Robust flood frequency analysis: Performance of EMA with multiple Grubbs-Beck outlier tests

Flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles. Parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods. A danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest. The identification and treatment of such Potentially Influential Low Floods (PILFs) frees a fitting algorithm to describe the distribution of the larger observations. This can allow parametric flood frequency analysis to be both efficient, and also robust to deviations from the proposed probability model's lower tail. Historically, PILF identification involved subjective judgement. We propose a new multiple Grubbs-Beck outlier test (MGBT) for objective PILF identification. MGBT PILF identification rates (akin to Type I errors) are reported for the lognormal (LN) distribution and the log-Pearson Type III (LP3) distribution with a variety of skew coefficients. MGBT PILF identification generally matched subjective identification from a recent California flood frequency study. Monte Carlo results show that censoring of PILFs identified by the MGBT algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm (EMA) for negatively skewed LP3 distributions and has little effect for zero or positive skews; simultaneously it protects against deviations from the LP3 in the lower tail, as illustrated by distorted LN examples. Thus, MGBT generally makes flood frequency analysis based on the LP3 distribution with EMA both more accurate and more robust.