WSP00375

• File Number: 8200.760
• Description: Yampa River General
• State: CO
• Basin: Yampa/White
• Water Division: 6
• Date: 1/1/1983
• Author: USGS
• Title: Simulated Effects of Anticipated Coal Mining on Dissolved Solids in Selected Tributaries of the Yampa River - Northwestern Colorado - 1983
• Water Supply Pro - Doc Type: Report/Study

I} O? 4JJ

MSE=X2+S2
,

(18)

With the equation in this form, Hem (1970) states that the coefficient b
should be about 0.60. From observed data for node 27 the coefficient b for
equation 15 is 0.58. Using a coefficient b of 0.58 and assuming the slopes
of the relations do not change in equations 13 and 14, the resulting equation
for Elk River at Clark (09241000) used in the model for node 22 is:

C=109Q-0.152. (16)

The equation used in the model for node 21 is:
C=956Q-0.383.

(17)

MODEL CALIBRATION

Observed or estimated data were entered into the model at each of the
input nodes. In order to calibrate the model, observed or estimated data were
computed for several internal nodes and all output nodes. These observed data
were compared against the model output for the particular nodes. Calibration
was done for nodes 15, 19, 20, and 27 (table 1). Calibration was performed by
changing parameters in the model in order that modeled output of discharge,
dissolved-solids concentration, and dissolved-solids load closely matched
observed data at the output nodes. Model parameters which were altered were
the regression coefficients in equations 2 and 4 and the coefficient E. in
-z.
equation 5.

The objective function that was considered during calibration
mean square error over the total 72 months the model was run
variable. The error function uses the logarithms of the differences
observed and predicted values. The mean square error is:

was the
for each
between

where:
MSE=mean square error,

x=mean of the differences between the logarithms (base e) of observed
and model prediction for each model variable for each month, and

s2=variance of the differences of the logarithms (base e) between the
observed and model prediction for each model variable for each
month.

In this equation, the first term is the bias from the true mean zero
second term is the variance. During calibration, the attempt is to
the bias (x) to zero with a minimum variance (s2).

and the
reduce

Hydrographs of observed variables and predicted variables for nodes 15,
19, 20, and 27 are shown in figures 3 through 14. An examination of these
figures gives a qualitative evaluation of the calibration of the variables.
The bias, variance, and mean square error of each variable for the same nodes
are given in table 4.

15