A Three Parameter Representation of the Shape and Size Distributions of Hailstones—A Case Study

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  • 1 Department of Meteorology University of Wisconsin—Madison, Madison, WI 53706
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Abstract

The characteristics of shapes and sizes of a sample of 679 hailstones, collected on 22 June 1976 during a hailstorm at Grover, Colorado, were analyzed using a three-parameter formula developed by us previously. These parameters are a, the horizontal dimension, c, the vertical dimension, and λ, the shape parameter. Once these three parameters are specified, both the shape and size of a hailstone are fixed. It is believed that this analysis produces the most complete and quantitative information about the hailstone shape and size distributions reported so far. The dataset of the three parameter also allows the relatively good reconstruction of the sizes and shapes of the original hailstones if desired. The results for this collection of hail show that the distributions of both horizontal and vertical dimensions can be described by gamma distributions, while the shape parameter can be described by an exponential distribution. Since the shape parameter basically describes the vertical asymmetry, it may provide additional information about the physics of particles in clouds and precipitation. The distributions of axial cross-sectional areas, surface areas, and volumes are also presented. They too can be described by gamma distributions. Finally, it was found that the geometrical quantities of the hailstones are best represented by a characteristic dimension rc, defined as the average of the horizontal and vertical dimension.

Abstract

The characteristics of shapes and sizes of a sample of 679 hailstones, collected on 22 June 1976 during a hailstorm at Grover, Colorado, were analyzed using a three-parameter formula developed by us previously. These parameters are a, the horizontal dimension, c, the vertical dimension, and λ, the shape parameter. Once these three parameters are specified, both the shape and size of a hailstone are fixed. It is believed that this analysis produces the most complete and quantitative information about the hailstone shape and size distributions reported so far. The dataset of the three parameter also allows the relatively good reconstruction of the sizes and shapes of the original hailstones if desired. The results for this collection of hail show that the distributions of both horizontal and vertical dimensions can be described by gamma distributions, while the shape parameter can be described by an exponential distribution. Since the shape parameter basically describes the vertical asymmetry, it may provide additional information about the physics of particles in clouds and precipitation. The distributions of axial cross-sectional areas, surface areas, and volumes are also presented. They too can be described by gamma distributions. Finally, it was found that the geometrical quantities of the hailstones are best represented by a characteristic dimension rc, defined as the average of the horizontal and vertical dimension.

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