Prepared in cooperation with the city of Wichita, Kansas

Model Documentation for Relations Between Continuous 

Real-Time and Discrete Water-Quality Constituents in 

the North Fork Ninnescah River Upstream from Cheney 

Reservoir, South-Central Kansas, 1999–2009

Open-File Report 2013–1014

U.S. Department of the Interior

U.S. Geological Survey

Model Documentation for Relations 

Between Continuous Real-Time and 

Discrete Water-Quality Constituents in the 

North Fork Ninnescah River Upstream from 

Cheney Reservoir, South-Central Kansas, 

1999–2009

By Mandy L. Stone, Jennifer L. Graham, and Jackline W. Gatotho

Prepared in cooperation with the city of Wichita, Kansas

Open-File Report 2013–1014

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: 2013

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Suggested citation:

Stone, M.L., Graham, J.L., and Gatotho, J.W., 2013, Model documentation for relations between continuous real-time 

and discrete water-quality constituents in the North Fork Ninnescah River upstream from Cheney Reservoir, southcentral Kansas, 1999–2009: U.S. Geological Survey Open-File Report 2013–1014, 101 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................1

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

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

Continuous Water-Quality Monitoring...............................................................................................2

Discrete Water-Quality Samples........................................................................................................2

Quality Assurance and Quality Control .............................................................................................3

Development of Regression Models to Compute Constituent Concentrations .........................4

Results of Regression Analysis for Selected Constituents.....................................................................5

Summary .....................................................................................................................................................100

References Cited........................................................................................................................................100

Figures

1. Map showing location of continuous real-time water-quality monitoring station 

and land use in the Cheney Reservoir watershed ..................................................................3

2. S+® output of regression model development using specific conductance (SC) as

an explanatory variable for dissolved solids (DS) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................40

3. S+® output graphs from simple linear regression analysis showing A,

log-transformed specific conductance (SC) versus log-transformed dissolved

solids (DS) concentrations; B, computed versus actual DS concentrations; C,

computed log-transformed DS concentrations versus regression residuals; and 

D, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................41

4. S+® output of regression model development using streamflow (Q) as an

explanatory variable for dissolved solids (DS) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................42

5. S+® output graphs from simple linear regression analysis showing A,

log-transformed streamflow (Q) versus log-transformed dissolved solids (DS)

concentrations; B, computed versus actual DS concentrations; C, computed

log-transformed DS concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................43
iv

6. S+

® output of regression model development using streamflow (Q) and specific 

conductance (SC) as explanatory variables for calcium (CA) concentrations for the

North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................44

7. S+

® output graphs from simple linear regression analysis using streamflow (Q)

and specific conductance (SC) as explanatory variables for calcium (CA) showing A, computed versus actual CA concentrations; B, computed log-transformed CA

concentrations versus regression residuals; and C, standard normal quantiles

versus regression residuals for the North Fork Ninnescah River upstream from

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009 ..................45

8. S+

® output of regression model development using specific conductance (SC) as

an explanatory variable for magnesium (MG) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................46

9. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed specific conductance (SC) versus log-transformed magnesium

(MG) concentrations; B, computed versus actual MG concentrations; C, computed

log-transformed MG concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................47

10. S+

® output of regression model development using specific conductance (SC) as

an explanatory variable for sodium (NA) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................48

11. S+

® output graphs of simple linear regression analysis showing 

A,

log-transformed specific conductance (SC) versus log-transformed sodium (NA)

concentrations; B, computed versus actual NA concentrations; C, computed

log-transformed NA concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................49

12. S+

® output of regression model development using streamflow (Q) as an

explanatory variable for sodium (NA) concentrations for the North Fork Ninnescah

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................50

13. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed streamflow (Q) versus log-transformed sodium (NA)

concentrations; B, computed versus actual NA concentrations; C, computed

log-transformed NA concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 071447800), south-central Kansas, 1999

through 2009 ................................................................................................................................51

14. S+

® output of regression model development using specific conductance (SC) 

as an explanatory variable for chloride (CL) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................52
v

15. S+

® output graphs from simple linear regression showing 

A, log-transformed 

specific conductance (SC) versus log-transformed chloride (CL) concentrations; B, computed versus actual CL concentrations; C, computed log-transformed CL 

concentrations versus regression residuals; and D, standard normal quantiles versus 

regression residuals for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.................................53

16. S+

® output of regression model development using streamflow (Q) as the

explanatory variable for chloride (CL) concentrations for the North Fork Ninnescah

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................54

17. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed streamflow (Q) versus log-transformed chloride (CL)

concentrations; B, computed versus actual CL concentrations; C, computed

log-transformed CL concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................55

18. S+

® output of regression model development using specific conductance (SC) as

an explanatory variable for potassium (K) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................56

19. S+

® output graphs from simple linear regression analysis using specific

conductance (SC) and log-transformed SC as explanatory variables for potassium

(K) concentrations showing A, computed versus actual K concentrations; B,

computed log-transformed K concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................57

20. S+

® output of regression model development using specific conductance (SC) as

an explanatory variable for sulfate (SO4) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................58

21. S+

® output graphs from simple linear regression analysis showing 

A, specific

conductance (SC) versus sulfate (SO4) concentrations; B, computed versus actual

SO4 concentrations; C, computed SO4 concentrations versus regression residuals;

and D, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................59

22. S+

® output of regression model development using streamflow (Q) as an

explanatory variable for sulfate (SO4) concentrations for the North Fork Ninnescah

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................60

23. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed streamflow (Q) versus sulfate (SO4) concentrations; B, computed

versus actual SO4 concentrations; C, computed SO4 concentrations versus

regression residuals; and D, standard normal quantiles versus regression residuals

for the North Fork Ninnescah River upstream from Cheney Reservoir (site

07144780), south-central Kansas, 1999 through 2009............................................................61
vi

24. S+

® output of regression model development using streamflow (Q) and specific

conductance (SC) as explanatory variables for alkalinity (ALK) concentrations for

the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................62

25. S+

® output graphs from simple linear regression analysis using streamflow (Q) 

and specific conductance (SC) as explanatory variables for alkalinity (ALK) 

concentrations showing A, computed versus actual ALK concentrations; B, 

computed log-transformed ALK concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central 

Kansas, 1999 through 2009 ........................................................................................................63

26. S+

® output of regression model development using streamflow (Q) and specific

conductance (SC) as explanatory variables for bicarbonate (HCO3) concentrations

for the North Fork Ninnescah River upstream from Cheney Reservoir (site

07144780), south-central Kansas, 1999 through 2009............................................................64

27. S+

® output graphs from simple linear regression analysis using streamflow (Q)

and specific conductance (SC) as explanatory variables for bicarbonate (HCO3)

concentrations showing A, computed versus actual HCO3 concentrations; B,

computed log-transformed HCO3 concentrations versus regression residuals, and C, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................65

28. S+

® output of regression model development using turbidity (TBY) as an

explanatory variable for total suspended solids (TSS) concentrations for the North

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................66

29. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed turbidity (TBY) versus log-transformed total suspended solids

(TSS) concentrations; B, computed versus actual TSS concentrations; C, computed

log-transformed TSS concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................67

30. S+

® output of regression model development using streamflow (Q) as an

explanatory variable for total suspended solids (TSS) concentrations for the North

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................68

31. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed streamflow (Q) versus log-transformed total suspended solids

(TSS) concentrations; B, computed versus actual TSS concentrations; C, computed

log-transformed TSS concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................69

32. S+

® output of regression model development using streamflow (Q) and turbidity

(TBY) as explanatory variables for suspended-sediment concentrations (SSC) for

the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................70
vii

33. S+

® output graphs from simple linear regression analysis using streamflow (Q)

and turbidity (TBY) as explanatory variables for suspended-sediment

concentrations (SSC) showing A, computed versus actual SSC concentrations; 

B, computed log-transformed SSC versus regression residuals; and C, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................71

34. S+

® output of regression model development using streamflow (Q) as an

explanatory variable for suspended-sediment concentrations (SSC) for the North

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................72

35. S+

® output graphs from simple linear regression analysis showing 

A, logtransformed streamflow (Q) versus log-transformed suspended-sediment 

concentrations (SSC); B, computed versus actual SSC concentrations; C, computed 

log-transformed SSC versus regression residuals; and D, standard normal quantiles 

versus regression residuals for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009 ..................73

36. S+

® output of regression model development using season (SIN and COS) and

turbidity (TBY) as explanatory variables for total nitrogen (TN) concentrations for

the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................74

37. S+

® output graphs from simple linear regression analysis using season (SIN and

COS) and turbidity (TBY) as explanatory variables for total nitrogen (TN)

concentrations showing A, computed versus actual TN concentrations; B,

computed log-transformed TN concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................75

38. S+

® output of regression model development using season (SIN and COS) and

turbidity (TBY) as explanatory variables for total nitrogen (TN) concentrations for

the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................76

39. S+

® output graphs from simple linear regression analysis using season (SIN and

COS) and streamflow (Q) as explanatory variables for total nitrogen (TN)

concentrations showing A, computed versus actual TN concentrations; B,

computed log-transformed TN concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................77

40. S+

® output of regression model development using turbidity (TBY) as an

explanatory variable for total Kjeldahl nitrogen (TKN) concentrations for the North

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................78

41. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed turbidity (TBY) versus log-transformed total Kjeldahl nitrogen

(TKN) concentrations; B, computed versus actual TKN concentrations; C,

computed log-transformed TKN concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork

Ninnescah River upstream from Cheney reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................79
viii

42. S+

® output of regression model development using turbidity (TBY) and specific

conductance (SC) as explanatory variables for organic nitrogen (ON)

concentrations for the North Fork Ninnescah River upstream from Cheney

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.................................80

43. S+

® output graphs from simple linear regression analysis using turbidity (TBY)

and specific conductance (SC) as explanatory variables for organic nitrogen (ON)

concentrations showing A, computed versus actual ON concentrations; B,

computed ON concentrations versus regression residuals; and C, standard normal

quantiles versus regression residuals for the North Fork Ninnescah River upstream

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.........81

44. S+

® output of regression model development using season (SIN and COS) and 

turbidity (TBY) as explanatory variables for nitrate (NO3) concentrations for the 

North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), 

south-central Kansas, 1999 through 2009...............................................................................82

45. S+

® output graphs from simple linear regression analysis using season (SIN and

COS) and turbidity (TBY) as explanatory variables for nitrate (NO3) concentrations

showing A, computed versus actual NO3 concentrations; B, computed NO3

concentrations versus regression residuals; and C, standard normal quantiles

versus regression residuals for the North Fork Ninnescah River upstream from

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009 ..................83

46. S+

® output of regression model development using season (SIN and COS) and

streamflow (Q) as explanatory variables for nitrate (NO3) concentrations for the

North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................84

47. S+

® output graphs from simple linear regression analysis using season (SIN and

COS) and streamflow (Q) as explanatory variables for nitrate (NO3) concentrations

showing A, computed versus actual NO3 concentrations; B, computed NO3

concentrations versus regression residuals; and C, standard normal quantiles

versus regression residuals for the North Fork Ninnescah River upstream from

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009 ..................85

48. S+

® output of regression model development using turbidity (TBY) as an

explanatory variable for total phosphorus (TP) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................86

49. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed turbidity (TBY) versus log-transformed total phosphorus (TP)

concentrations; B, computed versus actual TP concentrations; C, computed

log-transformed TP concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................87

50. S+

® output of regression model development using streamflow (Q) as an

explanatory variable for total phosphorus (TP) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................88

51. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed streamflow (Q) versus total phosphorus (TP) concentrations; B,

computed versus actual TP concentrations; C, computed TP concentrations versus

regression residuals; and D, standard normal quantiles versus regression residuals

for the North Fork Ninnescah River upstream from Cheney Reservoir (site

07144780), south-central Kansas, 1999 through 2009............................................................89
ix

52. S+

® output of regression model development using specific conductance (SC) as

an explanatory variable for orthophosphate (OP) concentrations for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................90

53. S+

® output graphs from simple linear regression analysis showing 

A, specific

conductance (SC) versus orthophosphate (OP) concentrations; B, computed

versus actual OP concentrations; C, computed OP concentrations versus

regression residuals; and D, standard normal quantiles versus regression residuals

for the North Fork Ninnescah River upstream from Cheney Reservoir (site

07144780), south-central Kansas, 1999 through 2009............................................................91

54. S+

® output of regression model development using turbidity (TBY) and specific

conductance (SC) as explanatory variables for fecal coliform bacteria (FC) densities

for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................92

55. S+

® output graphs from simple linear regression analysis using turbidity (TBY) and

specific conductance (SC) as explanatory variables for fecal coliform (FC)

densities showing A, computed versus actual FC densities; B, computed

log-transformed FC densities versus regression residuals; and C, standard normal

quantiles versus regression residuals for the North Fork Ninnescah River upstream

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.........93

56. S+

® output of regression model development using turbidity (TBY) and specific

conductance (SC) as explanatory variables for Escherichia coli bacteria (EC)

densities for the North Fork Ninnescah River upstream from Cheney Reservoir (site

07144780), south-central Kansas, 1999 through 2009............................................................94

57. S+

® output graphs from simple linear regression analysis using turbidity (TBY) and

specific conductance (SC) as explanatory variables for Escherichia coli bacteria

(EC) densities showing A, computed versus actual EC densities; B, computed

log-transformed EC densities versus regression residuals; and C, standard normal

quantiles versus regression residuals for the North Fork Ninnescah River upstream

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.........95

58. S+

® output of regression model development using streamflow (Q) as an

explanatory variable for Escherichia coli bacteria (EC) densities for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................96

59. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed streamflow (Q) versus log-transformed Escherichia coli bacteria

(EC) densities; B, computed versus actual EC densities; C, computed

log-transformed EC densities versus regression residuals; and D, standard normal

quantiles versus regression residuals for the North Fork Ninnescah River upstream

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.........97

60. S+

® output of regression model development using turbidity (TBY) as the

explanatory variable for total organic carbon (TOC) concentrations for the North

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................98

61. S+

® output graphs from simple linear regression analysis showing 

A,

log-transformed turbidity (TBY) versus log-transformed total organic carbon (TOC)

concentrations; B, computed versus actual TOC concentrations; C, computed

log-transformed TOC concentrations versus regression residuals; and D, standard

normal quantiles versus regression residuals for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................99
x

Tables

1. Christensen and others (2006), updated, and new regression models and summary

statistics for continuous concentration computations for the North Fork Ninnescah

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ..................................................................................................................................6

2. Dissolved solids, calcium, magnesium, sodium, and potassium simple linear

regression model datasets for the North Fork Ninnescah River upstream from

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009 ..................13

3. Chloride and sulfate simple linear regression model datasets for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................15

4. Alkalinity and bicarbonate simple linear regression model datasets for the North

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................17

5. Total suspended solids simple linear regression model dataset for the North Fork

Ninnescah River above Cheney Reservoir (site 07144780), south-central Kansas,

1999 through 2009 .......................................................................................................................19

6. Suspended-sediment concentration simple linear regression model dataset for the

North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780),

south-central Kansas, 1999 through 2009...............................................................................21

7. Total nitrogen simple linear regression model dataset for the North Fork Ninnescah

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................23

8. Total Kjeldahl nitrogen simple linear regression model dataset for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................25

9. Organic nitrogen simple linear regression model dataset for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................27

10. Nitrate simple linear regression model dataset for the North Fork Ninnescah River

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999

through 2009 ................................................................................................................................29

11. Total phosphorus simple linear regression model dataset using for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................31

12. Orthophosphate simple linear regression model dataset for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................33

13. Fecal coliform bacteria simple linear regression model dataset for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................35

14. Escherichia coli bacteria simple linear regression model dataset for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................37

15. Total organic carbon simple linear regression model dataset for the North Fork

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central

Kansas, 1999 through 2009 ........................................................................................................38
xi

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Volume

milliliter (mL) 0.0338 ounce, fluid (oz)

cubic foot (ft3) 28.32 cubic decimeter (dm3) 

Flow rate

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

milligram per liter (mg/L) 1 parts per million (ppm)

Mass

milligram (mg) 0.001 gram (g)

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

°F=(1.8×°C)+32

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

°C=(°F-32)/1.8

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

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

25 °C).

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

Abbreviations

adjr2 adjusted R2

Cp Mallow’s Cp

cooksD Cook’s distance

Df degrees of freedom

dfits change in fitted values

F-statistic ratio of the mean square of the regression to the estimated variance

F Value explained variance divided by unexplained variance

Max maximum

Mean Sq mean square

Min minimum

Nvars number of explanatory variables

p-value probability of observing a test statistic that is as extreme or more extreme 

than currently observed assuming that the null hypothesis is true

Pr(F) probability of observing a test statistic that is as extreme or more extreme 

than currently observed assuming that the null hypothesis is true

Pr(>|t|) probability of observing a test statistic that is as extreme or more extreme 

than currently observed assuming that the null hypothesis is true

press prediction error sum of squares

R-squared coefficient of determination (R2

)

resids residuals

Std. Error standard error

Stderr standard error

stnd.res standardized residuals

stud.res studentized residuals

Sum of Sq sum of squares 

t value coefficient divided by its standard error

yhat predicted values

1Q first quartile

3Q third quartile
Model Documentation for Relations Between Continuous 

Real-Time and Discrete Water-Quality Constituents in 

the North Fork Ninnescah River Upstream from Cheney 

Reservoir, South-Central Kansas, 1999–2009

By Mandy L. Stone, Jennifer L. Graham, and Jackline W. Gatotho

Abstract 

Cheney Reservoir in south-central Kansas is one of the 

primary sources of water for the city of Wichita. The North 

Fork Ninnescah River is the largest contributing tributary 

to Cheney Reservoir. The U.S. Geological Survey has operated a continuous real-time water-quality monitoring station 

since 1998 on the North Fork Ninnescah River. Continuously 

measured water-quality physical properties include streamflow, specific conductance, pH, water temperature, dissolved 

oxygen, and turbidity. Discrete water-quality samples were 

collected during 1999 through 2009 and analyzed for sediment, nutrients, bacteria, and other water-quality constituents. 

Regression models were developed to establish relations 

between discretely sampled constituent concentrations and 

continuously measured physical properties to estimate concentrations of those constituents of interest that are not easily 

measured in real time because of limitations in sensor technology and fiscal constraints. 

Regression models were published in 2006 that were 

based on a different dataset collected during 1997 through 

2003. This report updates those models using discrete and continuous data collected during January 1999 through December 

2009. Models also were developed for five new constituents, 

including additional nutrient species and indicator bacteria. 

The water-quality information in this report is important to the 

city of Wichita because it allows the concentrations of many 

potential pollutants of interest, including nutrients and sediment, to be estimated in real time and characterized over conditions and time scales that would not be possible otherwise.

Introduction

Cheney Reservoir (fig. 1), located in south-central Kansas, was constructed between 1962 and 1965 by the Bureau 

of Reclamation, U.S. Department of the Interior, to provide a 

municipal water supply for the city of Wichita, downstream 

flood control, wildlife habitat, and recreational areas. From 

1995 through 2010, water from Cheney Reservoir contributed 

between 51 and 69 percent of Wichita’s water supply (Ziegler 

and others, 2010). Water-supply needs and reliance on Cheney 

Reservoir will continue to increase with ongoing population 

growth and urban development. 

The U.S. Geological Survey (USGS), in cooperation 

with the city of Wichita, continuously has monitored water 

quality on the North Fork Ninnescah River upstream from 

Cheney Reservoir (USGS station 07144780; fig. 1) since 

October 1998. Streamflow has been measured continuously 

on the North Fork Ninnescah River above Cheney Reservoir 

since July 1965. Water budget analysis during 1997 through 

2003 indicated that the North Fork Ninnescah River contributes about 70 percent of the water flowing into the reservoir 

(Christensen and others, 2006). Water-quality monitoring on 

the North Fork Ninnescah River provides continuous measures 

of specific conductance, pH, water temperature, dissolved oxygen, and turbidity. Dozens of discrete water-quality samples 

have been collected at this site by USGS personnel and used 

to develop regression models establishing relations between 

continuously monitored water-quality physical properties and 

water-quality constituents of interest that are not monitored 

continuously. 

Purpose and Scope

The purpose of this report is to update and document 

regression models that establish relations between continuous 

and discrete water-quality data collected from the North Fork 

Ninnescah River upstream from Cheney Reservoir (USGS 

station 07144780; fig. 1). Regression models originally were 

published by Christensen and others (2006) using data collected during 1997 through 2003 for 15 water-quality constituents, including total suspended solids, suspended sediment, 

dissolved solids and major ions, total Kjeldahl nitrogen, total 

phosphorus, orthophosphate, and fecal coliform bacteria. In 

this report, those regression models are updated using data 
2 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

collected through 2009, and additional models are developed 

for nitrate, organic nitrogen, Escherichia coli (E. coli) bacteria, and total organic carbon. Models were updated to be more 

representative of water-quality conditions at this site and to 

evaluate whether relations have changed. The updated models 

are intended to replace existing models. These models are useful for evaluating concentrations of water-quality constituents 

to compare with water-quality criteria, evaluating variability 

during rapidly changing conditions, computing loads and 

yields to assess constituent transport through the watershed, 

and for providing more accurate load estimates compared 

to the original models published in 2006. The water-quality 

information in this report is important to the city of Wichita 

because it allows many potential pollutant concentrations of 

interest, including sediment and nutrient inputs, to be estimated in real time and characterized over conditions and time 

scales that would not otherwise be possible.

Description of Study Area

The Cheney Reservoir watershed is located in southcentral Kansas (fig. 1) and has a contributing drainage area of 

933 square miles (mi2). The North Fork Ninnescah River is the 

largest tributary to Cheney Reservoir. The North Fork Ninnescah River above Cheney Reservoir (USGS station 07144780), 

where continuous water-quality data have been collected since 

October 1998, has a drainage area of 734 mi2.

Land use in the Cheney Reservoir watershed predominately is rural (fig. 1); less than 1 percent of the land use in 

the watershed is classified as urban. All agricultural crops, 

including wheat, comprise about 55 percent of land use in the 

watershed above the North Fork Ninnescah River site. About 

25 percent of the North Fork Ninnescah River site’s watershed is grassland and about 18 percent is conservation reserve 

program land (Peterson and others, 2005).

