Mathematical Description of the Shape of Conical Hydrometeors

Pao-Kuan Wang Department of Meteorology, University of Wisconsin, Madison 53706

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Abstract

A mathematical function is presented to approximate the shape of conical hydrometeors such as conical graupel and hailstones and large falling raindrops. The function provides a method of parametric classification of conical hydrometeors. Steps and examples of fitting to real conical hydrometeors are given. The examples demonstrate that this function closely approximates the shape of these particles. Formulas for calculating the axial cross-sectional area, volume and area of the surface of revolution are given. The function will be useful in the future study of the physical properties of conical hydrometeors.

Abstract

A mathematical function is presented to approximate the shape of conical hydrometeors such as conical graupel and hailstones and large falling raindrops. The function provides a method of parametric classification of conical hydrometeors. Steps and examples of fitting to real conical hydrometeors are given. The examples demonstrate that this function closely approximates the shape of these particles. Formulas for calculating the axial cross-sectional area, volume and area of the surface of revolution are given. The function will be useful in the future study of the physical properties of conical hydrometeors.

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