A systematic method for analyzing parameterizations of unresolved physics in atmospheric general circulation models (GCM) is developed. Here, a linear model of the unresolved physics in CCM3 (the atmospheric GCM developed at the National Center for Atmospheric Research) is constructed using a single column version of CCM3. We then examine the most unstable modes, the fastest growing perturbations, and the response to the most likely perturbations by the linear model. This method provides a precise metric with which to analyze the behavior of the totality of the unresolved physics. By systematically removing the effect of individual parameterizations, the behavior of those individual parameterizations is also analyzed.

Results are shown that illustrate the utility of this method and examine the limits for which the linear approximation is valid. For tropical conditions in which convection is suppressed, all normal modes of the system are stable or have very small growth rates (time scales of several days). However, rapid perturbation growth can still occur through non-modal interaction. For conditions in which convection is promoted, large growth rates are found for normal modes in addition to the optimal perturbation. In that case, growth is primarily promoted by deep convection and vertical diffusion, while it is damped by large-scale stable condensation. The comparison of results from two different basic states demonstrate the nonlinearity of the single column model. Nevertheless, for even the convectively active basic state, linear behavior is apparent for several hours, comparable to the lifetime of tropical convection.