Extreme Storm Surge estimates and projection through the Metastatistical Extreme Value Distribution

Abstract:

The reliable estimation of the occurrence probability of extreme storm surges is crucial to quantify risk and to determine well-designed flood protection measures. This probability is estimated by fitting a suitable distribution to the observed extreme sea-level records. Uncertainty arises due to parameter estimation uncertainty and to the possible inability of the chosen distribution to capture the statistical properties of storm surge levels.

The traditional Extreme Value Theory is based on the use of the Generalized Extreme Value Distribution (GEVD) fitted either by considering block (typically yearly) maxima, or the observations that exceed a high threshold. This approach does not make full use of all observational information, thereby potentially not minimizing estimation uncertainty.

The recently-proposed Metastatistical Extreme Value Distribution (MEVD), in contrast, makes use of most of the observations and has been shown to outperform the classical GEVD in several applications.

Here, we comparatively apply the MEVD and the GEVD to long time series of storm surges (148 years - Venice, 110 years - Galveston, 94 years - New York) and a cross-validation approach is used to compare their performances in high-quantile estimation.

The MEVD approach is based on the definition of an ordinary values distribution (here a Generalized Pareto distribution) whose parameters are estimated on non-overlapping subsamples of fixed size. Here we experiment with subsamples of fixed size (5 yrs) and with variable subsample sizes determined by ensuring that each subsample contain at least 10 events/window. We also explore different threshold values to define independent events (MEVD) and to identify GPD excesses for POT, as well as the effect on uncertainty of different sample sizes (from 5 to 30 years).

We find the POT-GEVD and MEVD approaches to perform similarly once the above parameter choices are optimized. In particular, when considering short samples (5 yrs) and events with a high return time, all methods exhibit a similar underestimation of the actual quantile.

When larger lengths of the sample are considered (10-30 yrs), the median of the GEVD-POT estimation error does not change appreciably, while the median error in MEVD estimates tends to be closer to zero, corresponding to approximately unbiased estimates.