The surface of the ocean, and so such quantities as the significant wave height, H s , can be thought of as a random surface that develops over time. In this paper, we explore certain types of random fields in space and time, with and without dynamics that may or may not be driven by a physical law, as models for the significant wave height. Reanalysis data is used to estimate the sea-state motion which is modeled as a hidden Markov chain in a state space framework by means of an AR(1) process or in the presence of the dispersion relation. Parametric covariance models with and without dynamics are fitted to reanalysis and satellite data and compared to the empirical covariance functions. The derived models have been validated against satellite and buoy data.
Climate is changing due to global warming and many of the observed changes since the 1950s are unprecedented over many centuries to many thousands of years (IPCC, 2021). Since the end of the 20th century, the frequency and intensity of the strongest storms have been increasing in the North Atlantic (IPCC, 2013). Damage resulting from storm surges, sea level rise, and coastal flooding presents a major risk for Europe (IPCC, 2014). It is thus essential to investigate how extreme sea levels and storm surges change in a warming climate, in the perspective of predicting them and adapting coastal areas accordingly to future changes.Extreme high sea levels are the joint effect of mean sea level (MSL), tide, and storm surges. Storm surges are generated during extreme weather events such as extra-tropical storms or cyclones, and result from strong, large-scale atmospheric forcing (e.g., Dangendorf et al., 2016). The European coasts are regularly impacted by mid-latitude extra-tropical storms, which cause large surges, i.e., greater than 1 m. This may lead to huge economic losses and sometimes loss of human life. For example, the storm Xynthia hit the French coast severely on February 27 and 28, 2010, causing a large surge of 1.53 m in the harbor of La Rochelle (see location on Figure 1). This was the highest surge ever observed since the installation of the tide gauge in 1997; its return period was estimated to be greater than 100 yr (Pineau-Guillou et al., 2012). This exceptional storm event caused a major coastal flooding (Bertin et al., 2014). Forty-seven people were killed, around 10,000 people had to be evacuated, and the losses were estimated to more than 2.5 billion Euros (Genovese & Przyluski, 2013).
This work is motivated by the analysis of the extremal behavior of buoy and satellite data describing wave conditions in the North Atlantic Ocean. The available data sets consist of time series of significant wave height (Hs) with irregular time sampling. In such a situation, the usual statistical methods for analyzing extreme values cannot be used directly. The method proposed in this paper is an extension of the peaks over threshold (POT) method, where the distribution of a process above a high threshold is approximated by a max-stable process whose parameters are estimated by maximizing a composite likelihood function. The efficiency of the proposed method is assessed on an extensive set of simulated data. It is shown, in particular, that the method is able to describe the extremal behavior of several common time series models with regular or irregular time sampling. The method is then used to analyze Hs data in the North Atlantic Ocean. The results indicate that it is possible to derive realistic estimates of the extremal properties of Hs from satellite data, despite its complex space-time sampling.
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