Seasonal autoregressive modeling of a skew storm surge series

Autoregressive (AR) models have been widely used in several geophysical applications, as they represent a simple and practical option for modeling stochastic series. In this paper, we show that AR models can be adapted and are useful for the description of skew surge (i.e., a surge occurring at the time of a high tide) series. Namely, seasonal AR models of skew surge series are built on 35 sites located along the coasts of the European Atlantic Ocean, the English Channel and the Southern part of the North Sea. These models are presented and discussed. The estimation of the distribution of the residuals, modeled using a Normal Inverse Gaussian (NIG) distribution, is also discussed. AR models are advantageous for a number of reasons: (i) they provide information on the correlation length of the surge phenomena, (ii) they can be used to forecast short-term surge occurrences based on a limited set of past observations and (iii) they provide plausible information about longer series, which may have larger extremes than what is observed, permitting a statistical description of simulated extremes. These three characteristics and benefits are examined and discussed for a selected site, the Saint-Nazaire harbor (France), with respect to the storm surge that occurred during the Xynthia storm of February 2010.