression using data from October 

2007 through September 2010 was used to eliminate temporal 

trends in the error residuals. No temporal trends were detected 

with residuals when this later period was used. However, 

the regression equation developed using these later dates 

had a substantially poorer fit to the data, as indicated by an 

R2

 of 0.591 compared to 0.948 using data from November 

2004 through September 2010. This decrease in fit probably 

was caused by several phosphorus samples collected from 

2004 through 2007 being associated with extremely high 

streamflows (greater than the 2 percent streamflow exceedance 

probability), which had substantial leverage on the INSTC

regression. Because the trend was slight (p-value and tau 

were 0.02 and -0.16), this difference may indicate a slight 

tendency of the INSTC regressions to overestimate phosphorus 

concentrations. Additional runoff samples and relatively 

frequent updates of this regression using new data could 

improve regression estimates.

Turbidity and streamflow also were the variables selected 

to estimate phosphorus concentration using the INSTC

regression for the Beaty Creek station. Like the Colcord 

INSTC regression, positive turbidity and streamflow terms 

indicate increases of phosphorus concentration with runoff. 

The relation of phosphorus concentration with turbidity and 

streamflow is because of the association of phosphorus with 

sediment. When streamflow increases because of runoff, 

turbidity and phosphorus increase as runoff transports 

increasing concentrations of sediment-sorbed phosphorus. A 

quadratic turbidity term (FNU + FNU2) fits the phosphorus 

concentration data better than a linear turbidity term. This 

relation may indicate that at higher turbidity values, there may 

have been a decrease in the relation between turbidity with 

sediment at larger suspended-sediment concentrations (Gloria 

Ferrell, U.S. Geological Survey, written commun., 2011).
28 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Differences in the fit and types of variables from those 

used in previous INSTC regression equations (Christensen and 

others, 2008) may have been the result of new concentration 

data from 2007 through 2010 or changes in relations between 

phosphorus, turbidity, and streamflow. The previous INSTC

regression developed to estimate phosphorus at the Colcord 

station was nearly identical to the regression developed in 

this report. However, the INSTC regression developed to 

estimate phosphorus concentration at the Beaty Creek station 

in Christensen and others (2008) differed substantially from 

the new INSTC regression largely because the previous 

regressions did not include a quadratic turbidity term and were 

not log-transformed. Graphs of phosphorus concentration and 

turbidity using data collected from 2004 to 2010 indicated 

a logarithmic fit. The new INSTC regression developed for 

the Colcord station for this report had slightly reduced fit 

compared to the phosphorus regression in Christensen and 

others (2008) as indicated by a slight decrease in R2

 from 

0.958 to 0.948. The new INSTC regression developed for the 

Beaty Creek station for this report had reduced fit compared 

to the nitrogen regression in Christensen and others (2008) as 

indicated by a decrease in R2

 from 0.978 to 0.791 (table 6). 

Sediment

Turbidity was selected as the independent variable 

in the INSTC regression developed to estimate sediment 

concentrations at the Colcord station (table 6). Turbidity was 

positively correlated with phosphorus, indicating increases in 

phosphorus sorbed to sediments during runoff. Turbidity also 

was the independent variable in the INSTC regression used to 

estimate sediment concentration at the Beaty Creek station. 

A quadratic turbidity term (FNU + FNU2

) was used to fit the 

sediment concentration data better than a linear turbidity term, 

slightly improving regression fit, indicating that at greater 

turbidity, sediment concentrations may increase at a faster rate 

than at lesser turbidity.

Comparison of Regression-Based 

Load Estimates

Nitrogen, phosphorus, and sediment annual loads and 

yields were compared for the period 2005–10 for the Colcord 

station and 2006–10 for the Beaty Creek station using two 

regression methods. Annual total loads and mean annual total 

loads were from: (a) DML regressions used to estimate daily 

mean load based on streamflow, seasonality, and time (table 

3), and (b) INSTC regressions used to estimate instantaneous 

concentrations based on physical water-quality constituents 

(turbidity, specific conductance, temperature), streamflow, 

and seasonality (table 6). Accuracy of INSTC regressions were 

compared to alternate INSTC regressions using streamflow and 

time as the only independent variables in order to determine 

if inclusion of water-quality constituents in concentration and 

load estimation regression improves fit of the regression. 

Comparison of load estimates indicated that daily, 

annual, and mean annual loads varied substantially depending 

on the independent variables used to develop the regression 

equations. For each constituent at both stations, concentrations 

estimated from INSTC regressions with streamflow, 

seasonality, and physical water-quality parameters such as 

turbidity, temperature, and specific conductance, had better 

fit than estimates from alternate INSTC regressions that only 

included streamflow and seasonality, as indicated by R2

 and 

RMSE values (table 7). Regression-estimated loads using 

physical water-quality parameters are also useful because data 

are provided at more frequent intervals than a daily mean and 

can better describe variability in concentrations and loads. 

Because the majority of constituent load was delivered during 

a relatively small number of streamflow events, variability in 

hourly load estimation can be important in quantifying total 

loads. However, many instantaneous and daily load estimates 

for extreme high streamflow events were extrapolated beyond 

the range of water- quality and streamflow conditions for 

which the samples used to develop the regressions were 

collected, indicating that fit of load computations could be 

improved with data from additional high-flow samples.

Nitrogen

Estimates of mean annual nitrogen loads did not differ 

substantially between the two regression methods for either 

station (table 8, figs. 10-11). For both stations, the relative 

percent difference (RPD) between the mean annual total 

nitrogen and runoff-load estimates obtained by the two 

regression methods were within 2 percent. However, the RPD 

in mean annual nitrogen base-flow load was -12.1 percent 

for the Beaty Creek station (fig. 11). Estimated 90 percent 

prediction intervals were similar for annual total nitrogen 

loads estimated for the Colcord and Beaty Creek stations for 

both types of regressions (fig. 10).

The RPDs between annual total nitrogen loads estimated 

from the DML and INSTC regression equations ranged from 

-0.8 to 1.6 percent for the Colcord station and -22.5 to 12.4 

for the Beaty Creek station. For the Beaty Creek station, 

annual total nitrogen and runoff loads estimated from the DML

regression were less than those estimated from the INSTC

regression for 2006–08 but were greater than those estimated 

from the INSTC regression for 2009–10.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 29

Table 7. Alternate regression equations for estimating instantaneous concentrations of total nitrogen, total phosphorus, and 

suspended sediment using streamflow and seasonality parameters for Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek 

near Jay, Okla., streamflow-gaging stations, 2004–10.

[log10; base-10 logarithm; INSTC, estimated instantaneous concentration; TN, total nitrogen concentration in milligrams per liter; FNU, turbidity in formazin 

nephelometric units; Q, instantaneous streamflow in cubic feet per second; sin, sine; cos, cosine; SS, seasonality; R2, coefficient of determination; RMSE, root 

mean square error; ln, natural logarithm; TP, total phosphorus concentration in milligrams per liter; DEGC, temperature in degrees Celsius; Sed, 

suspended sediment concentration in milligrams per liter; SC, specific conductance in microsiemens per centimeter at 25 degrees Celsius]

Number of 

observations Instantaneous concentration regression model1 RMSE2 R2

Biascorrection 

factor3

Spavinaw Creek near Colcord, Okla. (071912213)

106 ln(INSTCTN) = 0.8054 + 0.1159*lnQ - 0.0091*(lnQ-5.03)2

 + 0.0183*sinSS + 0.2178*cosSS 0.068 0.697 1.01

102 INSTCTP = 0.0772 + 0.0002*Q 0.149 0.669 1.00

40 ln(INSTCSed) = -1.65 + 0.848*lnQ 0.54 0.549 1.59

Beaty Creek near Jay, Okla. (07191222)

111 ln(INSTCTN) = .4203 + 0.1427*lnQ - 0.0761*(lnQ-3.66)2

 + 0.0761*sinSS + 0.1690*cosSS 0.118 0.628 1.04

127 ln(INSTCTP) = -4.1145 + 0.368*lnQ + 0.051*(lnQ-3.66)2

 - 0.150*sinSS - 0.080*cosSS 0.184 0.747 1.10

37 ln(INSTCSed) = .125 + 0.4348*lnQ + 0.214*(lnQ-3.66)2 0.473 0.632 1.39

1

The seasonality parameter is computed as 2*pi*decimal date, which is the time parameter in decimal time.

