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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QT;:Q ~f
R 0

q./tJdt

(5)

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However, because qT(tJ is not perfectly related to qR(tJ, QR may not be the

best estimate of QT' Measurements made before, during, and after the year

may add additional information by means of the temporary rating shifts

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mentioned above. By accounting for the temporary shifts, another trace

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qc(tJ, can be developed, and QT can be estimated by a discretization of the

equation

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QC ~ f qC(tJdt
o

(6)

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The use of QC to estimate QT is current practice and, the difference between

QC and QT is the error of estimate of annual discharge. This error is denoted

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y, and minimization of its expected root-mean square is one of the objectives

of stream gaging efforts at many stations.

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Although it is not currently used as standard practice in the U.S.

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Geological Survey, that part of filter theory known as Optimal Estimation,

as described by Gelb (1974), could be used to construct the computed trace,

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qc(tJ and thus the estimate, QC' of annual discharge.

The three sources of discharge information, stage, time, and discharge

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measurements, could be used in a state-space framework (Gelb, 1974) to

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evaluate the accuracy of QC as an estimator of

Qm.
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However, the nonlinearity

of the general formulation of the discharge rating, illustrated in equation 3,

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would entail unnecessary difficulties. If a "reasonable" number of discharge

measurements is available to develop the discharge rating, the information

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contained in the correlative data can be removed by computing QR for the

annual time period and subtracting it from both QC and QT in the definition
of the error of annual discharge:

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zo

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