Abstract. In this paper we investigate some basic properties of the multi-model ensemble systems, which can be deduced from a general characteristic of statistical distributions of the ensemble members with the help of mathematical tools. In particular we show how to find optimal linear combination of model results, which minimizes the mean square error both in the case of uncorrelated and correlated models. By proving basic estimations we try to deduce general properties describing multi-model ensemble systems. We show also how mathematical formalism can be used for investigation of the characteristics of such systems.

[1] The aim of this work is to explore the effectiveness of theoretical information approaches for the reduction of data complexity in multimodel ensemble systems. We first exploit a weak form of independence, i.e. uncorrelation, as a mechanism for detecting linear relationships. Then, stronger and more general forms of independence measure, such as mutual information, are used to investigate dependence structures for model selection. A distance matrix, measuring the interdependence between data, is derived for the investigated measures, with the scope of clustering correlated/dependent models together. Redundant information is discarded by selecting a few representative models from each cluster. We apply the clustering analysis in the context of atmospheric dispersion modeling, by using the ETEX-1 data set. We show how the selection of a small subset of models, according to uncorrelation or mutual information distance criteria, usually suffices to achieve a statistical performance comparable to, or even better than, that achieved from the whole ensemble data set, thus providing a simpler description of ensemble results without sacrificing accuracy.Citation: Riccio A., A. Ciaramella, G. Giunta, S. Galmarini, E. Solazzo, and S. Potempski (2012), On the systematic reduction of data complexity in multimodel atmospheric dispersion ensemble modeling,

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