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