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Flood Frequency Estimates for the American River 49 The American River basin is in an area where map skew values change rapidly with location; hence the map skews are likely to be less reliable. For the location of the American River gage at Fair Oaks, the map value is about 0.0. Given the age of the Bulletin 17-B skew map and a concern with three-day volumes rather than annual peaks, the committee chose to estimate an alternative regional ("map") skew. This regional skew estimate is based on log skews computed from maximum annual three-day rain flood data from seven large west- slope Sierra rivers (USACE, 1998). For each of these discharge series there are about 25 more years of data than were used to construct the Bulletin l7-B skew map. The estimated log skews are given in Table 3.2. (Note that the skew for the Merced was adjusted to account for a low outlier. Bulletin 17-B procedures were used to detect and correct for the low outlier.) Averaging these values yields a regional skewness coefficient -0.1 for three-day flows. Estimating the standard error of our alternative regional skew estimate is complicated by the highly cross-correlated the flood data from the seven rivers. (The average pairwise correlation between the flood series is 0.89.) A Monte Carlo experiment was conducted to determine the sampling error of the average skewness coefficient for seven stations with n = 100 years of record when the correlation among concurrent flows was 0.89. While a single station had a standard error of 0.25 (variance 0.063), the standard error of the sample average of seven stations decreased by only 5%, to 0.21. (This result is consistent with a formula provided in Stedinger [1983].) We are in the unfortunate position of being unable to resolve with any precision the value of the sample skewness coefficient for the American River. More stations could be included in the analysis, but there are no other large basins in the northern and central Sierra Nevada that are like the American River. The two estimates of regional skew, 0.0 and -0.1, bracket the at-site skew of -0.06. The latter regional skew was derived specifically for three-day maxima and for large basins in the Sierra Nevada, like the American River, it would appear to be the more relevant of the two. Moreover, the former, based on the Bulletin l7-B skew map, is also limited in its precision by the high correlation among floods in the same year, and is based on shorter records for annual maxima. TABLE 3.1 Estimated Three-Day Discharge Magnimdes and 95% Confidence Limits 1862 Event Paleo Lower Paleo Upper Est. peak (cfs) 265,000 300,000 400,000 Est. three-Day Q (cfs mean) Ratio QJ!Qp Lower 95% conf. bound Ratio to Qp Upper 95% conf. bound Ratio to Qp 147,000 167,000 224,000 0.55 0.56 0.56 95,000 108,000 143,000 0.36 0.36 0.36 226,000 258,000 352,000 0.85 0.86 0.88 -