Analysing Spatial Directional data using Wrapped Gaussian processes

Directional data arise in various contexts such as oceanography (wave directions) and meteorology (wind directions), as well as with measurements on a periodic scale (weekdays, hours etc.). Our contribution is to introduce a model-based approach to handle periodic data in the case of measurements taken at spatial locations, anticipating structured dependence between these measurements. We formulate a wrapped Gaussian spatial process model for this setting, induced from a customary \textit{linear} Gaussian process.We build a hierarchical model to handle this situation and show that the fitting of such a model is possible using standard Markov chain Monte Carlo methods. Our approach enables spatial interpolation (and can accommodate measurement error). We illustrate with a set of wave direction data from the Adriatic coast of Italy, generated through a complex computer model.