A. Governing equations of the model
A.c. Dust Transport The dust mass mixing ratio is calculated by using the advection diffusion equation, which considers the gravitational settling of dust. The dust terminal velocity is calculated as follows(Conrath ,1975). is the density of the dust particle, is the radius of the dust particle, is atmospheric viscosity, is the mean free path of atmospheric gas at . In this study, we set = 3000 kgm-3, = 1.5×10-5 kgm-1sec-1, = 25 hPa, = 2.2×10-6 m. Equation (A.19) is applied for each dust particle with a different radius. However, for simplicity, the radius of a dust particle is assumed to be equal to the mode radius of a dust particle in Equation (A.38), which is the size distribution function of dust. It is assumed that dust injected from the surface to the atmosphere occurs when surface stress exceeds a threshold value . The dust flux from the surface is equivalent to that obtained by a wind tunnel experiment (White et al., 1997). The value of critical surface stress is described in Section 4.
A Numerical Simulation of Thermal Convection in the Martian Lower Atmosphere with a Two-Dimensional Anelastic Model