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<br />11 <br /> <br />c.onstraints in the model allow the production of ice crystals from the vapor only <br /> <br />in the",presence of water supersaturation within an updraft. <br /> <br />'".; <br /> <br />Sublimation <br /> <br />Sublimation of ice particles is allowed byasimplifiecHormof liquid con- <br /> <br />" <br /> <br />densation growth equation, neglecting the surface free energy and ventilation <br /> <br />effects. As shown by Fletcher (1966) and assuming spherical symmetry, the ice <br /> <br />sublimation equation is thus: <br /> <br />. 0 { DL2p <br />x = dx/dt = 41T r Dp (lIp. )[H-l] 1 + 2 v <br />. v Ice RgT K <br /> <br />F1 <br /> <br />(eq. 10) <br /> <br />where <br /> x = mass of ice in the ice particle <br /> 0 ti me rate of change of x <br /> x = <br /> Pv = cloud woter vapor density <br /> Pice = density of ice (assumed 0.9) <br /> H = relative hum idity (fractional) <br /> D = molecular diffusion coefficient <br /> K = thermal conductivity of air <br /> T = cloud temperature <br /> Rg = gas constant for water vapor <br /> L latent heat of condensation 1: <br /> = <br />Riming <br /> <br />The accretion of supercooled water on frozen particles by riming is <br /> <br />accounted for by a variant of the stochastic coalescence equation presented earlier. <br />