ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-9-9471-2009 <i>Est modus in rebus</i>: analytical properties of multi-model ensembles Potempski S. 1 2 Galmarini S. 1 European Commission – DG Joint Research Centre, Institute for Environment and Sustainability, 21020 Ispra VA, Italy Institute of Atomic Energy, 05-400 Otwock-Swierk, Poland 16 12 2009 9 24 9471 9489 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/9/9471/2009/acp-9-9471-2009.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/9/9471/2009/acp-9-9471-2009.pdf

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.

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