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<br />Flood Frequency Estimates for the American River <br /> <br />41 <br /> <br /> <br />G = G,/MSEG, + Gg/MSEG, <br />w 1/ MSEG, + 1/ MSEG, <br /> <br />Here Gw is the weighted skew coefficient, Gs is the station skew coefficient, and Gg <br />is the generalized regional estimate of the skew coefficient; !lfSE[-} is the mean <br />square error of the indicated variable. McCuen (1979) and Stedinger and Tasker <br />(1986a,b) discuss the development of skew coefficient maps and regression <br />estimators of Gg and MSE[GgJ. <br /> <br />Outliers <br /> <br />Unusual high or low annual floods are normally called outliers. Bulletin <br />17-B defmes outliers as "data points that depart significantly frorn the trend of the <br />remaining data." High outliers are retained unless historical information is identified <br />showing that such floods are the largest in a period longer than the systematic record. <br />Low outliers pose a problem. Due to the log transformation, one or more unusual <br />low flow values can distort the entire fitted frequency curve. To avoid this problem <br />Bulletin l7-B recommends a test of whether a low outlier is statistically significant <br />(IACWD, 1981; Stedinger et al., 1993). Flood peaks identified as low outliers are <br />omitted from the computation of X, S, and G, and a conditional probability <br />adjustment is applied to account for the omission. In practice the low outlier test <br />rarely leads to the identification of any more than a few outlying observations. <br /> <br />Historical and Paleoflood Information <br /> <br />Bulletin 17-B recommends a historical flood moment adjustment to account <br />for knowledge that a given number of events exceeded some discharge threshold <br />(Qh) in a period of known duration prior to the systematic flood record. This <br />adjustment, in effect, "fills in the ungaged portion of the historic period with an <br />appropriate number of replicates of the below-Qh portion of the systematic record" <br />(Kirby, 1981, p. c-47). Although the Bulletin 17-B historical adjustment ..vas <br />intended primarily for use with historical data, it can also be applied to paleoflood <br />data. <br /> <br />Alternative Treatments of Outliers and Historical and Paleoflood Information <br /> <br />Both outliers and historical and paleoflood data can be handled in the <br />framework of censored data. The influence of low outliers can be eliminated by <br />censoring below a low threshold. Historical and paleoflood data can be treated as <br />observations above a high threshold. Research subsequent to the publication of <br />Bulletin 17-B has identified efficient statistical methods for treating censored data. <br /> <br />- <br />