Hail Parameter Relations: A Comprehensive Digest

Abstract

Diagrams are presented which display the relationships between hailstone size distribution parameters and integral quantities defined in terms of these parameters. It is assumed that the hailstones are spherical and homogeneous, are distributed with respect to size according to a truncated exponential distribution, and that they fall in still air without rain. Some of the diagrams are shown to have application for size distributions other than exponential provided that the moments of the distribution are known. Hailfall-related integral quantities depicted are the total number of hailstones per unit volume, liquid water content, kinetic energy content, fluxes of mass and kinetic energy, median volume diameter, average diameter, mass-weighted average diameter, variance of the size distribution, and number of hailstones greater than a specified minimum diameter. Radar measurables are calculated using backscattering cross sections for spherical hailstones that are dry or coated with a thin film of liquid water of thickness t. The results are displayed on overlays for the hail parameter diagram for radar wavelengths of 3.21 cm and 10.0 cm for dry (t = 0.0) and wet (t = 0.01 cm) hail. Radar quantities shown on these overlays include the equivalent radar reflectivity factor, the mean Doppler fallspeed, the variance of the Doppler spectrum, and the ratio of the reflectivity factors for the above two radar wavelengths. Applications of the diagram are presented, one of which uses experimental hail parameters of several investigators. Another involves analysis of 1976 National Hail Research Experiment hailpad data and the results are plotted on the diagram. Empirical results deduced from these analyses are used to construct a second form of hail parameter diagram which is convenient for analyzing possible effects due to natural or artificial modification of the hail size distribution. Experimental hail parameters are also plotted on this diagram and empirical equations are derived from these data to illustrate the relationships implied by such empirical analyses between all pairs of hail parameters. These results also are used to assess the error introduced by neglect of the contribution to remote measurables due to rain.