Methods

Continuous and discrete water-quality data were collected at one inflow site on the North Fork Ninnescah River 

(fig. 1; USGS station 07144780, North Fork Ninnescah River 

above Cheney Reservoir), hereinafter referred to as the inflow 

site. The North Fork Ninnescah River is the largest contributing tributary to Cheney Reservoir, and thus one of the main 

contributors to reservoir water quality. Discrete water-quality 

samples routinely have been collected since February 1996. 

Continuous and discrete water-quality data collected by the 

USGS at the inflow site from January 1999 through December 2009 were used to develop updated and new site-specific 

regression models. 

Continuous Water-Quality Monitoring

Continuous water-quality data were collected from 

the inflow site and were recorded hourly. Streamflow was 

measured using standard USGS methods (Turnipseed and 

Sauer, 2010). The inflow site was equipped with a YSI 6600 

Extended Deployment System water-quality monitor that measured specific conductance, pH, water temperature, dissolved 

oxygen (YSI Clark cell or optical dissolved oxygen sensors), 

and turbidity (YSI model 6026 turbidity sensor). The YSI 

Clark cell dissolved-oxygen sensor was used from November 1998 through March 2008 and was replaced by the YSI 

optical dissolved-oxygen sensor in March 2008. The monitor 

was installed near the centroid of streamflow to best represent 

conditions across the width of the stream and was maintained 

in accordance with standard USGS procedures (Wilde, 2008; 

Wagner and others, 2006). Continuous streamflow and waterquality data were recorded hourly and are available on the 

USGS website at http://nrtwq.usgs.gov/ks.

The specific conductance, pH, water temperature, and 

dissolved oxygen sensors have wide ranges of operation (Wagner and others, 2006) that were not exceeded in this study. The 

YSI model 6026 turbidity sensor instrument maximum (1,700 

formazin nephelometric units, FNU) was not exceeded during 

1999 through 2009 and the maximum reading recorded at this 

site during the study period was 1,700 FNU. Continuous data 

during the study period generally required corrections of less 

than 10 percent, which classifies the data quality rating as 

good according to established guidelines (Wagner and others, 

2006). Time-series measurements occasionally were missing 

or deleted from the dataset because of equipment malfunction or excessive fouling caused by environmental conditions. 

During 1999 through 2009, less than 1 percent of the discharge record, 6 percent of the specific conductance record, 4 

percent of the pH record, 3 percent of the temperature record, 

8 percent of the dissolved oxygen record, and 7 percent of the 

turbidity record were missing or deleted. Missing and deleted 

data were because of issues with calibration of the Clark cell 

dissolved oxygen sensor, sensors becoming submerged in 

sand, sensors not having enough water to be submerged during 

low flow conditions, sensor fouling, data corrections greater 

than the maximum allowable 20 percent, and extremely cold 

temperatures causing icy conditions.

Discrete Water-Quality Samples

Discrete water-quality samples were collected over a 

range of streamflow conditions during January 1999 through 

December 2009 using depth- and width-integrating samplecollection techniques (Wilde, 2008; U.S. Geological Survey, 

2006). Samples collected using this approach are representative of the average chemical composition of the stream crosssectional area. All water samples were analyzed for dissolved 

solids and major ions, alkalinity, suspended solids and sediment, nutrients (nitrogen and phosphorus species), indicator 
Methods 3

SEDGWICK

COUNTY

KINGMAN

COUNTY

KIOWA

COUNTY

PRATT

COUNTY

PAWNEE

COUNTY

STAFFORD

COUNTY

EDWARDS

COUNTY

RENO

COUNTY

Stafford

Castleton

Cheney

Reservoir

07144780

Nester Creek

Sand Creek

Smoots Creek

Smoots Creek

S and Creek

Red Rock Cree k

Arkansas Ri ver

Sou th Fork Ninnescah Ri ver

Wolf Creek

North Fo r k Ninnesca h River

Irish Cree k

Pat Creek

Hunter C reek

Sa lt Cre ek

P ainter Creek

Spring Cree k

Gar Creek

Goose Cree

Si

k

lver Cre ek

Bear Cre ek

Sand Creek

Mead Creek

Sugar C reek

Rock Creek

Peace Creek

Spring Cre ek

Rattlesnake Creek

99°W 98°45'W 98°30'W 98°15'W 98°W 97°45'W

38°N

37°50'N

37°40'N

Base modified from U.S. Geological Survey

1:100,000-scale digital data, 2005

Land use data from Kansas Applied 

Remote Sensing Program (2006)

Wichita

EXPLANATION

U.S. Geological Survey station and identifier Land use (2005, modified from KLCP)

Urban

Cropland

Grassland

Conservation Reserve Program

Woodland

Water

Wheat

Cheney Reservoir

drainage area

0 5 10 20 Miles

0 5 10 20 Kilometers

bacteria, and organic carbon. Dissolved and suspended solids, 

major ions, alkalinity, nutrients (except for total Kjeldahl 

nitrogen), fecal coliform bacteria, and organic carbon were 

analyzed by the Wichita Municipal Water and Wastewater 

Laboratory in Wichita, Kansas according to standard methods 

(American Public Health Association and others, 1995). An 

incremental equivalence method was used for the alkalinity titrations. Bicarbonate concentrations were calculated by 

multiplying the alkalinity concentrations by 0.8202 (Rounds, 

2012). Selected replicate samples were sent to the USGS 

National Water Quality Laboratory in Lakewood, Colorado 

and analyzed according to methods presented in Fishman 

and Friedman (1989). E. coli bacteria was analyzed at the 

USGS Wichita Field Office in Wichita, Kansas using methods 

described by Wilde (2008). Suspended sediment was analyzed 

at the USGS Iowa Sediment Laboratory in Iowa City, Iowa 

according to methods described in Guy (1969). 

Quality Assurance and Quality Control

Replicate, standard reference, and blank samples were 

collected over a range of streamflow conditions as part of 

quality assurance/quality control (QA/QC). About 8 percent 

of discrete water-quality samples were QA/QC samples. 

Approximately 180 sequential replicate constituent pairs were 

Figure 1. Location of continuous real-time water-quality monitoring station and land use in the Cheney Reservoir watershed.

collected during 1999 through 2009 for the inflow site. Replicate samples were analyzed to identify variability in sampling 

and analysis methods (Wilde, 2008). Relative percentage 

difference (RPD) was used to evaluate differences in analyte 

concentrations detected in replicate water samples. The RPD 

was calculated using the following equation:

RPD A B A B = −  +









































/ ×

2

100 (1)

where A and B are concentrations in each replicate pair. Replicate pairs with an RPD within 10 percent were considered 

acceptable for inorganic constituents (Ziegler and Combs, 

1997). Replicate pairs with an RPD within 20 percent were 

considered acceptable for organic constituents (including total 

phosphorus), and RPDs within 50 percent were considered 

acceptable for bacterial analysis. The median RPD between 

all constituent replicate pairs was less than their respective 

acceptability limits. All constituent replicate pairs had median 

RPDs that were less than 5 percent, except for total Kjeldahl 

nitrogen (12 percent), total phosphorus (15 percent), E. coli

(25 percent), and suspended sediment (6 percent). Larger 

RPDs generally occurred when the values were near the 

method detection limit.
4 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Approximately 65 sequential constituent replicate pairs 

were analyzed by the Wichita Municipal Water and Wastewater Laboratory and the USGS National Water Quality Laboratory. The median RPD between laboratories for ions was 

6 percent. The median RPD between laboratories for nutrients 

was 12 percent. Larger nutrient RPDs generally occurred 

because of differences in laboratory method reporting levels 

and when the values were at or near the method reporting 

level. 

Blank sample analysis included approximately 210 

constituent concentrations. All constituents were below the 

method reporting level with the exception of ammonia. One 

ammonia value was 0.01 milligrams per liter (mg/L) above the 

method reporting level. Median blank bicarbonate concentration was 2.4 mg/L. Median blank alkalinity concentration was 

2.0 mg/L.

Standard reference samples were analyzed by the Wichita 

Municipal Water and Wastewater Laboratory at least annually and submitted to the USGS Branch of Quality Systems 

for sample analysis and evaluation of laboratory performance. 

Median major ion constituent RPDs ranged from 1 to 6 percent and median nutrient constituent RPDs ranged from 3 to 

5 percent during this study. Results are available at http://bqs.

usgs.gov/srs/.

Cross-sectional measurements were compared to the continuous measurements to provide verification that minimum 

bias occurred as a result of water-quality monitor location 

within the stream cross-section. The median RPD between 

cross-sectional and continuous monitor measurements was 

approximately 2 percent for all measurements. Larger differences (greater than 5 percent RPD) between cross-sectional 

and continuous monitor measurements occurred during stormwater runoff events when conditions were changing rapidly. 

Development of Regression Models to Compute 

Constituent Concentrations 

Models were developed using simple linear (ordinary 

least squares) regression analyses to relate discrete sample 

concentrations or densities of water-quality constituents to 

continuously measured water-quality physical properties (Helsel and Hirsch, 2002; Rasmussen and others, 2008). The methods used for the development of these models and quantifying 

uncertainty are described in detail in Rasmussen and others 

(2009). All data for this report were analyzed using TIBCO 

Spotfire S+® 8.1 for Windows® statistical software (TIBCO 

Software, Inc., 2008). 

To avoid false-positive quantification of a constituent, 

low concentrations are left-censored and reported as “less 

than” values by the laboratory (Childress and others, 1999). 

Two constituents had left-censored data: organic nitrogen 

(15 percent of samples) and orthophosphate (33 percent of 

samples). The left-censored data arbitrarily were assigned a 

value of one-half of the censoring level.

Although Christensen and others (2006) included 

discrete data collected in 1997 and 1998 in their regression 

analyses, these data were not included in the current analysis. 

Christensen and others (2006) used cross-sectional means of 

continuously measured physical properties as explanatory 

variables, whereas this current analysis uses continuously 

measured water-quality data after the Rasmussen and others 

(2009) protocol. Christensen and others (2006) also included 

discrete data collected by autosamplers as response variables; 

this report did not use autosampled data because the autosamples represented a relatively small part of the dataset and may 

not be representative of the average chemical composition of 

the stream cross-sectional area (Christensen and others, 2006; 

Rasmussen and others, 2008). Original models had numbers 

of discrete samples ranging from 20 to 127, with a median of 

27 (Christensen and others, 2006). The numbers of discrete 

samples for models in this report range from 22 to 61, with a 

median of 54.

All continuously measured variables and seasonal components (sine and cosine variables) were tested for significance 

(p-value less than 0.05) for each response variable. Concomitant in-stream continuous measurements were used to correspond with discrete measurements as described in Rasmussen 

and others (2009). In-stream continuous data corresponding to 

each discrete sample were determined from time-series datasets by using time-weighted averages of continuous data values 

recorded immediately before, during, and after the discrete 

sample collection. 

Outliers were identified and removed as described in 

Rasmussen and others (2009). Outliers in discrete samples 

primarily were removed when there was large heterogeneity in corresponding physical properties of cross-sectional 

data recorded during discrete sampling and when there were 

issues with nutrient laboratory analysis (such as an orthophosphate concentration being higher than the concomitant total 

phosphorus concentration). Overall, approximately 5 percent 

of the discrete-sample data were considered outliers and 

were removed from regression models. Three percent of the 

discrete-sample data was removed because of large heterogeneity in corresponding physical properties of cross-sectional 

data recorded during discrete sampling. One percent of the 

discrete-sample data was removed because of a large specific 

conductance value likely affected by road salt application. One 

percent of the discrete-sample data was removed because of 

laboratory analysis issues. Uncertainty in regression model 

predictions is unknown when the cross-sectional measurements vary greatly from the in situ measurements and when 

road salt is applied. 

Regression models were evaluated based on diagnostic statistics (R2

, coefficient of determination; Mallow’s Cp; 

RMSE, root mean square error; PRESS, prediction error sum 

of squares), patterns in residual plots, and the range and distribution of discrete and continuous data (Helsel and Hirsch, 

2002). All linear models were considered for each constituent, and the best model for each constituent was selected to 

maximize the amount of variance in the response variable that 
Results of Regression Analysis for Selected Constituents 5

is explained by the model (multiple R2 for models with one 

explanatory variable and adjusted R2 for models with more 

than one explanatory variable), that best fits the data (Mallow’s Cp

), and that minimized heteroscedasticity (irregular 

scatter) in the residual plots and uncertainty associated with 

computed values (RMSE and PRESS). Model simplicity also 

was considered for model selection because, as more variables 

are included, the likelihood increases that the variability of 

the system is not described by the sampling dataset. A second 

significant explanatory variable was added to the model when 

doing so substantially increased R2 and decreased Mallow’s 

Cp. 

Mean square error (MSE) and RMSE were calculated 

for each model to assess the variance between predicted and 

observed values (Helsel and Hirsch, 2002). The model standard percentage error (MSPE) was calculated as a percentage 

of the RMSE (Hardison, 1969). Because transformation of 

estimates back into original units results in a low biased estimate (Helsel and Hirsch, 2002), a bias correction factor (BCF) 

was calculated for models with logarithmically transformed 

response variables (Duan, 1983). Uncertainty associated with 

regression-computed constituent concentrations was quantified using 90-percent prediction intervals (Helsel and Hirsch, 

2002).

Results of Regression Analysis for 

Selected Constituents

Regression models for 15 constituents developed from 

data collected during 1997 through 2003 (Christensen and 

others, 2006) were updated and new models were developed 

for 5 additional constituents not described in Christensen and 

others (2006). The updated models were for dissolved solids, 

calcium, magnesium, sodium, chloride, potassium, sulfate, 

alkalinity, bicarbonate, total suspended solids, suspended 

sediment, total Kjeldahl nitrogen, total phosphorus, orthophosphate, and fecal coliform bacteria. The newly developed 

models were for the nutrient species total nitrogen, organic 

nitrogen, and nitrate; E. coli bacteria; and total organic carbon. 

Additional streamflow-based models of select constituents of 

interest were developed to allow computation of constituent 

concentrations when concomitant initial model real time data 

are unavailable. Streamflow-based models were developed 

for dissolved solids, sodium, chloride, sulfate, total suspended 

solids, suspended sediment, total nitrogen, nitrate, total 

phosphorus, and E. coli bacteria. Updated and newly developed models were developed from data collected during 1999 

through 2009. Models are shown in table 1. Model datasets 

are presented in tables 2–15 and TIBCO Spotfire S+® model 

(S+®) statistical output is presented in figures 2–61 (see the 

Abbreviations list in the front of this report for definitions of 

abbreviations used in the figures). 

Graphical S+® statistical output includes plots of 

the regression analysis for regression equations with one 

explanatory variable, computed versus measured (“actual”) 

concentrations, a comparison of estimated (“fitted”) concentrations and regression residuals (“residuals”), and a standard 

normal quantiles versus regression residuals plot. The plot of 

the fitted values and regression residuals indicates unexplained 

structure left in the residuals (TIBCO Software, Inc., 2008). 

The standard normal quantiles versus regression residuals 

plots the normal quantiles (“quantiles of standard normal”) 

against the regression residuals (“residuals”) and provides a 

visual test of the assumption that the model’s errors are normally distributed (TIBCO Software, Inc., 2008).

In general, model forms and the amount of variance 

explained by the models was similar between the original 

(Christensen and others, 2006) and updated models (table 1). 

The model forms for most updated models remained 

unchanged. Dissolved solids, calcium, magnesium, sodium, 

chloride, potassium, and sulfate were strongly positively 

correlated with specific conductance; the calcium model 

included streamflow as an additional explanatory variable. On 

average, the updated ion models explained 9 percent more of 

the variance in ion concentrations compared to the original 

models (table 1). Actual (measured) versus computed plots of 

dissolved solids, sodium, and chloride using streamflow as an 

explanatory variable indicate that relations may be different at 

higher concentrations compared to lower concentrations suggesting limitations in the utility of the streamflow-based model 

for these constituents (figs. 5B, 13B, 17B). 

The maximum pH for discrete water-quality samples 

associated with alkalinity titrations was 8.7. Alkalinity and 

bicarbonate were positively correlated with streamflow and 

specific conductance. The updated alkalinity model explained 

6 percent more variance in alkalinity concentrations than the 

original model and the updated bicarbonate model explained 5 

percent more variance than the original model (table 1).

Total suspended solids and suspended sediment were 

strongly positively correlated with turbidity. The updated 

suspended-sediment model also included streamflow as an 

explanatory variable and explained 5 percent more variance in suspended-sediment concentrations than the original 

model (table 1). The total suspended solids model that uses 

streamflow as an explanatory variable has a larger amount of 

variability when total suspended solids concentration is greater 

than about 150 mg/L than when total suspended solids concentration is less than about 150 mg/L (fig. 31B).

All nitrogen species and total phosphorus models 

included turbidity as an explanatory variable. Total nitrogen 

and nitrate models also included season as an explanatory 

variable. The updated total Kjeldahl nitrogen model explained 

9 percent more variance in total Kjeldahl nitrogen concentrations than the original model (table 1). The organic nitrogen 

model also included specific conductance as an explanatory 

variable, and the orthophosphorus model had specific conductance as the explanatory variable. Fecal coliform and Escherichia coli bacteria models were positively related to turbidity and negatively related to specific conductance. The total 

organic carbon model was positively related to turbidity.
6 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 milliliters]

Regression model Multiple 

R 2

Adjusted 

R 2

MSE RMSE

MSPE 

(upper)

MSPE 

(lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction 

interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Dissolved solids (DS), mg/L

Christensen and others (2006)

log(DS) = 0.910log(SC) + 0.0101 0.87 0.87 0.0044 0.0663 17 14 1.01 40 127 DS: 140–707 461 472 168

SC: 198–1,300 821 837 303

Updated

log(DS) = 0.892log(SC) + 0.0810 0.98 0.98 0.0006 0.0250 6 6 1.00 39 61 DS: 191–798 507 548 172

SC: 258–1,430 883 976 326

log(DS) = -0.225log(Q) + 3.19 0.68 0.67 0.0107 0.1036 27 21 1.03 40 61 DS: 191–798 507 548 172

Q: 9.4–3,725 564 223 873

Calcium (Ca), dissolved, mg/L

Christensen and others (2006)

log(Ca) = 0.724log(SC) - 0.387 0.76 0.76 0.0048 0.0767 19 16 1.02 40 127 Ca: 19.7–88.7 52.9 50.7 17.8

SC: 198–1,300 821 837 303

Updated

log(Ca) = 0.120log(Q) + 0.964log(SC) - 1.37 0.89 0.89 0.0023 0.0478 12 10 1.01 40 61 Ca: 23.2–86.6 53.4 54.7 15.8

Q: 9.4–3,725 564 223 873

SC: 258–1,430 883 976 326

Magnesium (Mg), dissolved, mg/L

Christensen and others (2006)

Mg = 0.0086(SC) +1.68 0.80 0.80 1.7500 1.3212 15 -15 1.00 39 127 Mg: 3.52–13.8 8.77 9.27 2.93

SC: 198–1,300 821 837 303

Updated

log(Mg) = 0.698log(SC) - 1.08 0.92 0.92 0.0017 0.0410 10 9 1.00 40 61 Mg: 3.66–13.0 9.26 10.0 2.63

SC: 258–1,430 883 976 326
Results of Regression Analysis for Selected Constituents 

7

Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 milliliters]

Regression model Multiple R 2 Adjusted R 2 MSE RMSE MSPE (upper) MSPE (lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction 

interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Sodium (Na), dissolved, mg/L

Christensen and others (2006)

log(Na) = 1.17log(SC) - 1.41 0.89 0.89 0.0061 0.0784 20 17 1.02 40 127 Na: 19.5–180 104 101 46.5

SC: 198–1,300 821 837 303

Updated

log(Na) = 1.33log(SC) - 1.86 0.99 0.98 0.0011 0.0330 8 7 1.00 40 61 Na: 22.8–185 117 130 53.4

SC: 258–1,430 883 976 326

log(Na) = -0.351log(Q) + 2.81 0.74 0.74 0.0187 0.1367 37 27 1.05 41 61 Na: 22.8–185 117 130 53.4

Q: 9.4–3,725 564 223 873

Chloride (Cl), dissolved, mg/L

Christensen and others (2006)

log(Cl) = 1.37log(SC) - 1.82 0.97 0.97 0.0018 0.0420 10 9 1.00 41 27 Cl: 34.0–289 155 159 71.0

SC: 322–1,250 844 903 297

Updated

log(Cl) = 1.39log(SC) - 1.90 0.96 0.96 0.0035 0.0591 15 13 1.01 40 48 Cl: 30.8–289 147 139 82.7

SC: 258–1,430 822 837 339

log(Cl) = -0.401log(Q) + 3.06 0.77 0.76 0.0212 0.1457 40 29 1.05 42 48 Cl: 30.8–289 147 139 82.7

Q: 15–3,725 697 321 942

Potassium (K), dissolved, mg/L

Christensen and others (2006)

log(K) = -0.0003(SC) + 0.944 0.54 0.54 0.0084 0.0917 24 19 1.02 40 127 K: 2.53–8.16 4.94 4.85 1.48

SC: 198–1,300 821 837 303

Updated

log(K) = -0.0011(SC) + 1.17log(SC) -1.80 0.73 0.72 0.0055 0.0740 19 16 1.01 40 61 K: 2.89–8.41 4.93 5.00 1.56

SC: 258–1,430 883 976 326
8 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 

milliliters]

Regression model Multiple 

R 2

Adjusted 

R 2

MSE RMSE

MSPE 

(upper)

MSPE 

(lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Sulfate (SO4), dissolved, mg/L

Christensen and others (2006)

log(SO4) = 0.961log(SC) - 1.26 0.85 0.85 0.0059 0.0765 19 16 1.01 41 27 SO4: 11.0–61.0 35.8 37.9 13.7

