Spatial analysis of wave direction data using wrapped Gaussian processes

TL;DR

This paper introduces a wrapped Gaussian spatial process model for analyzing directional data like wave directions, enabling spatial interpolation and handling measurement error, demonstrated on Adriatic coast wave data.

Contribution

It presents a novel hierarchical wrapped Gaussian process model for spatial directional data, with a practical MCMC fitting approach.

Findings

Model successfully interpolates wave directions across space.

Method accommodates measurement error in directional data.

Applied to complex wave data from the Adriatic coast.

Abstract

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.