## Document Type

Report

## Publication Date

January 1980

## Abstract

The flood magnitude for a given frequency or return period is estimated by fitting a probability distribution to the historical annual flood series. The log-Pearson type III distribution has been selected by the Water Resources Council for general use by the federal government, but practitioners should examine an annual flood series and use alternative distributions where they will produce better estimates. Empirical goodness of fit is one criterion for choosing a distribution, but the reasonableness of the assumptions theoretically associated with the form of the distribution should also be considered. In theory, extreme-value distributions are particularly applicable to flow series composed of the largest flow from each year of record. The Fisher-Tippett extreme-value function, commonly called the Gumbel distribution, has been widely used for flood frequency analysis, but it was found empirically inferior to the log=Pearson type III distribution by the Water Resources Council. The Gumbel is, however, only one of three alternative extreme-value functions, and these have not been systematically investigated fro applicability. All three are examined herein, and plotting tests are provided for making a selection. The generally most appropriate was found to be not the Gumbel distribution, which assumes neither an upper nor a lower bound to the possible flow flows, but rather a form adding a third parameter as an upper bound to the flood flow. The existence of such an upper bound seems reasonable hydrologically, and a maximum likelihood fit of this distribution to 14 stations around the world with over 50 years of record compares favorably with that with the log-Pearson type III distribution. More efficient parameter estimating techniques are, however, needed. The plotting tests for many series were found to exhibit a break between two linear portions suggesting that the recorded flows may in fact be drawn from two or more populations. The form of a distribution of a series drawn as a mixture from two populations is shown theoretically to be multiplicative with respect to the two functions (rather than having the more commonly used additive form). A five parameter distribution was applied to 11 long-term sequences shown by the plotting test to originate from nonhomogeneous sources. The fit was generally excellent.

## Recommended Citation

Canfield, Ronand V.; Olsen, D. R.; Hawkins, R. H.; and Chen, T. L., "Use of Extreme Value Theory in Estimating Flood Peaks from Mixed Populations" (1980). *Reports.* Paper 577.

https://digitalcommons.usu.edu/water_rep/577