Boundary Layer Height and Buoyancy Determine the Horizontal Scale of Convective Self-Aggregation

Organized rainstorms and their associated overturning circulations can self-emerge over an ocean surface with uniform temperature in cloud-resolving simulations. This phenomenon is referred to as convective self-aggregation. Convective self-aggregation is argued to be an important building block for tropical weather systems and may help regulate tropical atmospheric humidity and thereby tropical climate stability. Here the author presents a boundary layer theory for the horizontal scale lambda of 2D (x, z) convective self-aggregation by considering both the momentum and energy constraints for steady circulations. This theory suggests that lambda scales with the product of the boundary layer height h and the square root of the amplitude of density variation between aggregated moist and dry regions in the boundary layer, and that this density variation mainly arises from the moisture variation due to the virtual effect of water vapor. This theory predicts the following: 1) the order of magnitude of lambda is similar to 2000 km, 2) the aspect ratio of the boundary layer lambda/h increases with surface warming, and 3) lambda decreases when the virtual effect of water vapor is disabled. These predictions are confirmed using a suite of cloud-resolving simulations spanning a wide range of climates.