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JUNE 1983 UN, FARLEY AND OR VI LLE 1073 , rate. They attribute the difference to the role of in- 10-3 ternal circulation in the water film. Another inter- esting aspect of their study was the experimental dem- onstration of the role of the vapor transfer term in delaying the onset of melting until several degrees above OOC in evaporative: conditions. Whether the result is heating or coolingi the thermal effect of the mass change due to the vapor transfer is significant .' 10-4 to the meltmg process, whereas the mass transfer rate via the vapor phase is generally insignificant com- pared to the melting rate. Iq this study, we shall ignore the mass transfer via the v~por phase for ice particles '<Jl in the temperature regime:T ~ To. 'g: 5) THE BERGERON PROG:ESS In this model, cloud water and cloud ice are per- mitted to coexist between! 0 and -40oC. The Ber- geron process simulated in: Orville and Kopp (1977) is modified to a more reali'stic scheme developed by Hsie et at. (1980) and is used as a generation mech- anism for snow instead ofhilil as originally developed. Two terms, PSFW and RSFI. describe the rates at which cloud water and cloud ice, respectively, trans- form to snow by deposition and riming based on the growth of a 50 j.Lm radius ice crystal. The equations for these rates may be written as PSFW = N/so(alm~~o + -trE/wplcwRJsoU/so), (33) PSFI = le//tith (34) where al and a2 are temperature-dependent param- eters in the Bergeron process (taken from Koenig, 1971) and R/so, m/so and 'U/so are the radius, mass and terminal velocity of a $Oj.Lm size ice crystal. N/so is the number concentration (g-l) of the 50 j.Lm size , ice crystals and E/w is the collection efficiency of cloud ice for cloud water which is assumed to be 1 in this model. For more information, including a discussion of the temperature-dependent time scale t:.t I. the reader is referred to Hsie et at. (1980). , , 6) TRANSFORMATION R:\TES FOR SNOW Fig. 3 shows several of ~he production terms for snow for certain values of ~now, rain, hail, cloud ice or cloud water, and for representative environmental conditions. The abscissa represents the bulk water content of the accreting pafticles. The ordinate gives the transformation rates in: grams per gram per sec- ond. The curve for PSMLT ~s computed at +50C and water saturation conditions. Some additional points :are described here. Note that in Fig. 3, PRACS is gre~ter than PGACS. This can be explained by examining !the total number concen- tration of accreting particles Nt. For precipitating particles, Nt equals nOR (or nOG, nos for hail and snow, respectively) divided by ^R: (or ^G, As). The calcula- ........1... . .J.. ~~"'f'7,..t..'~"'""""'~-":";" (f) W f-o ~ 10-5 Z o f= u => o o a:: Il. 10-70 I 2 ACCRETING FIG. 3. Transfer rates for microphysical processes involving the snow field. The mixing ratio of the class of particle being accreted is set to be I g kg -1 unless otherwise noted. tions show that the concentration of raindrops is over 50 times greater than that for hail at the same water contents. This implies that given the same snow con- tent, the rain particles will accrete snow particles more effectively than does hail, although the differ- ence in fallspeeds offsets this to some degree. Fig. 3 also shows that PRACS is greater than PSACR, which again can be explained by the number concentration of the accreting particles, rain particles being a factor of 1.17 greater in number than snow particles, for the same mass contents. The rate offreezing of rain via the collision-freezing mechanism between rain and cloud ice (P1ACR) is not depicted in Fig. 3. This rate is much larger than the other rates depicted in Fig. 3 and is a reflection of the fact that rain is rapidly frozen in the presence of small amounts of cloud ice (Cotton, 1972). Production terms, PSFW and PSFI, which are also not presented in the figure, are much smaller than the other terms shown. For ICl fixed at 10-6 g g-l, PSFW ranges from