A Lagrangian Advection Scheme for Solving Cloud Droplet Diffusion Growth

Cloud drop diffusion growth is a fundamental microphysical process in warm clouds. In the present work, a new Lagrangian advection scheme (LAS) is proposed for solving this process. The LAS discretizes cloud drop size distribution (CDSD) with movable bins. Two types of prognostic variable, namely, bin radius and bin width, are included in the LAS. Bin radius is tracked by the well-known cloud drop diffusion growth equation, while bin width is solved by a derived equation. CDSD is then calculated with the information of bin radius, bin width, and prescribed droplet number concentration. The reliability of the new scheme is validated by the reference analytical solutions in a parcel cloud model. Artificial broadening of CDSD, understood as a by-product of numerical diffusion in advection algorithm, is strictly prohibited by the new scheme. The authors further coupled the LAS into a one-and-half dimensional (1.5D) Eulerian cloud model to evaluate its performance. An individual deep cumulus cloud studied in the Cooperative Convective Precipitation Experiment (CCOPE) campaign was simulated with the LAS-coupled 1.5D model and the original 1.5D model. Simulation results of CDSD and microphysical properties were compared with observational data. Improvements, namely, narrower CDSD and accurate reproduction of particle mean diameter, were achieved with the LAS-coupled 1.5D model.