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<br />FLOOD FREQUENCY ANALYSIS PROCEDURE <br /> <br />The following steps are offered as <br />guidelines for flood frequency analysis <br />based on extreme-value theory as presented <br />in this report. <br /> <br />1. Select a value for b in the order <br />of two or three times the magnitude of the <br />largest flood of record and plot the data in <br />the form of Figure 3. <br /> <br />2. If the plot in Step 1 is linear, <br />estimate parameters a, b, and c (Equation 6) <br />and apply the results for estimating flood <br />frequency. <br /> <br />3. If the plot in Step 1 is curved, <br />some other distribution is probably more <br />applicable, and alternatives should be <br />cons idered. <br /> <br />4. If the plot in Step 1 exhibits a <br />break, estimate parameters a, a', b, c, and <br />c1 (Equation 12). This is done by sub- <br />stituting Equations 22 and 23 in Equations 20 <br />and 21 and solving for al and !X2, estimat iog <br />61 and 62 from Equations 22 and 23, using <br />these four values to estimate a, ai, c, and <br />ct. Computer programming lists are presented. <br /> <br />CONCLUS IONS <br /> <br />The original objective of this research <br />was to develop and evaluate an extension of <br />extreme value theory for application to <br />estimating flood frequency relationships for <br />river flows drawn from nonhomogeneous popu- <br />lations. Before doing so, applications to <br />homogeneous data were cons idered, and a <br />functional f~rm that limits flows to a <br />maximum value was found prefer-able to the <br />widely used Gumbel form. A relationship waS <br />then derived for fitting data mixing two <br />distributions. The goodness-of-fit statistics <br />indicate excellent fit for these mixture <br />distributions (except when one of the sourceS <br />has very few observed values). <br /> <br />The mixture distribution, however, <br />has five parameters and therefore should <br /> <br />be capable of fitting a wide variety of <br />data sets. The real justification for its <br />application lies in its basis in extreme <br />value theory. It was demonstrated that <br />extreme-value distributions provide excellent <br />fit for many river systems. The method of <br />estimation (maximum likelihood) had some <br />inherent difficulties which may have produced <br />some of the poor fits. More efficient <br />estimation methods are now available and <br />should be tested. <br /> <br />Finally, extreme-value theory may not <br />apply to all river systems. A large carry- <br />over storage may, for example, violate the <br />hypothesis of the theory. However, the <br />results of this study indicate that the <br />theory does apply to many systems. <br /> <br />23 <br />