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<br />52 <br /> <br />Improving American River Flood Frequency Analyses <br /> <br /> <br />Case 4b: 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 4c: 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 4a and 4b are intended to bracket the results of using the <br />historical data with a skew estimated by EMA, while Case 4c gives a best estimate. <br /> <br />Case 5: Systematic Record and Historical and Paleoflood Information with Skew <br />Estimated by EMA (Sys. & Hist. & Paleo. wi EMA Skew) <br />The EMA is applied to the systematic record and the historical and <br />paleoflood information without specifYing the skew. This case has three subcases. <br /> <br />Case Sa: 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 95,000 cfs. All <br />floods in the 3,350 year period from approximately 1,500 RC. through 1847 A.D. <br />are less than 108,000 cfs (the lower 95% confidence limit of the lower paleoflood <br />non-exceedance threshold). <br />Case 5b: 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. All <br />floods in last 1,350 year period (prior to 1848) less than 352,000 cfs (the upper 95% <br />confidence limit of the upper paleoflood non-exceedance threshold). <br />Case 5c: 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. All floods in last 2,350 year <br />period (prior to 1848) less than 197,000 cfs (the median estimate of the three-day <br />flow associated with the average of the upper and lower paleoflood non-exceedance <br />limits). <br />Note that Cases 5a and 5b are intended to bracket the results of using the <br />historical and paleoflood data with a skew estimated by EMA, while Case 5c gives a <br />best estimate. <br /> <br />Results <br /> <br />Table 3.3 displays the results of the flood frequency analysis; Cases I, 3c, <br />and 5c are plotted in Figure 3.3. Estimates of Q,oo' the discharge with annual <br />exceedance probability of 1 in 100, range from about 87,000 cfs for the case with the <br />lowest paleoflood exceedance threshold (Case 5a), to 205,000 cfs for the case <br />duplicating the 1998 USACE estimate (Case 1). Excluding case I, which the <br />committee believes is based on too high a log-skew, and the cases using paleoflood <br />data, the range of estimates of QlOO is much smaller, from 169,000 cfs to 191,000 cfs. <br />Note that our best estimated distribution using the paleoflood information (Case 5c) <br />falls well below the data (Figure 3.3). The recommended distribution of three-day <br />flows for the American River at Fair Oaks is derived from Case 3c, which is based on <br />the use of a weighted log skew of -0.1 and the median estimator of the three-day <br />flow associated with the 1862 flood. The estimate of Q,oo for this case is 185,000 <br />cfs. There is little difference between case 3 c and 4c, where for case 4c the skew was <br />estimated with the systematic and historical data. <br /> <br />- <br />