Appendix H – RIV1 Modeling
H-2
Figure H-1. Examples of seasonal regression lines based on the running average log flows in
Vermillion and Embarrass River.
The approach described above of using running average flows and water quality data results in a stronger
statistical relationship because extreme values are “damped” out. However, to simulate the actual range of
observed water quality data, we assumed that they were normally distributed (Gaussian distribution) and
we established a time series of water quality by randomly selecting values from this normal distribution.
To generate the normally distributed values, the standard deviation and the mean of the water quality data
were needed. The mean was represented by the calculated value from the regression line created by the
running average of the log flows, and the standard deviation was based on the samples (before
transforming them into the log values) that are used to create the running average.
Figure H-2 shows an example of the derivation of the standard deviation for each flow. Final water
quality concentrations from subwatersheds had the predicted mean from the running average regression
line with the range derived from the standard deviation of the samples used for the running average. The
blue points show the example of the normal distributed possible concentration range estimated from this
method.
Vermillion River-fall
y = 0.4988x + 1.1119
R2 = 0.87
0
1
2
3
4
1 1.5 2 2.5 3 3.5
log flow
log fecal coliform
counts
Embarras River-summer
y = 0.1979x - 1.0125
R2 = 0.9032
-1.2
-1
-0.8
-0.6
-0.4
-0.2 0
0 0.5 1 1.5 2 2.5 3 3.5
log flow
log TP
Embarras River-fall
y = 0.2464x - 0.4893
R2 = 0.8664
-0.6
-0.4
-0.2
0
0.2
0.4
-0.5 0 0.5 1 1.5 2 2.5
log flow
log TKN
Embarras River-fall
y = 0.6431x - 1.7035
R2 = 0.8114
-2
-1.5
-1
-0.5
0
0.5
0 0.5 1 1.5 2 2.5 3 3.5
log flow
log NO2+NO3
