Statistical‐microphysical causes of rainfall variability in the tropics

Abstract

To elucidate links between statistical theories of rainfall phenomenology and kinematic/microphysical theories of rainfall production mechanisms, a system of partial differential equations is formulated from the air mass continuity, the water substance continuity, and the conservation of vertical momentum in deep tropical clouds during convection. Using observational evidence regarding the vertical structure of the model state variables and allowing for turbulent mixing of convecting elements with the environment, we integrate the conservation equations along the vertical to arrive at a set of equations for a space‐time description of the rainfall process. In the process of integration, we preserve advective storm velocities, and for the resultant numerical model, we use an explicit, antidiffusive numerical integration scheme to obtain rainfall estimates in space and time from given initial and boundary conditions. The advantage of the proposed model over current detailed dynamical cloud and mesoscale models of rainfall is its suitability for repetitive meso‐γ Monte‐Carlo simulation, necessary for statistical analysis that can support statistical‐dynamical theories. The link to statistical models comes from the synthetic generation of the input and boundary fields. Model input may be normalized to consist only of the spatiotemporal water vapor distribution and its vertical gradient, and the spatiotemporal distribution of the buoyancy acceleration due to thermal and pressure perturbations. Examples presented in this paper show the versatility of the model and its ability to reproduce known statistical properties of rainfields. On the basis of these preliminary studies it is conjectured that the rainfall intermittence in space and time over temporal scales greater than a few minutes and spatial scales greater than a few hundred meters originates in the dynamics and microphysics of the model and, possibly, in the intermittent nature of the water vapor field.