Non-Stationary Equivalent Storm Model for Long-Term Statistics of Ocean Storms

In the last decade many researchers focused on the study of non-stationary pattern of climatic variables., It is well established that marine signals e.g., significant wave height or sea water level exhibit a long-term trend due to climate change. The classical approach for the estimation of extreme values analyses may not be enough reliable. The need to account for non-stationarity has involved the development of non-stationary extreme value analysis (NS-EVA) approaches. The main idea is to modify the classical extreme value analysis approach by using non-stationary distributions instead of the stationary ones. Non-stationary probability distributions are analogue to the stationary ones, but their parameters are time dependent. The time dependency may involve all or some of the distribution parameters which may be expressed in different ways. In this paper, this basic concept is applied to develop a non-stationary Equivalent Storm Model (ESM) using the concept of Equivalent Triangular Storm (ETS). The ESM approach is a semi-analytical approach based on the statistic equivalence between actual and an associated simplified storm characterized by a standardized storm shape which leads to the equivalence of wave risk between actual storm sequence and simplified storm sequence at a given site. Due to the equality of wave risk between actual and simplified storm sequences, the problem of calculating return period of sea storm with assigned characteristics can be managed analytically referring to the standardized storm shape, providing very simple analytical formulae dependent on the significant wave height probability distribution and on a duration-intensity regression function at the considered site. The non-stationary ESM is achieved by substituting these two stationary functions with time dependent ones in a similar way as NS-EVA does. A data analysis is proposed to elucidate the differences on significant wave height return values estimation between stationary and non-stationary ESM approach due to non-stationarity of significant wave height and storm duration.