| Summary: | Distinct Empirical Orthogonal Functions (DEOF) analysis is a new method for the comparison of the modal structure in the variability of two data sets. This method is ideal to find the changes in the modes of variability in the data of two different time periods, e.g. today’s climate and a future climate change projection, but could also be used to compare modes of variability in climate models with observations or with other models. DEOF analysis is based on normal Empirical Orthogonal Function (EOF) analysis, but in a second step the DEOF patterns are computed via pairwise rotation of all EOF pattern in a way that the difference in explained variance between the two data sets gets maximized. Thus this method finds the pattern in each data set that strongest loses or gains importance in terms of explained variance relative to the other data set and quantifies the difference. We illustrate this method on the basis of several artificial stochastic processes and by literature examples, including the eastward shift of the North Atlantic Oscillation and the poleward shift of Southern Annular Mode in global warming. We further apply this method to a CMIP3 multi model ensemble to look how climate modes in the Northern Hemisphere are changing in future climate projections.
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