Segmentation of sea current fields by cylindrical hidden Markov models: a composite likelihood approach

Motivated by segmentation issues in studies of sea current circulation, we describe a hidden Markov random field for the analysis of spatial cylindrical data, i.e. bivariate spatial series of angles and intensities. The model is based on a mixture of cylindrical densities, whose parameters vary across space according to a latent Markov field. It enables segmentation of the data within a finite number of latent classes that represent the conditional distributions of the data under specific environmental conditions, simultaneously accounting for unobserved heterogeneity and spatial auto-correlation. Further, it parsimoniously accommodates specific features of environmental cylindrical data, such as circular–linear correlation, multimodality and skewness. Because of the numerical intractability of the likelihood function, estimation of the parameters is based on composite likelihood methods and essentially reduces to a computationally efficient expectation–maximization algorithm that iteratively alternates the maximization of a weighted composite likelihood function with weights updating. These methods are tested on simulations and exploited to segment the sea surface of the Gulf of Naples by means of meaningful circulation regimes.