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

I

I

*
x2(t) results in a new estimate, x2(t), that has a variance of error of

estimation,

I

* 2 ? '
P22(t) = at P22(t) + (1 - at)-p~2(t) + 2at(1 - at)ITt

(24)

I

I

where P~2(t) is the variance of the error of the backward estimate and at

is the weight given to the forward estimate,

I

b
at = P22 (t)
P 22 (t)

- 1T
t
b
+P22(t)

(25) .

- 2IT.
<-

I
I

The weight given to the backward estimate is l-at. Figure 6 shows that

the variance of the error of the optimum estimate is less than that of

either the forward or backward estimates taken alone.

I

Use of the Kalman filter to adjust discharges directly, as described

I

,herein, is a considerable deviation from the standard computational pro-

cedure, which adjusts the correlative data. For a station where discharge

I

is computed from a stage-discharge relation, the record of stage is

adjusted on the basis of apparent shifts in the relation at the time of

I

discharge measurement. Because of the form of the stage-discharge relation,

I

the standard procedure would result in larger magnitudes for x2 at high

stages and smaller magnitudes at low stages. The standard procedure is

I
I

analagous to the Kalman filter technique with a process noise, q, that is

a function of the stage. Equation 24 can be used with the average value of

I

a variable q to approximate the average variance of the estimate of xl'

The effects of these assumptions are examined in the following section.

I

28

I

I