WSP11570

• File Number: 8111.807
• Description: Arkansas River Compact Administration - Stream Gage Evaluation
• Basin: Arkansas
• Date: 1/1/1980
• Author: USGS
• Title: Cost-Effective Stream Gaging Strategies for the Lower Colorado River
• Water Supply Pro - Doc Type: Publication

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The Kalman filter provides a framework for optimally estimating values of

a random process when only imprecise measurements of the process are

available and also yields a measure of the accuracy of these estimates.

Temporal correlations are permissible in Kalman filtering.

At most of the stream gages in the Lower Colorado River Basin, there
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are not enough discharge measurements to perform a series of split-sample

analyses to define the error of estimation of discharge as a function of

the frequency of discharge measurement at the station. For that reason

the approach developed for this study is based on Kalman-filter theory

(Gelb,1974). Because all of the insight of the hydrographer cannot be

built into the filter model, certain simplifications were required. These

simplifications are enumerated below, and their effects on the estimation

of the accuracy of discharge computations are demonstrated by comparison

with the split-sample results for the station at the Colorado River below

Davis Dam.

In the Kalman-filter analogy of discharge computation, let qT(t) be

the true instantaneous discharge at time t and qM(t) be a measurement of

qT(t). In actuality the measurement, qM(t) , requires a finite amount of

time to accomplish. However, in standard stream gaging procedure, streamflow

measur,ements are made at times when qT(t) is as constant as possible during

the measurement interval. Furthermore, the measurement interval is very

brief relative to a year, which is the interval of interest here. Therefore,

qM(t) will be referred to as an instantaneous measurement with little loss

of veracity. In addition to the temporal disparity, discharge measurements

are subject to several other sources of error (Carter and Anderson, 1963).

The total error, v(t), in a measurement is equal to qM(t)

q~(t).

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