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APRIL 1995 MEYERS ET AL. 837 can be reasonably well approximated by the continuous gamma distributions as shown in Fig. 2. These gamma functions with shape parameter equal to 2 are of the form f(D) = :~ exp( - ~) , (3.1) where D is diameter and Dn is the scaling diameter. It was determined that Dn = 2.7 X 10-6 cm provides an excellent fit for the AgI-AgCl PSD from DeMott et al. ( 1983), while Dn = 1.5 X 10-6 is probably more char- acteristic of an aircraft generator PSD. The composite aircraft generator PSD was selected for the mesoscale model simulations as the most likely AgI-AgCl size distribution present following seeding on 18 December 1986. The consequence on ice for- mation compared to the use of the published ground generator PSD is demonstrated through the use of mi- crophysical parcel model simulations later in this sec- tion. In integrating DeMott's equations over the se- lected PSD, environmental dependencies on temper- ature, ice supersaturation, and water supersaturation were retained, and the results for each ice formation mechanism were fit to a computationally efficient polynomial. The total aerosol fraction nucleating ice by deposi- tion Fdep was found to be (273.16 - T) Fdep = a(Si - 1) + b To + C(Si - 1)2 (273.16 - T)2 + d To + e(Si - 1)3, (3.2) with constants To = 10.0 K, a = -3.25 X 10-3, b = 5.39 X 10-5, C = 4.35 X 10-2, d = 1.55 X 10-4, and e = -0.07. Here Si is the ice saturation ratio, Tis in kelvins, and this equation was taken to be valid when Si > 1.04 and T <= 268.2 K. The total aerosol fraction nucleating ice by condensation freezing Fcdf was pa- rameterized as (268.66 - T)3 2 Fedf = a To (Sw - 1) , with constants To = 10.0 K, a = 900.0. This result was taken to be valid when T < 268.66 K and water sat- uration ratio Sw > 1.0. In a similar way, for the im- mersion-freezing nucleation fraction Fimf, it was found that (3.3 ) ( 268.2 - T)b Fimf = a(Fimm) To ' (3.4 ) with To = 10.0 K, a = 0.0274, and b = 3.3, valid for T < 268.2 K. The use of this equation, however, also requires the knowledge of the fraction of nonactivated aerosol immersed in drops at any time and location (Fimm). This would be difficult to follow explicitly in 25 28 III W .J ~ 15 I- a: ([ II. I- Z ~ 18 a: w II. 5 8 o 8.B 1.2 1.6 2 (X le-6) 8.4 DIAMETER (em) FIG. 2. Particle size distributions for airborne and ground-based measurements. a mesoscale model with bulk microphysics. Fortu- nately, the analysis of the relative contributions ofthe different ice formation mechanisms for AgI-AgCl aerosols made later in this section justified the omission of immersion-freezing nucleation from the mesoscale seeding simulation. The equation is presented here for the sake of completeness. For contact-freezing nucleation, a parameterization was sought that would be compatible with the way that cloud water and scavenging of aerosols by cloud water are treated in RAMS. Namely, cloud droplet number concentration is fixed, cloud droplet diameter is al- lowed to vary, and aerosol size is fixed at one value. The geometric mean diameter of the artificial ice nuclei was taken as 2 X 10 -6 cm for use in calculating col- lection rates by cloud droplets in RAMS. Rather than using the activity of this average size, the fraction of the total AgI-AgCl aerosol population potentially ac- tive as contact-freezing nuclei (Fetf) was estimated by integrating the size-dependent equation given by DeMott ( 1994) over the selected size distribution. This gave Fctf= Fseav[a + b(Si - 1) + C(Si - 1)2 + d(Si - 1)3 + e(Si - 1)4 + f(Si - 1)5 + g(Si - 1)6), (3.5) where the constants are given by a = 0.0878, b = -3.7947, C = 52.3167, d = -255.4484, e = 568.3257, f= -460.4234, and g = -63.1248. The term Fscav is the fraction of the total aerosol population scavenged by cloud droplets in a given grid volume in one time