On Determining the Statistical Significance of Climate Experiments with General Circulation Models

Abstract

One of the key problems in analyzing the results of climate experiments with general circulation models (GCM's,) is the matter of estimating the statistical significance of a prescribed change response. This question involves separating the signal (that part of the response attributable to the prescribed change) and the noise (some measure of the inherent variability of model statistics). In this paper we present maps showing the geographical distribution of estimates of the standard deviations at each grid point for the January climatological statistics of the NCAR GCM based on a sample of five independent realizations. Also, a formalism for estimating the statistical significance of a prescribed change response is given based on the classical Student's t-test, and the implications of varying the sample size are discussed. The most telling implication of the results is that thus statistical significance questions could mean that a large percentage of total computational effort in a particular prescribed change GCM experiment series may have to be invested in generating a data base for the noise climatology. This suggests that careful advanced planning of proposed GCM experiments be made to maximize the chances for obtaining statistically significant results within a realistic computational budget.