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Quantifying the limits of convective parameterizations

[1] Quasi-equilibrium (QE) closure is an approximation that is expected to apply to a large ensemble of clouds under slowly changing weather conditions. It breaks down under rapidly changing conditions or when the domain size is too small to provide an adequate sample of the cloud field. We explore fluctuations about an equilibrium state as simulated by a three-dimensional cloud-resolving model. An ensemble of simulations is used to determine how the response to prescribed periodic large-scale forcing changes with the period of the forcing and the size of the averaging domain. The vertical profile of the forcing is loosely based on GATE data. Results are compared with those from constant forcing simulations. In the constant forcing simulations, the noise-to-signal ratio is nearly independent of forcing magnitude. With time-varying forcing, a considerable range of responses is found. As expected, the more slowly the forcing varies, the better the response is approximated by QE. Errors become large when the period of the forcing is less than 30 h, suggesting that the diurnal cycle cannot be accurately simulated with a QE closure. Nondeterministic variability becomes more significant with smaller domain sizes. For the cases studied, a domain width of at least 180 km is needed to obtain an adequate sample of the cloud population.