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A Laplace transform proof of the theorem of moments for the instantaneous unit hydrograph
Author(s) -
Diskin M. H.
Publication year - 1967
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/wr003i002p00385
Subject(s) - hydrograph , laplace transform , mathematics , method of moments (probability theory) , convolution (computer science) , runoff model , mathematical analysis , surface runoff , statistics , computer science , ecology , estimator , machine learning , artificial neural network , biology
Use is made of Laplace transforms to derive a general relationship for the moments about the origin of the three functions that appear in the convolution integral. The resulting equation can be used for the successive evaluation of the unknown moments of the instantaneous unit hydrograph from the known moments of the rainfall excess hyetograph and of the direct surface runoff hydrograph. Simplified forms of the moments equations are given for the moments of lowest orders. (Key words: Unit hydrograph; floods; streamflow)