Appendix 6 7

Appendix 6. Evaluation of logistic regression model performance for models

with turbidity or chlorophyll fluorescence as explanatory variables at the 

Wamego and De Soto sites on the Kansas River, Kansas Estimated probability of cyanobacteria occurrence at concentrations greater than 2,000 cells per milliliter

0

0.2

0.4

0.6

0.8

1.0

Turbidity set to 0 formazin nephelometric units (FNU)

Turbidity set to 1st quartile (14 FNU)

Turbidity set to 2nd quartile (30 FNU)

Turbidity set to 3rd quartile (76 FNU)

Threshold probability

for positive classification = 0.31

(Foster and Graham, 2016)

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan.

EXPLANATION

Month

Model form: Logit P=0.0887-0.875sin(2πD/365)-1.914cos(2πD/365)-0.0319(Turb); where P=probability of 

cyanobacteria presence (>2,000 cells/mL); Turb=turbidity in formazin nephelometric units (FNU); D=julian 

day of year; and Sin & Cos=seasonality component (Foster and Graham, 2016).

Figure 6.1. Estimated probability of cyanobacteria occurrence at concentrations greater than 2,000 cells per 

milliliter (cells/mL) at the Kansas River at Wamego site during a calendar year with turbidity held constant using 

quartiles (quartile values were calculated using continuous turbidity data collected from July 2012 through 

September 2016).
8 Cyanobacteria and Associated Toxins and Taste-and-Odor Compounds in the Kansas River, Kansas

0

0.2

0.4

0.6

0.8

1.0

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan.

Month

Estimated probability of cyanobacteria occurrence at 

concentrations greater than 10,000 cells per milliliter

Turbidity set to 0 formazin nephelometric units (FNU)

Turbidity set to 1st quartile (17 FNU)

Turbidity set to 2nd quartile (29 FNU)

Turbidity set to 3rd quartile (74 FNU)

EXPLANATION

Threshold probability

for positive classification = 0.48

(Foster and Graham, 2016)

Model form: Logit P=0.724-1.254sin(2πD/365)-3.725cos(2πD/365)-0.0928(Turb); where P=probability of cyanobacteria presence 

(>10,000); Turb=turbidity in formazin nephelometric units (FNU); D=julian day of year; and Sin & Cos=seasonality component 

(Foster and Graham, 2016).

Figure 6.2. Estimated probability of cyanobacteria occurrence at concentrations greater than 10,000 cells per 

milliliter (cells/mL) at the Kansas River at De Soto site during a calendar year with turbidity held constant using 

quartiles (quartile values were calculated using continuous turbidity data collected from July 2012 through 

September 2016).
Appendix 6 9

0

0.2

0.4

0.6

0.8

1.0

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan.

Month

Estimated probability of microcystin occurrence at 

concentrations greater than 0.1 microgram per liter

Turbidity set to 0 formazin nephelometric units (FNU)

Turbidity set to 1st quartile (14 FNU)

Turbidity set to 2nd quartile (30 FNU)

Turbidity set to 3rd quartile (76 FNU)

EXPLANATION

Threshold probability

for positive classification = 0.40

(Foster and Graham, 2016)

Model form: Logit P=-0.872-1.716sin(2πD/365)-1.313cos(2πD/365)+0.000349(Q)-0.0490 (Turb); where P=probability 

of microcystin presence (≥0.1 μg/L); Q=streamflow in cubic feet per second (ft3

/s); Turb=turbidity in formazin 

nephelometric units (FNU); D=julian day of year; and Sin & Cos=seasonality component (Foster and Graham, 2016).

Figure 6.3. Estimated probability of microcystin occurrence at concentrations greater than 0.1 microgram per 

liter (μg/L) at the Kansas River at Wamego site during a typical year (2015) with turbidity held constant using 

quartiles (quartile values were calculated using continuous turbidity data collected from July 2012 through 

September 2016).
10 Cyanobacteria and Associated Toxins and Taste-and-Odor Compounds in the Kansas River, Kansas

0

0.2

0.4

0.6

0.8

1.0

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. Jan.

Month

Estimated probability of geosmin occurrence at 

concentrations greater than 2.0 nanograms per liter

Chlorophyll set to 1st quartile (5.5 μg/L)

Chlorophyll set to 2nd quartile (10.9 μg/L)

Chlorophyll set to 3rd quartile (22.1 μg/L)

EXPLANATION

Threshold probability

for positive classification = 0.53

(Foster and Graham, 2016)

Chlorophyll set to 0 micrograms per liter (μg/L)

Model form: Logit P=1.325+0.830sin(2πD/365)+1.219cos(2πD/365)-0.0527(fChl); where P=probability of geosmin 

presence (>2.0 ng/L); fChl=sensor-measured chlorophyll fluorescence in micrograms per liter (μg/L); D=julian 

day of year; and Sin & Cos=seasonality component (Foster and Graham, 2016).

Figure 6.4. Estimated probability of geosmin occurrence at concentrations greater than 2.0 nanograms per 

liter (ng/L) at the Kansas River at Wamego site during a calendar year with chlorophyll held constant using 

quartiles (quartile values were calculated using continuous chlorophyll data collected from July 2012 through 

September 2016).

References Cited

Foster, G.M., and Graham, J.L., 2016, Logistic and linear 

regression model documentation for statistical relations 

between continuous real-time and discrete water-quality 

constituents in the Kansas River, Kansas, July 2012 through 

June 2015: U.S. Geological Survey Open-File Report 2016–

1040, 27 p. [Also available at https://doi.org/10.3133/

ofr20161040.]