2

In base-10 logarithmic units. Units can be converted to natural log by dividing by 2.3024.

3

From Duan (1983).

Table 8. Estimated mean annual total nitrogen, total phosphorus, and suspended-sediment loads and yields by using two different 

regression equations for streamflow-gaging stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10.

[NWIS, National Water Information System of the U.S. Geological Survey; DML, annual load computed from estimated concentrations from a regression 

using annual load estimated from a regression using streamflow, seasonality, and time (table 3); INSTC, annual load computed from estimated concentrations 

from a regression using physical water-quality constituents, streamflow, and seasonality (table 6); mi2, square mile; lb/yr, pound per year; lb/yr/mi2, pound per 

year per square mile; SEP, standard error of prediction; N, nitrogen; Differences between total load and the sum of the base-flow load plus runoff loads are 

caused by rounding]

Total nitrogen

Mean annual load

Station name 

(NWIS number)

Regression 

type

Total load1

(lb/yr as N)

Total yield1

(lb/yr/mi2 as N)

Base-flow 

load1

(lb/yr as N)

Base-flow 

yield1

(lb/yr/mi2 as N)

Runoff load2

(lb/yr as N)

Runoff yield2

(lb/yr/mi2 as N)

Load 

delivered 

during 

runoff

(percent)

Spavinaw 

Creek near 

Colcord, Okla. 

(071912213)

DML 1,440,000 8,830 348,000 2,135 1,100,000 6,750 76

INSTC 1,450,000 8,900 352,000 2,160 1,100,000 6,750 76

Beaty Creek 

near Jay, Okla. 

(07191222)

DML 448,000 7,570 55,500 938 392,000 6,620 88

INSTC 448,000 7,570 49,200 831 399,000 6,740 89
30 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Total phosphorus 

Mean annual loads

Station

Regression 

type

Total load1

(lb/yr as P)

Total yield1

(lb/yr/mi2 as P)

Base-flow 

load1

(lb/yr as P)

Base-flow 

yield1

(lb/yr/mi2 as P)

Runoff load2

(lb/yr as P)

Runoff yield2

(lb/yr/mi2 as P)

Load 

delivered 

during 

runoff

(percent)

Spavinaw 

Creek near 

Colcord, Okla. 

(071912213)

DML 73,700 452 7,390 45 66,300 407 90

INSTC 97,400 598 7,720 47 89,700 550 92

Beaty Creek 

near Jay, Okla. 

(07191222)

DML 43,700 738 1,180 20 42,500 718 97

INSTC 42,500 718 1,250 21 41,300 698 97

Suspended sediment

Mean annual loads

Station

Regression 

type

Total load1

(lb/yr as 

SS)

Total yield1

(lb/yr/mi2 as 

SS)

Base-flow 

load1

(lb/yr as N)

Base-flow 

yield1

(lb/yr/mi2 as N)

Runoff load2

(lb/yr as N)

Runoff yield2

(lb/yr/mi2 as N)

Load 

delivered 

during 

runoff

(percent)

Spavinaw 

Creek near 

Colcord, Okla. 

(071912213)

DML 65,000,000 399,000 1,760,000 10,800 63,200,000 388,000 97

INSTC 43,900,000 369,000 615,000 3,770 43,300,000 265,000 99

Beaty Creek 

near Jay, Okla. 

(07191222)

DML 80,300,000 1,360,000 111,000 1,880 80,200,000 1,350,000 100

INSTC 19,200,000 324,000 97,700 1,650 19,100,000 323,000 99

1

 Means of the base-flow loads are calculated from base-flow days data only.

2

 Means of the runoff loads are calculated from runoff days data only.

Table 8. Estimated mean annual total nitrogen, total phosphorus, and suspended-sediment loads and yields by using two different 

regression equations for streamflow-gaging stations in the Eucha-Spavinaw basin, Arkansas and Oklahoma, 2002–10.—Continued

[NWIS, National Water Information System of the U.S. Geological Survey; DML, annual load computed from estimated concentrations from a regression 

using annual load estimated from a regression using streamflow, seasonality, and time (table 3); INSTC, annual load computed from estimated concentrations 

from a regression using physical water-quality constituents, streamflow, and seasonality (table 6); mi2, square mile; lb/yr, pound per year; lb/yr/mi2, pound per 

year per square mile; SEP, standard error of prediction; N, nitrogen; Differences between total load and the sum of the base-flow load plus runoff loads are 

caused by rounding]
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 31

10,000,000

1,000,000

100,000

10,000

10,000,000

1,000,000

100,000

10,000

Annual total nitrogen load, in pounds as nitrogen

Spavinaw Creek near Colcord, Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

2005 2006 2007 2008 2009 2010

EXPLANATION

Year

DML regression estimate, annual 

load estimated from a regression 

using streamflow, seasonality, 

and time

INSTC regression estimate, annual 

load computed from estimated 

concentrations from a regression 

using physical water-quality 

constituents, streamflow, 

and seasonality

Estimated upper and lower

90-percent prediction intervals

Annual load not compared

Figure 10. Annual total nitrogen load estimated using two regression methods at Spavinaw Creek near Colcord, Oklahoma, and Beaty 

Creek near Jay, Okla., streamflow-gaging stations, 2005–10.
32 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

-5 0

-3 0

-1 0

10

30

50

-5 0

-3 0

-1 0

10

30

50

-5 0

-3 0

-1 0

10

30

50

Beaty Creek near Jay, Okla. (07191222)

Loads estimated from INSTC regression larger

than loads estimated from DML regression

Base-Flow Loads

Loads estimated from DML regression larger

than loads estimated from INSTC regression

Runoff Loads

Spavinaw Creek near Colcord, Okla. (071912213)

Relative percent difference

2006 2007 2008 2009 2010 Mean Annual

Total Load

2005–10

Total Loads

INSTC regression, regression used to estimate concentrations and loads 

where physical water-quality constituents, streamflow, and seasonality 

are independent variables.

DML regression, regression used to estimate loads where streamflow, 

seasonality and time are independent variable.

Figure 11. Comparison of relative percent differences between annual total nitrogen load estimated from two regression methods for 

Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near Jay, Okla., streamflow-gaging stations, 2006–10.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 33

Table 9. Wilcoxon signed-rank test results comparing daily loads estimated from two different regression methods at two streamflowgaging stations in the Eucha-Spavinaw basin, 2004–10.

[INSTC, estimated instantaneous concentrations, in mg/L; DML, daily mean load, in pounds per day; μ>0, mean difference is greater than zero; μ<0, mean 

difference is less than zero; p, probability value; p-values in bold indicate statistically significant differences between groups of data at 95-percent confidence 

level (probability value less than or equal to 0.05); --, not determined]

Station name 

(number)

Flow 

condition

Nitrogen Phosphorus Suspended sediment

Onesided 

test μ>0 

p-value1

Onesided 

test μ<0 

p-value1

Regression 

that 

estimated 

significantly 

greater 

daily loads

Onesided 

test μ>0 

p-value1

Onesided 

test μ<0 

p-value1

Regression 

that 

estimated 

significantly 

greater 

daily loads

Onesided 

test μ>0 

p-value1

Onesided 

test μ<0 

p-value1

Regression 

that 

estimated 

significantly greater 

daily loads

Spavinaw 

Creek near 

Colcord, 

Okla. 

