WMOD00462

• Contract/Permit #: 87-1999
• Title: Development of Empirical Equations of Ice Crystal Growth Microphysics for Modeling Analysis - Final Report
• Date: 9/1/1988
• Weather Modification - Doc Type: Report

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30

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growth environment is small with respect to the absolute temperature level
involved. Classical conduction and diffusion theories express the fluxes of
heat and water vapor between the environment and the outer boundary of
the resistance layer, and the transportations based on Knudsen's flow describe
the fluxes within the layer. Only parts of the heat and water vapor reaching
the particle surface through the resistance layer are conveyed to the ice
particle. Assuming the steady state fluxes and applying the appropriate
boundary conditions, the diffusion - kinetic equation, an expression
governing the rate of mass growth of the particle with respect to time under
the conditions mentioned above, becomes:

I

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.

dm
dt =

41tr(Si - 1)
L2 l'
( 2 + )
KRvT _fex P....,satDfy

(3.1)

.

where

.

fex=r I(r+ la),

(3.2)

f",/ = r I ( r + I)' ),

(3.3)

.

2aK(21tRa T 00)1/2
la = (2 - a)p(cv + Ra/2) ,

(3.4)

.

2yD ( 21t )1/2
1",/ = R T
2-y voo '

(3.5)

.

where m is the ice crystal mass, Si (= pool p 00, sat) the saturation ratio with
respect to ice , r the radius of the spherical ice particle, L the latent heat of
deposition, K the thermal conductivity, Rv specific gas constant for water

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