The moist parcel-in-cell method for modelling moist convection

We describe a promising alternative approach to modelling moist convection and cloud development in the atmosphere. Rather than using a conventional grid-based approach, we use Lagrangian parcels to represent key dynamical and thermodynamical variables. In the prototype model considered, parcels carry vorticity, mass, specific humidity, and liquid-water potential temperature. In this first study, we ignore precipitation, and many of these parcel attributes remain unchanged (i.e.are materially conserved). While the vorticity does change following the parcel motion, the vorticity tendency is readily computed and, crucially, unwanted numerical diffusion can be avoided. The model, called Moist Parcel-In-Cell (MPIC), is a hybrid approach which uses both parcels and a fixed underlying grid for efficiency: advection (here moving parcels) is Lagrangian whereas inversion (determining the velocity field) is Eulerian. The parcel-based representation of key variables has several advantages: (a) it allows an explicit subgrid representation; (b) it provides a velocity field which is undamped by numerical diffusion all the way down to the grid scale; (c) it does away with the need for eddy viscosity parametrizations and, in their place, it provides for a natural subgrid parcel mixing; (d) it is exactly conservative (i.e.there can be no net loss or gain of any theoretically conserved attribute); and (e) it dispenses with the need to have separate equations for each conserved parcel attribute; attributes are simply labels carried by each parcel. Moreover, the latter advantage increases as more attributes are added, such as the distributions of microphysical properties, chemical composition and aerosol loading.