A SIMPLE PROGNOSTIC CLOSURE ASSUMPTION TO DEEP CONVECTIVE PARAMETERIZATION:I

In this work,the problem of dependency of the predicted rainfall upon the grid-size in mesoscale numerical weather prediction models is addressed.We argue that this problem is due to (i) the violation of the quasi-equilibrium assumption,which is underlying most existing convective parameterization schemes,and states that the convective activity may be considered in instantaneous equilibrium with the larger-scale forcing;and (ii) the violation of the hydrostatic approximation,made in most mesoscale models,which would induce too large-scale circulation in occurrence of strong convection.On the contrary,meso-β and meso-α scale models,i.e.models with horizontal grid size ranging from 10 to 100 km,have a capacity to resolve motions with characteristic scales close to the ones of the convective motions.We hypothesize that a possible way to eliminate this problem is (i) to take a prognostic approach to the parameterization of deep convection,whereby the quantities that describe the activity of convection are no longer diagnosed from the instantaneous value of the large-scale forcing,but predicted by time-dependent equations,that integrate the large-scale forcing over time;(ii)to introduce a mesoscale parameter which varies systematically with the grid size of the numerical model in order to damp large-scale circulation usually too induced when the grid size becomes smaller (from 100 km to 10 km).We propose an implementation of this idea in the frame of one existing scheme,already tested and used for a long time at the French Weather Service.The results of the test through one-dimensional experiments with the Phase Ⅲ of GATE data are reported in this paper;and the ones on its implementation in the three-dimensional model with the OSCAR data will be reported in a companion paper.