SC: 322–1,250 844 903 297

Updated

SO4 = 0.0408(SC) - 0.002 0.87 0.87 29.56 5.4369 16 -16 1.00 40 48 SO4: 8.5–61.0 33.6 29.0 18.9

SC: 258–1,430 822 837 339

SO4 = -20.1log(Q) + 82.6 0.77 0.76 51.89 7.2035 21 -21 1.00 40 48 SO4: 8.5–61.0 33.6 29.0 18.9

Q: 15–3,725 697 321 942

Alkalinity (ALK), mg/L

Christensen and others (2006)

log(ALK) = 0.659log(SC) +0.241 0.81 0.80 0.0038 0.0614 15 13 1.01 41 27 ALK: 74–222 147 153 42

SC: 322–1,250 844 903 297

Updated

log(ALK) = 0.114log(Q) + 0.810log(SC) - 0.447 0.87 0.86 0.0022 0.0464 11 10 1.01 40 48 ALK: 74–215 149 156 38

Q: 15–3,725 697 321 942

SC: 258–1,430 822 837 339

Bicarbonate (HCO3), mg/L

Christensen and others (2006)

log(HCO3) = 0.669log(SC) + 0.296 0.81 0.80 0.0038 0.0617 15 13 1.01 41 27 HCO3: 86–271 179 187 51

SC: 322–1,250 844 903 297

Updated

log(HCO3) = 0.113log(Q) + 0.813log(SC) - 0.368 0.86 0.85 0.0023 0.0479 12 10 1.01 40 48 HCO3: 86–260 181 190 47

Q: 15–3,725 697 321 942

SC: 258–1,430 822 837 339
Results of Regression Analysis for Selected Constituents 

9

Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 

milliliters]

Regression model Multiple R 2 Adjusted R 2 MSE RMSE MSPE (upper) MSPE (lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Total suspended solids (TSS), mg/L

Christensen and others (2006)

log(TSS) = 0.893log(TBY6026) + 0.253 0.92 0.92 0.0233 0.1525 42 30 1.06 43 29 TSS: 8–696 156 55 186

TBY6026: 

7.9–575

154 40 188

log(TSS) = 0.682log(Q) + 0.431 0.61 0.59 0.1190 0.3454 122 55 1.34 54 29 TSS: 8–696 156 55 186

Q: 9.3–3,460 406 106 775

Updated

log(TSS) = 0.903log(TBY6026) + 0.252 0.87 0.87 0.0295 0.1718 49 33 1.08 42 57 TSS: 8–696 153 119 144

TBY6026: 13–600 136 110 138

 log(TSS) = 0.575log(Q) + 0.624 0.64 0.63 0.0810 0.2846 93 48 1.25 49 57 TSS: 8–696 153 119 144

Q: 9.4–3,725 600 238 892

Suspended-sediment concentration (SSC), mg/L

Christensen and others (2006)

log(SSC) = 1.10log(TBY6026) +0.0037 0.85 0.85 0.0589 0.2426 75 43 1.18 48 22 SSC: 22–2,150 385 93 625

TBY6026: 15–575 170 60.8 194

log(SSC) = 0.934log(Q) +0.043 0.76 0.78 0.0959 0.3097 104 51 1.26 51 22 SSC: 22–2,150 385 93 625

Q: 20–3,460 482 120 870

Updated

log(SSC) = 0.540log(Q) + 0.559log(TBY6026) - 0.110 0.90 0.90 0.0347 0.1862 54 35 1.09 43 52 SSC: 19–2,690 439 208 596

Q: 15–3,725 645 263 919

TBY6026: 13–600 146 113 139

log(SSC) = 0.861log(Q) + 0.209 0.82 0.81 0.0622 0.2494 78 44 1.18 47 52 SSC: 19–2,690 439 208 596

Q: 15–3,725 645 263 919
10 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 

milliliters]

Regression model Multiple 

R 2

Adjusted 

R 2

MSE RMSE

MSPE 

(upper)

MSPE 

(lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Nitrogen, total (TN), mg/L (TKN + NO NO 3 2

)

New

log(TN) = 0.0218sin(2πD/365) + 0.112cos(2πD/365) + 0.182log(TBY6026) - 0.0012 0.63 0.60 0.0077 0.0876 22 18 1.02 40 54 TN: 0.99–4.43 2.18 2.02 0.72

TBY6026: 12–600 141 113 140

log(TN) = 0.0209sin(2πD/365) + 0.105cos(2πD/365) + 0.0822log(Q) + 0.150 0.38 0.34 0.0127 0.1129 30 23 1.03 41 54 TN: 0.99-4.43 2.18 2.02 0.72

Q: 15–3,725 632 256 906

Nitrogen, ammonia plus organic (TKN), total, mg/L

Christensen and others (2006)

TKN = -0.0004(Q) + 0.0054(TBY6026) + 0.790 0.92 0.91 0.0881 0.2968 20 -20 1.00 41 20 TKN: 0.48–3.5 1.45 1.24 0.91

Q: 20–2,360 367 108 590

TBY6026: 15–532 151 41 177

Updated

log(TKN) = 0.426log(TBY6026) - 0.700 0.83 0.83 0.0079 0.0888 23 18 1.02 40 50 TKN: 0.48–3.40 1.57 1.55 0.69

TBY6026: 13–600 155 121 141

Organic Nitrogen (ON), mg/L (TKN - ammonia)

New

ON = 1.58log(TBY6026) + 1.04log(SC) - 4.65 0.82 0.81 0.0870 0.2950 21 -21 1.00 40 54 ON: <0.07–3.26 1.40 1.38 0.68

TBY6026: 12–600 140 113 140

SC: 258–1,430 857 935 337

Nitrate (NO3), mg/L

New

NO3 = 0.0519sin(2πD/365) + 0.619cos(2πD/365) - 0.389log(TBY6026) + 1.63 0.63 0.61 0.0954 0.3088 45 -45 1.00 39 61 NO3: 0.03–2.38 0.69 0.52 0.49

TBY6026: 

12–600

129 92 136

NO3 = 0.0903sin(2πD/365) + 0.652cos(2πD/365) - 0.278log(Q) + 1.55 0.60 0.58 0.1028 0.3206 46 -46 1.00 39 61 NO3: 0.03–2.38 0.69 0.52 0.49

Q: 9.40–3,725 564 223 873
Results of Regression Analysis for Selected Constituents 11

Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 

milliliters]

Regression model Multiple R 2 Adjusted R 2 MSE RMSE MSPE (upper) MSPE (lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Phosphorus, total (TP), mg/L

Christensen and others (2006)

TP = 0.0001(Q) + 0.0008(TBY6026) + 0.0863 0.84 0.83 0.0661 0.0661 33 -33 1.00 40 26 TP: 0.03–0.58 0.20 0.13 0.16

Q: 9.3–2,360 293 103 533

TBY6026: 

7.9–532

125 39.0 163

Updated

log(TP) = 0.611log(TBY6026) -1.829 0.83 0.82 0.0189 0.1375 37 27 1.05 42 55 TP: 0.04–0.58 0.27 0.26 0.16

TBY6026: 13–600 137 110 139

TP = 0.191log(Q) - 0.174 0.57 0.56 0.0115 0.1073 39 -39 1.00 40 55 TP: 0.04–0.58 0.27 0.26 0.16

Q: 9.4–3,725 596 238 904

Orthophosphate, filtered (OP), mg/L as phosphate

Christensen and others (2006)

OP = -0.0002(SC) + 0.237 0.84 0.83 0.0007 0.0263 66 -66 1.00 40 25 OP: <0.01–0.19 0.04 0.01 0.06

SC: 322–1,250 966 1,087 288

Updated

OP = -0.0002(SC) + 0.224 0.74 0.73 0.0011 0.0339 56 -56 1.00 40 54 OP: 0.01–0.23 0.06 0.03 0.07

SC: 317–1,430 907 977 311

Fecal coliform bacteria (FC), colonies/100 mL

Christensen and others (2006)

log(FC) = 0.714log(TBY6026) - 0.0016(SC) + 3.10 0.78 0.76 0.2230 0.4691 195 66 1.52 61 30 FC: 8–36,000 4,888 500 8,646

TBY6026: 

7.9–575

152 41 185

SC: 322–1,250 944 1,070 292

Updated

log(FC) = 0.761log(TBY6026) - 0.0013(SC) + 2.73 0.72 0.71 0.2367 0.4865 207 67 1.71 67 60 FC: 8–65,000 6,207 880 11,736

TBY6026: 13–600 138 120 134

SC: 200–1,430 843 896 333
12 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents Table 1. Christensen and others (2006), updated, and new regression models and summary statistics for continuous concentration computations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[R2, coefficient of determination; MSE, mean square error; RMSE, root mean square error; MSPE, model standard percentage error; %, percent; ±, plus or minus; n, number of discrete samples; mg/L, milligrams per liter; log, log10; SC, specific conductance in microsiemens per centimeter at 25 degress Celsius; Q, streamflow in cubic feet per second; TBY6026, turbidity from YSI sensor 6026 in formazin nephelometric units; TKN, total Kjeldahl nitrogen in milligrams per liter; NO NO 3 2, nitrate plus nitrate in milligrams per liter; sin, sine; D, day of year; cos, cosine; <, less than; colonies/100 mL, colonies per 100 

milliliters]

Regression model Multiple 

R 2

Adjusted 

R 2

MSE RMSE

MSPE 

(upper)

MSPE 

(lower)

Bias 

correction 

factor 

(Duan, 1983)

90% prediction interval, in ± %

Discrete data

n

Range of values 

in variable 

measurements

Mean Median

Standard 

deviation

Escherichia coli bacteria (EC), colonies/100 mL

New

log(EC) = 0.0032(TBY6026) - 0.0016(SC) + 4.01 0.87 0.85 0.0965 0.3106 104 51 1.20 49 22 EC: 17–30,000 5,086 1,400 8,319

TBY6026: 13–280 130 121 87.3

SC: 200–1,430 797 755 347

log(EC) = 0.977log(Q) + 0.650 0.73 0.71 0.1902 0.4361 173 63 1.45 59 22 EC: 17–30,000 5,086 1,400 8,319

Q: 15–4,780 993 402 1,321

Total organic carbon (TOC), mg/L

New

log(TOC) = 0.485log(TBY6026) + 0.0080 0.73 0.72 0.0183 0.1353 37 27 1.04 41 45 TOC: 2.5–20.5 11.2 12.6 5.3

TBY6026: 13–600 161 123 144
Results of Regression Analysis for Selected Constituents 13

Table 2. Dissolved solids, calcium, magnesium, sodium, and potassium simple linear regression model datasets for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in 

hhmm

Specific 

conductance, in 

microsiemens 

per centimeter 

at 25 degrees 

Celsius

Streamflow, 

in cubic feet 

per second

Dissolved 

solids, in 

milligrams 

per liter

Calcium, in 

milligrams 

per liter

Magnesium, 

in milligrams 

per liter

Sodium, in 

milligrams 

per liter

Potassium, 

in milligrams 

per liter

January 26, 1999 1150 1,195 106 677 84.9 11.7 164 2.89

April 16, 1999 1255 973 684 468 54.9 9.53 111 5.34

May 13, 1999 1025 1,138 98 654 78.0 13.0 173 3.03

May 24, 1999 1045 974 158 545 68.6 10.9 129 3.91

June 10, 1999 1200 1,125 86 641 59.8 12.3 155 2.92

June 25, 1999 1115 896 237 548 63.9 9.33 118 5.59

July 14, 1999 1120 1,078 63 618 56.3 11.1 159 3.47

July 29, 1999 0955 1,148 60 640 59.5 11.9 160 4.02

August 12, 1999 1035 1,150 43 658 55.9 11.8 171 3.56

August 26, 1999 1050 1,080 34 620 50.7 11.2 168 3.04

September 22, 1999 1120 1,165 49 657 66.2 10.6 161 3.18

December 2, 1999 1035 1,230 62 684 69.0 10.8 163 3.28

February 25, 2000 1040 841 256 486 54.4 9.00 104 6.34

April 27, 2000 1045 1,180 110 658 75.8 12.0 147 2.99

May 25, 2000 1020 1,190 60 656 65.4 11.9 163 3.14

June 21, 2000 1200 1,120 47 642 50.6 10.2 155 3.41

July 26, 2000 1150 896 117 532 54.7 8.67 130 6.36

August 29, 2000 1100 1,080 9.4 581 45.9 11.1 162 3.83

September 28, 2000 1030 1,058 20 608 47.5 10.3 154 3.33

October 26, 2000 1050 342 2,663 194 26.2 3.66 30.0 6.07

June 6, 2001 1135 342 1,753 198 29.1 4.54 31.0 5.61

September 4, 2001 1105 1,080 19 605 43.1 10.8 167 3.44

September 19, 20011 1025 343 188 359 40.9 6.15 81.2 5.51

June 12, 20021 1110 187 478 211 21.9 4.38 39.4 6.49

August 14, 2002 1135 398 347 239 30.2 4.70 45.0 6.29

March 18, 2003 1200 678 396 392 47.3 8.25 79.7 4.37

March 19, 2003 1220 342 2,245 224 27.6 4.99 34.5 5.81

April 21, 2003 1130 833 551 517 55.3 9.27 111 6.55

March 5, 2004 1210 445 1,968 355 35.1 5.79 50.1 5.91

May 14, 2004 1035 407 579 243 34.6 5.65 45.9 7.21

June 14, 2004 0945 576 238 331 39.3 6.64 63.4 8.41

September 8, 2004 1025 1,240 39 677 60.4 11.5 182 3.61

March 24, 2005 1015 1,060 381 621 69.0 12.4 144 5.17

May 16, 2005 1140 518 524 306 42.6 5.78 53.2 6.53

June 10, 2005 1055 258 1,100 191 23.2 4.43 22.8 6.00

June 13, 2005 0925 311 3,150 216 27.9 5.25 23.1 6.55

August 29, 2005 0935 707 256 420 52.2 6.68 83.0 8.05

March 2, 2006 0950 1,250 92 697 80.3 12.3 173 3.17
14 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 2. Dissolved solids, calcium, magnesium, sodium, and potassium simple linear regression model datasets for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in 

hhmm

Specific 

conductance, in 

microsiemens 

per centimeter 

at 25 degrees 

Celsius

Streamflow, 

in cubic feet 

per second

Dissolved 

solids, in 

milligrams 

per liter

Calcium, in 

milligrams 

per liter

Magnesium, 

in milligrams 

per liter

Sodium, in 

milligrams 

per liter

Potassium, 

in milligrams 

per liter

March 22, 20062 1130 1,665 144 952 100 16.8 238 5.45

May 1, 2006 1115 1,243 85 725 74.7 12.0 170 3.26

May 12, 2006 1030 1,120 156 639 73.0 11.3 149 5.28

June 5, 2006 1015 1,173 39 630 51.3 11.6 174 3.74

July 31, 2006 1030 1,150 15 637 41.5 11.8 185 3.95

September 7, 2006 1050 1,280 39 697 56.4 10.6 185 3.58

September 21, 2006 1000 1,230 24 667 56.1 11.1 174 3.77

January 9, 2007 1030 1,430 70 798 86.6 12.2 184 3.84

March 14, 2007 1020 1,280 67 696 71.8 11.8 174 2.93

March 22, 2007 1000 1,120 98 682 73.9 11.5 162 3.00

March 26, 2007 1040 976 295 597 60.4 9.46 139 5.00

March 31, 2007 1230 637 1,370 375 47.3 7.82 66.1 7.00

April 16, 2007 1215 724 751 437 54.5 8.54 85.7 6.00

May 7, 2007 1030 317 3,725 202 25.7 4.32 27.8 7.00

June 29, 2007 1025 701 401 427 54.9 8.44 74.5 7.00

September 4, 2007 1126 1,140 28 622 51.0 11.1 163 3.00

April 24, 2008 1140 569 269 335 43.8 8.09 61.8 6.00

May 9, 2008 1135 353 3,103 210 25.5 5.01 34.3 6.00

June 19, 2008 0945 978 223 527 65.4 9.65 114 5.00

September 15, 2008 1055 831 404 480 56.4 8.33 106 7.00

October 16, 2008 1010 589 839 362 43.5 6.96 71.0 7.00

March 31, 2009 1120 897 721 524 60.6 11.3 121 6.00

April 27, 2009 1215 478 2,150 306 39.5 8.37 47.6 6.00

June 17, 2009 1040 785 349 436 53.5 8.30 99.3 5.00

August 20, 2009 1050 1,095 103 632 65.6 9.97 149 5.00

September 10, 2009 1130 464 482 278 38.9 5.43 48.7 7.00

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.

2

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 15

Table 3. Chloride and sulfate simple linear regression model datasets for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, 

in hhmm

Specific conductance, 

in microsiemens per centimeter 

at 25 degrees Celsius

Streamflow, in 

cubic feet per 

second

Chloride, 

in milligrams per 

liter

Sulfate, in milligrams 

per liter

April 16, 1999 1255 973 684 127 29.0

June 10, 1999 1200 1,125 86 211 49.0

June 25, 1999 1115 896 237 164 29.0

July 29, 1999 0955 1,148 60 235 61.0

September 22, 1999 1120 1,165 49 254 52.8

December 2, 1999 1035 1,230 62 289 54.8

February 25, 2000 1040 841 256 159 41.2

October 26, 2000 1050 342 2,663 40.0 17.0

June 6, 2001 1135 342 1,753 34.0 11.0

September 4, 2001 1105 1,080 19 228 47.0

September 19, 20011 1025 343 188 116 39.2

June 12, 20021 1110 187 478 58.0 16.0

August 14, 2002 1135 398 347 59.0 23.0

March 18, 2003 1200 678 396 110 29.0

March 19, 2003 1220 342 2,245 46.0 14.0

April 21, 2003 1130 833 551 150 28.0

March 5, 2004 1210 445 1,968 64.0 26.0

May 14, 2004 1035 407 579 58.0 22.0

June 14, 2004 0945 576 238 92.0 32.0

September 8, 2004 1025 1,240 39 237 54.0

March 24, 2005 1015 1,060 381 185 41.8

May 16, 2005 1140 518 524 75.7 21.6

June 10, 2005 1055 258 1,100 31.3 12.8

June 13, 2005 0925 311 3,150 30.8 14.3

August 29, 2005 0935 707 256 109 27.7

March 2, 2006 0950 1,250 92 237 49.4

March 22, 20062 1130 1,665 144 239 52.1

May 1, 2006 1115 1,243 85 242 45.8

May 12, 2006 1030 1,120 156 193 46.8

June 5, 2006 1015 1,173 39 237 48.2

July 31, 2006 1030 1,150 15 253 50.2

September 7, 2006 1050 1,280 39 288 49.9

September 21, 2006 1000 1,230 24 263 47.8

January 9, 2007 1030 1,430 70 274 58.8

March 22, 2007 1000 1,120 98 230 49.0

March 26, 2007 1040 976 295 210 39.0

March 31, 2007 1230 637 1,370 81.0 24.0

April 16, 2007 1215 724 751 110 28.0

May 7, 2007 1030 317 3,725 50.0 8.50

June 29, 2007 1025 701 401 100 22.0
16 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 3. Chloride and sulfate simple linear regression model datasets for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, 

in hhmm

Specific conductance, 

in microsiemens per centimeter 

at 25 degrees Celsius

Streamflow, in 

cubic feet per 

second

Chloride, 

in milligrams per 

liter

Sulfate, in milligrams 

per liter

September 4, 2007 1126 1,140 28 240 46.0

April 24, 2008 1140 569 269 76.0 25.0

May 9, 2008 1135 353 3,103 40.0 12.0

June 19, 2008 0945 978 223 120 24.0

September 15, 2008 1055 831 404 150 30.0

October 16, 2008 1010 589 839 96.0 21.0

March 31, 2009 1120 897 721 150 38.0

April 27, 2009 1215 478 2,150 48.0 16.0

June 17, 2009 1040 785 349 120 22.0

August 20, 2009 1050 1,095 103 210 52.0

September 10, 2009 1130 464 482 63.0 19.0

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.

2

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 17

Table 4. Alkalinity and bicarbonate simple linear regression model datasets for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm Streamflow, in cubic 

feet per second

Specific 

conductance, in 

microsiemens per centimeter at 25 degrees 

Celsius

Alkalinity, in 

milligrams per liter

Bicarbonate, in 

milligrams per liter

April 16, 1999 1255 684 973 179 220

June 10, 1999 1200 86 1,125 176 220

June 25, 1999 1115 237 896 196 240

July 29, 1999 0955 60 1,148 172 210

September 22, 1999 1120 49 1,165 182 220

December 2, 1999 1035 62 1,230 192 230

February 25, 2000 1040 256 841 153 190

October 26, 2000 1050 2,663 342 74.0 86.0

June 6, 2001 1135 1,753 342 102 120

September 4, 2001 1105 19 1,080 132 160

September 19, 20011 1025 188 343 104 130

June 12, 20021 1110 478 187 74.0 90.0

August 14, 2002 1135 347 398 80.0 98.0

March 18, 2003 1200 396 678 143 170

March 19, 2003 1220 2,245 342 89.0 110

April 21, 2003 1130 551 833 174 210

March 5, 2004 1210 1,968 445 98.0 120

May 14, 2004 1035 579 407 104 130

June 14, 2004 0945 238 576 120 150

September 8, 2004 1025 39 1,240 172 210

March 24, 2005 1015 381 1,060 209 260

May 16, 2005 1140 524 518 126 150

June 10, 2005 1055 1,100 258 81.0 99.0

June 13, 2005 0925 3,150 311 101 120

August 29, 2005 0935 256 707 162 200

March 2, 2006 0950 92 1,250 202 250

March 22, 20062 1130 144 1,665 230 280

May 1, 2006 1115 85 1,243 200 240

May 12, 2006 1030 156 1,120 195 240

June 5, 2006 1015 39 1,173 144 180

July 31, 2006 1030 15 1,150 121 150

September 7, 2006 1050 39 1,280 152 180

September 21, 2006 1000 24 1,230 159 190

January 9, 2007 1030 70 1,430 215 260

March 22, 2007 1000 98 1,120 196 240

March 26, 2007 1040 295 976 160 200

March 31, 2007 1230 1,370 637 149 180

April 16, 2007 1215 751 724 164 200

May 7, 2007 1030 3,725 317 90.0 110
18 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 4. Alkalinity and bicarbonate simple linear regression model datasets for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in hhmm Streamflow, in cubic 

feet per second

Specific 

conductance, in 

microsiemens per centimeter at 25 degrees 

Celsius

Alkalinity, in 

milligrams per liter

Bicarbonate, in 

milligrams per liter

June 29, 2007 1025 401 701 170 210

September 4, 2007 1126 28 1,140 158 190

April 24, 2008 1140 269 569 136 170

May 9, 2008 1135 3,103 353 92.0 110

June 19, 2008 945 223 978 186 230

September 15, 2008 1055 404 831 144 180

October 16, 2008 1010 839 589 132 160

March 31, 2009 1120 721 897 174 210

April 27, 2009 1215 2,150 478 140 170

June 17, 2009 1040 349 785 166 200

August 20, 2009 1050 103 1,095 162 200

September 10, 2009 1130 482 464 104 130

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.

