A Relationship Between Hailstone Concentration and Size

Lawrence Cheng Alberta Research Council, Edmonton, Alberta, Canada T6H 5R7

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Marianne English Alberta Research Council, Edmonton, Alberta, Canada T6H 5R7

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Abstract

Hailstone size distributions have been determined from 41 time-resolved hailstone samples collected at the ground from seven storms that occurred in Alberta in the summer of 1980. Most size distributions were found to quite closely fit an exponential function of the form n(D) = n0e−λD. In studying variations in n0 and λ, it was found that a relationship exists between the two. In particular, correlation coefficients of ∼−0.9 were found when least-square linear regressions were fitted to the values of logn0 versus logλ. For Alberta storms, therefore, n0 can be expressed in terms of λ as n0 = 115λ3.63, and hail size distributions can be expressed in terms of the single parameter λ as n(D) = 115λ3.63e−λD. From an examination of hail size distributions from one storm that occurred in Switzerland, it appears likely that similar relationships can be determined for hailstorms from other regions.

Abstract

Hailstone size distributions have been determined from 41 time-resolved hailstone samples collected at the ground from seven storms that occurred in Alberta in the summer of 1980. Most size distributions were found to quite closely fit an exponential function of the form n(D) = n0e−λD. In studying variations in n0 and λ, it was found that a relationship exists between the two. In particular, correlation coefficients of ∼−0.9 were found when least-square linear regressions were fitted to the values of logn0 versus logλ. For Alberta storms, therefore, n0 can be expressed in terms of λ as n0 = 115λ3.63, and hail size distributions can be expressed in terms of the single parameter λ as n(D) = 115λ3.63e−λD. From an examination of hail size distributions from one storm that occurred in Switzerland, it appears likely that similar relationships can be determined for hailstorms from other regions.

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