Modified Richardson Number in Non-Uniform Saturated Moist Flow

As a useful index, i.e. the Richardson number Ri, is modified in non-uniform saturated moist flow, based on the fact that liquid water is partially dropped out in parcel air. This is more realistic in real moist atmosphere, especially in the rainfall process. The modified Ri presents adequately the influence of numerator, i.e. Brunt--Vaisala frequency (BVF), on instability. Compared to several former formulae generalized by Durran and Klemp, the modified Ri evidently decreases the stability in rainy regions. In theory, the modified BVF and Ri fix the discontinuity of latent heat release in the transition areas between saturated and unsaturated air by introducing the condensation probability function. Furthermore, the diagnostic analysis of the modified Ri validates the rationality of its application in the non-uniform sturated moist process.