2

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 19

Table 5. Total suspended solids simple linear regression model dataset for the North Fork Ninnescah River 

above Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Streamflow, in cubic 

feet per second

Total suspended 

solids, in milligrams 

per liter

January 26, 1999 1150 21 106 17

April 16, 1999 1255 128 684 309

May 13, 1999 1025 15 98 55

May 24, 1999 1045 138 158 119

June 10, 1999 1200 32 86 61

June 25, 1999 1115 120 237 148

July 29, 1999 0955 56 60 48

August 12, 1999 1035 51 43 35

August 26, 1999 1050 27 34 21

September 22, 1999 1120 22 49 30

December 2, 1999 1035 18 62 25

February 25, 2000 1040 272 256 422

April 27, 2000 1045 13 110 27

May 25, 2000 1020 27 60 38

June 21, 2000 1200 45 47 55

July 26, 2000 1150 123 117 142

August 29, 2000 1100 13 9.4 15

September 28, 2000 1030 22 20 8

October 26, 2000 1050 320 2,663 162

June 6, 2001 1135 250 1,753 212

September 19, 20011 1025 1,335 188 357

June 12, 20021 1110 965 478 582

August 14, 2002 1135 435 347 264

March 18, 2003 1200 600 396 696

March 19, 2003 1220 580 2,245 476

April 21, 2003 1130 130 551 124

March 5, 2004 1210 475 1,968 375

May 14, 2004 1035 210 579 100

June 14, 2004 0945 120 238 162

March 24, 2005 1015 105 381 120

May 16, 2005 1140 115 524 128

June 10, 2005 1055 240 1,100 250

June 13, 2005 0925 125 3,150 145

August 29, 2005 0935 140 256 172

March 2, 2006 0950 14 92 21

March 22, 2006 1130 71 144 87

June 5, 2006 1015 48 39 75

July 31, 2006 1030 31 15 24

September 7, 2006 1050 25 39 29

September 21, 2006 1000 13 24 15
20 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 5. Total suspended solids simple linear regression model dataset for the North Fork Ninnescah River 

above Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Streamflow, in cubic 

feet per second

Total suspended 

solids, in milligrams 

per liter

January 9, 2007 1030 22 70 30

March 14, 2007 1020 15 67 23

March 22, 2007 1000 39 98 74

March 26, 2007 1040 190 295 316

March 31, 2007 1230 220 1,370 459

April 16, 2007 1215 65 751 94

May 7, 2007 1030 170 3,725 211

June 29, 2007 1025 68 401 92

September 4, 2007 1126 15 28 22

April 24, 2008 1140 123 269 136

May 9, 2008 1135 253 3,103 283

June 19, 2008 0945 92 223 67

September 15, 2008 1055 74 404 146

October 16, 2008 1010 110 839 112

March 31, 2009 1120 220 721 364

April 27, 2009 1215 270 2,150 318

June 17, 2009 1040 140 349 201

August 20, 2009 1050 220 103 278

September 10, 2009 1130 280 482 258

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample 

collection.
Results of Regression Analysis for Selected Constituents 21

Table 6. Suspended-sediment concentration simple linear regression model dataset for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Streamflow, in cubic 

feet per second

Suspended-sediment 

concentration, 

in milligrams per liter

May 13, 1999 1025 15 98 67

May 24, 1999 1045 138 158 233

June 10, 1999 1200 32 86 28

June 25, 1999 1115 120 237 180

July 8, 1999 1400 90 76 62

July 29, 1999 0955 56 60 43

December 2, 1999 1035 18 62 22

April 27, 2000 1045 13 110 32

May 25, 2000 1020 27 60 44

June 21, 2000 1200 45 47 65

October 26, 2000 1050 320 2,663 2,100

June 6, 2001 1135 250 1,753 303

June 27, 2001 1155 48 77 94

September 19, 20011 1025 1,335 188 547

January 8, 2002 1120 50 81 93

May 13, 2002 1040 245 318 226

May 15, 2002 1100 66 130 91

June 12, 20021 1110 965 478 801

August 14, 2002 1135 435 347 468

March 18, 2003 1200 600 396 1,090

March 19, 2003 1220 580 2,245 2,150

April 21, 2003 1130 130 551 208

March 5, 2004 1210 475 1,968 2,690

May 14, 2004 1035 210 579 219

June 14, 2004 0945 120 238 187

March 24, 2005 1015 105 381 174

May 16, 2005 1140 115 524 295

June 10, 2005 1055 240 1,100 673

June 13, 2005 0925 125 3,150 747

August 29, 2005 0935 140 256 227

March 2, 2006 0950 14 92 51

March 22, 2006 1130 71 144 99

June 5, 2006 1015 48 39 52

July 31, 2006 1030 31 15 23

September 7, 2006 1050 25 39 46

September 21, 2006 1000 13 24 19

January 9, 2007 1030 22 70 82

March 14, 2007 1020 15 67 38

March 22, 2007 1000 39 98 72

March 26, 2007 1040 190 295 333
22 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 6. Suspended-sediment concentration simple linear regression model dataset for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—

Continued

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Streamflow, in cubic 

feet per second

Suspended-sediment 

concentration, 

in milligrams per liter

March 31, 2007 1230 220 1,370 1,240

April 16, 2007 1215 65 751 288

May 7, 2007 1030 170 3,725 1,390

June 29, 2007 1025 68 401 149

April 24, 2008 1140 123 269 208

May 9, 2008 1135 253 3,103 1,110

June 19, 2008 0945 92 223 139

September 15, 2008 1055 74 404 229

October 16, 2008 1010 110 839 1,060

March 31, 2009 1120 220 721 859

April 27, 2009 1215 270 2,150 967

June 17, 2009 1040 140 349 858

August 20, 2009 1050 220 103 292

September 10, 2009 1130 280 482 420

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample 

collection.
Results of Regression Analysis for Selected Constituents 23

Table 7. Total nitrogen simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.[hh, hours; mm, minutes; sin, sine; D, day of year; cos, cosine; <, less than]

Date Time, in hhmm sin(2πD/365) cos(2πD/365)

Turbidity, 

in formazin 

nephelometric 

units

Streamflow, 

in cubic feet 

per second

Total Kjeldahl 

nitrogen, 

in milligrams 

per liter

Nitrate plus nitrite, 

in milligrams per 

liter

Total nitrogen (Total 

Kjeldahl nitrogen plus 

nitrate plus nitrite), 

in milligrams per liter

January 26, 1999 1150 0.433 0.902 21 106 0.48 2.17 2.65April 16, 1999 1255 0.968 -0.251 128 684 1.60 0.02 1.62May 13, 1999 1025 0.753 -0.658 15 98 0.79 1.18 1.97May 24, 1999 1045 0.615 -0.788 138 158 1.20 1.34 2.54June 10, 1999 1200 0.362 -0.932 32 86 1.20 0.40 1.60June 25, 1999 1115 0.112 -0.994 120 237 1.70 0.32 2.02July 14, 1999 1120 -0.214 -0.977 28 63 1.20 0.38 1.58July 29, 1999 0955 -0.456 -0.890 56 60 1.30 0.40 1.70December 2, 1999 1035 -0.479 0.878 18 62 0.50 2.38 2.88February 25, 2000 1040 0.821 0.570 272 256 3.00 0.99 3.99April 27, 2000 1045 0.896 -0.444 13 110 0.58 1.10 1.68May 25, 2000 1020 0.588 -0.809 27 60 0.88 0.70 1.58June 21, 2000 1200 0.163 -0.987 45 47 0.91 0.52 1.43October 26, 2000 1050 -0.900 0.437 320 2,663 1.70 0.32 2.02June 6, 2001 1135 0.425 -0.905 250 1,753 1.40 0.28 1.68September 4, 2001 1105 -0.896 -0.444 39 19 1.20 0.34 1.54September 19, 20011 1025 -0.980 -0.201 1,335 188 3.40 0.93 4.33June 12, 20021 1110 0.329 -0.944 965 478 3.50 0.47 3.97August 14, 2002 1135 -0.681 -0.732 435 347 2.60 0.53 3.13March 18, 2003 1200 0.970 0.243 600 396 3.40 1.03 4.43March 19, 2003 1220 0.974 0.226 580 2,245 2.40 0.55 2.95April 21, 2003 1130 0.943 -0.333 130 551 1.40 0.47 1.87March 5, 2004 1210 0.900 0.437 475 1,968 3.00 0.75 3.75May 14, 2004 1035 0.730 -0.684 210 579 1.70 0.47 2.17June 14, 2004 0945 0.280 -0.960 120 238 1.50 0.44 1.94September 8, 2004 1025 -0.931 -0.366 12 39 0.45 0.92 1.37March 24, 2005 1015 0.990 0.142 105 381 1.40 0.78 2.18May 16, 2005 1140 0.718 -0.696 115 524 1.40 0.10 1.50June 10, 2005 1055 0.362 -0.932 240 1,100 1.80 0.32 2.12
24 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents Table 7. Total nitrogen simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued [hh, hours; mm, minutes; sin, sine; D, day of year; cos, cosine; <, less than] Date Time, in hhmm sin(2

πD/365) cos(2

πD/365)

Turbidity, 

in formazin 

nephelometric 

units

Streamflow, 

in cubic feet 

per second

Total Kjeldahl 

nitrogen, 

in milligrams 

per liter

Nitrate plus nitrite, 

in milligrams per 

liter

Total nitrogen (Total 

Kjeldahl nitrogen plus 

nitrate plus nitrite), 

in milligrams per liter

June 13, 2005 0925 0.313 -0.950 125 3,150 1.30 0.16 1.46

August 29, 2005 0935 -0.845 -0.534 140 256 1.60 0.40 2.00

March 2, 20062 0950 0.867 0.498 14 92 <0.1 1.90 1.95

March 22, 2006 1130 0.984 0.176 71 144 1.30 1.64 2.94

May 1, 2006 1115 0.872 -0.490 24 85 0.73 0.39 1.12

May 12, 2006 1030 0.764 -0.645 45 156 1.30 0.66 1.96

June 5, 2006 1015 0.441 -0.898 48 39 1.60 0.18 1.78

July 31, 2006 1030 -0.486 -0.874 31 15 1.20 0.03 1.23

September 7, 2006 1050 -0.918 -0.398 25 39 0.72 0.68 1.40

September 21, 2006 1000 -0.986 -0.167 13 24 0.49 0.50 0.99

January 9, 2007 1030 0.154 0.988 22 70 0.64 1.87 2.51

March 14, 2007 1020 0.951 0.309 15 67 0.55 1.17 1.72

March 22, 2007 1000 0.984 0.176 39 98 0.84 1.03 1.87

March 26, 2007 1040 0.994 0.107 190 295 2.10 0.63 2.73

March 31, 2007 1230 1.000 0.022 220 1,370 2.60 0.40 3.00

April 16, 2007 1215 0.968 -0.251 65 751 1.00 0.43 1.43

May 7, 2007 1030 0.817 -0.577 170 3,725 2.00 0.37 2.37

June 29, 2007 1025 0.043 -0.999 68 401 1.40 0.66 2.06

April 24, 2008 1140 0.918 -0.398 123 269 1.60 0.88 2.48

May 9, 2008 1135 0.786 -0.619 253 3,103 2.20 0.36 2.56

June 19, 2008 0945 0.197 -0.980 92 223 2.30 0.16 2.46

September 15, 2008 1055 -0.968 -0.251 74 404 1.50 0.34 1.84

October 16, 2008 1010 -0.961 0.276 110 839 1.60 0.72 2.32

March 31, 2009 1120 1.000 0.022 220 721 2.10 1.19 3.29

April 27, 2009 1215 0.903 -0.429 270 2,150 2.20 0.43 2.63

June 17, 2009 1040 0.247 -0.969 140 349 1.60 0.51 2.11

August 20, 2009 1050 -0.753 -0.658 220 103 2.10 0.85 2.95

September 10, 2009 1130 -0.937 -0.350 280 482 1.90 0.58 2.48

1Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.2Data point removed from final analysis because the total Kjeldahl nitrogen value was below the detection limit and likely erroneous.
Results of Regression Analysis for Selected Constituents 25

Table 8. Total Kjeldahl nitrogen simple linear regression model dataset for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes; <, less than]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Total Kjeldahl nitrogen, in 

milligrams per liter

January 26, 1999 1150 21 0.48

April 16, 1999 1255 128 1.60

May 13, 1999 1025 14.5 0.79

May 24, 1999 1045 138 1.20

June 10, 1999 1200 32 1.20

June 25, 1999 1115 120 1.70

July 29, 1999 0955 56 1.30

December 2, 1999 1035 18 0.50

February 25, 2000 1040 272 3.00

April 27, 2000 1045 13 0.58

May 25, 2000 1020 27 0.88

June 21, 2000 1200 45 0.91

October 26, 2000 1050 320 1.70

June 6, 2001 1135 250 1.40

September 19, 20011 1025 1,335 3.40

May 13, 2002 1040 245 2.00

June 12, 20021 1110 965 3.50

August 14, 2002 1135 435 2.60

March 18, 2003 1200 600 3.40

March 19, 2003 1220 580 2.40

April 21, 2003 1130 130 1.40

March 5, 2004 1210 475 3.00

May 14, 2004 1035 210 1.70

June 14, 2004 945 120 1.50

March 24, 2005 1015 105 1.40

May 16, 2005 1140 115 1.40

June 10, 2005 1055 240 1.80

June 13, 2005 0925 125 1.30

August 29, 2005 0935 140 1.60

March 2, 20062 0950 14 <0.1

March 22, 2006 1130 71 1.30

June 5, 2006 1015 48 1.60

July 31, 2006 1030 31 1.20

September 7, 2006 1050 25 0.72

September 21, 2006 1000 13 0.49

January 9, 2007 1030 22 0.64

March 14, 2007 1020 15 0.55

March 22, 2007 1000 39 0.84

March 26, 2007 1040 190 2.10

March 31, 2007 1230 220 2.60

April 16, 2007 1215 65 1.00
26 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 8. Total Kjeldahl nitrogen simple linear regression model dataset for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes; <, less than]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Total Kjeldahl nitrogen, in 

milligrams per liter

May 7, 2007 1030 170 2.00

June 29, 2007 1025 68 1.40

April 24, 2008 1140 123 1.60

May 9, 2008 1135 253 2.20

June 19, 2008 0945 92 2.30

September 15, 2008 1055 74 1.50

October 16, 2008 1010 110 1.60

March 31, 2009 1120 220 2.10

April 27, 2009 1215 270 2.20

June 17, 2009 1040 140 1.60

August 20, 2009 1050 220 2.10

September 10, 2009 1130 280 1.90

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample 

collection.

2

Data point removed from final analysis because the total Kjeldahl nitrogen value was below the detection limit and likely erroneous.
Results of Regression Analysis for Selected Constituents 27

Table 9. Organic nitrogen simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney Reservoir 

(site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes; <, less than]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Specific conductance, 

in microsiemens per 

centimeter at 25 degrees 

Celsius

Total Kjeldahl 

nitrogen, in 

milligrams per 

liter

Ammonia, in 

milligrams per 

liter

Organic 

nitrogen 

(total Kjeldahl 

nitrogen minus 

ammonia), in 

milligrams per 

liter

January 26, 1999 1150 21 1,195 0.48 0.08 0.40

April 16, 1999 1255 128 973 1.60 0.04 1.56

May 13, 1999 1025 15 1,138 0.79 0.10 0.69

May 24, 1999 1045 138 974 1.20 0.04 1.16

June 10, 1999 1200 32 1,125 1.20 <0.03 1.19

June 25, 1999 1115 120 896 1.70 0.14 1.56

July 14, 1999 1120 28 1,078 1.20 0.07 1.13

July 29, 1999 0955 56 1,148 1.30 0.21 1.09

December 2, 1999 1035 18 1,230 0.50 0.06 0.44

February 25, 2000 1040 272 841 3.00 0.13 2.87

April 27, 2000 1045 13 1,180 0.58 0.07 0.51

May 25, 2000 1020 27 1,190 0.88 0.05 0.83

June 21, 2000 1200 45 1,120 0.91 0.06 0.85

October 26, 2000 1050 320 342 1.70 <0.03 1.69

June 6, 2001 1135 250 342 1.40 0.03 1.37

September 4, 2001 1105 39 1,080 1.20 <0.03 1.19

September 19, 20011 1025 1,335 343 3.40 0.07 3.33

June 12, 20021 1110 965 187 3.50 0.09 3.41

August 14, 2002 1135 435 398 2.60 0.17 2.43

March 18, 2003 1200 600 678 3.40 0.14 3.26

March 19, 2003 1220 580 342 2.40 0.18 2.22

April 21, 2003 1130 130 833 1.40 <0.03 1.39

March 5, 2004 1210 475 445 3.00 0.27 2.73

May 14, 2004 1035 210 407 1.70 0.06 1.64

June 14, 2004 0945 120 576 1.50 0.03 1.47

September 8, 2004 1025 12 1,240 0.45 0.04 0.41

March 24, 2005 1015 105 1,060 1.40 0.12 1.28

May 16, 2005 1140 115 518 1.40 0.04 1.36

June 10, 2005 1055 240 258 1.80 0.10 1.70

June 13, 2005 0925 125 311 1.30 0.07 1.23

August 29, 2005 0935 140 707 1.60 0.06 1.54

March 2, 2006 0950 14 1,250 <0.1 0.03 0.02

March 22, 20062 1130 71 1,665 1.30 0.09 1.21

May 1, 2006 1115 24 1,243 0.73 0.03 0.70

May 12, 2006 1030 45 1,120 1.30 0.03 1.27

June 5, 2006 1015 48 1,173 1.60 0.04 1.56

July 31, 2006 1030 31 1,150 1.20 0.03 1.17
28 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 9. Organic nitrogen simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney Reservoir 

(site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes; <, less than]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Specific conductance, 

in microsiemens per 

centimeter at 25 degrees 

Celsius

Total Kjeldahl 

nitrogen, in 

milligrams per 

liter

Ammonia, in 

milligrams per 

liter

Organic 

nitrogen 

(total Kjeldahl 

nitrogen minus 

ammonia), in 

milligrams per 

liter

September 7, 2006 1050 25 1,280 0.72 <0.03 0.71

September 21, 2006 1000 13 1,230 0.49 0.03 0.46

January 9, 2007 1030 22 1,430 0.64 0.04 0.60

March 14, 2007 1020 15 1,280 0.55 0.03 0.52

March 22, 2007 1000 39 1,120 0.84 0.07 0.77

March 26, 2007 1040 190 976 2.10 0.03 2.07

March 31, 2007 1230 220 637 2.60 0.10 2.50

April 16, 2007 1215 65 724 1.00 0.06 0.94

May 7, 2007 1030 170 317 2.00 0.05 1.95

June 29, 2007 1025 68 701 1.40 0.05 1.35

April 24, 2008 1140 123 569 1.60 0.08 1.52

May 9, 2008 1135 253 353 2.20 0.68 1.52

June 19, 2008 0945 92 978 2.30 <0.03 2.29

September 15, 2008 1055 74 831 1.50 0.03 1.47

October 16, 2008 1010 110 589 1.60 0.10 1.50

March 31, 2009 1120 220 897 2.10 0.17 1.93

April 27, 2009 1215 270 478 2.20 0.10 2.10

June 17, 2009 1040 140 785 1.60 <0.03 1.59

August 20, 2009 1050 220 1,095 2.10 0.02 2.07

September 10, 2009 1130 280 464 1.90 0.08 1.82

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.

