Grey‐zone simulations of shallow‐to‐deep convection transition using dynamic subgrid‐scale turbulence models

We examine the ability of two dynamic turbulence closure models to simulate the diurnal development of convection and the transition from dry to shallow cumuli and then to deep convection. The dynamic models are compared with the conventional Smagorinsky scheme at a range of cloud‐resolving and grey‐zone resolutions. The dynamic schemes include the Lagrangian‐averaged, scale‐dependent dynamic Smagorinsky model and a Lagrangian‐averaged, dynamic mixed model. The conventional Smagorinsky model fails to reproduce the shallow convection stage beyond the large‐eddy simulation regime, continuously building up the convective available potential energy that eventually leads to an unrealistic deep convection phase. The dynamic Smagorinsky model significantly improves the representation of shallow and deep convection; however, it exhibits issues similar to the conventional scheme at coarser resolutions. In contrast, the dynamic mixed model closely follows the large‐eddy simulation results across the range of sub‐kilometre simulations. This is achieved by the combined effect of an adaptive length scale and the inclusion of the Leonard terms, which can produce counter‐gradient fluxes through the backscatter of energy from the subgrid to the resolved scales and enable appropriate non‐local contributions. A further sensitivity test on the inclusion of the Leonard terms on all hydrometeor fluxes reveals the strong interaction between turbulent transport and microphysics and the possible need for further optimisation of the dynamic mixed model coefficients together with the microphysical representation.