Hailstone Size Distributions and Their Relationship to Storm Thermodynamics

From ten storms, 184 time-resolved hailstone samples have been collected at the ground in Alberta. For each of the samples collected, hailstone size and concentration were determined and a truncated exponential distribution was fitted to the data. From the fitted size distributions an intercept parameter N0 and slope parameter Λ were obtained for each hail sample. It was found that the intercept parameters are related to the slope parameters by a power relationship of the form N0 = AΛb and that such a relationship applies to each storm individually. Furthermore, it appears that the exponent parameter of the power law b is constant from storm to storm, whereas the coefficient parameter A depends upon the storm thermodynamics. Relationships between the coefficient parameter A and cloud base temperature and maximum water mass flux are derived.