How to Express Hail Intensity—Modeling the Hailstone Size Distribution

Abstract

AbstractThe local intensity of hail can be expressed by a variety of variables, such as hail kinetic energy, maximum hailstone size, and radar reflectivity–driven algorithms. All of these variables are connected by the hailstone size distribution. In the United States, the Community Collaborative Rain, Hail and Snow Network (CoCoRaHS) provides more than 37 000 observations that describe the diameter of the smallest, average, and largest hailstone; duration of hail; and overall hailstone number density. We use these data and the assumption of an exponential hailstone size distribution aloft to model the rate of hailstones hitting the ground per unit area, time, and hailstone size bin during the passage of a hailstorm. We found that total hail kinetic energy is proportional to the diameter of the largest hailstone to a power of less than 2. To validate these results, we compared them with hailpad observations of the largest hailstone diameters and hail kinetic energies in southwestern France. As an example application, we calculate the probability mass function for the largest hailstone observed by a hailpad given the largest hailstone occurring in its vicinity. We use this model at Risk Management Solutions, Ltd. (RMS), to calculate the vulnerability of subjects at risk as a function of the diameter of the largest hailstone.