Mapes, B. E., 2004: Sensitivities of cumulus-ensemble rainfall in a cloud-resolving model with parameterized large-scale dynamics. J. Atmos. Sci., 61, 2308-2317.
The problem of closure in cumulus parameterization requires an understanding of the sensitivities of convective cloud systems to their large-scale setting. As a step toward such an understanding, this study probes some sensitivities of a simulated ensemble of convective clouds in a two-dimensional cloud-resolving model (CRM). The ensemble is initially in statistical equilibrium with a steady imposed background forcing (cooling and moistening). Large-scale stimuli are imposed as horizontally uniform perturbations nudged into the model fields over 10 min, and the rainfall response of the model clouds is monitored.
In order to reduce a major source of artificial insensitivity in the CRM, a simple parameterization scheme is devised to account for heating-induced large-scale (i.e., domain averaged) vertical motions that would develop in nature but are forbidden by the periodic boundary conditions. The effects of this large-scale vertical motion are parameterized as advective tendency terms that are applied as a uniform forcing throughout the domain, just like the background forcing. This parameterized advection is assumed to lag rainfall (used as a proxy for heating) by a specified time scale. The time scale determines (via a gravity wave spacetime conversion factor) the size of the large-scale region represented by the periodic CRM domain, which can be of arbitrary size or dimensionality.
The sensitivity of rain rate to deep cooling and moistening, representing an upward displacement by a large-scale wave of first baroclinic mode structure, is positive. Near linearity is found for ±1 K perturbations, and the sensitivity is about equally divided between temperature and moisture effects. For a second baroclinic mode (vertical dipole) displacement, the sign of the perturbation in the lower troposphere dominates the convective response. In this dipole case, the initial sensitivity is very large, but quantitative results are distorted by the oversimplified large-scale dynamics parameterization, which only allows for deep baroclinic mode responses. Imposition of moderate wind shear (10 m s-1 over the troposphere) has no significant impact on rain rate.