Appendix 1. Model Archival Summary for Chlorophyll Concentration 

at Station 06887500; Kansas River at Wamego, Kansas, during August 

30, 2012, through June 10, 2014

This model archival summary summarizes the chlorophyll (Chl; uncorrected for degradation products) concentration model developed 

to estimate Chl concentrations using YSI Model 6025 sensor-measured 15-minute chlorophyll fluorescence (fChl) data during August 

30, 2012, through June 10, 2014. 

Site and Model Information

Site number: 06887500

Site name: Kansas River at Wamego, Kansas

Location: Lat 39°11'54", long 96°18'19" referenced to North American Datum of 1927, in SW 1/4 NW 1/4 SE 1/4 sec.9, T.10 S., R.10 

E., Pottawatomie County, KS, Hydrologic Unit 10270102.

Equipment: A YSI 6600 water-quality monitor equipped with model 6025 fChl sensor was installed during August 2012 through June

2014. The monitor was housed in a 4-inch diameter galvanized steel pipe. Readings from the water-quality monitor were recorded 

every 15 minutes and transmitted by way of satellite, hourly. Sensor maximum was not exceeded during this time (operable range: 0 

to 400 micrograms per liter).

Date model was created: August 3, 2017

Model calibration data period and application date: August 30, 2012–June 10, 2014

Model-Calibration Dataset

All data were collected using U.S. Geological Survey protocols (U.S. Geological Survey, variously dated; 

https://water.usgs.gov/owq/FieldManual/; Wagner and others, 2006) and are stored in the National Water Information System (U.S. 

Geological Survey, 2018) database and available to the public. Calibration of the fChl sensor was periodically checked (quarterly), 

and recalibrated if needed, using the YSI-recommended Rhodamine WT dye solution and YSI-provided calibration tables (Yellow 

Springs Instruments, 2012). If recalibration was required, calibration check data were used to apply prorated calibration drift 

corrections to the sensor-measured fChl data during the sensor-deployment time period. Ordinary least squares analysis was used to 

develop regression models between sensor-measured fChl and laboratory-measured Chl (uncorrected for degradation products) at the 

Kansas River at Wamego, Kansas (Kans.), site using the open-source software package “R.” This model is specific to the Kansas 

River at Wamego site during this study period and cannot be applied to data collected from other sites on the Kansas River or data 

collected from other water bodies.

The final selected regression model is based on 25 concurrent measurements of sensor-measured fChl and laboratory-measured Chl 

collected during August 30, 2012, through June 10, 2014. Samples were collected throughout the range of continuously observed 

hydrologic conditions. No samples were below laboratory detection limits. Summary statistics and the complete model-calibration 

dataset are provided below. Studentized residuals from the final model were inspected for values greater than three or less than 

negative three. Values outside of that range were considered potential outliers and were investigated. None of the samples in this 

dataset were deemed outliers or removed from the model calibration dataset.

Chlorophyll Sampling Details

Cross-section samples were typically collected either from the downstream side of the bridge or instream within 100 feet of the bridge. 

The equal-width-increment method was used, and samples typically were composited for analysis. During August 2012 through June 

2014, cross-section samples were collected every 2 weeks during March through October, once a month during November through 

February, and during selected reservoir release and runoff events. A FISP US DH-95 or D-95 depth integrating sampler was used from 

the downstream side of the bridge. Additional detail on sample collection is available in Graham and others (2018). Chl (uncorrected 

for degradation products) was analyzed fluorometrically using U.S. Environmental Protection Agency Method 445.0 (Arar and 

Collins, 1997) modified for heated ethanol extraction (Sartory and Grobbelaar, 1984 and a fluorometer equipped with a flow-through 

cell (Knowlton, 1984) at the U.S. Geological Survey Kansas Water Science Center in Lawrence, Kans.
Model Development

Ordinary least squares regression analysis was done using R version 3.4.2 (R Core Team, 2017) with sensor-measured fChl as the 

explanatory variable for laboratory-measured Chl concentrations. The distribution of residuals was examined for normality, and the 

plots of residuals (the difference between the measured and computed values) were examined for homoscedasticity (meaning that their 

departures from zero did not change substantially over the range of computed values). 

Values for all the aforementioned statistics were computed and are included below along with all relevant sample data and more indepth statistical information. 

Model Summary

The following is a summary of final regression analysis for sensor-measured fChl and laboratory-measured Chl at the Kansas River at 

Wamego, Kans., streamgage (U.S. Geological Survey station number 06887500) during August 30, 2012, through June 10, 2014. A 

limitation in model predictive ability on the upper range of the observed concentrations is likely due to the small sample size (25) and 

can be seen in the cross-validation plots below.