(071912213)

Base-flow 

days

>0.9999 <0.0001 INSTC 0.336 0.664 -- <0.0001 >0.9999 DML

Runoff 

days

0.001 0.999 DML <0.0001 >0.9999 DML <0.0001 >0.9999 DML

High-flow 

days2

0.097 0.904 -- >0.9999 <0.0001 INSTC <0.0001 >0.9999 DML

Beaty Creek 

near Jay, 

Okla. 

(07191222)

Base-flow 

days

<0.0001 >0.9999 DML >0.9999 <0.0001 INSTC <0.0001 >0.9999 DML

Runoff 

days

<0.0001 >0.9999 DML <0.0001 >0.9999 DML <0.0001 >0.9999 DML

High-flow 

days2

0.010 0.990 DML 0.962 0.038 INSTC 0.405 0.595 --

1

 Differences greater than zero indicate that daily loads estimated from the DML regression were greater than those estimated from the INSTC regression. 

Differences less than zero indicate that daily loads estimated from the DML regression were less than those estimated from the INSTC regression. 

2

 Days in which daily mean streamflow was greater than the 2-percent streamflow exceedance probability.

Estimates of daily nitrogen load generally were greater 

from the DML regressions than the INSTC regressions, but 

differences varied depending on streamflow conditions. For 

the Colcord station, daily nitrogen loads for base-flow days 

estimated from the INSTC regression were significantly 

greater than the estimates from the DML regression, but daily 

nitrogen loads on runoff days estimated from the INSTC

regression were significantly less than the estimates from 

the DML regression (table 9). Daily nitrogen loads for the 

Beaty Creek station estimated using the INSTC regression 

were significantly less than those estimated using the DML

regression under all flow conditions. Load-duration curves 

indicated that differences in daily load estimates for the 

two types of regressions were generally small in magnitude 

(fig. 12). The load-duration curve indicated that nitrogen 

loads were greater for daily loads estimated from the INSTC

regression for the largest daily loads (less than 0.3 percent 

probability of exceedance).

Alternate INSTC nitrogen regressions that did not include 

physical water-quality constituents produced a poorer fit to 

field data than INSTC nitrogen regressions that did include 

physical water-quality constituents at both stations (fig. 13). 

For the Colcord station, the R2

 of the alternate INSTC nitrogen 

regressions were 0.697 compared to 0.777 percent for INSTC

nitrogen regressions. Use of water-quality constituents as 

independent variables only caused a slight improvement in fit 

for the INSTC nitrogen regression for the Beaty Creek station, 

where the R2

 of the alternate INSTC nitrogen regressions was 

0.628 compared to 0.647 for the INSTC nitrogen regression. 

Graphs of measured and estimated nitrogen concentrations for 

the alternate INSTC nitrogen regressions and INSTC nitrogen 

regressions at both stations indicated similar distributions of 

scatter about the one-to-one line, but one larger outlier on 

the alternate INSTC regressions at both stations may have 

decreased the fit of those regressions (fig. 13).
34 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

0. 1 1 10 100

1,000,000

100,000

10,000

1,000

100

10

1

1,000,000

100,000

10,000

1,000

100

10

1

Spavinaw Creek near Colcord, Okla. (071912213)

November 2004 - December 2010

Beaty Creek near Jay, Okla. (07191222)

March 2005 - December 2010

DML regression estimate

INSTC regression estimate

Probability of exceedance, in percent

Total nitrogen load, in pounds per day as nitrogen

INSTC regression estimate, daily load computed from estimated concentrations from

a regression using physical water-quality constituents, streamflow, and seasonality

DML regression estimate, daily load estimated from a regression using streamflow 

seasonality, and time

Figure 12. Comparison of duration curves for estimated daily nitrogen loads at Spavinaw Creek near Colcord, Oklahoma, and Beaty 

Creek near Jay, Okla., using two regression methods.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 35

2

4

6

8

10

0

2

4

6

8

10

0 2 4 6 8 10 0 2 4 6 8 10

1:1 Line

Spavinaw Creek near Colcord,

Okla. (071912213)

Spavinaw Creek near Colcord,

Okla. (071912213)

Beaty Creek near Jay,

Okla. (07191222)

Beaty Creek near Jay,

Okla. (07191222)

A B

Estimated total nitrogen concentration, 

in milligrams per liter as nitrogen

Measured total nitrogen concentration, 

in milligrams per liter as nitrogen

Figure 13. Comparison of measured and regression-estimated total nitrogen concentrations from (A) INSTC regressions that include 

physical water-quality constituents, streamflow, and seasonality as independent variables and (B) alternate INSTC

 regressions that 

include streamflow and seasonality as independent variables.

Phosphorus

Mean annual total phosphorus load estimates from the 

two regression methods did not differ substantially for the 

Beaty Creek station but were substantially different for the 

Colcord station (table 8, figs.14-15). The RPD between mean 

estimated annual total phosphorus loads at the Colcord station 

was 27.7 percent (fig. 15). In contrast to the Colcord station, 

the RPD in annual phosphorus total loads at the Beaty Creek 

station was -2.6 percent (fig. 15). The RPD in mean annual 

base-flow loads, which composed a relatively small proportion 

of the total loads (3-10 percent, table 8), was within 7 percent 

between regressions for data from both stations.

RPDs in annual phosphorus load estimates between the 

INSTC and DML regressions were variable by year for both 

stations, and relatively large for some years, ranging from 

-9.1 to 33.7 percent for the Colcord station and -10.9 to 14.9 

for the Beaty Creek station (fig. 15). For the Colcord station, 

DML total and runoff loads usually were less than INSTC loads 

for both stations from 2008 to 2010, equal to INSTC loads 

in 2007, and greater than INSTC loads in 2006. Because the 

years 2008 and 2009 had above-average streamflow and larger 

annual loads, differences in these years may have caused most 

of the mean annual differences. Differences in annual loads 

between the INSTC and DML regressions for the Beaty Creek 

station were variable by year, with no apparent pattern in years 

with above- or below-average streamflow and differences 

between annual DML and INSTC regression loads. 

Differences in estimates of daily phosphorus load 

from both regressions varied substantially for both stations, 

depending on streamflow conditions. For the Colcord station, 

daily phosphorus loads estimated from the INSTC regression 

were significantly greater than those from the DML regression 

for high-flow days, but daily phosphorus loads estimated from 

the INSTC regression were significantly less than those loads 

from the DML regression on all runoff days which included 

extremely high-flow days (table 9). For the Beaty Creek 

station, daily phosphorus loads estimated from the INSTC

regression were significantly greater than those from the 

DML regressions for extremely high-flow days and base-flow 
36 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10 Annual load not compared Annual total phosphorus load, in pounds

Spavinaw Creek near Colcord, Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

2005 2006 2007 2008 2009 2010

EXPLANATION

Year

1,000,000

10,000

1,000

100

100,000

1,000,000

10,000

1,000

100

100,000

DML regression estimate, annual 

load estimated from a regression 

using streamflow, seasonality, 

and time

INSTC regression estimate, annual 

load computed from estimated 

concentrations from a regression 

using physical water-quality 

constituents, streamflow, 

and seasonality

Estimated upper and lower

90-percent prediction intervals

Figure 14. Annual total phosphorus load estimated using two regression methods at Spavinaw Creek near Colcord, Oklahoma, and 

Beaty Creek near Jay, Okla., 2005–10.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 37

Spavinaw Creek near Colcord, Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

-50

-30

-10

10

30

50

-50

-30

-10

10

30

50

-50

-30

-10

10

30

50

Loads estimated from INSTC regression larger

than loads estimated from DML regression

Base-Flow Loads

Loads estimated from DML regression larger

than loads estimated from INSTC regression

Runoff Loads

Relative percent difference

2006 2007 2008 2009 2010 Mean Annual

Total Load

2006–10

Total Loads

INSTC regression, regression used to estimate concentrations and loads 

where physical water-quality constituents, streamflow, and seasonality 

are independent variables.

