Model-free environmental contours in higher dimensions

Abstract

This paper presents a method for estimating environmental contours in an arbitrary number of dimensions. The method, referred to as Direct-IFORM, does not require a model for the joint distribution of the variables. It can therefore be applied in higher dimensions without degradation in performance. The method involves multiple univariate analyses under rotations of the axes to estimate return values in various directions, which are used to form a contour. The method accounts for serial correlation in the observations, which removes the positive bias that occurs when this is neglected. An efficient open-source code is provided for estimating Direct-IFORM contours. A four-dimensional example is presented for contours of wind speed, wave height, wave period and wind-wave misalignment direction. The application of the method to the design of offshore wind turbines is discussed.