Comparisons of two moments‐based estimators that utilize historical and paleoflood data for the log Pearson type III distribution

Abstract

The expected moments algorithm (EMA) [Cohn et al., 1997] and the Bulletin 17B [Interagency Committee on Water Data, 1982] historical weighting procedure (B17H) for the log Pearson type III distribution are compared by Monte Carlo computer simulation for cases in which historical and/or paleoflood data are available. The relative performance of the estimators was explored for three cases: fixed‐threshold exceedances, a fixed number of large floods, and floods generated from a different parent distribution. EMA can effectively incorporate four types of historical and paleoflood data: floods where the discharge is explicitly known, unknown discharges below a single threshold, floods with unknown discharge that exceed some level, and floods with discharges described in a range. The B17H estimator can utilize only the first two types of historical information. Including historical/paleoflood data in the simulation experiments significantly improved the quantile estimates in terms of mean square error and bias relative to using gage data alone. EMA performed significantly better than B17H in nearly all cases considered. B17H performed as well as EMA for estimating X100 in some limited fixed‐threshold exceedance cases. EMA performed comparatively much better in other fixed‐threshold situations, for the single large flood case, and in cases when estimating extreme floods equal to or greater than X500. B17H did not fully utilize historical information when the historical period exceeded 200 years. Robustness studies using GEV‐simulated data confirmed that EMA performed better than B17H. Overall, EMA is preferred to B17H when historical and paleoflood data are available for flood frequency analysis.