4 Dust transport

The spatial distribution of dust mass mixing ratio $q$ is calculated by advection diffusion equation which considers gravitational settling of dust.

$$\DD{q}{t} + \frac{1}{\rho _{0}}\DP{}{z}(\rho _{0}Wq) = D(q).$$ (20)

The dust terminal velocity $W$ is calculated as follows (Conrath, 1975).

$$W = - \frac{4\rho _{d}gr^{2}}{18\eta} \left(1+2\frac{\lambda_{r}}{r}\frac{p_{r}}{P_{0}}\right).$$ (21)

$\rho _{d}$ is the density of dust particle, $r$ is the radius of dust particle, $\eta$ is atmospheric viscosity, $\lambda _{r}$ is the mean free path of atmospheric gas at $p_{r}$. The equation (21) is applied for each dust particle with different radius. However, the size distribution of dust is not considered here for simplicity and the radius of dust particle is supposed to be equal to the mode radius $r_{m}$ of dust particle in equation (38) which is the size distribution function of dust.

It is supposed that the dust injection from the surface to atmosphere occurs when the surface stress $\tau _{m}\equiv\vert F_{u}\vert$ exceeds some threshold value. The value of dust flux from the surface is constant.

Parameters

表 3: Parameters of dust transport model

Parameters	Standard Values	Note
$\rho _{d}$	3000 kgm${}^{-3}$	Conrath (1975)
$\eta$	1.5$\times10^{-5}$ kgm${}^{-1}$sec${}^{-1}$	〃
$p_{r}$	25 hPa	〃
$\lambda_{r}(p_{r})$	2.2 $\times 10^{-6}$m	〃
$r_{m}$	0.4$\mu$m	Toon et al. (1977)
$F_{q}$	3.7 $\times 10^{-6}$ kgm${}^{-2}$	White et al. (1997)
		( $\tau_{m} \geq \tau _{mc}$)
$\tau _{mc}$	0.01 Pa