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Linear error analysis of slope-area discharge determinations

Journal of Hydrology

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Abstract

The slope-area method can be used to calculate peak flood discharges when current-meter measurements are not possible. This calculation depends on several quantities, such as water-surface fall, that are subject to large measurement errors. Other critical quantities, such as Manning's n, are not even amenable to direct measurement but can only be estimated. Finally, scour and fill may cause gross discrepancies between the observed condition of the channel and the hydraulic conditions during the flood peak. The effects of these potential errors on the accuracy of the computed discharge have been estimated by statistical error analysis using a Taylor-series approximation of the discharge formula and the well-known formula for the variance of a sum of correlated random variates. The resultant error variance of the computed discharge is a weighted sum of covariances of the various observational errors. The weights depend on the hydraulic and geometric configuration of the channel. The mathematical analysis confirms the rule of thumb that relative errors in computed discharge increase rapidly when velocity heads exceed the water-surface fall, when the flow field is expanding and when lateral velocity variation (alpha) is large. It also confirms the extreme importance of accurately assessing the presence of scour or fill. ?? 1987.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Linear error analysis of slope-area discharge determinations
Series title:
Journal of Hydrology
Volume
96
Issue:
1-4
Year Published:
1987
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
125
Last page:
138
Number of Pages:
14