A linear stability analysis of stratocumulus convection driven by radiative cooling

Fully cloudy stratocumulus layers sometimes exhibit convective organization at a single dominant length scale with an aspect ratio (width/height) ≈ 1. We present a linear stability analysis of a radiatively-cooled cloud beneath a capping inversion and show that small aspect ratio modes are energetically favored over a broad range of inversion strengths and cooling depths. The integrated mode energy budgets indicate that, given a vertically limited region of radiative cooling, highly dissipative, localized convective modes can grow through efficient buoyancy production beneath the inversion. Including the effect of decoupling on the sub-cloud layer enhances this scale selection, but as the depth of the unstable layer is increased beyond 20% of the boundary layer depth, the critical Rayleigh number and the aspect ratio of the fastest growing mode approach that of a layer capped by a no-slip rigid lid.