Inhomogeneous Mixing in Lagrangian Cloud Models: Effects on the Production of Precipitation Embryos

Although small-scale turbulent mixing at the cloud edge has substantial effects on microphysics of clouds, most models do not represent these processes explicitly or parameterize them rather crudely. This study presents a first use of the so-called linear eddy model (LEM) to represent the unresolved turbulent mixing on the sub-grid scale (SGS) of large-eddy simulations (LES) with coupled Lagrangian cloud models (LCM). The introduced method utilizes the Lagrangian particles and their trajectories to provide the history of the air masses within each LES grid box, while the LEM is used to redistribute these air masses among the Lagrangian particles based on the local features of turbulence in accordance with the LES SGS model. Additionally, the new approach mitigates spurious supersaturations significantly.

At the low turbulence intensities, as found in the early stage of an idealized bubble cloud simulation, cloud edge SGS mixing tends to be inhomogeneous and the new approach is shown to be essential to produce large particles to initiate rain. At higher turbulence intensities, as found in a shallow cumulus test case, SGS mixing tends to be more homogeneous and the new approach did not significantly alter the results, indicating that a grid spacing of 20 m sufficient to resolve all relevant scales of inhomogeneous mixing. In both analyzed cases, droplet in-cloud residence times are shown to be important for the production of precipitation embryos in the absence of small-scale inhomogeneous mixing, either naturally due to strong turbulence or artificially by a too coarse resolution, or by not using the LEM as an SGS model.