2

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 29

Table 10. Nitrate simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes; sin, sine; D, day of year; cos, cosine]

Date Time, in hhmm sin(2πD/365) cos(2πD/365) Turbidity, in formazin 

nephelometric units

Streamflow, in 

cubic feet per 

second

Nitrate, in 

milligrams per 

liter

January 26, 1999 1150 0.4328 0.9015 21 106 2.17

April 16, 1999 1255 0.9679 -0.2512 128 684 0.44

May 13, 1999 1025 0.7527 -0.6584 15 98 1.18

May 24, 1999 1045 0.6153 -0.7883 138 158 0.87

June 10, 1999 1200 0.3617 -0.9323 32 86 0.40

June 25, 1999 1115 0.1117 -0.9937 120 237 0.32

July 14, 1999 1120 -0.2135 -0.9769 28 63 0.38

July 29, 1999 0955 -0.4559 -0.8900 56 60 0.38

August 12, 1999 1035 -0.6552 -0.7555 51 43 0.63

August 26, 1999 1050 -0.8165 -0.5773 27 34 0.74

September 22, 1999 1120 -0.9887 -0.1500 22 49 1.69

December 2, 1999 1035 -0.4787 0.8780 18 62 2.38

February 25, 2000 1040 0.8215 0.5702 272 256 0.99

April 27, 2000 1045 0.8958 -0.4444 13 110 1.10

May 25, 2000 1020 0.5878 -0.8090 27 60 0.70

June 21, 2000 1200 0.1628 -0.9867 45 47 0.52

July 26, 2000 1150 -0.4250 -0.9052 123 117 0.11

August 29, 2000 1100 -0.8543 -0.5197 13 9.4 0.37

September 28, 2000 1030 -0.9995 -0.0301 22 20 1.07

October 26, 2000 1050 -0.8996 0.4367 320 2,663 0.32

June 6, 2001 1135 0.4250 -0.9052 250 1,753 0.28

September 4, 2001 1105 -0.8958 -0.4444 39 19 0.34

September 19, 20011 1025 -0.9796 -0.2009 1,335 188 0.47

June 12, 20021 1110 0.3294 -0.9442 965 478 1.03

August 14, 2002 1135 -0.6808 -0.7325 435 347 0.55

March 18, 2003 1200 0.9701 0.2428 600 396 0.47

March 19, 2003 1220 0.9741 0.2261 580 2,245 0.75

April 21, 2003 1130 0.9428 -0.3335 130 551 0.47

March 5, 2004 1210 0.8996 0.4366 475 1,968 0.44

May 14, 2004 1035 0.7296 -0.6839 210 579 0.92

June 14, 2004 0945 0.2802 -0.9599 120 238 0.78

September 8, 2004 1025 -0.9307 -0.3657 12 39 0.10

March 24, 2005 1015 0.9899 0.1415 105 381 0.32

May 16, 2005 1140 0.7177 -0.6964 115 524 0.16

June 10, 2005 1055 0.3617 -0.9323 240 1,100 0.40

June 13, 2005 0925 0.3131 -0.9497 125 3,150 1.90

August 29, 2005 0935 -0.8453 -0.5344 140 256 0.39

March 2, 2006 0950 0.8675 0.4975 14 92 0.66

March 22, 20062 1130 0.9845 0.1755 71 144 0.18

May 1, 2006 1115 0.8717 -0.4900 24 85 0.03

May 12, 2006 1030 0.7639 -0.6454 45 156 0.68
30 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 10. Nitrate simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes; sin, sine; D, day of year; cos, cosine]

Date Time, in hhmm sin(2πD/365) cos(2πD/365) Turbidity, in formazin 

nephelometric units

Streamflow, in 

cubic feet per 

second

Nitrate, in 

milligrams per 

liter

June 5, 2006 1015 0.4405 -0.8977 48 39 0.50

July 31, 2006 1030 -0.4863 -0.8738 31 15 1.87

September 7, 2006 1050 -0.9176 -0.3975 25 39 1.17

September 21, 2006 1000 -0.9859 -0.1670 13 24 1.03

January 9, 2007 1030 0.1543 0.9880 22 70 0.63

March 14, 2007 1020 0.9511 0.3090 15 67 0.40

March 22, 2007 1000 0.9845 0.1755 39 98 0.43

March 26, 2007 1040 0.9942 0.1074 190 295 0.37

March 31, 2007 1230 0.9998 0.0215 220 1,370 0.66

April 16, 2007 1215 0.9679 -0.2512 65 751 0.82

May 7, 2007 1030 0.8165 -0.5773 170 3,725 0.85

June 29, 2007 1025 0.0430 -0.9991 68 401 0.35

September 4, 2007 1126 -0.8958 -0.4444 15 28 0.14

April 24, 2008 1140 0.9176 -0.3975 123 269 0.34

May 9, 2008 1135 0.7856 -0.6187 253 3,103 0.70

June 19, 2008 0945 0.1967 -0.9805 92 223 1.18

September 15, 2008 1055 -0.9679 -0.2512 74 404 0.42

October 16, 2008 1010 -0.9611 0.2761 110 839 0.51

March 31, 2009 1120 0.9998 0.0215 220 721 0.83

April 27, 2009 1215 0.9034 -0.4289 270 2,150 0.56

June 17, 2009 1040 0.2470 -0.9690 140 349 0.51

August 20, 2009 1050 -0.7527 -0.6584 220 103 0.83

September 10, 2009 1130 -0.9369 -0.3496 280 482 0.56

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.

2

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 31

Table 11. Total phosphorus simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Streamflow, in cubic 

feet per second

Total phosphorus, in 

milligrams per liter

January 26, 1999 1150 21 106 0.07

April 16, 1999 1255 128 684 0.21

May 13, 1999 1025 15 98 0.05

May 24, 1999 1045 138 158 0.24

June 10, 1999 1200 32 86 0.13

June 25, 1999 1115 120 237 0.26

July 29, 1999 0955 56 60 0.19

August 12, 1999 1035 51 43 0.13

August 26, 1999 1050 27 34 0.09

September 22, 1999 1120 22 49 0.09

December 2, 1999 1035 18 62 0.07

February 25, 2000 1040 272 256 0.58

April 27, 2000 1045 13 110 0.06

May 25, 2000 1020 27 60 0.07

June 21, 2000 1200 45 47 0.11

July 26, 2000 1150 123 117 0.26

August 29, 2000 1100 13 9.4 0.08

September 28, 20001 1030 22 20 0.03

October 26, 2000 1050 320 2,663 0.48

June 6, 2001 1135 250 1,753 0.44

September 19, 20012 1025 1,335 188 0.57

May 13, 2002 1040 245 318 0.45

June 12, 20022 1110 965 478 0.38

August 14, 2002 1135 435 347 0.52

March 18, 2003 1200 600 396 0.45

March 19, 2003 1220 580 2,245 0.51

April 21, 2003 1130 130 551 0.33

March 5, 2004 1210 475 1,968 0.51

May 14, 20041 1035 210 579 0.08

June 14, 2004 0945 120 238 0.34

March 24, 2005 1015 105 381 0.19

May 16, 2005 1140 115 524 0.23

June 10, 20051 1055 240 1,100 0.09

June 13, 2005 0925 125 3,150 0.18

August 29, 2005 0935 140 256 0.27

March 2, 2006 0950 14 92 0.04

March 22, 2006 1130 71 144 0.23

June 5, 2006 1015 48 39 0.26

July 31, 2006 1030 31 15 0.14

September 7, 2006 1050 25 39 0.13

September 21, 2006 1000 13 24 0.09
32 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 11. Total phosphorus simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Streamflow, in cubic 

feet per second

Total phosphorus, in 

milligrams per liter

January 9, 2007 1030 22 70 0.07

March 14, 2007 1020 15 67 0.10

March 22, 2007 1000 39 98 0.12

March 26, 2007 1040 190 295 0.49

March 31, 2007 1230 220 1,370 0.48

April 16, 2007 1215 65 751 0.31

May 7, 2007 1030 170 3,725 0.51

June 29, 2007 1025 68 401 0.45

September 4, 2007 1126 15 28 0.11

April 24, 2008 1140 123 269 0.34

May 9, 2008 1135 253 3,103 0.47

June 19, 2008 0945 92 223 0.31

September 15, 2008 1055 74 404 0.41

October 16, 2008 1010 110 839 0.45

March 31, 2009 1120 220 721 0.39

April 27, 2009 1215 270 2,150 0.42

June 17, 2009 1040 140 349 0.38

August 20, 2009 1050 220 103 0.31

September 10, 2009 1130 280 482 0.40

1

Data point removed from final analysis because of laboratory issues with phosphorus analysis. Dissolved phosphorus was greater than total phosphorus. 

2

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.
Results of Regression Analysis for Selected Constituents 33

Table 12. Orthophosphate simple linear regression model dataset for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm

Specific conductance, 

in microsiemens per centimeter at 25 degrees Celsius

Orthophosphate, in 

milligrams per liter

January 26, 1999 1150 1,195 0.02

April 16, 1999 1255 973 0.05

May 13, 1999 1025 1,138 <0.01

May 24, 1999 1045 974 0.02

June 10, 1999 1200 1,125 <0.01

June 25, 1999 1115 896 0.06

July 14, 1999 1120 1,078 0.02

July 29, 1999 0955 1,148 0.02

August 12, 1999 1035 1,150 <0.01

August 26, 1999 1050 1,080 <0.01

December 2, 1999 1035 1,230 <0.01

February 25, 2000 1040 841 <0.01

April 27, 2000 1045 1,180 0.01

May 25, 2000 1020 1,190 <0.01

June 21, 2000 1200 1,120 <0.01

July 26, 2000 1150 896 <0.01

August 29, 2000 1100 1,080 <0.01

September 28, 20001 1030 1,058 <0.01

October 26, 2000 1050 342 0.18

June 6, 2001 1135 342 0.18

September 4, 2001 1105 1,080 <0.01

September 19, 20012 1025 343 0.04

June 12, 20022 1110 187 0.19

August 14, 2002 1135 398 0.11

March 18, 2003 1200 678 0.05

March 19, 2003 1220 342 0.14

April 21, 2003 1130 833 0.07

March 5, 2004 1210 445 0.15

May 14, 20041 1035 407 0.16

June 14, 20043 0945 576 0.12

September 8, 2004 1025 1,240 0.02

March 24, 2005 1015 1,060 0.05

May 16, 2005 1140 518 0.04

June 10, 20053 1055 258 0.17

June 13, 20053 0925 311 0.16

August 29, 2005 0935 707 0.11

March 2, 2006 0950 1,250 0.02

March 22, 20064 1130 1,665 0.08

May 1, 2006 1115 1,243 0.02

May 12, 20063 1030 1,120 0.13
34 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 12. Orthophosphate simple linear regression model dataset for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in hhmm

Specific conductance, 

in microsiemens per centimeter at 25 degrees Celsius

Orthophosphate, in 

milligrams per liter

June 5, 2006 1015 1,173 0.02

July 31, 2006 1030 1,150 <0.01

September 7, 2006 1050 1,280 <0.01

September 21, 2006 1000 1,230 <0.01

January 9, 2007 1030 1,430 <0.01

March 14, 2007 1020 1,280 <0.01

March 22, 2007 1000 1,120 <0.01

March 26, 2007 1040 976 0.03

March 31, 2007 1230 637 0.14

April 16, 2007 1215 724 0.11

May 7, 2007 1030 317 0.21

June 29, 2007 1025 701 0.23

September 4, 2007 1126 1,140 <0.01

April 24, 2008 1140 569 0.14

May 9, 2008 1135 353 0.16

June 19, 2008 0945 978 0.04

September 15, 2008 1055 831 0.09

October 16, 2008 1010 589 0.19

March 31, 2009 1120 897 0.09

April 27, 2009 1215 478 0.13

June 17, 2009 1040 785 0.12

August 20, 2009 1050 1,095 0.04

September 10, 2009 1130 464 0.11

1

Data point removed from final analysis because of laboratory issues with phosphorus analysis. Dissolved phosphorus was 

greater than total phosphorus. 

2

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during 

sample collection.

3

Data point removed from final analysis because of laboratory issues with phosphorus analysis. Orthophosphorus was larger 

than dissolved phosphorus.

4

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 35

Table 13. Fecal coliform bacteria simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Specific conductance, in 

microsiemens per centimeter 

at 25 degrees Celsius

Fecal coliform bacteria, in 

colonies per 100 milligrams

January 26, 1999 1150 21 1,195 8.0

February 1, 1999 1055 120 1,060 200

April 15, 1999 1125 180 629 65,000

April 16, 1999 1255 128 973 5,700

May 13, 1999 1025 15 1,138 100

May 24, 1999 1045 138 974 760

June 10, 1999 1200 32 1,125 280

June 25, 1999 1115 120 896 780

July 29, 1999 0955 56 1,148 190

August 12, 1999 1035 51 1,150 1,000

August 26, 1999 1050 27 1,080 470

September 22, 1999 1120 22 1,165 320

December 2, 1999 1035 18 1,230 80

February 25, 2000 1040 272 841 13,000

April 27, 2000 1045 13 1,180 240

May 25, 2000 1020 27 1,190 100

June 21, 2000 1200 45 1,120 300

July 26, 2000 1150 123 896 700

August 29, 2000 1100 13 1,080 530

September 28, 2000 1030 22 1,058 330

October 26, 2000 1050 320 342 36,000

June 6, 2001 1135 250 342 5,900

September 19, 20011 1025 1,335 343 22,000

June 12, 20021 1110 965 187 6,700

August 14, 2002 1135 435 398 21,000

March 18, 2003 1200 600 678 10,000

March 19, 2003 1220 580 342 20,000

April 21, 2003 1130 130 833 2,500

March 5, 2004 1210 475 445 3,900

May 14, 2004 1035 210 407 11,000

June 14, 2004 0945 120 576 1,700

March 24, 2005 1015 105 1,060 3,200

May 16, 2005 1140 115 518 1,300

June 10, 2005 1055 240 258 810

June 13, 2005 0925 125 311 3,300

August 29, 2005 0935 140 707 590

March 2, 2006 0950 14 1,250 27

March 22, 20062 1130 71 1,665 220

June 5, 2006 1015 48 1,173 19

July 31, 2006 1030 31 1,150 400
36 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 13. Fecal coliform bacteria simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Specific conductance, in 

microsiemens per centimeter 

at 25 degrees Celsius

Fecal coliform bacteria, in 

colonies per 100 milligrams

September 7, 2006 1050 25 1,280 520

September 21, 2006 1000 13 1,230 330

January 9, 2007 1030 22 1,430 24

March 14, 2007 1020 15 1,280 95

March 22, 2007 1000 39 1,120 300

March 26, 2007 1040 190 976 1,100

March 31, 2007 1230 220 637 2,000

April 1, 2007 1600 120 572 11,000

April 16, 2007 1215 65 724 1,800

May 7, 2007 1030 170 317 20,000

May 24, 2007 1200 150 200 15,000

June 29, 2007 1025 68 701 710

September 4, 2007 1126 15 1,140 170

April 24, 2008 1140 123 569 6,700

May 9, 2008 1135 253 353 35,000

June 19, 2008 0945 92 978 900

September 15, 2008 1055 74 831 590

October 16, 2008 1010 110 589 8,700

March 31, 2009 1120 220 897 3,500

April 27, 2009 1215 270 478 35,000

June 17, 2009 1040 140 785 1,400

August 20, 2009 1050 220 1,095 860

September 10, 2009 1130 280 464 15,000

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.

2

Data point removed from final analysis because of the large specific conductance value likely affected by road salt application.
Results of Regression Analysis for Selected Constituents 37

Table 14. Escherichia coli bacteria simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, 

in hhmm

Turbidity, in formazin 

nephelometric units

Specific conductance, 

in microsiemens 

per centimeter at 25 

degrees Celsius

Streamflow, in cubic 

feet per second

Escherichia coli,

in colonies per 

100 milliliters

July 31, 2006 1030 31 1,150 15 340

September 7, 2006 1050 25 1,280 39 250

September 21, 2006 1000 13 1,230 24 140

January 9, 2007 1030 22 1,430 70 17

March 14, 2007 1020 15 1,280 67 82

March 26, 2007 1040 190 976 295 1,300

March 31, 2007 1230 220 637 1,370 6,000

April 1, 2007 1600 120 572 1,660 6,100

April 16, 2007 1215 65 724 751 1,500

May 7, 2007 1030 170 317 3,725 12,000

May 24, 2007 1200 150 200 4,780 6,700

June 29, 2007 1025 68 701 401 680

April 24, 2008 1140 123 569 269 2,600

May 9, 2008 1135 253 353 3,103 28,000

June 19, 2008 0945 92 978 223 670

September 15, 2008 1055 74 831 404 620

October 16, 2008 1010 110 589 839 6,300

March 31, 2009 1120 220 897 721 3,900

April 27, 2009 1215 270 478 2,150 30,000

June 17, 2009 1040 140 785 349 1,200

August 20, 2009 1050 220 1,095 103 800

September 10, 2009 1130 280 464 482 2,700
38 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Table 15. Total organic carbon simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Total organic carbon, 

in milligrams per liter

April 16, 1999 1255 128 10.7

June 10, 1999 1200 32 3.40

June 25, 1999 1115 120 7.60

July 29, 1999 0955 56 4.60

September 22, 1999 1120 22 3.00

December 2, 1999 1035 18 2.50

February 25, 2000 1040 272 9.70

October 26, 2000 1050 320 6.70

June 6, 2001 1135 250 7.40

September 19, 20011 1025 1,335 6.30

June 12, 20021 1110 965 22.5

August 14, 2002 1135 435 19.4

March 18, 2003 1200 600 15.9

March 19, 2003 1220 580 18.9

April 21, 2003 1130 130 13.7

March 5, 2004 1210 475 20.5

May 14, 2004 1035 210 12.9

June 14, 2004 0945 120 12.6

March 24, 2005 1015 105 9.90

May 16, 2005 1140 115 9.50

June 10, 2005 1055 240 15.4

June 13, 2005 0925 125 15.6

August 29, 2005 0935 140 12.6

March 2, 2006 0950 14 2.80

March 22, 2006 1130 71 9.00

June 5, 2006 1015 48 6.90

July 31, 2006 1030 31 5.70

September 7, 2006 1050 25 4.90

September 21, 2006 1000 13 4.20

January 9, 2007 1030 22 4.50

March 22, 2007 1000 39 5.50

March 26, 2007 1040 190 15.7

March 31, 2007 1230 220 18.7

April 16, 2007 1215 65 10.5

May 7, 2007 1030 170 16.4

June 29, 2007 1025 68 12.7

September 4, 2007 1126 15 4.21

April 24, 2008 1140 123 13.0

May 9, 2008 1135 253 15.3

June 19, 2008 0945 92 11.2

September 15, 2008 1055 74 12.9
Results of Regression Analysis for Selected Constituents 39

Table 15. Total organic carbon simple linear regression model dataset for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.—Continued

[hh, hours; mm, minutes]

Date Time, in hhmm Turbidity, in formazin 

nephelometric units

Total organic carbon, 

in milligrams per liter

October 16, 2008 1010 110 13.5

March 31, 2009 1120 220 17.4

April 27, 2009 1215 270 19.7

June 17, 2009 1040 140 15.5

August 20, 2009 1050 220 14.3

September 10, 2009 1130 280 16.4

1

Data point removed from final analysis because of atypically large heterogeneity in channel cross-sectional data during sample collection.
40 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGDS ~ LOGSC, data = DS, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.07485 -0.01183 -0.0008959 0.009746 0.1077

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.0810 0.0469 1.7274 0.0893 

 LOGSC 0.8916 0.0161 55.4096 0.0000 

Residual standard error: 0.02496 on 59 degrees of freedom

Multiple R-Squared: 0.9811 Adjusted R-squared: 0.9808 

F-statistic: 3070 on 1 and 59 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGSC -0.9977 

Analysis of Variance Table

Response: LOGDS

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGSC 1 1.913515 1.913515 3070.229 0

Residuals 59 0.036772 0.000623 

 model.formula nvars stderr adjr2 Cp press 

 LOGDS ~ LOGSC 1 0.02496494 98.08259 2.792865 0.04052048

Test criteria

leverage cooksD dfits 

 0.0984 0.798 0.362

Observations exceeding at least one test criterion

 LOGDS yhat resids stnd.res stud.res leverage cooksD dfits 

2 2.67 2.75 -0.0748 -3.03 -3.27 0.0191 0.0893 -0.456

20 2.29 2.34 -0.0520 -2.16 -2.24 0.0744 0.1880 -0.634

21 2.30 2.34 -0.0439 -1.83 -1.87 0.0741 0.1339 -0.528

27 2.55 2.44 0.1077 4.41 5.35 0.0441 0.4498 1.149

33 2.28 2.23 0.0506 2.16 2.23 0.1187 0.3138 0.818

34 2.33 2.30 0.0315 1.32 1.33 0.0879 0.0843 0.413

Figure 2. S+® output of regression model development using specific conductance (SC) as an 

explanatory variable for dissolved solids (DS) concentrations for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 41

Fitted : LOGSC

Residuals

2.4 2.6 2.8

-0.05 0.0 0.05 0.10

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.05 0.0 0.05 0.10

2.4 2.6 2.8 3.0 3.2

LOGSC

2.1

2.3

2.5

2.7

2.9

LOGDS

0 100 200 300 400 500 600 700 800

COMPUTED.DS.USING.SC

0

200

400

600

800

ACTUAL.DS

A B

C D

Figure 3. S+® output graphs from simple linear regression analysis showing A, log-transformed specific conductance (SC) versus 

log-transformed dissolved solids (DS) concentrations; B, computed versus actual DS concentrations; C, computed log-transformed 

DS concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
42 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGDS ~ LOGQ, data = DS, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.2396 -0.08065 0.01697 0.08353 0.1845

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.1891 0.0484 65.8379 0.0000

 LOGQ -0.2249 0.0203 -11.0809 0.0000

Residual standard error: 0.1036 on 59 degrees of freedom

Multiple R-Squared: 0.6754 Adjusted R-squared: 0.6699 

F-statistic: 122.8 on 1 and 59 degrees of freedom, the p-value is 4.441e-016 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9618 

Analysis of Variance Table

Response: LOGDS

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 1.317310 1.317310 122.787 4.440892e-016

Residuals 59 0.632977 0.010728 

 model.formula nvars stderr adjr2 Cp press 

 LOGDS ~ LOGQ 1 0.10357807 66.99434 6.949271 0.680932

Test criteria

leverage cooksD dfits 

 0.0984 0.798 0.362

Observations exceeding at least one test criterion

 LOGDS yhat resids stnd.res stud.res leverage cooksD dfits 

18 2.76 2.97 -0.206 -2.08 -2.14 0.0834 0.1960 -0.645

21 2.30 2.46 -0.163 -1.62 -1.64 0.0509 0.0700 -0.379

33 2.28 2.51 -0.224 -2.21 -2.28 0.0377 0.0954 -0.452

Figure 4. S+® output of regression model development using streamflow (Q) as an explanatory variable for 

dissolved solids (DS) concentrations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 43

Fitted : LOGQ

Residuals

2.4 2.5 2.6 2.7 2.8 2.9

-0.2 -0.1 0.0 0.1 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.2 -0.1 0.0 0.1 0.2

0.5 1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

2.1

2.3

2.5

2.7

2.9

LOGDS

200 400 600 800 1000

COMPUTED.DS.USING.Q

0

200

400

600

800

ACTUAL.DS

A B

C D

Figure 5. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus log-transformed 

dissolved solids (DS) concentrations; B, computed versus actual DS concentrations; C, computed log-transformed DS concentrations 

versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
44 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGCA ~ LOGQ + LOGSC, data = CA, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1095 -0.02992 -0.00139 0.04099 0.09087

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.3710 0.1981 -6.9211 0.0000

 LOGQ 0.1197 0.0171 6.9865 0.0000

 LOGSC 0.9641 0.0564 17.1014 0.0000

Residual standard error: 0.04779 on 58 degrees of freedom

Multiple R-Squared: 0.8907 Adjusted R-squared: 0.887 

F-statistic: 236.4 on 2 and 58 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) LOGQ 

LOGQ -0.8915 

LOGSC -0.9936 0.8375

Analysis of Variance Table

Response: LOGCA

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 0.4117400 0.4117400 180.2895 0

 LOGSC 1 0.6679043 0.6679043 292.4566 0

Residuals 58 0.1324588 0.0022838 

Variance inflation factors

 LOGQ LOGSC 

3.34962 3.34962

 model.formula nvars stderr adjr2 Cp press 

LOGCA ~ LOGQ + LOGSC 2 0.04778883 88.69516 3.00000 0.1492417

Test criteria

leverage cooksD dfits 

 0.148 0.849 0.444

Observations exceeding at least one test criterion

 LOGCA yhat resids stnd.res stud.res leverage cooksD dfits 

2 1.74 1.85 -0.1095 -2.41 -2.52 0.0939 0.2002 -0.810

22 1.63 1.71 -0.0707 -1.54 -1.56 0.0825 0.0714 -0.469

33 1.37 1.32 0.0482 1.11 1.11 0.1683 0.0825 0.498

40 1.62 1.72 -0.1007 -2.21 -2.29 0.0912 0.1634 -0.725

53 1.41 1.50 -0.0962 -2.09 -2.16 0.0756 0.1193 -0.617

Figure 6. S+® output of regression model development using streamflow (Q) and specific conductance (SC) 

as explanatory variables for calcium (CA) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 45

Fitted : LOGQ + LOGSC

Residuals

1.3 1.4 1.5 1.6 1.7 1.8 1.9

-0.10 -0.05 0.0 0.05

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.10 -0.05 0.0 0.05

.

