An anisotropic and inhomogeneous hidden Markov model for the classification of water quality spatio-temporal series on a national scale: the case of Scotland.

This work presents a case study about the evaluation of the water quality dynamics in each of the 56 major catchments in Scotland, for a period of 10 years. Data are obtained by monthly sampling of water contaminants, in order to monitor discharges from the land to the sea. We are interested in the multivariate time series of ammonia, nitrate, and phosphorus. The time series may present issues that make their analysis complex: non-linearity, non-normality, weak dependency, seasonality, and missing values. The goals of this work are the classification of the observations into a small set of homogeneous groups representing ordered categories of pollution, the detection of change-points, and the modeling of data heterogeneity. These aims are pursued by developing a novel spatio-temporal hidden Markov model, whose hierarchical structure was motivated by the data set to study: the observations are displayed on a cylindrical lattice and driven by an anisotropic and inhomogeneous hidden Markov random field. As a result, four hidden states were selected, showing that catchments could be grouped spatially, with a strong relationship with the dominating land use. This method represents a useful tool for water managers to have a nationwide picture in combination of temporal dynamics.