A Spectral Budget for the Size of Convective Self-Aggregation

To first order, the size of extra-tropical storms is set by the Rossby deformation radius, which scales inversely with the Coriolis parameter. However, what sets the size of convective clusters close to the Equator, where the Coriolis parameter is small, remains an open question. High resolution cloud-permitting simulations of non-rotating convection show the emergence of a dominant length scale, which has been referred to as convective self-aggregation. Furthermore, simulations in an elongated domain of size 12228km x 192km with a 3km horizontal resolution equilibrate to a wave-like pattern in the elongated direction, where the cluster size becomes independent of the domain size. These recent results motivate the question: How do radiation, convection and advection contribute to the emergence and evolution of a convective length scale?

First, we formulate a spectral budget that relates the evolution of the convective length scale to the vertically-integrated diabatic feedbacks. We link this budget to the moist static energy variance budget, widely used to diagnose diabatic feedbacks in cloud-permitting simulations. We then evaluate the radiative, convective and advective terms of this budget in a set of three-dimensional cloud-permitting simulations across a range of sea surface temperatures, using the System for Atmospheric Modeling. We find that the surface flux feedback (mostly latent heat flux) drives the convective cluster to a scale close to 1000km, while the radiative feedback (mostly longwave cloud feedback) stretches the convective clusters to larger scales, especially at low sea surface temperatures for which the radiative feedbacks are most intense. These first results explain why convective length scales are larger for low sea surface temperatures, and why the convective cluster size depends on the domain's size below 1000km. We run mechanism denial experiments to confirm our results, where the surface fluxes and/or the radiative cooling rates are homogenized across the horizontal domain. Our results underline the importance of observing and/or simulating surface fluxes, radiative and advective feedback across a wide range of spatial scales to understand the characteristics of turbulent moist convection.