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- 46 Improving American River Flood Frequency Analyses mean three-day discharges (Q3) from the 1905-1955 (unregulated) period. This equation, expressed in real (cfs) terms, is: Q3 = 1.031 * Qp 0.941 R2 = 0.937; standard error = 0.086 in log(10) units Although the log-space fit appears satisfactory, the use of this equation to predict volumes for events significantly larger than those used in estimating the equation would involve considerable extrapolation, with attending increases in confidence bounds, since the largest peak observed in this period was 180,000 cfs ey,'Y 1951). Several larger events occurred in the latter period (1956-1997), and a second equation was estimated that included these (reconstructed) data. This equation, based on 68 observations (low flows in 1964 and 1977 were excluded) is: Q3 = 0.922 * Q P 0.954 R2 = 0.952; standard error = 0.086 in log(10) units The second model differs very little from the model based on measured data only, suggesting that USACE procedures are not seriously biased (Figure 3.1). Since it appeared reasonable to assume an adequate degree of homogeneity between earlier and later records, a third equation was fitted to the upper 50% of the data in order to minimize the influence oflow observations, and to further reduce the error bounds on predicted volumes. This fmal equation, based on 35 observations (half measured, half reconstructed) was estimated as: (Figure 3.2) Q3 = 0394 * Q P 1.027 R2 = 0.885; standard error = 0.088 in log(10) units This equation was used to predict both the magnitude and the 95% confidence bounds of the three-day flow associated with the 1862 floods and the paleoflood threshold, as summarized in Table 3.1. Generalized Skew Coefficient A critical parameter in the development of a frequency curve in the Bulletin 1 7- B framework is the generalized skew coefficient. While on average the logarithms of annual peaks at U.s. gages have a skew near zero, floods in particular regions are thought to have skey,ness coefficients that can be greater or less than that value. Unfortunately, sample estimates of the coefficient of skewness are very unstable, even with long records. For example, even with a 90-year record, such as that available for the American River, the standard error of estimate of the sample skewness coefficient is 0.25. To help get around this large error and to stabilize estimates of flood exceedance probabilities and quantiles, Bulletin 17-B provides a skew map that can be used to compute a generalized skew. That map is based on 2,972 stations across the United States that had at least 25 years of record as of WY 1973. Efforts were employed to reject low outliers, but no effort was made to use historical information.