A hidden Markov approach to the analysis of space-time environmental data with linear and circular components

The analysis of bivariate space-time series with linear and circular components is complicated by (1) multiple correlations, across time, space and between variables, (2) different supports on which the variables are observed, the real line and the circle, and (3) the periodic nature of circular data. We describe a multivariate hidden Markov model that includes these features of the data within a single framework. The model integrates a circular von Mises Markov field and a Gaussian Markov field, with parameters that evolve in time according to a latent (hidden) Markov chain. It allows to describe the data by means of a finite number of time-varying latent regimes, associated with easily interpretable components of large-scale and small-scale spatial variation. It can be estimated by a computationally feasible Expectation-Maximization algorithm. In a case study of sea currents in the Northen Adriatic sea, it provides a parsimonious representation of the sea surface in terms of alternating environmental states.