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Climate Variability Studies and Model Intercomparison
PI: 
Jay Larson 
Institution: 
Argonne National Laboratory / The Australian Natio 
Abstract: 
Traditional statistical techniques in climatology emphasize primarily the computation of moments (i.e., means and variances), and correlations between variables. In spite of the arguable success of this approach, it is based on underlying assumptions (unimodality and linearity) that do not universally apply to the climate system. We are working on an alternate formulation of climate based on information theory. In this picture of climate the basic quantity for quantifying variability is the Shannon Entropy (SE) and the basic measure of association is the Mutual Information (MI). These quantities both have solid, useful connotations for discrete variables. For continuous variables, however, the SE is illdefined, possibly taking on negative or infinite values, but the MI is a welldefined and reliable quantity. Thus, the problem for continuous systems becomes one of finding a surrogate for the SE to quantify variability, and we have identified a number of candidate quantities.
The application for access to IPCC AR4 output is driven by an interest in applying these concepts to a large number of model output data sets.
We will begin by studying discretized variables (e.g., cloud amount expressed in octas or tenths), where we can compute both the SE and MI with confidence, using these metrics to quantify both spatial and temporal variability. Where possible, we will use SE and MI to quantify relative strengths in relationships between climate variables. We will do this for a wide variety of model output sets, and thus will be doing an intercomparison in the process. We will also apply the SE and MI to model data prepared (through intermesh interpolation) in a form that will allow 1) direct intermodel comparisons using information theory and 2) an assessment of the overall amount of information the models share (also called “redundancy”).
The application of information theory to continuous variables will be pursued as described above. Since the SE is not always well defined for continuous variables, we will experiment with various approaches to 1) discretizing the continuous data and then computing the SE and MI, and 2) using alternatives to the SE to calibrate the MI for use in model variability studies and model intercomparison.
The expected outcomes of this work are 1) a set of results applying informationtheoretic principles to assess climate variability, 2) a more general approach identify the existence of relationships among climate variables, and 3) a distinctly different and more general approach to model intercomparison. 
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