DML regression, regression used to estimate concentrations and loads 

where streamflow, seasonality, and time are independent variable.

Figure 15. Bar graphs of comparison of relative percent differences between annual total phosphorus load estimated from two 

regression methods for Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near Jay, Okla., 2006–10.
38 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

days, but daily phosphorus loads estimated from the INSTC

regression were significantly less than those loads from the 

DML regression on all runoff days, which included extremely 

high-flow days (table 9). However, load-duration curves 

indicated that these differences were small in magnitude 

for most days except for extremely high-flow days where 

differences were greater (fig. 16). Extremely high-flow days 

accounted for 73.4 percent of the total phosphorus load at 

the Colcord station from November 2004 to December 2010 

and 81.8 percent of the total phosphorus load at the Beaty 

Creek station from March 2005 to December 2010, which 

indicated that greater daily phosphorus loads estimated from 

the INSTC regressions probably substantially influence total 

load estimation.

Alternate INSTC phosphorus regressions not based on 

instantaneous measurement of physical properties produced 

a poorer fit to field data than INSTC phosphorus regressions, 

especially for the Colcord station. For the Colcord station, 

turbidity and streamflow are significantly better estimators 

of phosphorus than streamflow alone; the R2

 of the alternate 

INSTC phosphorus regression was 0.669 (table 7) compared 

to 0.948 for the INSTC phosphorus regression (table 6). 

This substantial difference in fit may indicate that the 

INSTC regression more accurately estimates load than then 

DML regression. Use of turbidity only resulted in a slight 

improvement in fit for the INSTC phosphorus regression for 

the Beaty Creek station, for which the R2

 of the alternate 

INSTC phosphorus regression was 0.749 compared to 0.791 

for INSTC regression. Plots of measured and estimated 

nitrogen concentrations for the alternate INSTC nitrogen 

regressions and INSTC nitrogen regressions at both stations 

indicated similar distributions of scatter about the one-toone line, but one substantial outlier on the alternate INSTC

phosphorus regression for the Colcord station, which was 

underestimated by the regression, may have caused poorer fit 

of that regression (fig. 17). 

The DML regression may have substantially 

underestimated the phosphorus load at the Colcord station 

in wet years because of poorer fit and use of daily mean 

streamflow in the DML regression. Differences in fit between 

INSTC and alternate INSTC regressions at the Colcord station 

indicate that the INSTC regression that included turbidity 

produced a better fit of annual load estimates than the 

DML regression that did not include turbidity. In addition 

to differences in fit, use of daily mean streamflow on days 

with large runoff may have caused underestimation of daily 

loads because a disproportionately large amount of the daily 

phosphorus load was transported at streamflow conditions 

greater than daily mean streamflow for these days. The 

days with the largest difference in daily phosphorus load 

generally also were the days with the largest difference 

between maximum instantaneous streamflow and mean 

daily streamflow at the Colcord station (fig. 18). This 

pattern occurred for both stations but was more apparent at 

the Colcord station than the Beaty Creek station (fig. 18). 

However, on January 8, 2008, turbidity readings exceeded 

the maximum sensor measurement at the Beaty Creek station 

causing underestimation of load from the INSTC regression for 

that day. The three days with the largest differences in daily 

load at the Colcord station were on March 18-19, and 

April 10, 2008. However, estimated instantaneous loads 

were extrapolated for some streamflows for those days 

because those streamflows were beyond the range used to 

develop the regression. Collection of additional runoff 

samples in the future will help to verify these loads and 

may make a substantial difference in fit of the mean annual 

phosphorus load.

Sediment

Mean annual total sediment loads estimated from 

the DML regression were substantially greater than those 

estimated from the INSTC regression for the Colcord and 

Beaty Creek stations (table 8, figs. 19-20). The RPD between 

mean annual total sediment loads at the Colcord station was 

-38.6 percent for the Colcord station and -122.7 percent for 

the Beaty Creek station (table 8, fig. 20). RPDs for baseflow loads, which made up a relatively small proportion of 

total loads (1-33 percent for the Colcord station and about 1 

percent for the Beaty Creek station), were -96.6 percent for the 

Colcord station and 13.1 for the Beaty Creek station.

Differences in annual load estimates between the INSTC

and DML regressions were variable by year for both stations 

but generally were less for the INSTC regression estimates 

than the DML regression estimates (fig. 20). For the Beaty 

Creek station, 90 percent prediction intervals were similar for 

annual total sediment loads estimated for both regressions for 

all years (fig. 19). RPDs in annual total load ranged from 

-65.9 to -35.9 percent for the Colcord station and -140 to 6.3 

percent for the Beaty Creek station (fig. 20). Differences in 

annual loads between the INSTC and DML regressions for the 

Colcord station were variable by year and had no apparent 

pattern in years with above- or below-average streamflow. 

The annual RPD was the greatest in 2008 for the Beaty Creek 

station (fig. 20). 

Estimated daily sediment loads were significantly 

greater for the DML regressions than the INSTC regressions 

for most flow conditions at both stations, with the 

exception of daily loads for high-flow days at Beaty Creek 

for which there was no significant difference (table 9). Loadduration curves indicated that these differences were relatively 

large in magnitude for most days for the Colcord station (fig. 

21). The largest difference in daily load between regressions at 

the Beaty Creek station was on January 8, 2008, which was an 

order of magnitude in difference (250,400,000 lbs estimated 

from the DML regression and 12,360,000 lbs estimated from 

the INSTC regression). The difference in daily loads between 

regression estimates for that day was 29 percent greater than 

the annual total load estimated from the INSTC regression for 

that year. A possible explanation for this difference may have 

been the uncertainty in the INSTC regression estimate for that 

day. On January 8, turbidity readings probably exceeded the 

maximum sensor measurement resulting in underestimation of 

load for that day. 
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 39

0.1 1 10 100

Spavinaw Creek near Colcord, Okla. (071912213)

November 2004 - December 2010

Beaty Creek near Jay, Okla. (07191222)

March 2005 - December 2010

DML regression estimate

INSTC regression estimate

Probability of exceedance, in percent

Total phosphorus load, in pounds per day as phosphorus

100,000

10,000

100

1,000

10

1

0.1

10,000

100,000

1,000

100

10

1

0.1

INSTC regression estimate, daily load computed from estimated concentrations from

a regression using physical water-quality constituents, streamflow, and seasonality

DML regression estimate, daily load estimated from a regression using streamflow 

seasonality, and time

Figure 16. Comparison of duration curves for estimated daily phosphorus loads at Spavinaw Creek near Colcord, Oklahoma, and Beaty 

Creek near Jay, Okla., using two regression methods.
40 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

0

0.5

1

1.5

2

0

0. 5

1

1.5

2

0 0.5 1 1.5 2 0 0.5 1 1.5 2

1:1 Line

A B

Estimated total phosphorus concentration, 

in milligrams per liter as phosphorus

Measured total phosphorus concentration, 

in milligrams per liter as phosphorus

Beaty Creek near Jay,

Okla. (07191222)

Beaty Creek near Jay,

Okla. (07191222)

Spavinaw Creek near Colcord,

Okla. (071912213)

Spavinaw Creek near Colcord,

Okla. (071912213)

Figure 17. Comparison of measured and regression-estimated total phosphorus concentrations from (A) INSTC regressions based on 

physical water-quality constituents, streamflow, and seasonality as independent variables and (B) alternate INSTC

 regressions based on 

streamflow and seasonality as independent variables.
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 41

Spavinaw Creek near Colcord, Okla. (071912213)

November 2004 - December 2010

Beaty Creek near Jay, Okla. (07191222)

March 2005 - December 2010

Daily phosphorus load estimated from INSTC regression minus daily phosphorus

 load estimated from DML regression, in pounds per day as phosphorus

0

40,000

30,000

20,000

10,000

-10,000

-20,000

-30,000

-40,000

0

40,000

30,000

20,000

10,000

-10,000

-20,000

-30,000

-40,000

Daily maximum streamflow minus daily mean streamflow, in cubic feet per second

INSTC regression, regression used to estimate concentrations and loads where physical water-quality 

constituents, streamflow, and seasonality are independent variables.

