Equilibrium Sizes of Cloud Droplets Condensed on Multi-sized CCN After In-size-Class and Inter-size-Class Competitive Growth

HR: 0800h
AN: A21C-0748 [Abstracts]
TI: Equilibrium Sizes of Cloud Droplets Condensed on Multi-sized CCN After In-size-Class and Inter-size-Class Competitive Growth
AU: * Shiba, S
EM: shiba@cheng.es.osaka-u.ac.jp
AF: Division of Chemical Engineering, Department of Materials Engineeing Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osa 560-8531 Japan
AU: Hirata, Y
EM: hirata@cheng.es.osaka-u.ac.jp
AF: Division of Chemical Engineering, Department of Materials Engineeing Science, Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osa 560-8531 Japan
AU: Yagi, S
EM: syagi@ise.setsunan.ac.jp
AF: Department of Industrial and Systems Engineering, Setsunan University, 17-8 Ikeda-nakamachi, Neyagawa, Osa 572-8508 Japan
AB: (Introduction) The equilibrium size of a cloud droplet condensed on a CCN is estimated by traditional Kť"{o}hler model derived from thermodynamic equilibrium between droplet and gas phases (Pruppacher and Klett, 1980). However, Kť"{o}hler model is based on the idealistic assumption that a cloud droplet grows in an infinitely large reservoir of water vapor at constant pressure and constant temperature. In application to realistic air parcels, this brings about two serious faults in size estimation (Shiba et al, 2003). The first is failure to consider competitive growth of plural droplets (i.e., effect of CCN number density). The second is limitation of the maximum allowable saturation ratio to get a definite droplet size. A new model applicable to competitive growth on multi-sized CCN has been developed, taking account of both water vapor reduction and temperature rise to remove above faults. (Mathematical Model) For multi-sized CCN of $n$ size-classes, $n+2$ governing equations are solved to estimate radius $a_{i}$ ($i=1, 2,., n$), saturation ratio $S$ and temperature $T$. They are derived from (1) $n$ equilibria between droplet chemical potential and vapor one, (2) conservation of mass, and (3) conservation of heat energy. (Model Calculations of Cloud Droplet Size) To do demonstrative calculations, three virtual air parcels (Types 1, 2, and 3) are arranged, combining CCN size [(small, medium, large) = (0.1, 0.5, 1.0) $ťmu$m] with CCN number [(most, average, least) = (750, 500, 250) cm$^{-3}$]. Types 1, 2, and 3 are small-CCN-rich parcel (750, 500, 250), even-CCN-distribution parcel (500, 500, 500), and large-CCN-rich parcel (250, 500, 750), respectively. Parenthesized CCN numbers are put in up-sized order of CCN. The more air parcel contains large CCN, the smaller droplet size becomes in any size-class regardless of parcel type. Droplet sizes in small and medium size-classes seem to be contrary to idea of in-size-class competition that less competitive growth produces larger cloud droplets. From the viewpoint of in-size-class competition we expect that small size-class droplets in large-CCN-rich air parcel becomes larger than that in small-CCN-rich air parcel, because number of small CCN in large-CCN-rich air parcel is less than that in small-CCN-rich air parcel. If cloud droplet size were controlled exclusively by in-size-class competition, as for small size-class, Type 3 air parcel [which contains the least (250 cm$^{-3}$) small CCN] would have the largest size droplet and Type 1 air parcel [which contains the most (750 cm$^{-3}$) small CCN] would have the smallest one. However, in any size-class, air parcel order according to droplet size is the same as that in the largest size-class (i.e., regardless of size-class, Types 1, 2 and 3 are in down-sized order of droplet). This means that the largest CCN controls not only in-size-class competition with themselves but also inter-size-class competition with smaller CCN. (Conclusions) Model calculations show that: (1) Equilibrium size of cloud droplet on multi-sized CCN is controlled by large size CCN; (2) Inter-size-class competitive growth brings about a kind of nonlinearity in mapping of CCN size distribution to cloud droplet size distribution.
DE: 9800 GENERAL OR MISCELLANEOUS
DE: 4801 Aerosols (0305)
DE: 3210 Modeling
SC: Atmospheric Sciences [A]
MN: 2004 AGU Fall Meeting