An Analytical Model of Two-Dimensional Mesoscale Circulation and Associated Properties Across Squall Lines

Abstract

Mesoscale convective systems (MCS) contribute about half of the world's precipitation and create flash flooding as well as other extreme weather events. Despite steady progress in research of these systems in the last several decades, better theoretical understanding is still needed to understand their dynamical organizations and to improve their forecasts in numerical models. By using the Moncrieff-Green horizontal vorticity equation, this paper presents an analytical model of one type of MCS, the steady-state squall lines. It describes the organization, propagation, and properties of mesoscale circulations of two-dimensional steady-state convective systems under sheared environment. Far-side solutions are formulated to illustrate the underlying physical processes of squall line flows. Numerical procedures are described to solve the model under general environmental conditions. The model leads to the following prediction of squall line properties: Given the environmental profiles of wind and convective available potential energy (CAPE), the propagation speed, the depths and mass fluxes of the tilted ascending front-to-rear flow, the overturning updraft, and the descending rear inflow of the squall line can be all determined from the cold pool buoyancy or CAPE. The squall lines are therefore self-organized dynamical systems that have limited degrees of freedom in their properties. The model advances the theoretical understanding of how mesoscale flow components interact to sustain organized convection. It provides a new tool to interpret squall line systems in high resolution models and to parameterize them in climate models.