Statistical Analysis of General Circulation Model Climate Simulation: Sensitivity and Prediction Experiments

Abstract

Evaluation of general circulation model (GCM) experiments presents one of the most challenging statistical inference problems in the study of climate. The problem is similar and comparable in difficulty to that encountered in empirical studies of global climate, because the data sets take the form of small samples of large numbers of cross-correlated climate statistics. Thus, in the absence of detailed a priori hypotheses the ability to detect all but the strongest of climate signals is severely limited. Most studies directed at this problem have followed the lead of Chervin and Schneider and have emphasized parametric techniques to solve the univariate or ?local? significance problem. Hasslemann was apparently the first to point out in the context of GCM problems that 1) a collection of ?local? tests has dubious value in the absence of a ?global? test, and 2) a sensitive global test is difficult to construct with multivariate methods without drastic a priori reduction in test dimensionality. Hasslemann's parametric strategy has subsequently guided a number of workers. Recently, in the vein of Mielke et al., Livezey and Chen, and Preisendorfer and Barnett, among others, have presented permutation or Monte Carlo approaches. These nonparametric methods obviate the need for limiting the choice of test statistics to those with known distributions. Examples are presented of the kinds of questions that GCM climate experiments address and how they have been answered, together with considerations on significance testing in future experiments. The principal goals of the narrative are to provide a comprehensive, critical overview of the topic for the nonspecialist, and a compact, discriminating guide to the subject's extensive literature for the GCM climate experimenter.