How to Express Hail Intensity—Modeling the Hailstone Size Distribution

Abstract

The 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.

Observational analysis and simulations of a severe hailstorm in northeastern Italy

“…16{1 − e −0.01319(D vicinity −1.123) } (mm) . 2In the case of a maximum diameter on the hailpad of 34.2 mm, the equation proposed by Grieser and Hill (2019) estimates 42 mm for the largest hailstone size in its vicinity. In agreement with this value, during the studied event the maximum documented hailstone diameter, provided by a picture taken by a storm chaser (Alessandro Fiorot) in Fontanafredda (9 km north of the hailpad shown in Figure 2a), was about 50 mm, which is significantly lower than 68 mm estimated by the factor-of-two rule.…”

“…More recently, Grieser and Hill (2019) refined the Smith and Waldvogel (1989) linear relation between the maximum observed hailstone size on the hailpad and in its vicinity with an exponential fit, which reduces the "factor of two" for hailpad-estimated hailsize lower than 60 mm (120 mm near the ground), while it increases that factor for giant hailstones. In practice, they propose to use the following equation:…”

Characteristics of hail hazard in South Africa based on satellite detection of convective storms

“…Leigh and Kuhnel (2001), for example, constructed a regional risk model based on such reports and loss data alone. Grieser and Hill (2019) used volunteer-collected hail observations in the United States (Reges et al, 2016) to model the rate of hailstones hitting the ground per unit area, time, and hailstone size bin during the passage of a hailstorm. Based on that data, they set up a model to calculate the vulnerability of subjects at risk as a function of the diameter of the largest hailstone, which can be transferred to other regions.…”

Estimation of Maximum Hail Diameters from FY-4A Satellite Data with a Machine Learning Method

“…Hailstone size is closely related to the momentum of its falling, which directly affects the magnitude of damage [9][10][11]. Larger hail would cause more severe damage and significant losses.…”