Spatial clustering of curves with an application of satellite data

Abstract

Water quality indicators are important to identify risks to the environment, society and human health. The European Community Water Framework Directive establishes guidelines for the classification of all water bodies across Europe and chemical and biological indicators were used to this scope. In particular, the Chlorophyll type A index (Chl-a) is a shared indicator of trophic status and monitoring activities may be useful to explain its spatial distribution and to discover local dangerous behaviours (for example the anoxic events). Differently by the classical approach based on an “average” values over a period, we propose a functional clustering model that takes into account temporal and spatial dependence of Chl-a concentrations in the Adriatic Sea for defining appropriate clusters of sites. We use satellite monthly data, during the period 2002–2012, and we model the spatial dependence among the sites by means of a Markov random field model. Compared to similar attempts in literature by Jiang and Serban (2012) our formulation includes spatial covariates. This inclusion allows for more flexibility to obtain more homogeneous and representative clusters of sites in the Adriatic Sea. The estimation of the model and the identification of the number of clusters are carried out using a pseudolikelihood function. A small simulation study complements the real data analysis.