Numerical diffusion and turbulent mixing in convective self-aggregation

Convective Self-Aggregation (CSA) is a common feature of idealized numerical simulations of the tropical atmosphere in Radiative-Convective Equilibrium (RCE). However, at coarse grid resolution where deep convection is not fully resolved, the occurrence of this phenomenon is extremely sensitive to subgrid-scale processes. This study examines the role of mixing and entrainment, provided by the turbulence model and the implicit numerical diffusion. The study compares the results of two models, WRF and SAM, by varying turbulence models, initial conditions, and horizontal spatial resolution. At a coarse grid resolution of 3 km, the removal of turbulent mixing prevents CSA in models with low numerical diffusivity but is preserved in models with high numerical diffusivity. When the horizontal grid resolution is refined to 1 km, CSA can only be achieved by increasing explicit turbulent mixing, even with a small amount of shallow clouds. Therefore, the sensitivity of CSA to horizontal grid resolution is not primarily caused by the decrease in shallow clouds. The analysis of the total water path spectrum suggests that the amplitude of initial humidity perturbations introduced by convection in the free troposphere is the key factor. This amplitude is regulated by turbulent mixing and diffusion at small scales. Prior to the onset of CSA, increased mixing makes updrafts more sensitive to the dryness of the free troposphere, which strengthens the moisture-convection feedback. This leads to an increased distance between convective cores and a stronger humidity perturbation in the free troposphere, which can destabilize the RCE state.