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Show APPENDIX A TREATMENT OF PRECIPITATION PHYSICS IN THE NUMERICAL MODEL In order to calculate the location and rate of precipitation in the numerical orographic precipitation model, it is necessary to account for the formation and growth of ice crystals, and to specify their fallout trajectories. The mathematical formulation developed for the m?del is described here. The derivation of the basic equations for growth of particles closely follows the work of Juisto (1967). 1. Ice Phase Mic rophysics Assuming for the present that suitable sites are available for nucleation, and following Jiusto (1967), the growth of an ice crystal by diffusion can be expressed as follows: dm dt where G = 47T C GS. = 1 Dfv p.1 p.1 (1) 2 [l + DL fv] R T2 K (2) V The primary difficulty in the use of this equation for growth computations is that the factor C varies with temperature. For the present discussion, the crystal form considered is that of a dendrite, hence C = 2r / 11 • Thus equation (1) becomes: dm/ dt = 8 G S. r t>. 1 1 1 (3) The relation betwe e n dendrite mass and radius is obtained from empirical data of Nakaya and Terada (1935) as, m Thus, = 1 _5 . 2 x 10 dr/dt = 8/3 x 10 -4 3 r 2 (4) (5) f. GS . 1 1 which, upon integrating, gives t = 3. 8 x 10 G f. S. 1 -4 1 (r - r o (6) ) The thermodynamic function G, and the supersaturation S., vary with cloud 1 340 i |
