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The Arakawa-Schubert (A-S) cumulus parameterization is evaluated by performing semiprognostic tests against data simulated by a cumulus ensemble model (CEM). The CEM is a two-dimensional cloud model for simulating the formation of an ensemble of cumulus clouds under prescribed large-scale conditions. Three simulations, two with vertical wind shear and one without, are performed with identical (time-varying) large-scale advective effects. The semiprognostic tests follow a procedure similar to that used by Lord except that simulated data averaged over the entire domain or selected subdomains of the CEM provide the “observed” large-scale conditions. Detailed comparisons were made between the results of simulation and parameterization. The results include comparisons of surface precipitation rate, apparent heat source, apparent moisture sink, updraft mass flux, and downdraft mass flux. Two different sets of tests were performed. One is the standard A-S parameterization with the cloud work function (CWF) quasi equilibrium, and the other allows CWF nonequilibrium by taking into account the simulated time change of the CWF. The tests show that the A-S parameterization is basically valid in spite of the existence of mesoscale organization in cumulus convection. In particular, the assumption of CWF quasi equilibrium is more accurate for inputs averaged over smaller subdomain sizes that resolve some mesoscale processes. On the other hand, errors due to the nondiagnostic aspect of cumulus convection are more significant for inputs averaged over larger subdomain sizes. Errors due to the inherent nondeterministic aspect of cumulus convection appear to be more significant for inputs averaged over smaller subdomain sizes. A modified A-S parameterization with a convective-scale downdraft formulation was also tested against the simulated data. The inclusion of downdrafts slightly improves the results of semiprognostic tests. The impact of downdrafts on the subcloud layer may depend significantly on the subdomain size.
Xu et al. (Tue,) studied this question.