WSP12351

• File Number: 8273.300
• Description: Colorado River Basin Salinity Control - Federal Agencies - USGS
• Basin: Colorado Mainstem
• Water Division: 5
• Date: 9/1/1988
• Author: USGS
• Title: Estimation of Natural Dissolved Solids Discharge in the Upper Colorado River Basin - Western United States
• Water Supply Pro - Doc Type: Report/Study

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Selection of Model Form

An equation commonly used to relate the concentration of dissolved solids
to streamflow (Hall, 1970 and 1971; Lane, 1975; Steele, 1976; DeLong, 1977) is
of the form:

b
C '" aQ ,

(1)

where

C '" dissolved-solids concentration, in milligrams per liter;
Q = streamflow, in cubic feet per second;
a '" an empirical coefficient; and
b = an empirical exponent.

The data available for this report were monthly dissolved-solids dis-
charge, streamflow, and data representing the level of development in the
Upper Colorado River Basin, Dissolved-solids discharge (D) is the product of
dissolved-solids concentration and streamflow:

D = CQ.

(2)

Combining equations 1 and 2 yields:

D = aQb+1,

(3)

Equation 3 relates dissolved-solids discharge to streamflow. However,
the model selected for this report needed to incorporate independent variables
representing water-resources development. In addition, the relation between
dissolved-solids and streamflow in the fitted model had to be reasonable for
natural conditions when all the development variables were set equal to zero,
Three model forms were tested to determine wh1ch would most adequately meet
the requirements. These were:

Additive model:

b
Da = aQN + L ciXi

(4)

Power model:

= aQab O(Xi+ l)ci , and

(5)

Da

Exponential model:

b
= aQa exp(LC.X.)
1 1

(6 )

Da

where

historical dissolved-solids discharge, in tons per month;
natural streamflow, in acre-feet per month;

D =
a
Q =
N

Qa =

x. =
1

historical streamflow, in acre-feet per month;

development variables (appropriate units); and

c. = the coefficient or exponent for the ith development
1

variable.

16