DML regression, regression used to estimate loads where streamflow, seasonality, and time are 

independent variable.

0.1 1 10 100 1,000 10,000 100,000

Figure 18. Comparison of difference in daily mean streamflow to difference in estimated phosphorus load between two regression 

methods at Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near Jay, Okla.
42 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

2005 2006 2007 2008 2009 2010 Annual load not compared

Spavinaw Creek near Colcord, EXPLANATION

Okla. (071912213)

Beaty Creek near Jay, Okla. (07191222)

Suspended-sediment annual load, in pounds

Year

1,000,000,000

10,000,000

1,000,000

100,000

10,000

1,000,000,000

10,000,000

100,000,000

100,000,000

1,000,000

100,000

10,000

DML regression estimate, annual 

load estimated from a regression 

using streamflow seasonality, 

and time

INSTC regression estimate, annual 

load computed from estimated 

concentrations from a regression 

using physical water-quality 

constituents, streamflow, 

and seasonality

Estimated upper and lower

90 percent prediction intervals

Figure 19. Suspended-sediment annual total load estimated using two regression methods, Spavinaw Creek near Colcord, and Beaty 

Creek near Jay, Oklahoma, 2005–10. 
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 43

Beaty Creek near Jay, Okla. (07191222)

Loads estimated from INSTC regression larger

than loads estimated from DML regression

Base-Flow Loads

Loads estimated from DML regression larger

than loads estimated from INSTC regression

-150

-100

-50

0

50

100

150 Runoff Loads

Spavinaw Creek near Colcord, Okla. (071912213)

Relative percent difference

2006 2007 2008 2009 2010 Mean Annual

Total Load

2005–10

Total Loads

INSTC regression, regression used to estimate concentrations and loads 

where physical water-quality constituents, streamflow, and seasonality 

are independent variables.

DML regression, regression used to estimate loads where streamflow, 

seasonality and time are independent variable.

-150

-100

-50

50

100

150

-150

-100

-50

50

100

150

Figure 20. Comparison of relative percent differences between suspended-sediment annual total load estimated from two regression 

methods for Spavinaw Creek near Colcord, Oklahoma, and Beaty Creek near Jay, Okla., 2006–10.
44 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

INSTC regression estimate, daily load computed from estimated 

concentrations from a regression using physical water-quality 

constituents, streamflow, seasonality.

DML regression estimate, daily load estimated from a regression 

using streamflow seasonality and time.

Spavinaw Creek near Colcord, Okla. (071912213)

November 2004 - December 2010

Beaty Creek near Jay, Okla. (07191222)

March 2005 - December 2010

0.1 1 10 100

Total suspended-sediment load, in pounds per day

100,000,000

10,000,000

1,000,000

100,000

10,000

1,000

100

10

1

100,000,000

10,000,000

1,000,000

100,000

10,000

1,000

100

10

1

0.1

DML regression estimate

INST regression estimate C

Probability of exceedance, in percent

Figure 21. Comparison of duration curves for estimated daily suspended-sediment loads at Spavinaw Creek near Colcord, Oklahoma, 

and Beaty Creek near Jay, Okla., streamflow-gaging stations using two regression methods. 
Streamflows, Loads, and Instantaneous Concentrations in the Eucha-Spavinaw Basin, 2002–10 45

Alternate INSTC sediment regressions that did not 

incorporate physical constituent data values produced poorer 

fits to field data than INSTC sediment regressions, especially 

for the Colcord station. For the Colcord station, turbidity is 

a substantially better estimator of sediment than streamflow. 

Streamflow was not a statistically significant estimator of 

sediment when turbidity was included in the regression. The 

R2

 of the alternate INSTC sediment regression was 0.549 

compared to 0.830 for the INSTC sediment regression for the 

Colcord station. Use of turbidity as an independent variable 

improved the fit for the INSTC sediment regression for the 

Beaty Creek station but to a lesser extent for the Colcord 

station. The R2

 of the alternate INSTC sediment regression was 

0.632 compared to 0.757 for INSTC sediment regression for 

the Beaty Creek station. Graphs of measured and estimated 

nitrogen concentrations for the INSTC sediment regressions at 

both stations indicated closer distributions of scatter about the 

one-to-one line compared to the alternate INSTC regressions 

(fig. 22). Several substantial outliers on the alternate INSTC

sediment regression for both stations may have caused poorer 

fit of those regressions. 

Large differences in daily, annual, and mean annual 

loads between regression methods may be caused by 

differences in streamflow-estimated sediment load (DML

regression) compared to turbidity-estimated sediment load 

(INSTC regression). Differences in fit between turbidity-based 

INSTC regressions and alternate streamflow-based INSTC

regressions indicate that the turbidity-based regression (the 

INSTC regression) produced a better fit of load estimate 

than the DML regression. One possible explanation for 

overestimation of sediment load from the DML regression is 

that during large runoff, streamflow is sustained for a longer 

period of time than turbidity values, causing larger estimates 

of sediment load from streamflow than from turbidity as 

described by Rasmussen and others (2005), which compared 

streamflow-based sediment regressions to turbidity-based 

sediment regressions. 

A B

0 400 800 1,200 1,600 0 400 800 1,200 1,600

1:1 Line

Estimated suspended-sediment concentration, 

in milligrams per liter

Measured suspended-sediment concentration, 

in milligrams per liter

2,500

2,000

1,500

1,000

500

0

1,600

1,400

1,200

1,000

800

600

400

200

0

Beaty Creek near Jay,

Okla. (07191222)

Beaty Creek near Jay,

Okla. (07191222)

Spavinaw Creek near Colcord,

Okla. (071912213)

Spavinaw Creek near Colcord,

Okla. (071912213)

Figure 22. Comparison of measured and regression-estimated suspended-sediment concentrations from (A) INSTC regressions based 

on physical water-quality constituents, streamflow, and seasonality as independent variables and (B) alternate INSTC

 regressions based 

on streamflow and seasonality as independent variables.
46 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Evaluation of Temporal Trends in 

Nitrogen, Phosphorus, and Sediment 

Concentrations in the Eucha-Spavinaw 

Basin, 2002–10

City of Tulsa staff, members of the TMUA Board, and 

other parties wish to know whether BMPs and other measures 

have led to improvements in water quality in the EuchaSpavinaw basin. Millions of dollars have been spent to more 

effectively control discharges of nitrogen and phosphorus 

compounds from point and nonpoint sources in the basin and 

in treating drinking water to remove algal chemicals.

No statistically significant temporal trends were detected 

for flow-adjusted nitrate plus nitrite-nitrogen or total nitrogen 

concentrations at the five stations. However, there were 

significant trends in phosphorus concentrations at all stations 

(table 10, figs. 23-27). Significant downward trends in baseflow phosphorus concentrations were detected at all Spavinaw 

Creek stations except for the Maysville station, where a slight 

upward trend (less than 0.01 mg/L/yr) was detected. No trend 

was detected for base-flow phosphorus concentrations at 

the Beaty Creek station. Significant downward trends were 

detected in the phosphorus concentration of runoff samples 

at all Spavinaw Creek stations except for the Maysville 

station, where no trend was detected. A slight upward trend 

for phosphorus concentration (0.01 mg/L/yr, 4.17 percent per 

year) was observed in runoff samples from the Beaty Creek 

station. Significant upward trends in phosphorus generally 

were less than significant downward trends in phosphorus. 

