TABLE 5.1 Summary of Three-Day Flood Quantile Estimates for the American River at Fair Oaks Using the Expected Moments Algorithm (EMA)a

Data and Assumptions:


Systematic Observations:

1905 - 1997

Historical Period:

1848 - 1904

Historical Flood

1862; 147,000b

Upper Bound for Remainder of Historical Period


Paleoflood Observations:

not included

Estimated Distribution Moments:


Log(10) Mean:


Log(10) Std. Deviation:


Log(10) Skewness Coefficient:


Estimated Three-Day Mean Flood Quantiles and 90% Confidence Intervalsc:

Q10 (Pexceed = 0.10)

72,500 cfs (60,000 cfs; 88,000 cfs)

Q20 (Pexceed = 0.05)

101,000 cfs (81,000 cfs; 126,000 cfs)

Q50 (Pexceed = 0.02)

145,000 cfs (109,000 cfs; 192,000 cfs)

Q100 (Pexceed = 0.01)

185,000 cfs (131,000 cfs; 257,000 cfs)

Q200 (Pexceed = 0.005)

230,000 cfs (154,000 cfs; 338,000 cfs)

a Flood quantile estimates are based on rain floods only.

b Corresponds to estimated 1862 three-day mean Q.

c Based on the LPIII fitted using a log skew of -0.1 to the systematic record and the historical record from 1848 that included the historical 1862 flood.

Sensitivity analysis using the recommended approach indicates that censoring below various flows with exceedance probabilities ranging from about 0.94 to 0.31 does not significantly affect the estimated distribution.

The committee chose not to apply the expected probability adjustment to the distribution obtained by application of the expected moments algorithm.

In developing the recommended flood frequency distribution, it was decided not to use paleoflood information recently obtained by the U.S. Bureau of Reclamation. Use of the paleoflood data implies that the log skew is much more negative, and as a result when the paleoflood data is used with the systematic and historical data, the resulting fitted log-Pearson type III distribution does not provide an adequate description of the flood flow frequency relationships for floods with exceedance probabilities from 0.5 up to and beyond 0.002.

Beyond Bulletin 17-B

While its preferred estimate of the frequency distribution of three-day rain flood flows on the American River is consistent with the systematic and historical data, the committee is uncomfortable with extrapolating it much beyond the flow with an exceedance probability of 0.005. Use of the recommended distribution to estimate the exceedance probabilities of two recent PMF estimates yields values that

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