Estimation and Clustering of Directional Wave Spectra

The directional wave spectrum (DWS) describes the energy of sea waves as a function of frequency and direction. It provides useful information for marine studies and guides the design of maritime structures. One of the challenges in the statistical estimation of DWS is to account for the circular nature of direction. To address this issue, this paper considers the 1-dimensional case of the direction-only DWS (DWSd) and applies the circular regression to smooth the DWSd observations. This paper then improves an existing clustering algorithm by incorporating circular smoothing in the clustering algorithm, automating the determination of the optimal number of clusters, and designing a more appropriate smoothing parameter selection procedure for data with correlated errors. Our simulation studies reveal an improvement in the performance of estimating the underlying DWSd using the circular smoother. Finally, the linear and circular smoothers are compared by clustering two real datasets, one from the Sofar Ocean network and the second from a buoy located at the Red Sea. For the Sofar Ocean data, clustering with the two smoothers results in different number of clusters. For the Red Sea data, a cluster with a peak at the boundary is only identified when the circular smoother is used. Supplementary materials accompanying this paper appear online.