A significant upward trend in phosphorus concentrations 

from base-flow samples occurred at the Maysville station on 

Spavinaw Creek (3.5 percent per year), whereas, significant 

downward trends in phosphorus concentrations ranged from 

-2.0 to -12.5 percent per year for base-flow samples and 

from -5.40 to -12.9 percent per year for runoff samples 

(table 10). There were significant downward trends in 

phosphorus concentrations in base-flow and runoff samples 

collected at the Spavinaw Creek near Cherokee City, 

Sycamore, and Colcord, Okla., streamflow-gaging stations 

(-4.9 to -12.9 percent per year).

Significant trends in sediment concentrations varied by 

station and stream. There were significant downward trends in 

sediment concentration during runoff conditions ranging from 

-1.53 to -1.81 percent per year at the Maysville, Sycamore, 

and Beaty Creek stations but no significant trends in sediment 

concentration during runoff conditions at the Cherokee City or 

Colcord stations (table 10, figs. 28-30).

Decreased phosphorus content of effluent from the 

Decatur wastewater-treatment plant following upgrades to 

the plant in 2006 may have contributed to downward trends 

in phosphorus concentrations at the three closest downstream 

Spavinaw Creek stations. However, the downward trend in 

phosphorus concentration began prior to the changes in the 

Decatur wastewater-treatment plant. The trend slopes for baseflow and runoff components of total phosphorus concentration 

at the Cherokee City station (fig. 24), the station nearest to 

the Decatur wastewater-treatment plant, were larger (-0.02 

and -0.03 mg/L/year, respectively) than the trend slopes 

of phosphorus concentrations at the downstream stations 

(table 10). Decreases in phosphorus concentrations during 

runoff as well as base-flow conditions also were measured 

at the stations further downstream from the wastewatertreatment plants. In streams affected by wastewater discharge, 

streambed sediments can act as phosphorus storage zones 

(Haggard and others, 2001) and are a source of phosphorus to 

downstream locations (Reddy and others, 1999; Haggard and 

Stoner, 2009). Therefore, mobilization of streambed sediments 

during runoff conditions may coincide with transport of 

phosphorus sorbed to those sediments. Decreased phosphorus 

concentrations in runoff samples may have been caused by 

decreases in phosphorus content of sediments in Columbia 

Hollow downstream from the plant (fig. 1). However, the 

largest decreases in phosphorus concentrations occurred 

prior to reductions in phosphorus from the Decatur 

wastewater-treatment plant in 2006, which indicates that the 

observed trends are not solely explained by improvements to 

the plant (figs. 24-26).

Other possible explanations for significant downward 

trends in phosphorus may be consequences of BMP 

implementation and reduction in poultry-litter applications, 

but these explanations were not supported by the trend 

analysis because downward trends in phosphorus 

concentrations were not observed at the Maysville or Beaty 

Creek stations (figs. 23 and 27), even though BMPs were 

implemented in the basins upstream from those stations. 

BMPs were not implemented in much of the Spavinaw basin 

until 2003. BMPs were implemented in the Beaty Creek 

basin in 1998; however, a slight upward trend in phosphorus 

concentration was detected for that station (fig. 27, table 10).

Runoff samples collected at the Beaty Creek station 

had a statistically significant upward trend in phosphorus 

concentrations and a significant downward trend in sediment 

concentration (table 10), indicating that the amount of 

phosphorus sorbed to sediment during runoff may have 

increased with time even though sediment concentrations 

decreased or that the dissolved component of phosphorus 

increased relative to the sediment-sorbed component. BMPs 

implemented in Beaty Creek basin from 1998 to 2003 may 

have caused decreases in sediment transport from hilltops or 

streambanks. However, BMPs may not have caused decreases 

in phosphorus concentrations because long-term phosphorus 

storage in channel sediments may be a persistent source of 

phosphorus in the future (Phillips and others, 2005). 
Evaluation of Temporal Trends in Nitrogen, Phosphorus, and Sediment Concentrations in the Eucha-Spavinaw Basin, 2002–10 47

Table 10. Results of Kendall’s tau and Seasonal Kendall tests of time trends of concentrations of nitrate plus nitrite, total nitrogen, total 

phosphorus, and suspended sediment in water samples collected at streamflow-gaging stations in the Eucha-Spavinaw basin, Arkansas 

and Oklahoma, 2002–10.

[Tau, Kendall’s tau; P-Value, probability level; SK, Seasonal Kendall trend test; KT, Kendall-Thiel trend test; results shaded in blue are statistically significant 

upward trends at a p-value of 0.05; results shaded in green are statistically significant downward trends at a p-value of less than or equal to 0.05; --, not reported] 

Constituent

Base flow Runoff

Trend 

test1

Flow 

adjustment2 Tau

pvalue

Slope 

(mg/L/

yr)

Slope 

(percent/yr)

Trend 

test1

Flow 

adjustment2 Tau

PvalueSlope 

(mg/L/yr)

Slope 

(percent/yr)

Spavinaw Creek near Maysville, Ark. (07191160)

Total nitrate plus 

nitrite SK yes -0.074 0.631 -- -- SK no 0.230 0.213 -- --

Total nitrogen SK yes -0.015 0.955 -- -- SK yes 0.149 0.393 -- --

Total phosphorus SK no +0.313 0.020 <0.01 +3.5 SK yes 0.080 0.649 -- --

Suspended 

sediment not analyzed KT yes -0.280 0.009 -2.7 -1.53

Spavinaw Creek near Cherokee City, Ark. (07191179)

Total nitrate plus 

nitrite SK yes -0.203 0.309 -- -- SK yes 0.192 0.168 -- --

Total nitrogen SK yes -0.188 0.325 -- -- SK yes 0.131 0.386 -- --

Total phosphorus SK yes -0.800 0.003 -0.02 -12.5 SK yes -0.613 0.006 -0.03 -12.9

Suspended 

sediment not analyzed KT yes -0.112 0.303 -- --

Spavinaw Creek near Sycamore, Okla. (07191220)

Total nitrate plus 

nitrite KT yes -0.027 0.814 -- -- SK yes 0.218 0.118 -- --

Total nitrogen KT yes -0.026 0.825 -- -- SK yes 0.172 0.179 -- --

Total phosphorus KT no -0.604 <0.001 <0.01 -2.0 SK yes -0.540 0.027 -0.01 -5.40

Suspended 

sediment not analyzed KT yes -0.251 0.023 -2.7 -1.81

Spavinaw Creek near Colcord, Okla. (071912213)

Total nitrate plus 

nitrite SK yes -0.233 0.201 -- -- SK yes 0.161 0.098 -- --

Total nitrogen SK yes -0.267 0.168 -- -- SK yes 0.097 0.579 -- --

Total phosphorus SK no -0.451 0.010 <0.01 -4.9 SK yes -0.441 0.016 -0.02 -6.53

Suspended 

sediment not analyzed KT yes -0.159 0.092 --

Beaty Creek near Jay, Okla. (07191222)

Total nitrate plus 

nitrite SK yes 0.086 0.681 -- -- SK yes 0.213 0.234 -- --

Total nitrogen SK yes 0.061 0.812 -- -- SK yes 0.191 0.224 -- --

Total phosphorus SK yes 0.357 0.055 -- -- SK yes +0.330 0.039 +0.01 +4.17

Suspended 

sediment not analyzed KT yes -0.270 0.004 -1.5 -1.59

1

 Kendall-Thiel trend test used when adequate seasons could not be defined for use in Seasonal Kendall trend test according to standard thresholds discussed in 

Schertz and others (1991).

2

 Flow-adjustment was only applied if concentrations in the given dataset were significantly correlated to streamflow at the time of sample collection at a 

p-value of less than or equal to 0.05.
48 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Spavinaw Creek near Maysville, Ark. (07191160)

Base-flow samples

Runoff samples

LOESS trend line for base-flow samples

LOESS trend line for runoff samples

75th percentile of

flow-weighted phosphorus

concentrations from

relatively undeveloped

basins of the United States

(Clark and others, 2000)

Spavinaw Creek near Maysville, Ark. (07191160)

Runoff Samples1

1

Total phosphorus concentrations from base-flow samples were not flow-adjusted.

