How Big Is the 100-Year Flood? Log-Pearson Type III Estimates for Five Large US Rivers, the Wilson–Hilferty Approximation, and the Weight of Low Outliers

Bridges, levees and dams in the United States are designed for floods with a 1% annual exceedance probability, usually estimated by fitting a log-Pearson Type III distribution to annual peak flows. I fit it to the systematic peak-flow records of five large rivers, from 96 to 152 years long, using USGS data. I derive the Wilson–Hilferty approximation to the Pearson III frequency factor from the gamma distribution and show that its error at the 1% probability is below 0.8% for skews between −1 and 2 but reaches −1.2% at a skew of 3; in the five fits it changes the 100-year flood by 0.04% to 0.35%. The 90% parametric-bootstrap intervals for the 100-year flood are wide, for example 604,628 to 905,746 cfs around 734,172 cfs for the Susquehanna at Harrisburg. Two other sources of uncertainty are larger. The 100-year flood estimated from the second half of each record differs from the first-half estimate by 10% to 34%, partly because the station skew has a sampling standard deviation of about 0.29 in a half-record. And the treatment of low outliers matters: removing two low peaks on the Wabash raises the 100-year flood from 316,674 to 335,560 cfs and cuts the fitted return period of the 1913 flood from 48,700 to 1,306 years.