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<br />. <br /> <br />7 <br /> <br />Beheng (1978) performed calculations of graupel developnent. <br /> <br />. <br /> <br />e <br /> <br />His calculations included: <br /> <br />i) simul taneous treatment of <br /> <br />coalescence and graupel growth; ii) interaction between the <br /> <br />graupel growth and the droplet spectrum, so that the growing <br /> <br />. <br /> <br />graupel depleted the cloud water; i i i) stochastic collisions. <br /> <br />When coalescence occurred simultaneously with the riming process <br /> <br />the two interacted strongly. <br /> <br />The depletion of the water by the <br /> <br />. <br /> <br />growing graupel led to tile inhibition of the coalescence process. <br /> <br />Heymsfield (1982) calculated the growth rates of a variety of <br /> <br />.e <br /> <br />particle types by diffusion, accretion, "dry" or "wet" growth and <br /> <br />melting. <br /> <br />The particlE!s were grown in a region of updraft. <br /> <br />At <br /> <br />LWC=l g m-3, frozen drops grew most rapidly, followed in order by <br /> <br />graupel, aggregates and planar crystals. <br /> <br />This model is described <br /> <br />. <br /> <br />in section 4.1 and is the basis for many of the calculations in <br /> <br />this thesis. <br /> <br />Heymsfield and Pflaum (1985) calculated the growth of graupel <br /> <br />.e <br /> <br />and compared wi th experimental graupel growth of pflaum and <br /> <br />Pruppacher (1979). <br /> <br />~~he calculations were performed using the <br /> <br />basic growth equations of diffusion and accretion. The <br /> <br />. <br /> <br />accretional growth was calculated using four methods of collection <br /> <br />efficiency: <br /> <br />First, the momentum approach, where the results of <br /> <br />Pflaum and Pruppacher (1979) were used which showed the graupel <br /> <br />. <br /> <br />collection kernal to be equal to that of a water drop with the <br /> <br />same momentum. <br /> <br />Second, a theoretical approach developed by Hall <br /> <br />e <br /> <br />(1980) and Rasmussen and Heymsfield (1985) which uses Pflaum and <br /> <br />. <br /> <br />Pruppacher I s finding that the parameter controlling the trajectOl::Y <br /> <br />Ie <br />I <br />