Towards a new hybrid cumulus parametrization scheme for use in non-hydrostatic weather prediction models

摘要

Classical mass flux parametrization schemes for cumulus convection generally transport heat and moisture only but do not include a net mass transport. This is well justified for large grid spacings comprising the whole convective circulation in the local grid column, such that all convective mass fluxes locally cancel out. A conceptual problem arises for finer grid spacings as used in contemporary numerical weather prediction (NWP) models, when convection becomes partially resolvable. This problem can be overcome by the hybrid approach presented here. Only updraft and downdraft are parametrized with a net mass transport; the environmental subsidence is treated by the grid-scale equations. The total mass flux in the continuity equation is split intoa grid-scale and a subgrid-scale contribution. This parametrization scheme is designed for use in any nonlinear, non-hydrostatic and fully compressible NWP model. We here have chosen the Lokal-Modell (LM) of Deutscher Wetterdienst. Idealized dry mass lifting experiments (without convective heat transport) demonstrate the feasibility of the hybrid approach. Entrainment causes grid-scale convergence and the detrained air, if set to the environmental temperature, spreads mainly horizontally on the grid. Gravity waves are generated when convection starts and ends. Whereas their amplitude depends on the details of the switching on and off of convection, the stationary state (after about 30 minutes) does not. Four model runs with different grid spacings (3.5km to 28 km) confirm that the mass exchange between the model grid and the parametrization scheme is independent of the chosen grid spacing. Total mass in a convective circulation cell is conserved to better than 0.1%, but only if the damping layer at the upper boundary of the LM is shifted to above 20 km. For moist convection (with convective heat transport), a simple cloud model for an updraft has been set up. As the detrained air at the cloud top is colder than the environment, it moves down by about 1 km but then mainly spreads horizontally again over several tens of kilometres as in the dry case without convective heat transport. The hybrid mass flux approach with both a grid-scale and a subgrid-scale contribution may fill the gap between coarse-grid models (grid spacing > 50 km) with classical parametrization schemes, and very highly resolved explicit convection modelling (with a grid spacing of the order of 100 m).