A theoretical model of multi-regime convection in a stratocumulus-topped boundary layer

The possible effects on stratocumulus circulations caused by drizzle and radiative cooling or heating are investigated theoretically using a simple Nonlinear Dynamical System (NDS). These effects are incorporated implicitly via the background temperature profile, and are expressed as departures from neutral conditions. These neutral conditions are assumed to be dry adiabatic in the surface, sub-cloud and inversion regions, and moist adiabatic in the cloud region. The NDS domain is divided into six distinct regions that represent those commonly observed in the planetary boundary layer (PBL): 1) the surface layer, 2) the sub-cloud layer, 3) the cloud-base layer, 4) the cloud layer, 5) the cloud-top layer, and 6) the capping inversion. The NDS successfully represents the effects of the capping inversion. Circulations are limited in their upward extent by the inversion, and would only penetrate into it when surface forcing rates are quite large. Surprisingly, when there are identical forcing rates but different initial conditions for the dynamic and thermodynamic flelds, the NDS yields two solutions throughout a wide range of cloud-base stabilities. This range covers the transition from a stable to an unstable cloud-base layer (layer 3 above). The first solution is a steady one having a decoupled form, with separate circulations in the sub-cloud region and the cloud region. The second solution is a temporally varying one exhibiting periodic coupling. The circulation in this case starts as a shallow eddy near the surface. This eddy grows into a deeper plume that penetrates into the inversion before finally dying and beginning the process again. The existence of these two fundamentally different solutions for the same forcing rates, or multi-regime convection, suggests that the PBL response to a particular forcing rate may depend critically on the initial conditions of the dynamic and thermodynamic fields. As a consequence, future modeling efforts of the PBL should consider a broad range of initial flelds.