Appendix 3. Model Archival Summary for Chlorophyll Concentration

at Station 06887500; Kansas River at Wamego, Kansas, during June 10, 

2014, through September 30, 2016

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

to estimate Chl concentrations using Xylem YSI EXO2 sensor-measured 15-minute chlorophyll fluorescence (fChl) data during June 

10, 2014, through September 30, 2016. 

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 Xylem YSI EXO2 water-quality monitor equipped with a fChl sensor was installed during June 2014 through 

September 2016. 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 (μg/L).

Date model was created: August 3, 2017

Model calibration data period and application date: June 10, 2014–September 30, 2016

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 43 concurrent measurements of sensor-measured fChl and laboratory-measured Chl 

collected during June 10, 2014, through September 30, 2016. 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. One of the sensor-measured fChl

samples, from May 18, 2015, was deemed an outlier and removed from the model calibration dataset. The sensor-measured fChl value

of 79.98 μg/L was likely biased high due to turbidity interference from a recent reservoir release. The corresponding laboratorymeasured Chl was 7.24 μg/L. This was the only data pair in which sensor-measured fChl was greater than laboratory-measured Chl. 

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 June 2014 through 

September 2016, 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 (USGS station number 06887500) during June 10, 2014, through September 30, 2016.

Chl concentration-based model:

CChllEE = 1.9 × ff hll + 4.12

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 Xylem YSI EXO2 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 = + 1.9 * fChl + 4.12

Variable Summary Statistics

 Chl fChl

Minimum 1.99 3.24

1st Quartile 10.40 5.08

Median 25.50 9.78

Mean 30.90 14.10

3rd Quartile 49.00 21.00

Maximum 95.40 49.00

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 43

Standard error (RMSE) 9.93

Upper Model standard percentage error (MSPE) 32.1

Lower Model standard percentage error (MSPE) 32.1

Coefficient of determination (R2) 0.829

Adjusted Coefficient of Determination (Adj. R2) 0.825

Explanatory Variables

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

(Intercept) 4.12 2.430 1.7 9.74e-02

fChl 1.90 0.135 14.1 2.48e-17
Correlation Matrix

 Intercept fChl

Intercept 1.000 -0.782

fChl -0.782 1.000

Outlier Test Criteria

Leverage Cook's D DFFITS 

 0.0698 0.1056 0.3050 

Flagged Observations

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

3 95.4 78.4 17.00 1.85 1.900 0.1380 0.2730 0.762

6 67.5 52.3 15.20 1.57 1.600 0.0465 0.0602 0.354

7 73.2 68.5 4.63 0.49 0.486 0.0952 0.0127 0.158

26 83.2 97.3 -14.10 -1.64 -1.670 0.2480 0.4400 -0.959

28 59.3 69.5 -10.20 -1.08 -1.080 0.0990 0.0641 -0.359

30 53.7 72.4 -18.70 -2.00 -2.070 0.1110 0.2480 -0.732

32 42.2 55.7 -13.50 -1.40 -1.410 0.0545 0.0561 -0.339

35 56.5 26.1 30.40 3.10 3.490 0.0244 0.1200 0.553
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: 13.50

 Mean MSE of folds: 104.00

 Median MSE of folds: 86.60

 Maximum MSE of folds: 220.00

(Mean MSE of folds) / (Model MSE): 1.05
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

13 6/11/2014 25.5 5.9 15.3 10.1 1.02 --

 1 6/30/2014 19.2 6.13 15.8 3.38 0.355 --

 2 7/14/2014 95.4 39.1 78.4 17 1.79 --

 3 7/28/2014 49 21.3 44.6 4.4 0.549 --

 5 8/11/2014 67.5 25.3 52.3 15.2 1.38 --

 6 8/25/2014 73.2 33.9 68.5 4.63 0.689 --

 7 9/8/2014 5.85 7.55 18.5 -12.6 -1.38 --

 8 9/22/2014 29.4 18.5 39.3 -9.95 -1.13 --

 9 10/6/2014 57.4 25.8 53.2 4.19 0.482 --

10 10/20/2014 10.4 8.12 19.6 -9.14 -0.931 --

11 11/17/2014 9.7 4.2 12.1 -2.4 -0.0581 --

12 12/15/2014 10.4 5.5 14.6 -4.18 -0.355 --

14 2/9/2015 23.2 11.6 26.1 -2.82 -0.116 --
15 3/9/2015 21.3 7.52 18.4 2.93 0.294 --

16 4/6/2015 42.4 17.8 38 4.41 0.617 --

17 5/4/2015 58 21 44 14 1.25 --

19 6/1/2015 9.13 4.95 13.5 -4.4 -0.418 --

20 6/15/2015 3.48 4.68 13 -9.54 -1.02 --

21 6/29/2015 5.95 5.28 14.2 -8.21 -0.765 --

22 7/13/2015 13.8 7.24 17.9 -4.05 -0.294 --

23 7/27/2015 17.2 9.78 22.7 -5.5 -0.617 --

24 8/10/2015 28 14.5 31.7 -3.73 -0.234 --

25 8/24/2015 83.2 49 97.3 -14.1 -1.79 --

27 9/8/2015 59.3 34.4 69.5 -10.2 -1.25 --

28 9/21/2015 44.7 21.8 45.6 -0.952 0.0581 --

29 10/5/2015 53.7 35.9 72.4 -18.7 -2.2 --

31 10/19/2015 42.2 27.1 55.7 -13.5 -1.55 --

33 11/16/2015 20.5 12 26.9 -6.45 -0.689 --

34 12/14/2015 56.5 11.6 26.1 30.4 2.2 --

35 1/11/2016 1.99 3.24 10.3 -8.29 -0.845 --

36 2/8/2016 7.8 4.3 12.3 -4.49 -0.482 --

37 3/3/2016 35.1 16 34.5 0.528 0.234 --

38 4/4/2016 42.4 13.5 29.7 12.7 1.13 --

40 5/2/2016 26.8 7.94 19.2 7.58 0.845 --

41 5/16/2016 12.1 4.48 12.6 -0.536 0.175 --

42 6/6/2016 8.15 3.92 11.6 -3.42 -0.175 --

43 6/20/2016 5.53 3.42 10.6 -5.09 -0.549 --

45 7/11/2016 29.7 10.8 24.7 4.98 0.765 --

46 7/25/2016 58.2 20 42.1 16.1 1.55 --

47 8/8/2016 10.7 4.2 12.1 -1.42 0 --

49 8/22/2016 27.8 7.94 19.2 8.58 0.931 --

51 9/12/2016 12.9 5.08 13.8 -0.877 0.116 --

52 9/26/2016 14.9 3.88 11.5 3.4 0.418 --
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.

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/.]

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: Chlorophylls, water, in situ, fluorometric method, excitation at 470 +-15 nm, 

emission at 685 +-20 nm, micrograms per liter (parameter code 32318).

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

(Helsel and Hirsch, 2002).
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, EXO user manual—Advanced water quality monitoring 

platform: Yellow Springs Instruments, 137 p.