Introduction

An issue that has perplexed the minds of great meteorologists for many years now, and still does, is the determination of the length of time that it takes for rain to form and fall to the ground (Knight and Miller1993). This problem has been the center of much past and present research. First, nucleation occurs, followed by condensation growth, and finally drops begin to grow to a size that is large enough that the probability of a collision becomes non-negligible. This size seems to be around diameters of about 41 μm. Until drops grow to this size by vapor diffusion and collection from very small droplets, or if aerosols of the size of ultra-giant cloud condensation nuclei are available, droplets may not grow to the size necessary for rapid coalescence. If they do, then rapid coalescence or collection growth begins to dominate. In general, it takes some time for a few particles finally to reach about D = 82 mm, a size where more rapid coalescence can take place.

Collection growth can be presented as a relatively straightforward two-body collection continuous growth problem or a complex, statistical collection problem. Both of these are included in the discussion that follows. A primary mode by which hydrometeors come together is by differing fallspeeds such that particles of different sizes, densities, or shapes fall at differing speeds, which allows collisions to occur.