A stochastic parcel model for shallow cumulus convection (Formerly paper 2.6)

Stochastic parcel models have been used in the past to explain the observed variability of temperature, moisture and vertical velocity inside shallow cumulus clouds (Raymond and Blyth 1986; Kain and Fritsch 1990; Emanuel 1991; Hu 1997). In these models, the mixing-rate of each individual parcel was often fixed. Here we derive an expression for the lateral entrainment rate of such a rising air-parcel, and we find that the entrainment-rate is coupled to the dynamics of the parcel, introducing some important feedback mechanisms. Because of these feedbacks, parcels with different properties can have the same expression for the mixing-rate, making a stochastic model less arbitrary and ad-hoc.

We validate this parcel-model stochastically on LES data. The characteristics of the buoyant part of the clouds are reproduced: the decreasing fractional cover and increasing liquid water content with height, the vertical dynamics and mass-flux, the conserved properties and the marginally buoyant state. The model also produces the variability typical for shallow cumulus.

A special limit of our model describes a bulk-volume in a cloud-ensemble. We will analyse this special case to explain its characteristics, and show its potential use as a parameterization in convective schemes of large-scale models.