Clustering a Global Field of Atmospheric Profiles by Mixture Decomposition of Copulas

This work focuses on the clustering of a large dataset of atmospheric vertical profiles of temperature and humidity in order to model a priori information for the problem of retrieving atmospheric variables from satellite observations. Here, each profile is described by cumulative distribution functions (cdfs) of temperature and specific humidity. The method presented here is based on an extension of the mixture density problem to this kind of data. This method allows dependencies between and among temperature and moisture to be taken into account, through copula functions, which are particular distribution functions, linking a (joint) multivariate distribution with its (marginal) univariate distributions. After a presentation of vertical profiles of temperature and humidity and the method used to transform them into cdfs, the clustering method is detailed and then applied to provide a partition into seven clusters based, first, on the temperature profiles only; second, on the humidity profiles only; and, third, on both the temperature and humidity profiles. The clusters are statistically described and explained in terms of airmass types, with reference to meteorological maps. To test the robustness and the relevance of the method for a larger number of clusters, a partition into 18 classes is established, where it is shown that even the smallest clusters are significant. Finally, comparisons with more classical efficient clustering or model-based methods are presented, and the advantages of the approach are discussed.