NUMERICAL CONVERGENCE OF THE DYNAMICS OF A GCM

Atmospheric general circulation models (GCMs) are characterized by man y features but especially by: (1) the manner of discretizing the gover ning equations and of representing the variables involved at a given r esolution, and (2) the manner of parameterizing unresolved physical pr ocesses in terms of those resolved variables. These two aspects of mod el formulation are not independent and it is difficult to untangle the ir intertwined effects when assessing model performance. The attempt h ere is to separate these aspects of GCM behaviour and to ask, ''Given a perfect parameterization of the physical processes in a model, what resolution is needed to capture the dominant dynamical aspects of the atmospheric climate?'' Alternatively, ''At what resolution do the dyna mics of a GCM converge''? The perfect parameterization approach assume s that the calculation of the physical terms returns the ''correct'' r esult at all resolutions. In the idealized case, a time-independent fo rcing is one of the simplest that satisfies this condition. However, e xperiments show that it is difficult for the dynamics of a GCM to bala nce a time-independent forcing with atmosphere-like flows and structur es. The model requires, and the atmosphere presumably includes, physic al feedback mechanisms which act so as to maintain the kinds of flows and structures that are observed. Resolution experiments are performed with a simplified forcing function for the thermodynamic equation whi ch combines a dominant time-independent specified forcing with a weak linear relaxation feedback. These experiments show that the dynamics o f the GCM have essentially converged at T32 and certainly by T63 which is the next resolution considered. This is shown by the constancy of structures, variances, covariances, transports and energy budgets with increasing resolution. Experiments with an alternative forcing propos ed by Held and Suarez, which has the form of a linear relaxation, show somewhat less evidence of convergence at these resolutions. In both c ases the ''physics'' are known by assumption. However, the form and na ture of the forcing is different, as is the behaviour with resolution. The implication for the real system is that the resolution required f or simulating the dynamical aspects of climate is rather modest. The s imulated climate does, however, apparently depend on the ability to co rrectly and consistently parameterize the physical processes in a GCM, involving both forcing and feedback mechanisms, as a function of reso lution.