Schneider, Tapio and Griffies, Stephen M. (1999) A Conceptual Framework for Predictability Studies. Journal of Climate, 12 (10). pp. 3133-3155. ISSN 0894-8755. http://resolver.caltech.edu/CaltechAUTHORS:SCHNjc99
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A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probability distribution of prediction errors. For univariate Gaussian predictions, the PP reduces to conventional predictability measures that are based upon the ratio of the rms error of a model prediction over the rms error of the climatological mean prediction. Since climatic variability on intraseasonal to interdecadal timescales follows an approximately Gaussian distribution, the emphasis of this paper is on multivariate Gaussian random variables. Predictable and unpredictable components of multivariate Gaussian systems can be distinguished by predictable component analysis, a procedure derived from discriminant analysis: seeking components with large PP leads to an eigenvalue problem, whose solution yields uncorrelated components that are ordered by PP from largest to smallest. In a discussion of the application of the PP and the predictable component analysis in different types of predictability studies, studies are considered that use either ensemble integrations of numerical models or autoregressive models fitted to observed or simulated data. An investigation of simulated multidecadal variability of the North Atlantic illustrates the proposed methodology. Reanalyzing an ensemble of integrations of the Geophysical Fluid Dynamics Laboratory coupled general circulation model confirms and refines earlier findings. With an autoregressive model fitted to a single integration of the same model, it is demonstrated that similar conclusions can be reached without resorting to computationally costly ensemble integrations.
|Additional Information:||© Copyright by American Meteorological Society 1999 (Manuscript received September 24, 1998, in final form January 19, 1999) We wish to express our thanks to Jeff Anderson and Arnold Neumaier, who drew our attention to some of the referenced literature on climatic predictability and discriminant analysis, respectively. Jeff Anderson, Ruth Michaels, Thomas Müller, Arnold Neumaier, Heidi Swanson, and Jens Timmer carefully read drafts of this paper. We gratefully acknowledge their comments and criticism, which led to substantial improvements in the final version.|
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|Deposited On:||20 Jul 2006|
|Last Modified:||26 Dec 2012 08:57|
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