  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 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.
