Cloud Top Entrainment Instability

The criterion for instability of dry air mixing into a cloud top is determined both graphically and mathematically. It is found to be identical to the buoyancy-flux instability criterion of Randall (1976) based on stratocumulus mixed-layer jump-model equations which yield a cloud top jump in θe, for marginal stability of order Δθe=−1 to −3 K (θe), is equivalent potential temperature). Numerical calculations from a three-dimensional boundary-layer turbulence model with stratocumulus are examined from the viewpoint of cloud top entrainment instability. The entrainment rate is found to increase decisively when Δθe, drops below the critical value. The resulting rapid entrainment is found to dry out the cloud from the bottom up, leaving the cloud-base height intact; in conjunction with the negative Δθe value, this causes ∂θe/∂z in the cloud layer to become negative. This in turn sets the stage for the final phase of stratocumulus breakup, whereby conditional instability of the first kind begins to operate and the cloud fraction becomes small.