Modeling supersaturation and subgrid-scale mixing with two-moment bulk warm microphysics

This paper describes further developments of a two-moment warm rain bulk microphysics scheme suitable for addressing the indirect impact of atmospheric aerosols on ice-free clouds in large-eddy simulation (LES) models. The emphasis is on the prediction of supersaturation, activation of cloud droplets, and the representation of microphysical transformations during parameterized turbulent mixing. A comprehensive approach is proposed that is capable of simulating droplet activation at the cloud base, in the cloud interior due to increasing updraft strength, and at the lateral edges due to entrainment. Such an approach requires high spatial resolution to capture maximum supersaturation at cloud base as well as to resolve entraining eddies that lead to additional activation above the cloud base. This approach can be used as a benchmark for developing and testing schemes suitable for lower spatial resolutions. A novel approach for predicting the supersaturation field is proposed, with an emphasis on its application in an Eulerian framework. This approach produces consistency among the thermodynamic variables and mitigates the problem of spurious cloud-edge supersaturation noted in the past. A new subgrid scheme is also developed to treat microphysical transformations during turbulent entrainment and mixing. This scheme is designed to be as flexible as possible, allowing for the entire range of mixing scenarios from homogeneous to extremely inhomogeneous. The above developments are applied in 2D simulations of moist convection for an idealized rising thermal, assuming either pristine or polluted aerosol conditions. The mixing scenario has a substantial impact on the cloud microphysical and optical properties. As expected, extremely inhomogeneous mixing results in substantially smaller mean droplet number concentration, larger effective radius, and smaller cloud optical depth compared to the run with homogeneous mixing. The subgrid mixing of cloud condensation nuclei (CCN) and formation of CCN from evaporated droplets during extremely inhomogeneous mixing are relatively less important for this case.