Functional Data Analysis and Wave Profiles During a Storm

Abstract

Functional Data Analysis is a set of statistical tools developed to perform statistical analysis on data having a functional form. In our case we consider the one-dimensional wave profiles registered during a North-Sea storm as functional data. The waves are defined as the surface height between two consecutive downcrossings. Data is split into 20-minute periods and after registration of the waves to the interval [0,1], the mean wave is obtained along with the first two derivatives of this mean profile. We analyze the shape of these mean waves and their derivatives and show how they change as a function of the significant wave height for the corresponding time interval. We also look at the evolution of the energy, as represented by the phase diagram, as a function of significant wave height. The results show the asymmetry in vertical and horizontal scales for real data. To consider how the individual waves vary we perform a Functional Principal Component Analysis of wave profiles, dividing previously the waves into groups according to their height and comparing with waves measured during a non-storm period. The results suggest that the modes of variation of wave profiles do not depend on wave height or sea condition.