The natural horizontal scale of convective self-aggregation

Randomly distributed small-scale convection can spontaneously organize into a large-scale quasi-steady circulation with a convecting moist patch (rising branch) and a non-convecting dry patch (sinking branch). This phenomenon is often referred to as convective self-aggregation. Convective self-aggregation is considered to be crucial to various organized dynamical and cloud patterns in the real tropical atmosphere (e.g., tropical cyclones and the Madden-Julian Oscillation) and has been studied extensively using cloud-resolving models (CRMs). Here I ask, what sets the horizontal scale (L) of convective self-aggregation at steady state? By combining the momentum and energy constraints in the boundary layer, I derive a scaling theory, which suggests that L increases with the effective pressure difference between the dry and moist patches, and that L decreases with the radiative cooling rate at the top of the boundary layer. This theory is consistent with results of CRM simulations over a wide range of sea surface temperatures. One use of this theory is to understand why the emergence of convective self-aggregation depends on the domain size of CRMs. In this presentation, I will test the hypothesis that convective self-aggregation will disappear if the CRM domain size is much smaller than the natural horizontal scale of convective self-aggregation.