Johnson [1993] identified a number of important considerations for
precipitation to form during the limited lifetime of a typical cumulus
cloud. He showed, using a continuous collection parcel model, that in
order to develop precipitation during the limited lifetime of a typical
cumulus cloud (30 minutes or less), mass doubling times for the growing
particles must be on the order of 3 minutes or less. The model results
also show that for a 3 minute mass doubling time, effective coalescence
growth will require embryos larger than about 70 microns diameter, and
water contents greater than 0.7 gm
. This embryo size is larger
than those usually suggested as being necessary to start active
coalescence growth, the difference being the time limitation for
effective coalescence growth. The smaller ``initiation'' diameters
referred to in the literature refer to those droplet sizes for which
collision efficiencies first become large enough to begin to support
an active coalescence process at all.
The above study by Johnson [1993] did not consider the details of particle trajectories. The recent studies by Rauber et al. [1991] and Kogan [1993] draw attention to the importance of recycling hydrometeor trajectories to the development of large raindrops. Rauber et al. [1991] showed through a detailed analysis of aircraft observations from Hawaiian clouds that the development of large (4-8 mm) raindrops requires a recirculating trajectory such that the precipitating particles in the downdraft get entrained back into the updraft for additional growth. Kogan [1993] shows through a modeling study that larger particles with higher terminal velocities are more likely to stay close to the cloud and be recycled rather than being carried away from the cloud by the upper-level outflow.