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     using none toincoporate none on web,windows applicationc# generate barcode 0 L02 and N2 are S2 s total none for none mass and number concentration, respectively; S2 first attains a Golovin shape; S2 s relative mass variance is 1 (increasing from prior smaller values); S2 obtains a mean-mass radius of $41 mm; and r(gm) is the threshold radius corresponding to the minimum in the mass between the two modes of the total liquid spectrum.. iPhone OS The determination of T2 is i mportant to modelers because T2 was the only time for which Berry and Reinhardt (1974b) tabulated both the rain mass and rain number concentration from a bin model. The other timescales defined by Berry and Reinhardt (1974b) are: TH ($1.1T2), which denotes the time at which the developing S2 mass distribution curve forms a hump; and T ($1.

25T2), which denotes the time at which the radius of the predominant mass of the joint S1 + S2 (bimodal) distribution first reaches a radius of 50 mm.. 9.2 Schemes for cloud droplets to drizzle and raindrops The focus first will be on t he earliest timescale presented in Berry and Reinhardt (1974b), T2, as both mass and number concentration are defined. After converting to SI units, making some corrections to typesetting errors in Berry and Reinhardt, and converting radius to diameter, the resulting timescale is given as ^ T 2 fsg 3:72 s kg m 3 mm h nmmo 0:5 106 D0 fmg b m 7:5fmmgL kg m. 9:3 :. The second equation involved in the Berry and Reinhardt (1974b) scheme is shown in their Eq. 18, Fig. 9, as the following for total mass,   n o 1 0 3 3 0 4 ^2 gm 3 10 4 104 4 mm L rb fcmg rf fcmg 0:4fmmg cm 9:4 2:7 10 2 fmmg 4 L0 g m 3 : Pruppacher and Klett (1981) were perhaps first to suggest that (9.

3) and (9.4) could be combined to obtain an average rate of change in rain mixing ratio ^ during T2 for a bulk microphysics model:  0  ^ max L2 ; 0 1 dQzw 1 1  : Qzw CNcw kg kg s 9:5 dt r max T 0 ; 0 ^. Berry and Reinhardt (1974b) none for none do not propose this average mixing ratio rate; this is probably because they only consider those curve fits to data as an intermediate step (Berry and Reinhardt 1974b, p. 1825) to their parameterization, and because these authors (Berry and Reinhardt 1974c,d) present a way to evaluate precise rates at any arbitrary time (rather than average rates via a characteristic timescale). Nevertheless, the simple form is what all subsequent bulk microphysics modelers have used and what is herein designated as the Berry and Reinhardt (1974b) parameterization or Berry and Reinhardt (1974b) scheme .

There are some limitations to the Berry and Reinhardt (1974b) scheme. First, it unfortunately does not give the remaining cloud-water number concentration NTcw at T2, and therefore an average dNTcw/dt (owing to S1 self-collection and S1 accretion by S2) cannot be derived. Next, adequate mass and number concentration rates are difficult to define since the S1 and S2 distributions overlap.

Also, Cohard and Pinty (2000) have noted that cloud accretion by rain and rain self-collection both appear twice for some. Autoconversions and conversions size ranges: once implicitly none none within the Berry and Reinhardt (1974b) scheme, and again when explicitly parameterized. This results in double counting of particles. Finally, Berry and Reinhardt (1974b) write that the parameterization is based upon initial values of cloud droplets only in the range from 20 D0 f 36 mm; 9:6 .

where f L/Z (L is the liqu id-water content, Z is the reflectivity); and only with the relative variance var M given as lying between 0:25 var M 1; 9:7 . which corresponds to a Golov none for none in-distribution shape parameter with limits 0 < vcw < 3. Cohard and Pinty s (2000) formulation is given as   ^zw;inv s 1 106 1 D var M 1=6 7:5 Qcw r=3:72; 9:8 T 2 cw ^ Lzw kg m 3 and dqzw kg kg dt.
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