A novel method for the distribution and extrapolation of extreme sea state parameters

Abstract

This paper proposes a novel transformation KDE (Kernel Density Estimation) method in order to more accurately calculate the sea state parameter distribution tails and to extrapolate well. Implementation of this novel method starts with using the Box-Cox formulation to transform the original dataset into a new sample having a density g that can be more easily estimated using the ordinary KDE (Kernel Density Estimation) method. One can then “backtransform” the estimate of g to obtain the estimate of the probability density distribution of the original dataset. The rationale for choosing the Box-Cox formulation is that it is a convex transformation and therefore can reduce the positive skewness of the unimodal density of a typical sea sate parameter (significant wave height, zero-up-crossing period, etc.). Our proposed novel transformation KDE method has been applied in predicting the probability distribution tails of two datasets, and its accuracy has been clearly substantiated by comparing with the prediction results obtained using the traditional parametric approaches and the ordinary KDE (Kernel Density Estimation) method. This novel transformation KDE method has subsequently been applied for deriving a 50-year environmental contour line based on one of the aforementioned datasets. The derived contour line has been compared with those predicted by using a traditional parametric approach and the ordinary KDE method, and the efficiency and accuracy of our proposed novel method have been once again convincingly validated. The research results demonstrate that our novel transformation KDE method can be utilized as a useful tool for the distribution and extrapolation of extreme sea state parameters.