20 30 40 50 60 70 80

COMPUTED.CA.USING.Q.AND.SC

0

20

40

60

80

ACTUAL.CA

C

A B

Figure 7. S+® output graphs from simple linear regression analysis using streamflow (Q) and specific conductance (SC) as explanatory 

variables for calcium (CA) showing A, computed versus actual CA concentrations; B, computed log-transformed CA concentrations 

versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
46 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGMG ~ LOGSC, data = MG, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1213 -0.02679 0.003214 0.01909 0.1361

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.0822 0.0770 -14.0606 0.0000

 LOGSC 0.6975 0.0264 26.4042 0.0000

Residual standard error: 0.04098 on 59 degrees of freedom

Multiple R-Squared: 0.922 Adjusted R-squared: 0.9207 

F-statistic: 697.2 on 1 and 59 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGSC -0.9977 

Analysis of Variance Table

Response: LOGMG

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGSC 1 1.170948 1.170948 697.183 0

Residuals 59 0.099093 0.001680 

 model.formula nvars stderr adjr2 Cp press 

 LOGMG ~ LOGSC 1 0.04098222 92.06541 2.706622 0.1079854

Test criteria

leverage cooksD dfits 

 0.0984 0.798 0.362

Observations exceeding at least one test criterion

 LOGMG yhat resids stnd.res stud.res leverage cooksD dfits 

20 0.563 0.685 -0.1213 -3.08 -3.33 0.0744 0.380 -0.943

33 0.646 0.599 0.0472 1.23 1.23 0.1187 0.101 0.452

34 0.720 0.656 0.0642 1.64 1.67 0.0879 0.130 0.517

58 0.923 0.787 0.1361 3.39 3.74 0.0379 0.226 0.742

Figure 8. S+® output of regression model development using specific conductance (SC) as an 

explanatory variable for magnesium (MG) concentrations for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 47

Fitted : LOGSC

Residuals

0.6 0.7 0.8 0.9 1.0 1.1

-0.10 -0.05 0.0 0.05 0.10

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.10 -0.05 0.0 0.05 0.10

2.4 2.6 2.8 3.0 3.2

LOGSC

0.5

0.7

0.9

1.1

LOGMG

2 4 6 8 10 12 14

COMPUTED.MG.USING.SC

2

4

6

8

10

12

ACTUAL.MG

C

A B

D

Figure 9. S+® output graphs from simple linear regression analysis showing A, log-transformed specific conductance (SC) versus 

log-transformed magnesium (MG) concentrations; B, computed versus actual MG concentrations; C, computed log-transformed 

MG concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
48 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGNA ~ LOGSC, data = NA, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.08809 -0.01781 -0.002292 0.02416 0.05946

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.8615 0.0620 -30.0234 0.0000

 LOGSC 1.3295 0.0213 62.4796 0.0000

Residual standard error: 0.03301 on 59 degrees of freedom

Multiple R-Squared: 0.9851 Adjusted R-squared: 0.9849 

F-statistic: 3904 on 1 and 59 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGSC -0.9977 

Analysis of Variance Table

Response: LOGNA

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGSC 1 4.254731 4.254731 3903.701 0

Residuals 59 0.064305 0.001090 

 model.formula nvars stderr adjr2 Cp press 

 LOGNA ~ LOGSC 1 0.03301397 98.48588 6.550423 0.06965938

Test criteria

leverage cooksD dfits 

 0.0984 0.798 0.362

Observations exceeding at least one test criterion

 LOGNA yhat resids stnd.res stud.res leverage cooksD dfits 

23 1.65 1.59 0.0589 1.836 1.874 0.0557 0.0994 0.455

28 1.66 1.61 0.0538 1.676 1.703 0.0531 0.0788 0.403

33 1.36 1.34 0.0143 0.461 0.458 0.1187 0.0143 0.168

34 1.36 1.45 -0.0881 -2.794 -2.974 0.0879 0.3762 -0.923

43 2.26 2.33 -0.0687 -2.126 -2.194 0.0420 0.0992 -0.460

Figure 10. S+® output of regression model development using specific conductance (SC) as an 

explanatory variable for sodium (NA) concentrations for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 49

Fitted : LOGSC

Residuals

1.4 1.6 1.8 2.0 2.2

-0.05 0.0 0.05

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.05 0.0 0.05

2.4 2.6 2.8 3.0 3.2

LOGSC

1.2

1.4

1.6

1.8

2.0

2.2

2.4

LOGNA

0 50 100 150 200

COMPUTED.NA.USING.SC

0

50

100

150

200

ACTUAL.NA

A

C

B

D

Figure 11. S+® output graphs of simple linear regression analysis showing A, log-transformed specific conductance (SC) versus 

log-transformed sodium (NA) concentrations; B, computed versus actual NA concentrations; C, computed log-transformed NA 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
50 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGNA ~ LOGQ, data = Na, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.3833 -0.0946 0.0231 0.09604 0.277

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.8099 0.0639 43.9399 0.0000

 LOGQ -0.3514 0.0268 -13.1139 0.0000

Residual standard error: 0.1367 on 59 degrees of freedom

Multiple R-Squared: 0.7446 Adjusted R-squared: 0.7402 

F-statistic: 172 on 1 and 59 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9618 

Analysis of Variance Table

Response: LOGNA

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 3.215783 3.215783 171.9742 0

Residuals 59 1.103254 0.018699 

 model.formula nvars stderr adjr2 Cp press 

 LOGNA ~ LOGQ 1 0.1367451 74.02307 5.067156 1.187213

Test criteria

leverage cooksD dfits 

 0.0984 0.798 0.362

Observations exceeding at least one test criterion

 LOGNA yhat resids stnd.res stud.res leverage cooksD dfits 

18 2.21 2.47 -0.258 -1.97 -2.02 0.0834 0.1768 -0.610

33 1.36 1.74 -0.383 -2.86 -3.05 0.0377 0.1602 -0.605

34 1.36 1.58 -0.217 -1.65 -1.67 0.0719 0.1053 -0.466

57 2.08 1.81 0.277 2.06 2.12 0.0285 0.0621 0.363

Figure 12. S+® output of regression model development using streamflow (Q) as an explanatory 

variable for sodium (NA) concentrations for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 51

Fitted : LOGQ

Residuals

1.6 1.8 2.0 2.2 2.4

-0.4 -0.2 0.0 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.4 -0.2 0.0 0.2

0.5 1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

1.2

1.6

2.0

2.4

LOGNA

0 50 100 150 200 250 300

COMPUTED.NA.USING.Q

0

50

100

150

200

250

ACTUAL.NA

B

C

A

D

Figure 13. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus logtransformed sodium (NA) concentrations; B, computed versus actual NA concentrations; C, computed log-transformed NA 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 071447800), south-central Kansas, 1999 through 2009.
52 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGCL ~ LOGSC, data = CL, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1695 -0.03047 0.01382 0.04013 0.1298

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.8984 0.1180 -16.0909 0.0000

 LOGSC 1.3868 0.0410 33.8255 0.0000

Residual standard error: 0.05914 on 46 degrees of freedom

Multiple R-Squared: 0.9613 Adjusted R-squared: 0.9605 

F-statistic: 1144 on 1 and 46 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGSC -0.9974 

Analysis of Variance Table

Response: LOGCL

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGSC 1 4.001980 4.001980 1144.166 0

Residuals 46 0.160895 0.003498

 model.formula nvars stderr adjr2 Cp press 

 LOGCL ~ LOGSC 1 0.05914158 96.05097 1.53727 0.1765017

Test criteria

leverage cooksD dfits 

 0.125 0.8 0.408

Observations exceeding at least one test criterion

 LOGCL yhat resids stnd.res stud.res leverage cooksD dfits 

1 2.10 2.25 -0.1416 -2.43 -2.57 0.0275 0.0834 -0.433

9 1.53 1.62 -0.0848 -1.49 -1.51 0.0750 0.0901 -0.430

36 1.70 1.57 0.1298 2.30 2.41 0.0865 0.2498 0.743

41 2.08 2.25 -0.1695 -2.91 -3.18 0.0278 0.1207 -0.538

45 1.68 1.82 -0.1362 -2.35 -2.48 0.0383 0.1099 -0.494

Figure 14. S+® output of regression model development using specific conductance (SC) as an 

explanatory variable for chloride (CL) concentrations for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 53

Fitted : LOGSC

Residuals

1.6 1.8 2.0 2.2 2.4

-0.15 -0.10 -0.05 0.0 0.05 0.10

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.15 -0.10 -0.05 0.0 0.05 0.10

2.4 2.6 2.8 3.0 3.2

LOGSC

1.4

1.6

1.8

2.0

2.2

2.4

LOGCL

0 50 100 150 200 250 300

COMPUTED.CL.USING.SC

0

100

200

300

ACTUAL.CL

C

A B

D

Figure 15. S+® output graphs from simple linear regression showing A, log-transformed specific conductance (SC) versus 

log-transformed chloride (CL) concentrations; B, computed versus actual CL concentrations; C, computed log-transformed CL 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
54 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGCL ~ LOGQ, data = CL, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.346 -0.09134 0.02241 0.1038 0.261

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 3.0610 0.0826 37.0506 0.0000

 LOGQ -0.4010 0.0327 -12.2547 0.0000

Residual standard error: 0.1457 on 46 degrees of freedom

Multiple R-Squared: 0.7655 Adjusted R-squared: 0.7604 

F-statistic: 150.2 on 1 and 46 degrees of freedom, the p-value is 4.441e-016 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9671 

Analysis of Variance Table

Response: LOGCL

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 3.186761 3.186761 150.178 4.440892e-016

Residuals 46 0.976115 0.021220 

 model.formula nvars stderr adjr2 Cp press 

 LOGCL ~ LOGQ 1 0.1456705 76.04216 3.316772 1.056413

Test criteria

leverage cooksD dfits 

 0.125 0.8 0.408

Observations exceeding at least one test criterion

 LOGCL yhat resids stnd.res stud.res leverage cooksD dfits 

10 2.36 2.55 -0.195 -1.40 -1.42 0.0905 0.0979 -0.447

21 1.50 1.84 -0.346 -2.42 -2.57 0.0390 0.1190 -0.517

28 2.40 2.60 -0.192 -1.39 -1.41 0.1036 0.1122 -0.479

Figure 16. S+® output of regression model development using streamflow (Q) as the explanatory variable 

for chloride (CL) concentrations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 55

Fitted : LOGQ

Residuals

1.6 1.8 2.0 2.2 2.4 2.6

-0.3 -0.2 -0.1 0.0 0.1 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.3 -0.2 -0.1 0.0 0.1 0.2

1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

1.4

1.6

1.8

2.0

2.2

2.4

2.6

LOGCL

0 100 200 300 400

COMPUTED.CL.USING.Q

0

100

200

300

ACTUAL.CL

C

A B

D

Figure 17. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus logtransformed chloride (CL) concentrations; B, computed versus actual CL concentrations; C, computed log-transformed CL 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
56 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGK ~ SC + LOGSC, data = K, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1576 -0.05541 -0.003193 0.05333 0.1994

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.7980 0.6242 -2.8806 0.0056 

 SC -0.0011 0.0002 -6.5201 0.0000 

 LOGSC 1.1690 0.2627 4.4495 0.0000 

Residual standard error: 0.07405 on 58 degrees of freedom

Multiple R-Squared: 0.7329 Adjusted R-squared: 0.7237 

F-statistic: 79.58 on 2 and 58 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) SC 

 SC 0.9749 

LOGSC -0.9990 -0.9834

Analysis of Variance Table

Response: LOGK

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SC 1 0.7641589 0.7641589 139.3684 0.00000000000

 LOGSC 1 0.1085549 0.1085549 19.7984 0.00003959515

Residuals 58 0.3180148 0.0054830

Variance inflation factors

 SC LOGSC 

30.30338 30.30338

 model.formula nvars stderr adjr2 Cp press 

LOGK ~ SC + LOGSC 2 0.07404738 72.37146 3.00000 0.3558819

Test criteria

leverage cooksD dfits 

 0.148 0.849 0.444

Observations exceeding at least one test criterion

 LOGK yhat resids stnd.res stud.res leverage cooksD dfits 

24 0.640 0.798 -0.158 -2.186 -2.26 0.0521 0.0875 -0.530

33 0.778 0.749 0.029 0.453 0.45 0.2537 0.0233 0.262

43 0.584 0.385 0.199 2.918 3.13 0.1488 0.4963 1.310

Figure 18. S+® output of regression model development using specific conductance (SC) as an 

explanatory variable for potassium (K) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 57

Fitted : SC + LOGSC

Residuals

0.4 0.5 0.6 0.7 0.8

-0.1 0.0 0.1 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.1 0.0 0.1 0.2

2 3 4 5 6

COMPUTED.K.USING.SC

2

4

6

8

ACTUAL.K

C

A B

Figure 19. S+® output graphs from simple linear regression analysis using specific conductance (SC) and log-transformed SC as 

explanatory variables for potassium (K) concentrations showing A, computed versus actual K concentrations; B, computed logtransformed K concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North 

Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
58 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = SO4 ~ SC, data = SO4, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-15.94 -2.564 0.1872 3.105 14.14

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.0020 2.0754 -0.0009 0.9992

 SC 0.0408 0.0023 17.4635 0.0000

Residual standard error: 5.437 on 46 degrees of freedom

Multiple R-Squared: 0.8689 Adjusted R-squared: 0.8661 

F-statistic: 305 on 1 and 46 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

SC -0.9258 

Analysis of Variance Table

Response: SO4

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SC 1 9015.111 9015.111 304.9746 0

Residuals 46 1359.769 29.560 

 model.formula nvars stderr adjr2 Cp press 

 SO4 ~ SC 1 5.436929 86.60872 2.835275 1457.633

Test criteria

leverage cooksD dfits 

 0.125 0.8 0.408

Observations exceeding at least one test criterion

 SO4 yhat resids stnd.res stud.res leverage cooksD dfits 

4 61 46.9 14.1 2.66 2.85 0.0405 0.149 0.586

41 24 39.9 -15.9 -2.97 -3.27 0.0254 0.115 -0.527

Figure 20. S+® output of regression model development using specific conductance (SC) as an 

explanatory variable for sulfate (SO4) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 59

Fitted : SC

Residuals

10 20 30 40 50 60

-15 -10 -5 0 5 10 15

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-15 -10 -5 0 5 10 15

200 400 600 800 1000 1200 1400

SC

0

20

40

60

SO4

10 20 30 40 50 60

COMPUTED.SO4.USING.SC

0

20

40

60

ACTUAL.SO4

B

C

A

D

Figure 21. S+® output graphs from simple linear regression analysis showing A, specific conductance (SC) versus sulfate (SO4) 

concentrations; B, computed versus actual SO4 concentrations; C, computed SO4 concentrations versus regression residuals; and 

D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
60 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = SO4 ~ LOGQ, data = SO4, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-11.43 -6.472 -0.3668 5.413 14.13

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 82.5695 4.0854 20.2107 0.0000

 LOGQ -20.0745 1.6180 -12.4071 0.0000

Residual standard error: 7.204 on 46 degrees of freedom

Multiple R-Squared: 0.7699 Adjusted R-squared: 0.7649 

F-statistic: 153.9 on 1 and 46 degrees of freedom, the p-value is 3.331e-016 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9671 

Analysis of Variance Table

Response: SO4

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 7987.909 7987.909 153.9373 3.330669e-016

Residuals 46 2386.971 51.891

 model.formula nvars stderr adjr2 Cp press 

 SO4 ~ LOGQ 1 7.203518 76.49263 1.189501 2587.379

Test criteria

leverage cooksD dfits 

 0.125 0.8 0.408

Observations exceeding at least one test criterion

 SO4 yhat resids stnd.res stud.res leverage cooksD dfits 

4 61.0 46.9 14.13 2.00 2.08 0.0431 0.0904 0.440

10 47.0 57.1 -10.13 -1.47 -1.49 0.0905 0.1081 -0.471

28 50.2 59.3 -9.06 -1.33 -1.34 0.1036 0.1018 -0.455

Figure 22. S+® output of regression model development using streamflow (Q) as an explanatory variable 

for sulfate (SO4) concentrations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 61

Fitted : LOGQ

Residuals

10 20 30 40 50 60

-10 -5 0 5 10 15

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-10 -5 0 5 10 15

1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

0

20

40

60

SO4

10 20 30 40 50 60

COMPUTED.SO4.USING.Q

0

20

40

60

ACTUAL.SO4

C

A B

D

Figure 23. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus sulfate (SO4) 

concentrations; B, computed versus actual SO4 concentrations; C, computed SO4 concentrations versus regression residuals; and 

D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
62 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGALK ~ LOGQ + LOGSC, data = ALK, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1253 -0.03398 0.007513 0.03147 0.07802

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.4469 0.2121 -2.1064 0.0408

 LOGQ 0.1136 0.0193 5.8909 0.0000

 LOGSC 0.8101 0.0595 13.6066 0.0000

Residual standard error: 0.0464 on 45 degrees of freedom

Multiple R-Squared: 0.8661 Adjusted R-squared: 0.8601 

F-statistic: 145.5 on 2 and 45 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) LOGQ 

LOGQ -0.8998 

LOGSC -0.9923 0.8415

Analysis of Variance Table

Response: LOGALK

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 0.2278944 0.2278944 105.8508 2.118306e-013

 LOGSC 1 0.3985991 0.3985991 185.1386 0.000000e+000

Residuals 45 0.0968839 0.0021530 

Variance inflation factors

 LOGQ LOGSC 

3.425637 3.425637

 model.formula nvars stderr adjr2 Cp press 

LOGALK ~ LOGQ + LOGSC 2 0.04640018 86.01147 3.00000 0.1119638

Test criteria

leverage cooksD dfits 

 0.188 0.852 0.5

Observations exceeding at least one test criterion

 LOGALK yhat resids stnd.res stud.res leverage cooksD dfits 

8 1.87 1.99 -0.1253 -2.81 -3.06 0.0774 0.221 -0.887

21 1.91 1.85 0.0569 1.36 1.37 0.1831 0.137 0.648

28 2.08 2.16 -0.0817 -1.90 -1.96 0.1449 0.205 -0.808

Figure 24. S+® output of regression model development using streamflow (Q) and specific conductance (SC) 

as explanatory variables for alkalinity (ALK) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 63

Fitted : LOGQ + LOGSC

Residuals

1.9 2.0 2.1 2.2 2.3

-0.10 -0.05 0.0 0.05

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.10 -0.05 0.0 0.05

65 90 115 140 165 190 215

COMPUTED.ALK.USING.Q.AND.SC

50

100

150

200

ACTUAL.ALK

C

A B

Figure 25. S+® output graphs from simple linear regression analysis using streamflow (Q) and specific conductance (SC) as 

explanatory variables for alkalinity (ALK) concentrations showing A, computed versus actual ALK concentrations; B, computed logtransformed ALK concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the 

North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
64 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGHCO3 ~ LOGQ + LOGSC, data = HCO3, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1443 -0.03119 0.006959 0.02818 0.08358

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.3677 0.2190 -1.6792 0.1001

 LOGQ 0.1126 0.0199 5.6560 0.0000

 LOGSC 0.8134 0.0614 13.2375 0.0000

Residual standard error: 0.04789 on 45 degrees of freedom

Multiple R-Squared: 0.8608 Adjusted R-squared: 0.8546 

F-statistic: 139.1 on 2 and 45 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) LOGQ 

LOGQ -0.8998 

LOGSC -0.9923 0.8415

Analysis of Variance Table

Response: LOGHCO3

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 0.2362125 0.2362125 102.9856 3.274048e-013

 LOGSC 1 0.4019175 0.4019175 175.2308 0.000000e+000

Residuals 45 0.1032141 0.0022936

 

Variance inflation factors

 LOGQ LOGSC 

3.425637 3.425637

 model.formula nvars stderr adjr2 Cp press 

LOGHCO3 ~ LOGQ + LOGSC 2 0.04789203 85.45866 3.0000 0.1192452

Test criteria

leverage cooksD dfits 

 0.188 0.852 0.5

Observations exceeding at least one test criterion

 LOGHCO3 yhat resids stnd.res stud.res leverage cooksD dfits 

8 1.93 2.08 -0.1443 -3.14 -3.51 0.0774 0.275 -1.016

21 2.00 1.94 0.0598 1.38 1.40 0.1831 0.143 0.661

28 2.18 2.25 -0.0767 -1.73 -1.77 0.1449 0.169 -0.730

Figure 26. S+® output of regression model development using streamflow (Q) and specific conductance (SC) 

as explanatory variables for bicarbonate (HCO3) concentrations for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 65

