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NOVEMBER 1978 LARRY VARDIMAN 2179 5. Results The most critical pararl,Jeters in this study were found to be the relative velocity between crystals and the degree of rime. If the relative velocity for all crystal sizes is increased by 10% the rate of fragment generation increases by 50%. This is true because an increase in relative velocity affects both the collision frequency and the fragment generation function. The effect on the fragment generation function is to in- crease the change in momentum which produces a nonlinear change in the number of fragments generated. The crystal combination which has the greatest relative velocity between crystals is graupel and un- rimed plane dendrites. However, neither graupel nor unrimed plane dendrites generate a large number of fragments, so a greater effect was found between graupel and rimed crystals. The greatest rate of secondary particle generation was found between heavily rimed plane dendrites and graupel although ther,e was little difference from that between mod- erately rimed plane dendrites and graupel or lightly rimed spatial crystals and graupel. Apparently, the reduction in relative velocity is more than compen- sated for by the ability of rimed crystals to produce fragments. The magnitude of ice multiplication due to the generation of secondary particles is less than a factor of 10 for every possible combination of crystal types and size distributions without accretion and diffusion. The broader the distribution of either or both crystal types colliding in a cloud, the greater the rate of fragmentation. This is apparently an effect of shifting a greater concentration of crystals to larger sizes by a broader distribution. The larger the crystals, the greater the relative velocities and the greater the ability to produce fragments. Ice multiplication be- comes less for smaller and narrower size distributions E c5- 0.10 10 , ~ " ~ z Q l- e:( a: ~ 0.05 ILl u Z o u and lighter rimed crystals. The generation of secondary particles is effectively zero unless graupel or heavily rimed particles are present. When accretion and diffusion are allowed to occur during fragmentation the concentration of crystals continues to increase as a function of the rate of accretion and diffusion and the ice multiplication can become greater than a factor of 10. 6. Conclusions The results of this study were somewhat different than had been expected. The presen~ce of fragments and numerous irregular crystals beneath convective cells (Vardiman, 1972) led to the belief that me- chanical. fracturing of unrimed dendrites would explain part of the observed excess in ice crystal concentra- tions. It was also thought that this process might possibly be general enough to explain high crystal concentrations observed in many other cloud con- ditions. The findings from the model, based on ex- perimentally derived fragment generation functions, eliminate further consideration of unrimed crystals as a source of more than minor numbers of in-cloud fragments. The model does predict, however, that under certain cloud conditions, significant fragmenta- tion can occur, namely, when relatively large con- centrations of rimed crystals are present. Since rela- tively large concentrations of rimed crystals are required before secondary particle generation can proceed, this mechanism cannot explain the occurrence of excess crystal concentrations at warm temperatures, as observed by Mossop (1972). Even though mechani- cal fracturing of rimed crystals by crystal-crystal col- lision cannot explain ice multiplication in general, it may still be important in certain cloud situations. The following cloud types exemplify the possible --- TIME = o minutes ........... TIME = 5minutes -l.'ME = 10minutes (0) 2 345 DIAMETER (mm) FIG. 9. Change in size distribution of graupel due to collision with heavily rimed plane dendrites. i ; ;~J",,,,",,,,:iw-. .~.~~ ~~,~J~L;~~i&ff;~~~&;~~~~~~~~~'r.t~,L~...,~.:!:~;~~vi~,,',;_,', -.~~~~:;;fi~~~~~*"-