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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where h(t) is the water-surface elevation, also known as stage or gage-height,

and cO' cl' c2' and c3 are coefficients that mayor may not be functions of

time.

If it is assumed that the correlative data are exact and continuous in

time and that sufficient discharge measurements have been made such that the

effects of x2(t) and v(t) are negligible, an exact and continuous trace of

qR(t) can be developed for any period of interest. The unobservable

random variable, x2(t), which is the difference between the trace of qR(t)

and the unobservable trace of qx(t) , is used herein as one of the primary

state variables in the Kalman-filter technique; x2(t) replaces qX(t) in the

formulation because it more nearly satisfies the filter assumptions.

In actuality, the correlative data are neither exact nor continuous.

Records are lost when recorders malfunction. Several procedures are

available to reconstruct lost record; however, none of these fully replaces

the information that was contained in the lost record. For this reason

the assumption of exact and continuous correlative data will cause an under-

estimation of the actual uncertainty in an estimate of annual mean discharge.

Because more record will tend to be lost with infrequent visits, uncertainty

in the real world will be somewhat more sensitive to visit frequency than

the exact-and-continuous assumption will indicate. In this study, the

lost-record considerations are considered to be secondary and negligible to

the other effects of record computation.

The true total discharge during one year is defined by

1
Q = J
X 0

qx(tJ dt

(4)

The value of QX can be approximated from the trace of qR(tJ by

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