Year

0.1

1.0

0.02

1.0

2.0

0.0

-1.0

-2.0

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

2.0

Total phosphorus concentration, 

in milligrams per liter as phosphorus

Total phosphorus concentration residuals from LOESS

regression, in natural log of milligrams per liter as phosphorus

A

B

Figure 23. Phosphorus concentrations and LOESS trend lines at Spavinaw Creek near Maysville, Arkansas, showing (A) total 

phosphorus concentrations with time, and (B) flow-adjusted total phosphorus concentrations (error residuals) from a LOESS regression.
Evaluation of Temporal Trends in Nitrogen, Phosphorus, and Sediment Concentrations in the Eucha-Spavinaw Basin, 2002–10 49

Spavinaw Creek near Cherokee City, Ark. (07191179)

Spavinaw Creek near Cherokee City, Ark. (07191179)

Base-flow samples

Runoff samples

LOESS trend line for base-flow samples

LOESS trend line for runoff samples

Year

0.1

1.0

2.0

0.02

75th percentile of flow-weighted phosphorus concentrations from relatively

undeveloped basins of the United States (Clark and others, 2000)

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

1.0

2.0

0.0

-1.0

-2.0

Total phosphorus concentration, 

in milligrams per liter as phosphorus

Total phosphorus concentration residuals from LOESS

regression, in natural log of milligrams per liter as phosphorus

A

B

Figure 24. Total phosphorus concentrations and LOESS trend lines at Spavinaw Creek near Cherokee City, Arkansas, showing (A) total 

phosphorus concentrations with time, and (B) flow-adjusted total phosphorus concentrations (error residuals) from a LOESS regression.
50 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Spavinaw Creek near Sycamore, Okla. (07191220)

Base-flow samples

Runoff samples

LOESS trend line for base-flow samples

LOESS trend line for runoff samples

0.1

1.0

2.0

0.02

75th percentile of flow-weighted phosphorus concentrations from relatively

undeveloped basins of the United States (Clark and others, 2000)

1.0

2.0

0.0

-1.0

-2.0

Spavinaw Creek near Sycamore, Okla. (07191220)

Total phosphorus concentrations from base-flow samples were not flow adjusted.

Year

2002 2003 2004 2005 2006 2007 2008 2009 2010

Total phosphorus concentration, 

in milligrams per liter as phosphorus

Total phosphorus concentration residuals from LOESS

regression, in natural log of milligrams per liter as phosphorus

A

B

Runoff Samples1

1

Figure 25. Total phosphorus concentrations and LOESS trend lines at Spavinaw Creek near Sycamore, Oklahoma, showing (A) total 

phosphorus concentrations with time, and (B) flow-adjusted total phosphorus concentrations (error residuals) from a LOESS regression.
Evaluation of Temporal Trends in Nitrogen, Phosphorus, and Sediment Concentrations in the Eucha-Spavinaw Basin, 2002–10 51

Spavinaw Creek near Colcord, Okla. (071912213)

Base-flow samples

Runoff samples

LOESS trend line for base-flow samples

LOESS trend line for runoff samples

Year

0.1

1.0

0.02

75th percentile of flow-weighted phosphorus 

concentrations from relatively undeveloped 

basins of the United States (Clark and others, 2000)

1.0

2.0

0.0

-1.0

-2.0

Spavinaw Creek near Colcord, Okla. (071912213)

Runoff Samples1

1 Total phosphorus concentrations from base-flow samples were not flow adjusted.

2002 2003 2004 2005 2006 2007 2008 2009 2010

2.0

Total phosphorus concentration, 

in milligrams per liter as phosphorus

Total phosphorus concentration residuals from LOESS

regression, in natural log of milligrams per liter as phosphorus

A

B

Figure 26. Total phosphorus concentrations and LOESS trend lines at Spavinaw Creek near Colcord, Oklahoma, showing (A) total 

phosphorus concentrations with time, and (B) flow-adjusted total phosphorus concentrations (error residuals) from a LOESS regression.
52 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Beaty Creek near Jay, Okla. (07191222)

Base-flow samples

Runoff samples

LOESS trend line for base-flow samples

LOESS trend line for runoff samples

Year

0.1

1.0

2.0

75th percentile of flow-weighted

phosphorus concentrations from

relatively undeveloped basins 

of the United States (Clark and 

others, 2000)

1.0

2.0

0.0

-1.0

-2.0

Beaty Creek near Jay, Okla. (07191222)

0.01

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Total phosphorus concentration, 

in milligrams per liter as phosphorus

Total phosphorus concentration residuals from LOESS

regression, in natural log of milligrams per liter as phosphorus

A

B

Figure 27. Total phosphorus concentrations and LOESS trend lines at Beaty Creek near Jay, Oklahoma, showing (A) total phosphorus 

concentrations with time, and (B) flow-adjusted total phosphorus concentrations (error residuals) from a LOESS regression.
Evaluation of Temporal Trends in Nitrogen, Phosphorus, and Sediment Concentrations in the Eucha-Spavinaw Basin, 2002–10 53

Figure 28. Suspended-sediment concentrations and LOESS trend lines at Spavinaw Creek near Maysville, Arkansas, showing 

(A) suspended-sediment concentrations with time, and (B) flow-adjusted suspended-sediment concentrations (error residuals) from a 

LOESS regression.

2002 2003 2004 2005 2006 2007 2008 2009 2010

-3

-2

-1

0

1

2

Spavinaw Creek near Maysville, Ark. (07191160) Runoff Samples

Spavinaw Creek near Maysville, Ark. (07191160) Runoff Samples

1

10

100

1,000

3,000

LOESS Trend Line

Year

Suspended-sediment, in milligrams per liter Suspended-sediment concentration residuals from LOESS

regression, in natural log of milligrams per liter

A

B
54 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

Spavinaw Creek near Sycamore, Okla. (07191220) Runoff Samples

LOESS trend line

Year

2002 2003 2004 2005 2006 2007 2008 2009 2010

-1

0

1

Spavinaw Creek near Sycamore, Okla. (07191220) Runoff Samples

1

10

100

1,000

3,000

2

-2

Suspended-sediment, in milligrams per liter Suspended-sediment concentration residuals from LOESS

regression, in natural log of milligrams per liter

A

B

Figure 29. Suspended-sediment concentrations and LOESS trend lines at Spavinaw Creek near Sycamore, Oklahoma, showing 

(A) suspended-sediment concentrations with time, and (B) flow-adjusted suspended-sediment concentrations (error residuals) from a 

LOESS regression.
Evaluation of Temporal Trends in Nitrogen, Phosphorus, and Sediment Concentrations in the Eucha-Spavinaw Basin, 2002–10 55

Beaty Creek near Jay, Okla. (07191222) Runoff Samples

1

10

100

1,000

3,000

LOESS Trend Line

Beaty Creek near Jay, Okla. (07191222) Runoff Samples

2002 2003 2004 2005 2006 2007 2008 2009 2010

-2

-1

0

1

2

3

Suspended-sediment, in milligrams per liter Suspended-sediment concentraton residuals from LOESS regression, in natural log of milligrams per liter

-3

4

Year

2011

A

B

Figure 30. Suspended-sediment concentrations and LOESS trend lines at Beaty Creek near Jay, Oklahoma, showing (A) suspendedsediment concentrations with time, and (B) flow-adjusted suspended-sediment concentrations (error residuals) from a LOESS egression.
56 Nitrogen, Phosphorus, and Suspended Sediment in the Eucha-Spavinaw Basin, 2002–10

The significant upward trend in phosphorus 

concentrations in base-flow samples at the Maysville station 

could not be easily explained because there are no known 

substantial point sources of nitrogen and phosphorus upstream 

from this station, and increases in BMP implementation 

and reduction in poultry-litter application started in this 

basin in 2003–04. Similar to upward trends in phosphorus 

concentrations from runoff samples at Beaty Creek, long-term 

phosphorus storage in channel sediments may have served as a 

source of phosphorus in this stream.

