THE DEVELOPMENT OF THE SIZE DISTRIBUTION OF RAINDROPS DURING THEIR FALL

Abstract

Numerical methods are used to study the changes in the distribution of raindrops with size and in the radar echo, as rain falls. Changes brought about by collisions among the drops, by accretion of cloud, and by evaporation are considered. The distribution assumed aloft is that actually observed at the ground. This is justified, because the changes in the form of the distribution are found to be slight: an exponential type of distribution law would seem to be applicable at all heights. This result is taken to mean that the processes investigated cannot by themselves produce the distributions observed at the ground from distributions of a very different sort, or from the broad distributions of snow. A mechanism as yet unknown, probably involving drop break-up, would seem to be required. The work is done both for ?continuous rain,? where conditions at all levels are assumed to be constant in time, and for showers, where they are assumed to be initially the same at all levels. Unequal rates of fall of raindrops tend to increase the vertical extent of the radar echo in time. The calculated rates of motion of echo top and base depend critically on range and radar sensitivity; they are in reasonable agreement with those observed. Where necessary, the rate of depletion of cloud due to rain falling through it is taken into account. A simple theory of this process, by Dr. K. L. S. Gunn, is described in an appendix.