A mixed-phase bulk orographic precipitation model with embedded convection

A novel analytical model for mixed-phase, unblocked and unseeded orographic precipitation with embedded convection is developed and evaluated. The model takes an idealized background flow and terrain geometry and calculates the area-averaged precipitation rate and other microphysical quantities. The results provide insight into key physical processes, including cloud condensation, vapour deposition, evaporation and sublimation, as well as precipitation formation and sedimentation (fallout). To account for embedded convection in nominally stratiform clouds, diagnostics for purely convective and purely stratiform clouds are calculated independently and combined using weighting functions based on relevant dynamical and microphysical time-scales. An in-depth description of the model is presented, as well as a quantitative assessment of its performance against idealized, convection-permitting numerical simulations with a sophisticated microphysics parametrization. The model is found to reproduce the simulation diagnostics accurately over most of the parameter space considered.