Multiplication of Ice Particles in Slightly Supercooled Cumulus

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  • 1 Department of Mathematics, University of Manchester, England
  • | 2 Physics Department, University of Manchester, Institute of Science and Technology, England
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Abstract

A stochastic model of ice particle multiplication is outlined in which ice splinters are produced by riming and possibly also by the splintering of individual drops on freezing. The splinters may grow into rimers or be captured by supercooled drops, causing the drops to freeze and become rimers. The possibility of splinter-capture by supercooled drops reduces the average waiting time between the birth of a splinter and its subsequent development into a splinter-producing rimer. This reduction of the waiting time greatly enhances the growth rate of the ice particle population. In a particular calculation, with drops present, a multiplication factor of 104 is achieved in about 50 min if Mp (the number of ice splinters ejected per unit mass of rime) is 1 mg−1; this time is reduced to 10 min if we take the much higher values of Mp≈140 found by Hallett and Mossop. The corresponding times in the absence of drops are about 74 and 37 min respectively.

Abstract

A stochastic model of ice particle multiplication is outlined in which ice splinters are produced by riming and possibly also by the splintering of individual drops on freezing. The splinters may grow into rimers or be captured by supercooled drops, causing the drops to freeze and become rimers. The possibility of splinter-capture by supercooled drops reduces the average waiting time between the birth of a splinter and its subsequent development into a splinter-producing rimer. This reduction of the waiting time greatly enhances the growth rate of the ice particle population. In a particular calculation, with drops present, a multiplication factor of 104 is achieved in about 50 min if Mp (the number of ice splinters ejected per unit mass of rime) is 1 mg−1; this time is reduced to 10 min if we take the much higher values of Mp≈140 found by Hallett and Mossop. The corresponding times in the absence of drops are about 74 and 37 min respectively.

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