The Two‐Energies Turbulence Scheme Coupled to the Assumed PDF Method

An update of the two‐energy turbulence scheme is presented, the 2TE + APDF scheme. The original version of the two‐energy scheme is able to successfully model shallow convection without the need of an additional parameterization for non‐local fluxes. However, the performance of the two‐energy scheme is worse in stratocumulus cases, where it tends to overestimate the erosion of the stable layers. We have identified the causes: the non‐local stability parameter does not consider local stratification, the scheme lacks an internal parameter that could distinguish between a shallow convection regime and a stratocumulus regime, and it uses an inflexible turbulence length scale formulation. To alleviate this problem, we propose several modifications: an update of the stability parameter, a modified computation of the turbulence length scale, and the introduction of the entropy potential temperature to distinguish between a shallow convection and a stratocumulus regime. In addition, the two‐energy scheme is coupled to a simplified assumed probability density function method in order to achieve a more universal representation of the cloudy regimes. The updated turbulence scheme is evaluated for several idealized cases and one selected real case in the ICOsahedral Nonhydrostatic (ICON) modeling framework. The results show that the updated scheme corrects the overmixing problem in the stratocumulus cases. The performance of the updated scheme is comparable to the operational setup, and can be thus used instead of the operational turbulence and shallow convection scheme in ICON. Additionally, the updated scheme improves the coupling with dynamics, which is beneficial for the modeling of coherent flow structures in the atmospheric boundary layer.