  Convective self-aggregation refers to a phenomenon in which random convection
can self-organize into large-scale clusters over an ocean surface with uniform
temperature in cloud-resolving models. Previous literature studies convective
aggregation primarily by analyzing vertically integrated (VI) moist static
energy (MSE) variance. That is the global MSE variance, including both the
local MSE variance at a given altitude and the covariance of MSE anomalies
between different altitudes. Here we present a vertically resolved (VR) MSE
framework that focuses on the local MSE variance to study convective
self-aggregation. Using a cloud-resolving simulation, we show that the
development of self-aggregation is associated with an increase of local MSE
variance, and that the diabatic and adiabatic generation of the MSE variance is
mainly dominated by the boundary layer (BL). The results agree with recent
numerical simulation results and the available potential energy analyses
showing that the BL plays a key role in the development of self-aggregation. We
further present a detailed comparison between the global and local MSE variance
frameworks in their mathematical formulation and diagnostic results,
highlighting their differences.
