On the Growth of Large Hail

Abstract

Calculation of the trajectories of precipitation particles growing in a simplified thunderstorm updraft model shows some effects that have a bearing on understanding the mechanism of water storage in thunderstorms, the growth of large hailstones, and the techniques to be used in hail prevention. The updraft model is characterized by a region of inflow overlain by one of outflow, with the vertical component of air velocity increasing along inflowing streamlines and decreasing along outflowing streamlines. For simplicity, streamlines are assumed to be arcs of circles in the vertical plane, and the velocity distribution in this plane is equivalent to solid rotation. Air density is assumed constant everywhere, and particles are assumed to move horizontally at the same speed as the air and vertically at a speed equal to the vertical component of air velocity minus their terminal velocity. In such a flow regime, the motion of particles is along families of concentric circles centered on the intersection between the locus of points of zero horizontal air velocity and the vertical air speed isotach corresponding to the terminal fall speed of the particle (called the ?balance point? of the particle). Particles of different sizes move along different families of circular trajectories, and consideration of the way in which these families intersect illustrates the large dispersion in the directions of motion of the different components of the precipitation size spectrum at each point in the cloud. Growth of particles is specified as a linear increase of fall speed with time, sawtooth fashion for liquid drops (to simulate the spontaneous breakup responsible for the Langmuir chain reaction), and continuous for hail particles. The results of trajectory calculations show: (1) that in the region of the balance points of large raindrops (diameter = 3?5 mm) the drop trajectories are of an indefinitely (timewise) recirculating character, indicating a tendency to store water in that region (identified with the ?accumulation zone? introduced by Russian hail researchers) ; (2) that in the higher speed regions of the updraft, drop trajectories lead to ejection of the drop from the storm and little or no storage of water (identified with the ?echo-free vault? introduced by English cloud dynamicists) ; (3) that hail embryos, in the form of frozen large raindrops, start their growth in the region of liquid water storage and move along looping trajectories that carry them across the up draft to the region of highest velocities at a rate such that they achieve fall speeds (size) about equal to the maximum updraft speed; and (4) that introducing cloud seeding material into the high speed updraft core should be ineffective for hail prevention due to rapid ejection from the storm. Seeding material should be introduced directly into the accumulation zone (Russian method) or at points below the cloud where the airflow will carry it through the accumulation zone.