Joint spatio-temporal analysis of a linear and a directional variable: space-time modeling of wave heights and wave directions in the Adriatic Sea

In various marine operations, it is useful to have a better understanding of factors that influence sea motion and to provide more accurate forecasts. In particular, we are motivated by data on wave heights and outgoing wave directions over a region in the Adriatic sea during the time of a storm, with the overarching goal of understanding the association between wave directions and wave heights and enabling improved prediction of wave behavior. Our contribution is to develop a fully model-based approach to capture joint structured spatial and temporal dependence between a linear and an angular variable. Model fitting is carried out using a suitable data augmented Markov chain Monte Carlo (MCMC) algorithm. We illustrate with data outputs from a deterministic wave model for a region in the Adriatic Sea. The proposed joint model framework enables both spatial inter- polation and temporal forecasting.