A hybrid bulk-bin approach to model warm-rain processes

This paper presents a hybrid approach to model warm-rain processes, merging the diverse schemes of bulk and detailed (bin) microphysics. In the bulk scheme, the key assumption is that the exact saturation is maintained inside a cloud. In contrast, the supersaturation inside a cloud is predicted in the bin scheme and is applied to calculate the diffusional growth of cloud droplets. Predicting the supersaturation is numerically cumbersome, however, and typically requires spatial and temporal resolutions that are significantly higher than those that can be applied in the bulk scheme. At the same time, supersaturations inside clouds are small, and the condensate amounts in bulk and bin schemes differ insignificantly. This critical observation forms a starting point for the hybrid bulk–bin approach. In this approach, when the cloud water first appears, the activation scheme inserts cloud droplets at the low end of the bin representation. Subsequent diffusional and eventually accretional growth shift the spectrum toward larger sizes so that the saturation inside a cloud is maintained. Details of the hybrid approach are discussed in this paper, and the validation against the traditional bin scheme in a framework of the adiabatic rising parcel is presented. Before the scheme can be applied to the multidimensional cloud model, a 1D advection–condensation problem of Grabowski and Smolarkiewicz is used to address the issue of the numerical difficulties that finite-difference schemes experience near cloud edges. In the bulk case, these are in the form of condensation rate overshoots and undershoots; and this aspect requires special attention in the hybrid scheme. A novel approach is developed that provides a physically consistent solution near cloud edges using the hybrid bulk–bin scheme. The key is to allow grid boxes near the edges to be partly cloudy and to include spectral changes of cloud droplets that take this into account. Application of the hybrid scheme to an idealized 2D problem of moist thermal rising from rest and producing rain illustrates the application of the scheme to practical problems of cloud dynamics and warm-rain microphysics.