A statistical model for the incidence of large hailstones on solar collectors

Abstract

A statistical model is described for estimating the risk of impacts by large hail on any ground installation (such as a solar collector array). The model is based on data for three frequency distributions: hailstone size, hailfall count (number of hailstones per m 2 per storm), and number of haildays per year. Other than parameters derived from meteorological data, the parameters of the model required to describe a particular installation are the number of years of surface exposure and the area of the exposed surface. The independent variable is the critical hailstone diameter, D. The result given by the model is the probability of a hailstone of diameter D or greater striking a given surface area in a given number of years. Thus it is possible to determine the “probable maximum hailstone size”, a convenient index of hail risk. Alternatively, the “mean time between hits” may may be computed for a given size of hailstone. However, the meteorological data for estimating hail risk are sparse at this time, covering few geographic locations; much of the information available is deficient in sampling consistency and/or sample size. For general application of the model, more detailed data on hailfall in many geographic locations is needed. This model improves on previous work in including all three of the distributions needed to characterize the variability of large hail incidence: hailstone size, count and storm frequency, and in identifying better analytical expressions for these distributions: a special β function for hailstone size, a γ function for hailfall count, and a Poisson function or a negative binomial function for annual hailday frequency. The independence of these three random variables is also discussed.