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<br />- 20- <br /> <br />41T R3 g <br />3 Pp <br /> <br />P v 2 <br />c -----.!.- 1T R 2 , <br />w 2 <br /> <br />b <br /> <br />(9) <br /> <br />where R is the radius, Pp the particle density, c the drag coefficient, and v ! the ter- <br />minal fall speed. w tl <br /> <br />" <br /> <br />This leads to a free fall speed or terminal velocity of <br /> <br />vt <br /> <br />/ 8 Pp g I <br />3~R <br />w <br /> <br />(10) <br /> <br />Different velocities during fall lead to the possibility that larger particles <br />may catch up with smaller, slower moving ones. This may result in a coalescence or <br />aggregation which can be described by a collection efficiency [the fraction of ~smaller <br />particles in the swept-out volume (of the larger particle) which are being captured by the <br />larger particle] or a breakup probability if two drops are involved. ; <br />! <br />Mass accretion by capturing of water or ice particles represents a t~ansfer of <br />enthalpy and thus also affects the heat transfer. It controls together with the heat <br />transfer by conduction and convection and the thermal equivalent of the molecul~r mass <br />transfer, the amount of accreted water which can be frozen after impact on a growing hail- <br />stone. Any resulting heating or cooling of the surrounding air needs to be inc;luded in the <br />thermodynamic equation. <br /> <br />CCN <br />I <br />C()\lDENSATION <br />l <br />DROPLETS <br />I <br />COALESCENCE <br />CONDENSATION <br />~ <br />DROPS <br />I <br /> <br />COALESCENCE <br /> <br />"iKUP <br /> <br />WARM RAIN <br /> <br />IN <br /> <br />CCN <br />I VAPOUR 4 <br />ICE CRYSTALS <br />DROPLET~ - - - -t-ACCRETION- -~ <br />: \ GRAUPEL SNOW <br /> <br />I \ ~ I <br />I \ <br />DRbPS \ - - - ACCRETION - -~ <br /> <br />: HAIL <br />I <br />COALESCENCE <br />BREAKUP <br />I <br />I <br />, + <br /> <br />MELTING <br /> <br />v <br /> <br />COLD RAIN <br /> <br />hgUfte 2a. Sc.hematic. diagftam J.>howing the evofution <br />06 Waftm and Cold Rain, J.>tatr-Ung 6ftom <br />c.loud c.ondenJ.>a:t-<-on nuc.lei (CCN) and ic.e <br />nuc.lei { IN J. <br /> <br />~ <br />