Characterization of storm wave asymmetries with functional data analysis

Functional data analysis (FDA) is a set of tools developed to perform statistical analysis on data having a functional form. In our case we consider the one-dimensional wave surface profiles registered during a North-Sea storm as functional data. The data is split into 20 min intervals within which an individual wave is defined as the profile between two consecutive downcrossings. After registration of these individual waves to the interval 0, 1], the mean wave profile for the entire 20 min interval 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, which is a measure of the severity of the sea 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. Comparison with a Gaussian wave simulation model calculated from the actual wave spectra shows important differences in symmetry and shape of the average wave and seem to indicate that the greatest difference in the distribution of energy during the wave cycle lies in the second and fourth quarters of the wave period. FDA can be applied to derive information on the individual and average wave profiles and also provide an understanding of the variation in energy throughout the wave phase.