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<br />Flood Frequency Estimates for the American River <br /> <br />51 <br /> <br /> <br />coefficients for I-day, 3-day, and 7-day are -0.157, -0.096, and -0.138, which average <br />to -0.130. After rounding to nvo-decimal digits, skew values for all three durations <br />support choice of -0.10 as the skewness coefficient for three-day volumes on the <br />American River. <br /> <br />Alternative Freq uency Estimates for the American River Data <br /> <br />The committee chose five cases (with subcases) to explore alternate <br />estimates of the probability distribution of three-day average rain flood discharges on <br />the American River at Fair Oaks. The first case duplicates the USACE analysis <br />(USACE, 1998). The remaining four cases vary with respect to the skew estimate <br />and the use of historical and paleoflood data. All cases are consistent with the spirit <br />of Bulletin 17- B. <br /> <br />Case 1: Systematic Record wilh Zero Skew (Sys. wi Zero Skew) <br />This is a duplication of the USACE approach (without the expected <br />probability correction), using the conventional method of moments, as specified in <br />Bulletin 17-B. <br /> <br />Case 2: Systematic Record with Weighted Skew (Sys. wi Skew -0.1) <br />This case is based on the committee's estimate of weighted skew equal to <br />-0.1, using the conventional method of moments, as specified in Bulletin 17-B. <br /> <br />Case 3: Syslematic Record and Historical Data with Weighted Skew (Sys. & His!. wi <br />Skew -0.1) <br />Historical information is added in this case, through the use of the expected <br />moments algorithm (EMA). Three subcases are run. <br /> <br />Case 3a: Three-day discharge for 1862 flood between the 95% confidence <br />limits of 95,000 cfs and 226,000 cfs; all other floods in period 1848-1904 between 0 <br />and 95,000 cfs. <br />Case 3b: Three-day discharge for 1862 flood between 95,000 cfs and <br />226,000 cfs; all other floods in period 1848-1904 between 0 and 226,000 cfs. <br />Case 3c: Three-day discharge for 1862 flood equal to 147,000 cfs; all other <br />floods in period 1848-1904 between 0 and 147,000 cfs. <br />Note that Cases 3a and 3b are intended to bracket the results of using the <br />historical data with a fixed skew, while 3c gives a best estimate. <br /> <br />Case 4: Systematic Record and Historical Data with Skew &timated by EMA (Sys. & <br />Hist. wi EMA Skew) <br />The EMA is applied to the systematic record and the historical information <br />without specifYing the skew; hence the skew is estimated by the EMA. This case has <br />three subcases. <br /> <br />Case 4a: Three-day discharge for 1862 flood between 95,000 cfs and <br />226,000 cfs; all other events in period 1848-1904 between 0 and 95,000 cfs. <br /> <br />- <br />