Significant decreases in sediment concentrations at the 

Maysville, Sycamore, and Beaty Creek stations (figs. 28-30, 

table 10) indicated that BMPs may have reduced erosion of 

hillslopes and streambanks. However, because there were no 

significant trends in sediment concentration at the Cherokee 

City and Colcord stations, changes in sediment transport 

caused by BMPs probably were variable and affected by local 

sediment erosion and deposition in Spavinaw Creek. Because 

no significant trends in sediment concentrations were observed 

for the Colcord station, the flow-adjusted sediment load to 

Lake Eucha contributed from Spavinaw Creek may not have 

decreased over the study period. However, because a majority 

of the sediment load to Lake Eucha may have been contributed 

from the Beaty Creek basin (table 5), flow-adjusted sediment 

contributions to Lake Eucha may have decreased over the 

study period.

Summary

The City of Tulsa, Oklahoma, uses Lake Eucha and 

Spavinaw Lake in the Eucha-Spavinaw basin in northwestern 

Arkansas and northeastern Oklahoma for public water supply. 

The City has spent millions of dollars from 1998 through 2005 

to eliminate taste and odor problems in the drinking water 

from the Eucha-Spavinaw system that have been attributed 

to blue-green algae. Increases in algal biomass in the lakes 

may be caused by increases in nitrogen and phosphorus 

concentrations in the lakes derived from streams discharging 

to the lakes. 

In July 2001, the U.S. Geological Survey, in cooperation 

with the city of Tulsa supplemented monthly water-quality 

sampling with six runoff samplings per year for four stations 

on Spavinaw Creek and one station on Beaty Creek to better 

characterize water-quality conditions over the range of 

streamflows in the basin.

Daily mean load (DML) regression equations were 

developed using data collected from 2002–10 to estimate 

nitrogen, sediment, and phosphorus loads and yields at the 

five streamflow-gaging stations in the basin. Instantaneous 

nitrogen, phosphorus, and sediment concentrations were 

estimated from regression equations (instantaneous-continuous 

or INSTC regressions). INSTC regressions were developed 

to estimate real-time nitrogen, phosphorus, and sediment 

concentrations using continuous measurements of physical 

water-quality constituents and streamflow in conjunction 

with periodic water-quality samples from 2004–10 for the 

Beaty Creek and Colcord stations. INSTC regressions also 

were used to estimate daily and annual load for these three 

constituents. Daily, annual, and mean annual loads estimated 

from these two regression methods were compared for the 

Beaty and Colcord stations for 2005–10. DML regressions 

for nitrogen and phosphorus had better fit to field data than 

DML regressions for sediment for all stations as indicated 

by coefficient of determination (R2

) values. Differences in 

nitrogen and phosphorus loads and yields were similar to those 

reported for the period 2002-09 in the basin. The range in 

the runoff component of the mean annual total nitrogen load 

was 66 to 71 percent for the Spavinaw Creek stations and 87 

percent for Beaty Creek. The range in the runoff component 

of the mean annual total phosphorus load was 78 to 92 percent 

for the Spavinaw Creek stations and 97 percent for Beaty 

Creek. The range in the runoff component of the mean annual 

total sediment load was 96 to 99 percent for the Spavinaw 

Creek stations and 100 percent for Beaty Creek. Runoff 

components of nitrogen and phosphorus were about 1 to 2 

percent less for 2002–10 than those in 2002–09. 

As estimated from the DML regression, Spavinaw Creek 

and Beaty Creek contributed a mean annual total nitrogen load 

of 1,640,000 pounds per year (lbs/yr), a mean annual total 

phosphorus load of 100,000 lbs/yr, and a mean annual total 

sediment load of 116,000,000 lbs/yr to Lake Eucha. Annual 

nitrogen and phosphorus loading to Lake Eucha computed 

from 2002–10 were 2.5 to 7.8 percent less than from 2002–09, 

indicating that nitrogen and phosphorus loads in 2010 were 

less than average compared to 2002–09.

Comparison of load-estimation equations indicated 

that daily, annual, and mean annual load estimates varied 

substantially depending on the independent variables used to 

develop regressions and on streamflow conditions. Fit cannot 

be compared between the DML and INSTC regressions using 

the changes in R2

, but alternate INSTC regressions that used 

streamflow and seasonality indicated potential differences 

in fit between the regression methods. For all nitrogen, 

phosphorus, and sediment at both stations, concentrations 

estimated from INSTC regressions fit the field data better than 

estimates from alternate INSTC regressions as indicated by R2

and root-mean-square error (RMSE). 

Mean annual nitrogen loads computed by both types 

of regression methods were not substantially different for 

the Beaty Creek and Colcord stations (within 2 percent). 

Mean annual total phosphorus loads were not substantially 

different between regression methods for both stations. The 

DML regression may have substantially underestimated 

phosphorus load at the Colcord station in wet years because 

of poorer fit and use of daily mean streamflow, which may 
References Cited 57

have underestimated loads during peak-flow conditions. Mean 

annual total sediment loads estimated from the DML regression 

were substantially greater than those estimated from the 

INSTC regression for both stations. The relative percent 

differences between those two types of regression estimates 

mean annual total sediment loads at the Colcord station were 

-38.6 percent for the Colcord station and -122.7 percent 

for the Beaty Creek station. The DML regression may have 

substantially overestimated sediment load at both stations in 

wet years, which notably affected computation of mean annual 

phosphorus load.

Trends in flow-adjusted nitrate-nitrate, nitrogen, 

phosphorus, and sediment concentrations were analyzed for 

the five stations for the period 2002–10. Significant temporal 

trends were not detected for nitrate plus nitrite-nitrogen or 

total nitrogen concentrations for either flow condition at 

any of the stations. Significant upward trends in phosphorus 

concentrations were observed for the Maysville station for 

base-flow samples and for runoff samples from the Beaty 

Creek station and ranged from 3.5 to 4.2 percent per year. 

Significant downward trends in phosphorus concentrations 

from base-flow and runoff samples were observed for the 

Cherokee City, Sycamore, and Colcord stations and ranged 

from -4.9 to -12.9 percent per year. No significant downward 

trends in sediment concentration were observed for the 

Maysville, Sycamore, and Beaty Creek stations, which ranged 

from -1.5 to -1.8 percent per year, and no significant trends in 

sediment concentration were observed for the Cherokee City 

or Colcord stations.

Reduction in phosphorus discharges from the Decatur, 

Arkansas, wastewater-treatment plant following upgrades to 

the plant in 2006 may have contributed to downward trends 

in phosphorus concentrations at the three closest Spavinaw 

Creek stations downstream from the plant. However, the 

largest decreases in phosphorus concentrations took place 

prior to reduction in phosphorus discharges in 2006. Causes 

of downward trends in phosphorus concentrations at the 

downstream Spavinaw Creek stations prior to changes in the 

wastewater-treatment plant in 2006 and implementation of 

best management practices in 2003 to 2004 are unknown.

Significant upward trends in phosphorus concentrations 

and significant downward trends in sediment concentrations 

at the Beaty Creek station were observed for runoff samples, 

indicating that the amount of phosphorus adsorbed to sediment 

transported during runoff may have increased with time 

even though sediment concentrations decreased. Factors 

contributing to a significant upward trend in phosphorus 

concentration in base-flow samples from the Maysville station 

were unknown. Decreases in sediment concentrations at the 

Maysville, Sycamore, and Beaty Creek stations indicate that 

best management practices may have contributed to local 

decreases in sediment erosion.

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