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<br />be used with historical and paleoflood information. The Expected Moments <br />Algorithm is as efficient as standard maximum likelihood approaches and works well <br />with the log-Pearson type III distribution. <br /> <br />EXPECTED PROBABILITY <br /> <br />- <br />44 <br /> <br />Improving American River Flood Frequency Analyses <br /> <br /> <br />Flood frequency analysis often focuses on estimation of the flood quantile <br />x l-q, the quantile that will be exceeded with probability q = lIT. However, different <br />statistical estimators of Xl-q have different properties (Stedinger, 1997; Beard, <br />1997). Most estimators provide an almost unbiased estimator of x l-q : <br /> <br />E[ .1:1_q ] '" xl_q <br /> <br />However, interest may be in a value that in the future will be exceeded with <br />probability fl., so that <br /> <br />p{x > XI_q l", q <br /> <br />when both X and XI_q are viewed as random variables. If a very long record is <br />available, these two criteria would lead to almost the same design value. With short <br />records, they lead to different estimates because of the effect of the uncertainty in the <br />estimated parameters. <br />Beard (1978) developed the expected probability correction to ensure that <br />the second criterion is met. However, this correction generally increases the bias in <br />estimated damages calculated for dwellings and economic activities located at fIXed <br />locations in a basin (Stedinger, 1997). This paradox arises because the estimated T- <br />year flood is a (random) level computed by the hydrologist based on the fitted <br />frequency distribution, whereas the expected damages are calculated for human and <br />economic activities at fixed flood levels. Recently NRC (1995) concluded that, for <br />the economic evaluation of projects, an expected probability adjustment should not <br />be made because of the upward bias it introduces. Beard (1997, 1998) disagreed with <br />that conclusion. Although a correction for expected probability may be appropriate <br />in some decision-making frameworks, the committee decided not to apply such a <br />correction to its recommended American River frequency distribution. <br /> <br />SUMMARY OF COMMfITEE APPROACH <br /> <br />In estimating the probability distribution of three-day rain flood discharges <br />for the American River at Folsom, the committee decided to adopt an overall <br />approach that was consistent with the philosophy of Bulletin 17- B guidelines. This <br />includes the assumption of the log-Pearson type III distribution and estimation based <br />on preserving log-space moments. Estimation was based on traditional method of <br />moments and the Expected Moments Algorithm. The latter method was chosen over <br />maximum likelihood and other methods because it (1) can be applied readily to the <br />