Chl concentration model:

CChllEE = 2.05 × ff hll + 6.55

where 

ChlE = regression estimated chlorophyll (uncorrected for degradation products) concentration in micrograms per liter; and 

fChl = sensor-measured chlorophyll fluorescence in micrograms per liter.
R Output for the relation between YSI model 6025 sensor-measured chlorophyll 

fluorescence and laboratory-measured chlorophyll concentration; 06887500; 

Kansas River at Wamego, Kansas

Model Statistics, Data, and Plots

Definitions for terms used in this output can be found at the end of this 

document. 

Model

ChlE = + 2.05 * fChl + 6.55

Variable Summary Statistics

 Chl fChl

Minimum 6.0 4.07

1st Quartile 18.5 9.20

Median 30.8 13.20

Mean 43.0 17.80

3rd Quartile 55.2 21.40

Maximum 119.0 50.80

Box Plots
Exploratory Plots

Red line shows the locally weighted scatterplot smoothing (LOWESS).
Basic Model Statistics

For a detailed explanation of the terms used below, refer to Helsel and Hirsch (2002).

 

Number of Observations 25

Standard error (RMSE) 16.5

Upper Model standard percentage error (MSPE) 38.3

Lower Model standard percentage error (MSPE) 38.3

Coefficient of determination (R2) 0.755

Adjusted Coefficient of Determination (Adj. R2) 0.744

Explanatory Variables

 Coefficients Standard Error t value Probability(>|t|)

(Intercept) 6.55 5.440 1.20 2.41e-01

fChl 2.05 0.244 8.41 1.79e-08
Correlation Matrix

 Intercept fChl

Intercept 1.000 -0.796

fChl -0.796 1.000

Outlier Test Criteria

Leverage Cook's D DFFITS 

 0.120 0.106 0.400 

Flagged Observations

 Chl Estimate Residual Standard Residual Studentized Residual Leverage Cook's D DFFITS

15 73.7 111.0 -36.900 -2.6500 -3.1000 0.2790 1.360000 -1.93000

16 87.4 50.4 37.000 2.3000 2.5600 0.0429 0.119000 0.54300

17 91.8 51.3 40.600 2.5200 2.9000 0.0436 0.145000 0.61900

35 102.0 99.0 2.630 0.1790 0.1760 0.2040 0.004130 0.08890

36 119.0 108.0 10.300 0.7280 0.7210 0.2640 0.095100 0.43200

38 84.9 85.3 -0.386 -0.0252 -0.0247 0.1340 0.000049 -0.00968
Statistical Plots

Cross Validation

Fold - equal partition of the data (10 percent of the data)

Large symbols – observed value of a data point removed in a fold

Small symbols – recomputed value of a data point removed in a fold

Recomputed regression lines – adjusted regression line with one fold removed

 

 Minimum MSE of folds: 33.80

 Mean MSE of folds: 289.00

 Median MSE of folds: 128.00

 Maximum MSE of folds: 876.00

(Mean MSE of folds) / (Model MSE): 1.07
Red line - Model MSE 

Blue line - Mean MSE of folds

Model-Calibration Data Set

 Date Chl fChl Computed Residual Normal Censored

 0 ChlE Quantiles Values

 5 9/10/2012 38.3 15.3 37.9 0.417 0.303 --

 6 9/24/2012 30.8 15.6 38.6 -7.79 -0.765 --

 7 10/15/2012 27.1 11.6 30.3 -3.14 -0.2 --

 8 10/29/2012 18.5 13.2 33.7 -15.2 -1.07 --

10 12/17/2012 19.8 8.6 24.2 -4.38 -0.303 --

11 1/14/2013 20.3 9.68 26.4 -6.13 -0.409 --

12 2/11/2013 24.8 9.2 25.4 -0.563 0 --

13 3/11/2013 28.7 10.2 27.5 1.27 0.409 --

14 4/8/2013 73.7 50.8 111 -36.9 -1.98 --

15 5/6/2013 87.4 21.4 50.4 37 1.53 --

16 5/20/2013 91.8 21.8 51.3 40.6 1.98 --

17 6/3/2013 43 7.84 22.6 20.4 1.26 --

18 6/17/2013 15.7 7.85 22.6 -6.91 -0.52 --
19 7/1/2013 8.6 4.4 15.6 -6.97 -0.637 --

