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<br />Table 2 illustrates various examples of regional equations for the entire <br />state of California. These equations make no assumptions regarding statistical <br />distribution or skew. Both characteristics are inherent in the data used to develop the <br />regression equations. These predeveloped USGS regional equations mayor may not <br />be as good as ones developed specifically for the region of interest, but th'ey'are <br />already available and development of regional equations is an expensive approach. <br /> <br />In contrast to the USGS type of regional equations shown above, the <br />U.S. Army Corps of Engineers (USACE) usually develop regional frequency equations <br />as documented in EM 1110-2-1415. The USACE type equations are of the following <br />form: <br /> <br />o = X + kS <br /> <br />(3) <br /> <br />X = aAbL 0(1 +I)d <br /> <br />(4) <br /> <br />S = eAfGgLh <br /> <br />k = <br />S = <br /> <br />flood peak for varying frequency (cts) <br />mean of the logarithms of annual series peak <br />events (cts) <br />log Pearson type 11 deviates <br />Standard deviation of the logarithms annual <br />series peak flood events (Cts) <br />various (some are logarithmic) quantifiable physical <br />basin characteristics <br />represent regression constants <br />represent regression coefficients <br /> <br />where: 0 = <br />X = <br /> <br />A,L,I&G = <br /> <br />a&e = <br /> <br />b,c,d,f,g&h = <br /> <br />The USACE methods assume a log Pearson type III distribution for "k" <br />values anda weighted skew coefficient, for peak flood events. The equation provides <br />a peak flow for various frequency levels associated with the value of "k". Values of <br />"k" are found in various lJSACE literature such as the EM 1110-2-1415. <br /> <br />Other governmental agencies (i.e.. City and County) have developed <br />regional frequency equations but may be difficult to locate. <br /> <br />Regardless of the source of the equations, the user must identify the <br />standard error of estimate (Se) associated with the equation. The standard error of <br />estimate defines the possible range of error in the value of flow predicted by the <br />regression equation. Assuming tile error is log normally distributed, there is a 68% <br />chance that the "true values" of flow is within + 1- 1 SE and a 95% chance that R is <br />within + 1- 2 Se. <br /> <br />7-88 <br />