A Theory for Buoyancy and Velocity Scales in Deep Moist Convection

Buoyancy and velocity scales for dry convection in statistical equilibrium were derived in the early twentieth century by Prandtl, but the scaling of convective velocity and buoyancy, as well as the fractional area coverage of convective clouds, is still unresolved for moist convection. In this paper, high-resolution simulations of an atmosphere in radiative-convective equilibrium are performed using the Weather Research and Forecasting (WRF) model, a three-dimensional, nonhydrostatic, convection-resolving, limited-area model. The velocity and buoyancy scales for moist convection in statistical equilibrium are characterized by prescribing different constant cooling rates to the system. It is shown that the spatiotemporal properties of deep moist convection and buoyancy and velocity scales at equilibrium depend on the terminal velocity of raindrops and a hypothesis is developed to explain this behavior. This hypothesis is evaluated and discussed in the context of the numerical results provided by the WRF model. The influence of domain size on radiative-convective equilibrium statistics is also assessed. The dependence of finescale spatiotemporal properties of convective structures on numerical and physical details is investigated.