20 7/15/2013 43 17 41.3 1.74 0.52 --

21 8/5/2013 9.23 9.96 27 -17.7 -1.53 --

23 8/19/2013 9.27 9.3 25.6 -16.3 -1.26 --

24 9/9/2013 51.9 23.2 54.1 -2.23 -0.0996 --

26 10/21/2013 55.2 18.8 45.1 10 0.906 --

29 12/16/2013 6 4.07 14.9 -8.89 -0.906 --

32 3/10/2014 16.6 4.93 16.7 -0.106 0.2 --

33 4/7/2014 48.9 16.1 39.6 9.35 0.765 --

34 5/5/2014 102 45.1 99 2.63 0.637 --

35 5/19/2014 119 49.7 108 10.3 1.07 --

37 6/2/2014 84.9 38.4 85.3 -0.386 0.0996 --

Definitions

References Cited

Arar, E.J., and Collins, G.B., 1997, Method 445.0—In vitro determination of 

chlorophyll a and pheophytin a in marine and freshwater algae by 

fluorescence (rev. 1.2): U.S. Environmental Protection Agency, Office of 

Research and Development, 22 p.

Cleveland, W.S., 1979, Robust locally weighted regression and smoothing

scatterplots: Journal of the American Statistical Association, v. 74, p. 

829–836.

Chl: Chlorophyll a, fluorometric method, uncorrected, micrograms per liter (parameter 

code 32217).

ChlE: Estimated chlorophyll concentration, micrograms per liter.

Cook’s D: Cook’s distance (Helsel and Hirsch, 2002).

DFFITS: Difference in fits statistic (Helsel and Hirsch, 2002).

Leverage: An outlier’s measure in the x direction (Helsel and Hirsch, 2002).

LOWESS: Locally weighted scatterplot smoothing (Cleveland, 1979; Helsel and Hirsch,

2002).

MSE: Model standard error (Helsel and Hirsch, 2002).

MSPE: Model standard percentage error (Helsel and Hirsch, 2002).

Probability(>|t|): The probability that the independent variable has no effect on the

dependent variable (Helsel and Hirsch, 2002).

RMSE: Root mean square error (Helsel and Hirsch, 2002).

fChl: Chlorophyll, total, water, fluorometric, 650-700 nanometers, in situ sensor, 

micrograms per liter (parameter code 62361).

t value: Student’s t value; the coefficient divided by its associated standard error

(Helsel and Hirsch, 2002).
Graham, J.L., Foster, G.M., Williams, T.J., Mahoney, M.D., May, M.R., and Loftin, 

K.A., 2018, Water-quality conditions with an emphasis on cyanobacteria and associated 

toxins and taste-and-odor compounds in the Kansas River, Kansas, July 2012 through 

September 2016: U.S. Geological Survey Scientific Investigations Report 2018–5089, 55 

p., https://doi.org/10.3133/sir20185089.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in water resources—Hydrologic 

analysis and interpretation: U.S. Geological Survey Techniques of Water-Resources

Investigations, book 4, chap. A3, 510 p.

Knowlton, M.F., 1984, Flow-through microcuvette for fluorometric determination of 

chlorophyll: Water Resources Bulletin, v. 20, p. 1198–1205.

R Core Team, 2017, R——A language and environment for statistical computing: Vienna, 

Austria, R Foundation for Statistical Computing. [Also available at https://www.Rproject.org/.]

Sartory, D.P., and Grobbelaar, J.U., 1984, Extraction of chloro¬phyll a from 

freshwater phytoplankton for spectrophotomet¬ric analysis: Hydrobiologia, v. 114, no. 

3, p. 177–187.

U.S. Geological Survey, variously dated, National field manual for the collection of

water-quality data: U.S. Geological Survey Techniques of Water-Resources

Investigations, book 9, chaps. A1–A9 [variously paged].

U.S. Geological Survey, 2018, National Water Information System—Web interface: accessed 

January 2017 at https://doi.org/10.5066/F7P55KJN.

Wagner, R.J., Boulger, R.W., Jr., Oblinger, C.J., and Smith, B.A., 2006, Guidelines 

and standard procedures for continuous water-quality monitors—Station operation, 

record computation, and data reporting: U.S. Geological Survey Techniques and 

Methods, book 1, chap. D3, 51 p. + 8 attachments, accessed April 10, 2006, at 

https://pubs.water.usgs.gov/tm1d3.

Yellow Springs Instruments, 2012, 6-Series Multiparameter Water Quality Sondes—User 

manual: Yellow Springs Instruments, 379 p.