Fitted : LOGQ + LOGSC

Residuals

2.0 2.1 2.2 2.3 2.4

-0.15 -0.10 -0.05 0.0 0.05

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.15 -0.10 -0.05 0.0 0.05

90 140 190 240

COMPUTED.HCO3.USING.Q.AND.SC

50

100

150

200

250

ACTUAL.HCO3

C

A B

Figure 27. S+® output graphs from simple linear regression analysis using streamflow (Q) and specific conductance (SC) as 

explanatory variables for bicarbonate (HCO3) concentrations showing A, computed versus actual HCO3 concentrations; B, computed 

log-transformed HCO3 concentrations versus regression residuals, and C, standard normal quantiles versus regression residuals for the 

North Fork Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
66 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGTSS ~ LOGTBY, data = TSS, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.5663 -0.08246 0.01373 0.07905 0.439

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.2523 0.0927 2.7205 0.0087 

 LOGTBY 0.9033 0.0473 19.1125 0.0000 

Residual standard error: 0.1718 on 55 degrees of freedom

Multiple R-Squared: 0.8691 Adjusted R-squared: 0.8668 

F-statistic: 365.3 on 1 and 55 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGTBY -0.9694 

Analysis of Variance Table

Response: LOGTSS

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGTBY 1 10.77767 10.77767 365.2859 0

Residuals 55 1.62276 0.02950 

 model.formula nvars stderr adjr2 Cp press 

 LOGTSS ~ LOGTBY 1 0.1717695 86.67574 1.202253 1.752887

Test criteria

leverage cooksD dfits 

 0.105 0.799 0.375

Observations exceeding at least one test criterion

 LOGTSS yhat resids stnd.res stud.res leverage cooksD dfits 

3 1.740 1.30 0.439 2.63 2.79 0.0591 0.2181 0.700

18 0.903 1.47 -0.566 -3.37 -3.74 0.0409 0.2414 -0.773

19 2.210 2.52 -0.306 -1.82 -1.86 0.0450 0.0782 -0.404

26 2.000 2.35 -0.350 -2.07 -2.14 0.0309 0.0683 -0.381

Figure 28. S+® output of regression model development using turbidity (TBY) as an explanatory variable 

for total suspended solids (TSS) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 67

Fitted : LOGTBY

Residuals

1.5 2.0 2.5

-0.6 -0.4 -0.2 0.0 0.2 0.4

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4

1.1 1.6 2.1 2.6

LOGTBY

0.5

1.0

1.5

2.0

2.5

3.0

LOGTSS

0 100 200 300 400 500 600

COMPUTED.TSS.USING.TBY

0

200

400

600

ACUTAL.TSS

C

B A

D

Figure 29. S+® output graphs from simple linear regression analysis showing A, log-transformed turbidity (TBY) versus log-transformed 

total suspended solids (TSS) concentrations; B, computed versus actual TSS concentrations; C, computed log-transformed TSS 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
68 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGTSS ~ LOGQ, data = TSS, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.5578 -0.1812 -0.01994 0.1864 0.7242

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.6243 0.1411 4.4240 0.0000 

 LOGQ 0.5753 0.0581 9.9018 0.0000 

Residual standard error: 0.2846 on 55 degrees of freedom

Multiple R-Squared: 0.6406 Adjusted R-squared: 0.6341 

F-statistic: 98.05 on 1 and 55 degrees of freedom, the p-value is 7.938e-014 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9636 

Analysis of Variance Table

Response: LOGTSS

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 7.944119 7.944119 98.04663 7.938095e-014

Residuals 55 4.456314 0.081024 

 model.formula nvars stderr adjr2 Cp press 

 LOGTSS ~ LOGQ 1 0.2846469 63.40984 30.6069 4.761309

Test criteria

leverage cooksD dfits 

 0.105 0.799 0.375

Observations exceeding at least one test criterion

 LOGTSS yhat resids stnd.res stud.res leverage cooksD dfits 

18 0.903 1.37 -0.467 -1.69 -1.72 0.0630 0.0964 -0.447

19 2.210 2.59 -0.385 -1.40 -1.41 0.0666 0.0700 -0.378

22 2.843 2.12 0.724 2.57 2.72 0.0203 0.0684 0.391

31 2.161 2.64 -0.475 -1.74 -1.77 0.0734 0.1192 -0.498

45 2.324 2.68 -0.354 -1.30 -1.31 0.0806 0.0740 -0.387

Figure 30. S+® output of regression model development using streamflow (Q) as an explanatory variable 

for total suspended solids (TSS) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 69

Fitted : LOGQ

Residuals

1.5 2.0 2.5

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

0.5 1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

0.5

1.0

1.5

2.0

2.5

3.0

LOGTSS

0 100 200 300 400 500 600

COMPUTED.TSS.USING.Q

0

200

400

600

ACUTAL.TSS

C

A B

D

Figure 31. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus logtransformed total suspended solids (TSS) concentrations; B, computed versus actual TSS concentrations; C, computed log-transformed 

TSS concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
70 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGSSC ~ LOGQ + LOGTBY, data = SSC, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.4998 -0.08841 -0.002607 0.1056 0.4714

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.1103 0.1187 -0.9292 0.3573 

 LOGQ 0.5400 0.0663 8.1439 0.0000 

 LOGTBY 0.5589 0.0877 6.3748 0.0000 

Residual standard error: 0.1862 on 49 degrees of freedom

Multiple R-Squared: 0.8993 Adjusted R-squared: 0.8952 

F-statistic: 218.8 on 2 and 49 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) LOGQ 

 LOGQ -0.2530 

LOGTBY -0.4221 -0.7587

Analysis of Variance Table

Response: LOGSSC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 13.77122 13.77122 397.0356 0.000000e+000

 LOGTBY 1 1.40951 1.40951 40.6375 6.172674e-008

Residuals 49 1.69957 0.03469 

Variance inflation factors

 LOGQ LOGTBY 

2.356401 2.356401

 model.formula nvars stderr adjr2 Cp press 

LOGSSC ~ LOGQ + LOGTBY 2 0.1862393 89.52069 3.00000 1.888522

Test criteria

leverage cooksD dfits 

 0.173 0.851 0.48

Observations exceeding at least one test criterion

 LOGSSC yhat resids stnd.res stud.res leverage cooksD dfits 

12 2.48 2.98 -0.500 -2.76 -2.98 0.0560 0.1510 -0.725

47 3.03 2.61 0.416 2.28 2.39 0.0425 0.0771 0.504

Figure 32. S+® output of regression model development using streamflow (Q) and turbidity (TBY) as 

explanatory variables for suspended-sediment concentrations (SSC) for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 71

Fitted : LOGQ + LOGTBY

Residuals

1.5 2.0 2.5 3.0

-0.4 -0.2 0.0 0.2 0.4

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.4 -0.2 0.0 0.2 0.4

300 800 1300 1800

COMPUTED.SSC.USING.Q.AND.TBY

-100

400

900

1400

1900

2400

ACTUAL.SSC

C

A B

Figure 33. S+® output graphs from simple linear regression analysis using streamflow (Q) and turbidity (TBY) as explanatory variables 

for suspended-sediment concentrations (SSC) showing A, computed versus actual SSC concentrations; B, computed log-transformed 

SSC versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
72 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGSSC ~ LOGQ, data = SSC, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.5193 -0.1469 -0.02211 0.1559 0.5931

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.2092 0.1441 1.4515 0.1529 

 LOGQ 0.8606 0.0578 14.8818 0.0000 

Residual standard error: 0.2494 on 50 degrees of freedom

Multiple R-Squared: 0.8158 Adjusted R-squared: 0.8121 

F-statistic: 221.5 on 1 and 50 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9708 

Analysis of Variance Table

Response: LOGSSC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 13.77122 13.77122 221.4674 0

Residuals 50 3.10908 0.06218 

 model.formula nvars stderr adjr2 Cp press 

 LOGSSC ~ LOGQ 1 0.2493625 81.21322 31.73686 3.353123

Test criteria

leverage cooksD dfits 

 0.115 0.8 0.392

Observations exceeding at least one test criterion

 LOGSSC yhat resids stnd.res stud.res leverage cooksD dfits 

12 2.48 3.00 -0.519 -2.14 -2.23 0.0558 0.1357 -0.541

21 3.43 3.04 0.386 1.60 1.62 0.0604 0.0818 0.411

27 2.87 3.22 -0.347 -1.45 -1.47 0.0818 0.0938 -0.438

Figure 34. S+® output of regression model development using streamflow (Q) as an explanatory variable 

for suspended-sediment concentrations (SSC) for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 73

Fitted : LOGQ

Residuals

1.5 2.0 2.5 3.0

-0.4 -0.2 0.0 0.2 0.4 0.6

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.4 -0.2 0.0 0.2 0.4 0.6

1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

1.0

1.5

2.0

2.5

3.0

3.5

LOGSSC

0 500 1000 1500 2000

COMPUTED.SSC.USING.Q

0

500

1000

1500

2000

2500

ACTUAL.SSC

C

B A

D

Figure 35. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus logtransformed suspended-sediment concentrations (SSC); B, computed versus actual SSC concentrations; C, computed log-transformed 

SSC versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
74 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGTN ~ SIN + COS + LOGTBY, data = TN, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1782 -0.04105 0.01431 0.05001 0.1447

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.0012 0.0513 -0.0235 0.9814 

 SIN 0.0218 0.0173 1.2584 0.2141 

 COS 0.1118 0.0220 5.0822 0.0000 

 LOGTBY 0.1818 0.0260 7.0011 0.0000 

Residual standard error: 0.08755 on 50 degrees of freedom

Multiple R-Squared: 0.6254 Adjusted R-squared: 0.6029 

F-statistic: 27.82 on 3 and 50 degrees of freedom, the p-value is 1.003e-010 

Correlation of Coefficients:

 (Intercept) SIN COS 

 SIN 0.0792 

 COS 0.1375 -0.1148 

LOGTBY -0.9546 -0.1946 0.0271

Analysis of Variance Table

Response: LOGTN

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SIN 1 0.0803847 0.0803847 10.48781 0.002137292

 COS 1 0.1836119 0.1836119 23.95589 0.000010690

 LOGTBY 1 0.3756877 0.3756877 49.01608 0.000000006

Residuals 50 0.3832291 0.0076646 

Variance inflation factors

 SIN COS LOGTBY 

1.05247 1.013377 1.039364

 model.formula nvars stderr adjr2 Cp press 

LOGTN ~ SIN + COS + LOGTBY 3 0.08754760 60.28766 4.000000 0.4586760

Test criteria

leverage cooksD dfits 

 0.222 0.882 0.544

Observations exceeding at least one test criterion

 LOGTN yhat resids stnd.res stud.res leverage cooksD dfits 

3 0.29447 0.153 0.142 1.70 1.74 0.0961 0.0770 0.566

9 0.45939 0.315 0.145 1.82 1.86 0.1729 0.1726 0.851

14 0.30535 0.484 -0.178 -2.23 -2.33 0.1694 0.2542 -1.052

31 0.04922 0.214 -0.165 -1.95 -2.01 0.0688 0.0703 -0.546

36 -0.00436 0.161 -0.166 -2.02 -2.08 0.1204 0.1392 -0.771

Figure 36. S+® output of regression model development using season (SIN and COS) and turbidity 

(TBY) as explanatory variables for total nitrogen (TN) concentrations for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 75

Fitted : SIN + COS + LOGTBY

Residuals

0.2 0.3 0.4 0.5

-0.15 -0.10 -0.05 0.0 0.05 0.10 0.15

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.15 -0.10 -0.05 0.0 0.05 0.10 0.15 1.0 1.5 2.0 2.5 3.0 3.5

COMPUTED.TN.USING.TBY

0

1

2

3

4

ACTUAL.TN

C

A B

Figure 37. S+® output graphs from simple linear regression analysis using season (SIN and COS) and turbidity (TBY) as explanatory 

variables for total nitrogen (TN) concentrations showing A, computed versus actual TN concentrations; B, computed log-transformed 

TN concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
76 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

 *** Linear Model *** 

Call: lm(formula = LOGTN ~ SIN + COS + LOGQ, data = TN, na.action = na.exclude) 

Residuals: 

 Min 1Q Median 3Q Max 

 -0.2292 -0.06353 0.01046 0.05958 0.2388 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.1503 0.0650 2.3109 0.0250 

 SIN 0.0209 0.0233 0.8990 0.3730 

 COS 0.1049 0.0284 3.6985 0.0005 

 LOGQ 0.0822 0.0266 3.0923 0.0032 

Residual standard error: 0.1129 on 50 degrees of freedom 

Multiple R-Squared: 0.3772 Adjusted R-squared: 0.3398 

F-statistic: 10.09 on 3 and 50 degrees of freedom, the p-value is 0.00002619 

Correlation of Coefficients: 

 (Intercept) SIN COS 

 SIN 0.2196 

 COS 0.1957 -0.0945 

LOGQ -0.9529 -0.3395 -0.0310 

Analysis of Variance Table 

Response: LOGTN 

Terms added sequentially (first to last) 

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SIN 1 0.0803847 0.0803847 6.30888 0.01528828 

 COS 1 0.1836119 0.1836119 14.41053 0.00039846 

 LOGQ 1 0.1218415 0.1218415 9.56256 0.00324482 

Residuals 50 0.6370753 0.0127415 

 Variance inflation factors 

 SIN COS LOGQ 

 1.144573 1.013607 1.135441 

 model.formula nvars stderr adjr2 Cp press 

 LOGTN ~ SIN + COS + LOGQ 3 0.1128783 33.98270 4.000000 0.7442692 

 Test criteria 

 leverage cooksD dfits 

 0.222 0.882 0.544 

 Observations exceeding at least one test criterion 

 LOGTN yhat resids stnd.res stud.res leverage cooksD dfits 

14 0.30535 0.459 -0.154 -1.54 -1.56 0.2215 0.1692 -0.834 

17 0.49554 0.268 0.227 2.09 2.16 0.0685 0.0802 0.587 

28 0.16435 0.345 -0.181 -1.69 -1.73 0.1090 0.0878 -0.604 

36 -0.00436 0.225 -0.229 -2.15 -2.23 0.1076 0.1393 -0.776 

53 0.46982 0.231 0.239 2.18 2.27 0.0610 0.0774 0.579 

Figure 38. S+® output of regression model development using season (SIN and COS) and streamflow 

(Q) as explanatory variables for total nitrogen (TN) concentrations for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 77

variables for total nitrogen (TN) concentrations showing A, computed versus actual TN concentrations; B, computed log-transformed 

TN concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

Figure 39. S+® output graphs from simple linear regression analysis using season (SIN and COS) and streamflow (Q) as explanatory 

Fitted : SIN + COS + LOGQ

Residuals

0.2 0.3 0.4

-0.2 -0.1 0.0 0.1 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.2 -0.1 0.0 0.1 0.2

1.3 1.8 2.3 2.8 3.3

COMPUTED.TN.USING.Q

0

1

2

3

4

ACTUAL.TN

C

B A
78 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGTKN ~ LOGTBY, data = TKN, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.1799 -0.05763 -0.009309 0.04722 0.2251

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.6997 0.0562 -12.4495 0.0000

 LOGTBY 0.4259 0.0275 15.4685 0.0000

Residual standard error: 0.08875 on 48 degrees of freedom

Multiple R-Squared: 0.8329 Adjusted R-squared: 0.8294 

F-statistic: 239.3 on 1 and 48 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) 

LOGTBY -0.9747 

Analysis of Variance Table

Response: LOGTKN

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGTBY 1 1.884674 1.884674 239.2752 0

Residuals 48 0.378077 0.007877 

 model.formula nvars stderr adjr2 Cp press 

 LOGTKN ~ LOGTBY 1 0.0887502 82.94318 1.01267 0.4118841

Test criteria

leverage cooksD dfits 

 0.12 0.8 0.4

Observations exceeding at least one test criterion

 LOGTKN yhat resids stnd.res stud.res leverage cooksD dfits 

1 -0.319 -0.139 -0.180 -2.09 -2.17 0.0636 0.1490 -0.567

8 -0.301 -0.165 -0.136 -1.59 -1.62 0.0719 0.0979 -0.450

14 0.146 0.321 -0.175 -2.01 -2.08 0.0360 0.0757 -0.402

Figure 40. S+® output of regression model development using turbidity (TBY) as an explanatory variable 

for total Kjeldahl nitrogen (TKN) concentrations for the North Fork Ninnescah River upstream from 

Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 79

Fitted : LOGTBY

Residuals

-0.2 0.0 0.2 0.4

-0.1 0.0 0.1 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.1 0.0 0.1 0.2

1.1 1.6 2.1 2.6

LOGTBY

-0.5

-0.3

-0.1

0.1

0.3

0.5

LOGTKN

0.5 1.0 1.5 2.0 2.5 3.0

COMPUTED.TKN.USING.TBY

0

1

2

3

ACTUAL.TKN

C

A B

D

Figure 41. S+® output graphs from simple linear regression analysis showing A, log-transformed turbidity (TBY) versus log-transformed 

total Kjeldahl nitrogen (TKN) concentrations; B, computed versus actual TKN concentrations; C, computed log-transformed TKN 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney reservoir (site 07144780), south-central Kansas, 1999 through 2009.
80 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = ON ~ LOGTBY + LOGSC, data = ON, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.6905 -0.2012 -0.0441 0.1487 0.7088

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -4.6450 1.0758 -4.3177 0.0001

 LOGTBY 1.5834 0.1293 12.2472 0.0000

 LOGSC 1.0406 0.3024 3.4416 0.0012

Residual standard error: 0.295 on 51 degrees of freedom

Multiple R-Squared: 0.8204 Adjusted R-squared: 0.8134 

F-statistic: 116.5 on 2 and 51 degrees of freedom, the p-value is 0 

Correlation of Coefficients:

 (Intercept) LOGTBY 

LOGTBY -0.8498 

LOGSC -0.9881 0.7623

Analysis of Variance Table

Response: ON

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGTBY 1 19.24951 19.24951 221.1226 0.000000000

 LOGSC 1 1.03110 1.03110 11.8444 0.001162786

Residuals 51 4.43973 0.08705

 

Variance inflation factors

 LOGTBY LOGSC 

2.387615 2.387615

 model.formula nvars stderr adjr2 Cp press 

ON ~ LOGTBY + LOGSC 2 0.2950484 81.33586 3.0000 5.038485

Test criteria

leverage cooksD dfits 

 0.167 0.85 0.471

Observations exceeding at least one test criterion

 ON yhat resids stnd.res stud.res leverage cooksD dfits 

4 1.16 1.85 -0.690 -2.40 -2.53 0.0527 0.1071 -0.596

10 2.87 2.25 0.618 2.19 2.27 0.0830 0.1442 0.684

18 3.26 2.70 0.560 2.03 2.10 0.1293 0.2049 0.810

43 1.95 1.49 0.461 1.66 1.69 0.1137 0.1180 0.606

47 2.28 1.58 0.709 2.44 2.57 0.0325 0.0668 0.472

Figure 42. S+® output of regression model development using turbidity (TBY) and specific conductance 

(SC) as explanatory variables for organic nitrogen (ON) concentrations for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 81

Fitted : LOGTBY + LOGSC

Residuals

0.5 1.0 1.5 2.0 2.5

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.0 0.5 1.0 1.5 2.0 2.5

COMPUTED.ON.USING.TBY.AND.SC

0

1

2

3

ACTUAL.ON

C

A B

Figure 43. S+® output graphs from simple linear regression analysis using turbidity (TBY) and specific conductance (SC) as 

explanatory variables for organic nitrogen (ON) concentrations showing A, computed versus actual ON concentrations; B, computed 

ON concentrations versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
82 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = NO3 ~ SIN + COS + LOGTBY, data = NO3, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.5598 -0.2033 -0.02083 0.1656 0.7258

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.6308 0.1618 10.0789 0.0000

 SIN 0.0519 0.0557 0.9304 0.3561

 COS 0.6194 0.0753 8.2222 0.0000

 LOGTBY -0.3892 0.0853 -4.5632 0.0000

Residual standard error: 0.3088 on 57 degrees of freedom

Multiple R-Squared: 0.6277 Adjusted R-squared: 0.6081 

F-statistic: 32.04 on 3 and 57 degrees of freedom, the p-value is 2.877e-012 

Correlation of Coefficients:

 (Intercept) SIN COS 

 SIN 0.2178 

 COS 0.0921 -0.1429 

LOGTBY -0.9523 -0.2992 0.0876

Analysis of Variance Table

Response: NO3

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SIN 1 0.035685 0.035685 0.37418 0.5431685

 COS 1 7.144058 7.144058 74.90901 0.0000000

 LOGTBY 1 1.985835 1.985835 20.82247 0.0000273

Residuals 57 5.436079 0.095370 

 

Variance inflation factors

 SIN COS LOGTBY 

1.115139 1.023158 1.1008

 model.formula nvars stderr adjr2 Cp press 

NO3 ~ SIN + COS + LOGTBY 3 0.3088200 60.81138 4.000000 6.441167

Test criteria

leverage cooksD dfits 

 0.197 0.881 0.512

Observations exceeding at least one test criterion

 NO3 yhat resids stnd.res stud.res leverage cooksD dfits 

1 2.17 1.699 0.471 1.63 1.66 0.1295 0.0993 0.640

11 1.69 0.964 0.726 2.43 2.55 0.0663 0.1050 0.679

12 2.38 1.661 0.719 2.51 2.64 0.1393 0.2545 1.060

20 0.32 0.880 -0.560 -1.98 -2.03 0.1588 0.1843 -0.882

42 0.50 1.043 -0.543 -1.83 -1.87 0.0795 0.0724 -0.550

60 0.83 0.272 0.558 1.88 1.92 0.0734 0.0696 0.540

Figure 44. S+® output of regression model development using season (SIN and COS) and turbidity (TBY) as 

explanatory variables for nitrate (NO3) concentrations for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 83

Fitted : SIN + COS + LOGTBY

Residuals

0.5 1.0 1.5

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6

0.05 0.30 0.55 0.80 1.05 1.30 1.55 1.80

COMPUTED.NO3.USING.TBY

0.0

0.5

1.0

1.5

2.0

2.5

ACTUAL.NO3

C

A B

Figure 45. S+® output graphs from simple linear regression analysis using season (SIN and COS) and turbidity (TBY) as explanatory 

variables for nitrate (NO3) concentrations showing A, computed versus actual NO3 concentrations; B, computed NO3 concentrations 

versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
84 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Figure 46. S+® output of regression model development using season (SIN and COS) and streamflow (Q) 

as explanatory variables for nitrate (NO3) concentrations for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.

