HR: 17:00h
AN: A12F-05    [PDF]
TI: Equilibrium Cloud Droplet Size due to Competitive Condensational Growth on Mono-size Plural CCN
AU: * Shiba, S
EM: shiba@cheng.es.osaka-u.ac.jp
AF: Osaka University, 1-3 Machikaneyama, Toyonaka, 5608531 Japan
AU: Hirata, Y
EM: hirata@cheng.es.osaka-u.ac.jp
AF: Osaka University, 1-3 Machikaneyama, Toyonaka, 5608531 Japan
AU: Yagi, S
EM: yagi@ise.setsunan.ac.jp
AF: Setsunan University, 17-8 Ikedanakamachi, Neyagawa, 5728508 Japan
AB: {\bf Introduction}\\ The equilibrium size of the cloud droplet condensed on cloud condensation nucleus (CCN) is commonly estimated by traditional K\"{o}hler model derived from the thermodynamic equilibrium between liquid and gas phases separated by a curved interface. However, K\"{o}hler model is based on the idealistic assumption that the cloud droplet grows in an infinitely large reservoir of water vapor at constant pressure and constant temperature. As for application of K\"{o}hler model to more realistic air parcels, this brings about two major faults in the droplet size estimation. The first is the limitation of the maximum allowable saturation ratio. The limitation produces curious situation as the equilibrium size cannot be decided in case of larger saturation ratios than the critical saturation ratio. The second is the inability to distinguish competitive growth of plural droplets from non-competitive growth of a single droplet. In other words, K\"{o}hler model fails to consider the effect of CCN number density on droplet size. A new model free of these faults has been made by supplementing mass and heat conservation equations to the traditional K\"{o}hler equation. \\ \\ {\bf Mathematical Model for Cloud Droplet Size} \\ The new model consists of three governing equations and enables to estimate radius $a_{\rm e}$, saturation ratio $S_{\rm e}$ and temperature $T_{\rm e}$ in equilibrium state. The governing equations are derived from (1) equilibrium of the droplet chemical potential $\mu_{\rm w}$ with the vapor one $\mu_{\rm v}$ as: $ \mu_{\rm {w}}(S_{\rm e}, T_{\rm e}, a_{\rm e}) = \mu_{\rm {v}}(S_{\rm e}, T_{\rm e}, a_{\rm e}) $, (2) mass conservation represented by liquid water mass $m_{\rm w}$ and vapor water mass $m_{\rm v}$ as: $ d(m_{\rm w}+m_{\rm v}) = 0 $, and (3) heat energy conservation represented by enthalpy $h_{\rm x}$ per unit mass of $m_{\rm x}$ (suffix x gets w, v and a for liquid water, vapor water and air, respectively) as: $ d(m_{\rm w}h_{\rm w}+m_{\rm v}h_{\rm v}+m_{\rm a}h_{\rm a}) = 0 $. The equilibrium gives the relation between $a_{\rm e}$ and $S_{\rm e}$ (similar to K\"{o}hler equation). The mass conservation enables to obtain $S_{\rm e}$ from initial saturation ratio $S_{0}$. The heat energy conservation relates $T_{\rm e}$ with initial temperature $T_{0}$. \\ \\ {\bf Conclusions} \\ Numerical simulations by the new model show that: (1) Reduction of equilibrium cloud droplet radius $a_{\rm e}$ with increase in CCN number density $N$, i.e., reduction due to competitive growth, becomes more remarkable with increase in initial saturation ratio $S_0$; (2) Equilibrium temperature increase $T_{\rm e}-T_{0}$ from initial temperature $T_{0}$ with increase in $N$ is not monotonous but has the minimum value; (3) $T_{\rm e} - T_0$ by competitive growth is too small to have an effect on $a_{\rm e}$, but, it seems to be large enough to make the air parcel statically unstable and trigger off the thermal convection in the atmosphere.
DE: 0305 Aerosols and particles (0345, 4801)
DE: 0320 Cloud physics and chemistry
SC: Atmospheric Sciences [A]
MN: 2003 Fall Meeting