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1074 JOURNAL OF CLIMATE AND APPLIED METEOROLOGY VOLUME 22 \ \ 0.8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ "- " "- ...... ...... ...... x ...... o xX xxoooooooo ....____ XXxx 00 --- x x Xx Xx = OBSERVATION ~ 0.7 z w Q 06 ll.. ll.. W z Q5 o ~ 04 w ..J 603 u 0.2 o 0.1 00 FIG. 4. Collection efficiencies assumed in the model compared with laboratory observations. The symbol X is for 127 I'm spheres collecting 8-18 I'm crystals. The symbol 0 is for 360 I'm spheres collecting 8-18 I'm crystals (Hosler and Hallgren, 1961). about 4.5 X 10-11 g g-I S-I to 6.9 X 10-10 g g-I S-I, when Icw is in the range of 10-4 to IO-z g g-I, PSFI ranges from 8.8 X 10-10 to 3.2 X 10-9 g g-I S-I, with ICI in the range of 5 X 10-8 to 10-4 g g-I. In the production rates PSAC1 [(22)] and PGACS [(29)], we used assumed collection efficienciesEsI and EGs, given respectively by (23) and (30). A similar temperature dependence has been assumed for the rate coefficients for. PSAUT [(21)] and PGAUT [(37)]. Unfortunately, there have been few experimental studies of ice collecting ice and no theoretical studies due to the complexity of the problem. Fig. 4 compares the assumed collection efficiencies to the values de- rived from laboratory studies as reported by" Hosler and Hallgren (1961). The obvious disa.greement be- tween the assumed and observed collection efficien- cies is due to the fact that the observed values were obtained at ice saturation. In a related study, Hosler et al. (1957) note considerably higher efficiencies at ice supersaturation, the efficiency increasing with in- creasing temperature. In a somewhat different vein, Passarelli (1978) deduced a mean aggregation effi- ciency of 1.4 :t 0.6 from aircraft data. He noted ef- ficient aggregation extended down to the -12 to - 15 oC range and attributed the difference between his findings and laboratory studies to the fact that nature produces more elaborate crystals and larger sizes. The assumed collection efficiencies reflect the results quoted above in a number of ways: (ii) Efficiencies are highest at OOC, consistent with the indirect evidence of efficient aggregation in this region provided by the radar "bright band." (iii) The trend to higher than observed values in the intermediate temperature range seems justified due to the likelihood of ice supersaturation in this regime. (iv) ESI is greater than,EGs consistent with the rel- ative ease with which ice crystals are collected by snow crystals as opposed to hard ice spheres as in- dicated by Nakaya (1954). /. . d. Production term for hail Both dry and wet growth of hail are considered in this model, while only dry growth is considered in Chang (1977). The total production term for hail can be written as: (i) If the temperature is below OOC (T < To): PG = PGAUT + PGFR + PGDRy (or PGWET) + PSACR( 1 - (h) + PRACS( 1 - oz) + PRAC1 X (1 - (3) + P1ACR(1 - (3) + PGSUB(1 - (1)' (35) (ii) If the temperature is above OOC (T ~ To): PG = PGMLT + PGACS' (36) The definition of 01, Oz and 03 are given by (20). The two sets of coupled terms present in (35) [PRACt. P1ACR and PRACS, PSACR], are given earlier by (25), (26) and (27), (28). For PRAC1 arid P1ACR, hail will be produced only when the mixing ratio of rain (/R) ex- ceeds 10-4 gg-I. For PSACR and PRACS, hail production results when the mixing ratio of either rain or snow exceeds 10-4 g g-I. 1) SNOW CRYSTAL AGGREGATION, Rimed snow crystals may collide and aggregate to form graupel or hail. The aggregation rate is assumed to follow the form used to express the aggregation of cloud ice to form snow [Eq. (21)]. The aggregation rate may be expressed as PGAUT = uz(/s - Iso), (37) where Uz is a rate coefficient (s-'), and Iso is a mass threshold for snow; Iso is set somewhat arbitrarily at 6 X 10-4 g g-I as in Chang (1977). The rate coefficient Uz is assumed to be temperature dependent and is given as Uz = 10-3 exp[0.09(T - To)]. (38) (i) The assumed efficiencies, especially EGs, are Note that the temperature dependence of the rate close to the observations at low temperatures where coefficient is the same as that used for the collection ice saturation is more likely. efficiency of hail for snow [(30)].