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<br />23 <br /> <br />this mass by collision of two smaller ice particles <br /> <br />to form one of this size. In all the cases presented <br /> <br />in this research, the ice-ice coalescence coefficient <br /> <br />is assumed to be zero and thus C2 = 0 <br /> <br />B2 = loss of ice particles of this size due to melting <br /> <br />to smaller ice sizes and formation of liquid drops <br /> <br />from the melted water <br /> <br />F 1 - gain of ice particles of this mass due to freezing of <br /> <br />preexisting water drops having the same mass <br /> <br />~ <br /> <br />Numerical Methods <br /> <br />The previous section has presented a self-consistent system of dynamic, <br /> <br />thermodynamic, and continuity equations which can be used to represent the problem <br /> <br />of interest; evolution and microphysical development of precipitation in an isolated <br /> <br />cold cumulus cloud. The next task is to transform these theoretical relations into a <br /> <br />practical system of Eulerian equations capable of solution by finite difference schemes <br /> <br />in currently available digital computers. <br /> <br />An immediate problem arises in determining a quantized size distribution of <br /> <br />particle sizes to permit adequate resolution of small particles while retaining large <br /> <br />particles without an excessive number of particle size categories. The problem is <br /> <br />one of dynamic range; the mass scale from small cloud drop to large hailstones spans <br /> <br />about 12 orders of magnitude. <br />