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Note on ‘The accuracy of the prediction of floods of high return period’
Author(s) -
Nash J. E.,
Amorocho J.
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/wr003i002p00635
Subject(s) - standard deviation , hydrometeorology , mathematics , statistics , value (mathematics) , flood myth , notation , exponential function , return period , magnitude (astronomy) , monte carlo method , work (physics) , period (music) , calculus (dental) , mathematical analysis , physics , meteorology , arithmetic , thermodynamics , history , precipitation , medicine , archaeology , dentistry , astronomy , acoustics
While pursuing further studies on this subject our attention has been directed by the reference in the WMO ‘ Guide to Hydrometeorological Practices ’ [1965] to the work of Kaczmerek [1957], which was unknown to us at the time of writing the above paper [ Nash and Amorocho , 1966]. In Kaczmerek's work, a formula for the standard deviation of estimates of the magnitude of a flood of given return period is derived. This formula may be written in our notation as It agrees with equation 14 of our paper, except for the coefficient of K . The difference between the two formulas arises in the evaluation by us of the coefficient of correlation between the mean and the standard deviation of samples drawn from a double exponential universe. Using a Monte Carlo process, we obtained a value of 0.56 for this quantity. A value of 0.62, which is not inconsistent with our results, would render the two formulas identical. Kaczmerek's treatment of the problem, and his derivations, were entirely analytical and, we believe, are superior to ours. It is gratifying, however, that we obtained such close agreement with his results by a completely different approach.