*** Linear Model ***

Call: lm(formula = NO3 ~ SIN + COS + LOGQ, data = NO3, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.5831 -0.2364 -0.004877 0.1657 0.798

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 1.5501 0.1676 9.2518 0.0000 

 SIN 0.0903 0.0625 1.4444 0.1541 

 COS 0.6524 0.0779 8.3741 0.0000 

 LOGQ -0.2782 0.0713 -3.9020 0.0003 

Residual standard error: 0.3206 on 57 degrees of freedom

Multiple R-Squared: 0.5989 Adjusted R-squared: 0.5777 

F-statistic: 28.36 on 3 and 57 degrees of freedom, the p-value is 2.361e-011 

Correlation of Coefficients:

 (Intercept) SIN COS 

SIN 0.3848 

COS 0.1855 -0.1040 

LOGQ -0.9520 -0.4695 -0.0094

Analysis of Variance Table

Response: NO3

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SIN 1 0.035685 0.035685 0.34727 0.5579937

 COS 1 7.144058 7.144058 69.52146 0.0000000

 LOGQ 1 1.564567 1.564567 15.22538 0.0002545

Residuals 57 5.857348 0.102760 

Variance inflation factors

 SIN COS LOGQ 

1.302438 1.015401 1.288456

 model.formula nvars stderr adjr2 Cp press 

NO3 ~ SIN + COS + LOGQ 3 0.3205628 57.774461 4.000000 6.944896

Test criteria

leverage cooksD dfits 

 0.197 0.881 0.512

Observations exceeding at least one test criterion

 NO3 yhat resids stnd.res stud.res leverage cooksD dfits 

1 2.17 1.614 0.556 1.85 1.89 0.1180 0.1139 0.690

11 1.69 0.893 0.797 2.57 2.71 0.0612 0.1073 0.690

12 2.38 1.582 0.798 2.67 2.83 0.1310 0.2689 1.099

20 0.32 0.801 -0.481 -1.69 -1.72 0.2154 0.1967 -0.902

36 1.90 1.407 0.493 1.61 1.64 0.0894 0.0638 0.513

40 0.03 0.613 -0.583 -1.89 -1.94 0.0774 0.0753 -0.562
Results of Regression Analysis for Selected Constituents 85

Fitted : SIN + COS + LOGQ

Residuals

0.0 0.5 1.0 1.5

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8

0.0 0.5 1.0 1.5

COMPUTED.NO3.USING.Q

-0.1

0.4

0.9

1.4

1.9

2.4

ACTUAL.NO3

C

A B

Figure 47. S+® output graphs from simple linear regression analysis using season (SIN and COS) and streamflow (Q) as explanatory 

variables for nitrate (NO3) concentrations showing A, computed versus actual NO3 concentrations; B, computed NO3 concentrations 

versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
86 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

 *** Linear Model *** 

Call: lm(formula = LOGTP ~ LOGTBY, data = TP, na.action = na.exclude) 

Residuals: 

 Min 1Q Median 3Q Max 

 -0.281 -0.09675 -0.01903 0.08665 0.3666 

Coefficients: 

 Value Std. Error t value Pr(>|t|) 

(Intercept) -1.8294 0.0757 -24.1638 0.0000 

 LOGTBY 0.6106 0.0385 15.8472 0.0000 

Residual standard error: 0.1375 on 53 degrees of freedom 

Multiple R-Squared: 0.8257 Adjusted R-squared: 0.8224 

F-statistic: 251.1 on 1 and 53 degrees of freedom, the p-value is 0 

Correlation of Coefficients: 

 (Intercept) 

LOGTBY -0.9696 

Analysis of Variance Table 

Response: LOGTP 

Terms added sequentially (first to last) 

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGTBY 1 4.747262 4.747262 251.133 0 

Residuals 53 1.001879 0.018903 

 

 model.formula nvars stderr adjr2 Cp press 

 LOGTP ~ LOGTBY 1 0.1374896 82.24461 1.397491 1.077901 

Test criteria 

 leverage cooksD dfits 

 0.109 0.799 0.381 

 Observations exceeding at least one test criterion 

 LOGTP yhat resids stnd.res stud.res leverage cooksD dfits 

22 -0.347 -0.133 -0.214 -1.62 -1.65 0.0781 0.1110 -0.479 

31 -1.420 -1.139 -0.281 -2.11 -2.19 0.0653 0.1562 -0.578 

44 -0.344 -0.710 0.367 2.69 2.87 0.0186 0.0686 0.395

Figure 48. S+® output of regression model development using turbidity (TBY) as an explanatory 

variable for total phosphorus (TP) concentrations for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 87

Fitted : LOGTBY

Residuals

-1.0 -0.8 -0.6 -0.4 -0.2

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

1.1 1.6 2.1 2.6

LOGTBY

-1.5

-1.1

-0.7

-0.3

LOGTP

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

COMPUTED.TP.USING.TBY

0.0

0.2

0.4

0.6

ACTUAL.TP

C

A B

D

Figure 49. S+® output graphs from simple linear regression analysis showing A, log-transformed turbidity (TBY) versus log-transformed 

total phosphorus (TP) concentrations; B, computed versus actual TP concentrations; C, computed log-transformed TP concentrations 

versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
88 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = TP ~ LOGQ, data = TP, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.3131 -0.06473 -0.003157 0.06227 0.295

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) -0.1744 0.0552 -3.1612 0.0026 

 LOGQ 0.1908 0.0227 8.3927 0.0000 

Residual standard error: 0.1073 on 53 degrees of freedom

Multiple R-Squared: 0.5706 Adjusted R-squared: 0.5625 

F-statistic: 70.44 on 1 and 53 degrees of freedom, the p-value is 2.653e-011 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.965 

Analysis of Variance Table

Response: TP

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 0.8107083 0.8107083 70.43751 2.653244e-011

Residuals 53 0.6100093 0.0115096 

 model.formula nvars stderr adjr2 Cp press 

 TP ~ LOGQ 1 0.1072829 56.25317 1.293694 0.654852

Test criteria

leverage cooksD dfits 

 0.109 0.799 0.381

Observations exceeding at least one test criterion

 TP yhat resids stnd.res stud.res leverage cooksD dfits 

12 0.58 0.285 0.295 2.78 2.97 0.0184 0.0721 0.407

29 0.18 0.493 -0.313 -3.04 -3.31 0.0782 0.3919 -0.965

Figure 50. S+® output of regression model development using streamflow (Q) as an explanatory variable for 

total phosphorus (TP) concentrations for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 89

Fitted : LOGQ

Residuals

0.0 0.1 0.2 0.3 0.4 0.5

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

0.5 1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

0.0

0.1

0.2

0.3

0.4

0.5

0.6

TP

0.0 0.1 0.2 0.3 0.4 0.5

COMPUTED.TP.USING.Q

0.0

0.1

0.2

0.3

0.4

0.5

0.6

ACTUAL.TP

C

A B

D

Figure 51. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus total 

phosphorus (TP) concentrations; B, computed versus actual TP concentrations; C, computed TP concentrations versus regression 

residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
90 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = OP ~ SC, data = OP, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.09096 -0.01705 0.0003533 0.01675 0.132

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.2243 0.0143 15.6578 0.0000

 SC -0.0002 0.0000 -12.0588 0.0000

Residual standard error: 0.0339 on 52 degrees of freedom

Multiple R-Squared: 0.7366 Adjusted R-squared: 0.7315 

F-statistic: 145.4 on 1 and 52 degrees of freedom, the p-value is 1.11e-016 

Correlation of Coefficients:

 (Intercept) 

SC -0.9467 

Analysis of Variance Table

Response: OP

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 SC 1 0.1670741 0.1670741 145.4137 1.110223e-016

Residuals 52 0.0597458 0.0011490 

 model.formula nvars stderr adjr2 Cp press 

 OP ~ SC 1 0.03389627 73.15283 1.369267 0.06430480

Test criteria

leverage cooksD dfits 

 0.111 0.799 0.385

Observations exceeding at least one test criterion

 OP yhat resids stnd.res stud.res leverage cooksD dfits 

28 0.04 0.131 -0.0910 -2.75 -2.95 0.0480 0.1908 -0.662

42 0.21 0.167 0.0428 1.32 1.33 0.0864 0.0824 0.409

43 0.23 0.098 0.1320 3.95 4.67 0.0268 0.2147 0.776

49 0.19 0.118 0.0719 2.16 2.25 0.0382 0.0929 0.448

Figure 52. S+® output of regression model development using specific conductance (SC) as an explanatory 

variable for orthophosphate (OP) concentrations for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 91

Fitted : SC

Residuals

0.0 0.05 0.10 0.15

-0.05 0.0 0.05 0.10

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.05 0.0 0.05 0.10

200 400 600 800 1000 1200 1400

SC

-0.05

0.00

0.05

0.10

0.15

0.20

OP

0.00 0.05 0.10 0.15

COMPUTED.OP.USING.SC

0.00

0.05

0.10

0.15

0.20

ACTUAL.OP

A B

C D

Figure 53. S+® output graphs from simple linear regression analysis showing A, specific conductance (SC) versus orthophosphate 

(OP) concentrations; B, computed versus actual OP concentrations; C, computed OP concentrations versus regression residuals; and 

D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream from Cheney Reservoir (site 

07144780), south-central Kansas, 1999 through 2009.
92 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGFC ~ LOGTBY + SC, data = FC, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-1.289 -0.2806 0.0566 0.296 1.202

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 2.7269 0.6447 4.2300 0.0001 

 LOGTBY 0.7608 0.2162 3.5193 0.0009 

 SC -0.0013 0.0003 -4.2657 0.0001 

Residual standard error: 0.4865 on 57 degrees of freedom

Multiple R-Squared: 0.7167 Adjusted R-squared: 0.7067 

F-statistic: 72.09 on 2 and 57 degrees of freedom, the p-value is 2.22e-016 

Correlation of Coefficients:

 (Intercept) LOGTBY 

LOGTBY -0.9637 

 SC -0.9135 0.7896

Analysis of Variance Table

Response: LOGFC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGTBY 1 29.82038 29.82038 125.9757 0.00000000000

 SC 1 4.30732 4.30732 18.1962 0.00007592688

Residuals 57 13.49277 0.23672 

Variance inflation factors

 LOGTBY SC 

2.655678 2.655678

 model.formula nvars stderr adjr2 Cp press 

LOGFC ~ LOGTBY + SC 2 0.4865339 70.67186 3.00000 14.91702

Test criteria

leverage cooksD dfits 

 0.15 0.849 0.447

Observations exceeding at least one test criterion

 LOGFC yhat resids stnd.res stud.res leverage cooksD dfits 

1 0.903 2.15 -1.25 -2.62 -2.77 0.0438 0.1048 -0.593

32 2.908 4.20 -1.29 -2.76 -2.94 0.0770 0.2115 -0.848

36 1.279 2.45 -1.18 -2.46 -2.58 0.0368 0.0771 -0.504

Figure 54. S+® output of regression model development using turbidity (TBY) and specific conductance 

(SC) as explanatory variables for fecal coliform bacteria (FC) densities for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 93

Fitted : LOGTBY + SC

Residuals

2.0 2.5 3.0 3.5 4.0

-1.0 -0.5 0.0 0.5 1.0

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-1.0 -0.5 0.0 0.5 1.0

0 10000 20000 30000 40000

COMPUTED.FC.USING.TBY.AND.SC

0

20000

40000

60000

ACTUAL.FC

C

A B

Figure 55. S+® output graphs from simple linear regression analysis using turbidity (TBY) and specific conductance (SC) as 

explanatory variables for fecal coliform (FC) densities showing A, computed versus actual FC densities; B, computed log-transformed FC 

densities versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
94 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGEC ~ TBY + SC, data = EC, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.7392 -0.1274 0.04522 0.2341 0.3727

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 4.0075 0.3063 13.0839 0.0000

 TBY 0.0032 0.0010 3.2199 0.0045

 SC -0.0016 0.0003 -6.3227 0.0000

Residual standard error: 0.3106 on 19 degrees of freedom

Multiple R-Squared: 0.8681 Adjusted R-squared: 0.8542 

F-statistic: 62.54 on 2 and 19 degrees of freedom, the p-value is 4.381e-009 

Correlation of Coefficients:

 (Intercept) TBY 

TBY -0.8336 

SC -0.9187 0.6271

Analysis of Variance Table

Response: LOGEC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 TBY 1 8.207095 8.207095 85.09731 1.899300e-008

 SC 1 3.855518 3.855518 39.97690 4.556139e-006

Residuals 19 1.832429 0.096444 

Variance inflation factors

 TBY SC 

1.6483 1.6483

 model.formula nvars stderr adjr2 Cp press 

LOGEC ~ TBY + SC 2 0.3105538 85.42418 3.00000 2.65851

Test criteria

leverage cooksD dfits 

 0.409 0.87 0.739

Observations exceeding at least one test criterion

 LOGEC yhat resids stnd.res stud.res leverage cooksD dfits 

4 1.23 1.81 -0.580 -2.10 -2.33 0.205 0.377 -1.18

11 3.83 4.17 -0.346 -1.28 -1.30 0.244 0.176 -0.74

22 3.43 4.17 -0.739 -2.64 -3.23 0.186 0.532 -1.54

Figure 56. S+® output of regression model development using turbidity (TBY) and specific conductance 

(SC) as explanatory variables for Escherichia coli bacteria (EC) densities for the North Fork Ninnescah River 

upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 95

Fitted : TBY + SC

Residuals

2.0 2.5 3.0 3.5 4.0

-0.6 -0.4 -0.2 0.0 0.2 0.4

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.6 -0.4 -0.2 0.0 0.2 0.4

0 5000 10000 15000 20000

COMPUTED.EC.USING.TBY.AND.SC

0

5000

10000

15000

20000

25000

30000

ACTUAL.EC

C

B A

Figure 57. S+® output graphs from simple linear regression analysis using turbidity (TBY) and specific conductance (SC) as 

explanatory variables for Escherichia coli bacteria (EC) densities showing A, computed versus actual EC densities; B, computed logtransformed EC densities versus regression residuals; and C, standard normal quantiles versus regression residuals for the North Fork 

Ninnescah River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
96 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

 *** Linear Model ***

Call: lm(formula = LOGEC ~ LOGQ, data = EC, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-1.222 -0.2419 0.05747 0.2634 0.7469

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.6500 0.3572 1.8194 0.0839 

 LOGQ 0.9769 0.1341 7.2838 0.0000 

Residual standard error: 0.4361 on 20 degrees of freedom

Multiple R-Squared: 0.7262 Adjusted R-squared: 0.7125 

F-statistic: 53.05 on 1 and 20 degrees of freedom, the p-value is 4.811e-007 

Correlation of Coefficients:

 (Intercept) 

LOGQ -0.9655 

Analysis of Variance Table

Response: LOGEC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGQ 1 10.09095 10.09095 53.05305 4.81067e-007

Residuals 20 3.80410 0.19020 

 model.formula nvars stderr adjr2 Cp press 

 LOGEC ~ LOGQ 1 0.4361248 71.25377 7.886898 4.898533

Test criteria

leverage cooksD dfits 

 0.273 0.816 0.603

Observations exceeding at least one test criterion

 LOGEC yhat resids stnd.res stud.res leverage cooksD dfits 

1 2.53 1.78 0.747 1.96 2.12 0.2336 0.583 1.17

4 1.23 2.45 -1.222 -2.95 -3.82 0.0954 0.458 -1.24

Figure 58. S+® output of regression model development using streamflow (Q) as an explanatory variable for 

Escherichia coli bacteria (EC) densities for the North Fork Ninnescah River upstream from Cheney Reservoir 

(site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 97

Fitted : LOGQ

Residuals

2.0 2.5 3.0 3.5 4.0

-1.0 -0.5 0.0 0.5

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-1.0 -0.5 0.0 0.5

1.0 1.5 2.0 2.5 3.0 3.5

LOGQ

1

2

3

4

LOGEC

0 5000 10000 15000 20000 25000

COMPUTED.EC.USING.Q

0

5000

10000

15000

20000

25000

30000

ACTUAL.EC

C

A B

D

Figure 59. S+® output graphs from simple linear regression analysis showing A, log-transformed streamflow (Q) versus logtransformed Escherichia coli bacteria (EC) densities; B, computed versus actual EC densities; C, computed log-transformed EC densities 

versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah River upstream 

from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
98 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

*** Linear Model ***

Call: lm(formula = LOGTOC ~ LOGTBY, data = TOC, na.action = na.exclude)

Residuals:

 Min 1Q Median 3Q Max 

-0.3964 -0.03895 0.01692 0.09365 0.2074

Coefficients:

 Value Std. Error t value Pr(>|t|) 

(Intercept) 0.0080 0.0931 0.0856 0.9322 

 LOGTBY 0.4848 0.0451 10.7565 0.0000 

Residual standard error: 0.1353 on 43 degrees of freedom

Multiple R-Squared: 0.7291 Adjusted R-squared: 0.7228 

F-statistic: 115.7 on 1 and 43 degrees of freedom, the p-value is 9.015e-014 

Correlation of Coefficients:

 (Intercept) 

LOGTBY -0.9763 

Analysis of Variance Table

Response: LOGTOC

Terms added sequentially (first to last)

 Df Sum of Sq Mean Sq F Value Pr(F) 

 LOGTBY 1 2.116599 2.116599 115.7032 9.015011e-014

Residuals 43 0.786614 0.018293 

 model.formula nvars stderr adjr2 Cp press 

 LOGTOC ~ LOGTBY 1 0.1352529 72.27529 1.375876 0.8628375

Test criteria

leverage cooksD dfits 

 0.133 0.801 0.422

Observations exceeding at least one test criterion

 LOGTOC yhat resids stnd.res stud.res leverage cooksD dfits 

6 0.398 0.617 -0.219 -1.69 -1.73 0.0866 0.136 -0.533

8 0.826 1.222 -0.396 -3.00 -3.34 0.0487 0.231 -0.756

9 0.869 1.170 -0.301 -2.27 -2.39 0.0383 0.103 -0.478

Figure 60. S+® output of regression model development using turbidity (TBY) as the explanatory variable 

for total organic carbon (TOC) concentrations for the North Fork Ninnescah River upstream from Cheney 

Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
Results of Regression Analysis for Selected Constituents 99

Fitted : LOGTBY

Residuals

0.6 0.8 1.0 1.2

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

Quantiles of Standard Normal

Residuals

-2 -1 0 1 2

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2

1.1 1.6 2.1 2.6

LOGTBY

0.2

0.4

0.6

0.8

1.0

1.2

1.4

LOGTOC

0 5 10 15 20 25

COMPUTED.TOC.USING.TBY

0

5

10

15

20

ACTUAL.TOC

C

B A

D

Figure 61. S+® output graphs from simple linear regression analysis showing A, log-transformed turbidity (TBY) versus log-transformed 

total organic carbon (TOC) concentrations; B, computed versus actual TOC concentrations; C, computed log-transformed TOC 

concentrations versus regression residuals; and D, standard normal quantiles versus regression residuals for the North Fork Ninnescah 

River upstream from Cheney Reservoir (site 07144780), south-central Kansas, 1999 through 2009.
100 Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents

Summary 

Cheney Reservoir in south-central Kansas is one of the 

primary sources of water for the city of Wichita. The North 

Fork Ninnescah River is the largest contributing tributary 

to Cheney Reservoir. The U.S. Geological Survey has operated a continuous real-time water-quality monitoring station 

since 1998 on the North Fork Ninnescah River. Continuously 

measured water-quality physical properties include streamflow, specific conductance, pH, water temperature, dissolved 

oxygen, and turbidity. Discrete water-quality samples were 

collected during 1999 through 2009 and analyzed for sediment, nutrients, bacteria, and other water-quality constituents. 

Regression models were developed to establish relations 

between discretely sampled constituent concentrations and 

continuously measured physical properties to estimate concentrations of those constituents of interest that are not easily 

measured in real time because of limitations in sensor technology and fiscal constraints. The water-quality information in 

this report is important to the city of Wichita because it allows 

the concentrations of many potential pollutants of interest, 

including nutrients and sediment, to be estimated in real time 

and characterized over conditions and time scales that would 

not be possible otherwise. Regression models based on data 

collected during 1997 through 2003 were published in 2006. 

This report updates those models using discrete and continuous data collected during January 1999 through December 

2009. The 2006 models for dissolved solids, sodium, chloride, 

sulfate, calcium, magnesium, potassium, alkalinity, bicarbonate, total suspended solids, suspended-sediment concentration, 

total Kjeldahl nitrogen, total phosphorus, orthophosphate, and 

fecal coliform bacteria were updated. New regression models 

were developed for total nitrogen, nitrate, organic nitrogen, 

Escherichia coli bacteria, and total organic carbon.

In general, model forms and the amount of variance 

explained by the models was similar between the original and 

updated models. The model forms for most updated models 

remained unchanged. Ions were strongly positively correlated 

with specific conductance. Sediment was positively correlated 

with turbidity. Nutrients were generally positively correlated 

with turbidity. Some nutrient species included either season or 

specific conductance as explanatory variables. Bacteria was 

positively correlated to turbidity and negatively correlated 

with specific conductance.

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Publishing support provided by: 

Rolla Publishing Service Center

For additional information concerning this publication, contact:

Director, USGS Kansas Water Science Center 

4821 Quail Crest Place

Lawrence, KS 66049

(785) 842–9909

Or visit the Kansas Water Science Center Web site at:

http://ks.water.usgs.gov

Stone and others—Model Documentation for Relations Between Continuous Real-Time and Discrete Water-Quality Constituents—Open-File Report 2013–1014