Reining in Log-Pearson Type III Flow-Frequency Estimates — Applying a Reasonable Bound through the Skew Parameter

In the United States, the flow-frequency distribution established for use by federal agencies is the log-Pearson Type III (LP3). Fitting an LP3 requires the estimation of three log-space parameters: mean, standard deviation, and coefficient of skewness (skew). The resulting flow-frequency estimates for extreme floods are very sensitive to the value of the skew parameter. Many researchers and practitioners have made attempts to better estimate the skew, e.g., through regional skew maps and relating skew to physical watershed characteristics. These attempts have been mainly unsuccessful. In practice, using unfiltered LP3 fitted parameters to estimate project design flows and their associated confidence limits for floods greater than those recorded has lead to extreme flow estimates, which often exceed perceived physical basin limits. In order to improve the LP3 extrapolations, a simple procedure was developed by which the skew parameter was adjusted such that the resulting flow-frequency estimates respected the physical basin limits. This procedure was applied to several major watersheds of the Sacramento and San Joaquin River system in California. In this application, the skew was adjusted such that the probable maximum flood had an annual exceedance probability (AEP) of 1-in-10,000 or less. Monte Carlo simulations were performed with an assumed underlying test flood-frequency distribution. The distribution was sampled with representative flood record lengths (50 and 100 years). Estimates and confidence limits of commonly used design frequencies (1-in-10 to 1-in-500 AEP) and the risk of flooding in the next 50 years were computed using both the standard (Bulletin 17B) procedure and the procedure with the described skew adjustment. The design flood estimates were compared for reasonableness and consistency with the expected, underlying test distribution values.