The influence of melting on hailstone size distribution

Abstract

The physical properties of hailstones registered by a hailpad network (size distribution, mass, kinetic energy) are essential data for the establishment of a regional hail climatology. Nevertheless, when comparing these data to the same properties of hailstones inside the cloud, the melting process must be taken into account. This paper presents a brief theoretical study of the changes effected on hailstone size distribution due to the melting process. The paper is based on previous studies dealing with the melting of hailstones before they reach the ground. The aim is to analyze the influence of this melting process on hailstone size distribution. An initial melting simulation was carried out in order to achieve this aim. Despite the common assumption that hailstone size distribution on the ground is exponential, it was found that when the in-cloud size distribution is exponential, on the ground, there are fewer small hailstones than what would be expected in an exponential distribution. The data registered by the hailpad network in León (Spain) for 1 year were used to estimate the size of every hailstone before the melting process. The results show that the hailstone size distribution simulated inside the cloud resembles more closely an exponential distribution than the hailstones on the ground. The type of hailstone size distribution inside the cloud will be the starting point for calculating the hailstone size distribution on the ground. Several equations describing the melting processes are used to calculate a new probability density function that initially corresponds to an exponential distribution that undergoes a partial melting process. The result is a function that is not monotonously decreasing like the exponential function, but rather a function that has a peak for a given size. This new function fits better the data found than the exponential function and actually resembles the gamma function.