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Determination of Optimal Flood Protection Levels With Small Exceedance Probabilities
Author(s) -
Shane Richard M.,
Gaver Donald P.
Publication year - 1969
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr005i006p01223
Subject(s) - flood myth , intensity (physics) , statistics , range (aeronautics) , parametric statistics , quadratic equation , environmental science , mathematics , magnitude (astronomy) , sensitivity (control systems) , function (biology) , hydrology (agriculture) , geology , geotechnical engineering , geography , engineering , physics , geometry , archaeology , quantum mechanics , astronomy , aerospace engineering , electronic engineering , evolutionary biology , biology
A technique for selecting flood protection levels that exceed mean flood intensities by a large amount is based on a probability model derived from the assumption that base flow floods occur at random with exponentially distributed magnitudes. It is a parametric approach involving the estimation of two statistical parameters by the method of maximum likelihood. The sensitivity of the results to errors made in choosing the correct flood intensity distribution is examined by computing the loss when the flood intensities are log normally distributed. This loss is shown to be small over a wide range of parameter values likely to be encountered. Through the use of a quadratic loss function it is shown that the expected loss is inversely proportional to the length of record. Furthermore if the existing level of protection exceeds the mean peak flood intensity by a large amount, then parameter estimation losses can be quite large, even when a record of considerable length is available. The quadratic loss function also demonstrates that the loss is due primarily to errors in estimating the expected flood intensity.