2. Numerical model
2.a. Outline of the model The 2D model system consists of the atmosphere and the grand surface. The effect of planetary rotation is not considered. The model atmosphere is composed of ideal gas. The atmospheric constituent is assumed to CO2 only and its condensation and sublimation are not considered. The values of soil density, thermal conductivity and specific heat are constant each other. The surface topography is not considered. Atmospheric model The governing equation of model atmospheric dynamics is the 2D anelastic system (Ogura and Phillips, 1962). The thickness of convection layer in dust-free Mars calculated by 1D model (Flasar and Goody, 1976; Pollack et al., 1979) is almost equal to that of the scale hight estimated by using planetary equilibrium temperature of Mars (Zurek et al., 1992). It is adequate to apply the anelastic system to Martian atmospheric convection whose depth is almost equal to the scale hight, since density stratification is taken into consideration in the anelastic system. Turbulent parametarization The subgrid turbulent mixing is evaluated by the formula of Klemp and Wilhelmson (1978). The value of turbulent diffusion coefficient for heat is equal to that for momentum. The surface momentum and heat fluxes are given by the bulk formulae, where the bulk coefficients depend on static stability and vertical wind shear (Louis, 1979). The bulk coefficient for heat transport has same value of that for momentum. The roughness length for the bulk coefficients is 1 cm (Sutton et al, 1978). These turbulent models have been developed in order to simulate the turbulent mixing in the terrestrial atmosphere. In this study, we assume that these turbulent models are also applicable to the turbulence in the Martian atmosphere. Dust transport The spatial distribution of dust is calculated by advection diffusion equation which considers gravitational settling of dust. The representation of dust terminal velocity follows Conrath (1975). The radius of dust particle is constant value (0.4 μm). The value of dust flux from the surface is those obtained by wind tunnel experiment (White et al.,1997). The value of critical surface stress is described in Section 4. Radiation The radiative transfer of CO2 atmosphere is calculated by a Goody narrow band model which considers 15 μm band in infrared wavelength and 4.3, 2.7, 2.0 μm band in near infrared wavelength. The values of absorption line intensities and widths in each band are same as those of Houghton (1986). The radiative transfer of dust is calculated by δ-Eddington approximation model which considers two bands in infrared wavelength region (5-11.6, 20-200 μm) and one band in solar wavelength region (0.1-5 μm). The values of band width and optical parameters of dust (extinction efficiency, single scattering albedo, asymmetry factor) in each band are same as those of Forget et al. (1999) except in 11.6-20 μm band which is not considered in our model. Grand surface The grand temperature is calculated by 1D thermal conduction equation. The values of soil density, thermal conductivity and specific heat are same as those of Kieffer et al. (1977) standard model.
A numerical simulation of thermal convection in the Martian lower atmosphere.