4 Dust transport

In the advection diffusion equation of dust ( equation (20) in Part I), the advection term $[\mbox{DQADV}]_{i,j}^{n}$ is evaluated by the forth order centered scheme and the vertical advection term associated with the gravitational settling $[\mbox{DQFALL}]_{i,j}^{N}$ is evaluated by the first order upstream scheme. In time integration, the forward scheme is adapted for the friction terms $[\mbox{DQDIF}]_{i,j}^{N}$, $[\mbox{DQNLD}]_{i,j}^{N}$ and the gravitational settling term $[\mbox{DQFALL}]_{i,j}^{N}$. Representation of $[\mbox{DQADV}]_{i,j}^{n}$, $[\mbox{DQDIF}]_{i,j}^{N}$ and $[\mbox{DQNLD}]_{i,j}^{N}$ are same as those of (22), (24) and (42).

$$q_{i,j}^{n+1} = q_{i,j}^{N} + dt \left\{ [\mbox{DQADV}]_... ... [\mbox{DQFALL}]_{i,j}^{N}+ [\mbox{DQNLD}]_{i,j}^{N} \right\}$$ (49)

$$\mbox{DQFALL}_{i,j}^{n} = - \frac{1}{\rho _{0,j}\Delta z_{j}} \left\{ FQf_{z(i,j+\frac{1}{2})}^{n}-FQf_{z(i,j-\frac{1}{2})}^{n} \right\},$$ (50)

$$FQf_{z(i,j-\frac{1}{2})}^{n} = - \frac{4\rho _{d}gr_{mod}^{2}}{18\eta }\left( 1 + 2\frac{\lambda _{r}}{r_{mod}}\frac{p_{r}}{P_{0,j}}\right) \rho _{0,j}q_{i,j}^{n},$$