Environmental conditions in semi-enclosed basins: A dynamic latent class approach for mixed-type multivariate variables

The identification of typical environmental conditions from multiple time series of linear and circular observations requires classification methods that account for the dependence across variables and in time. Motivated by a case study of sea conditions, we take a latent-class approach to classification, relying on a multivariate hidden Markov model. The model integrates multivariate von Mises and log-normal densities to describe the distribution that wind speed and wave height as well as wind and wave direction take under different latent regimes, with parameters that depend on the evolution of an unobserved Markov chain. The estimation of the model is facilitated by a hybrid algorithm that combines an EM algorithm with direct maximization of the log-likelihood. Our analysis of marine data from two locations in the Mediterranean shows that a hidden Markov approach to classification can be successfully employed for identifying interpretable marine conditions in complex orographic settings.