2. Numerical model
2.a. Outline of the model The model domain consists of an atmosphere and a ground soil layer. The effect of planetary rotation is not included. The atmosphere is regarded as ideal gas. The atmospheric constituent is assumed to be CO2 only and its condensation and sublimation are not considered. The values of soil density and soil thermal properties are horizontally uniform. There is no surface topography. Atmospheric model The wind and temperature fields of the model atmosphere are described by a two-dimensional version of the anelastic system of Ogura and Phillips, 1962. According to the results obtained by vertical one-dimensional models (e.g., Flasar and Goody, 1976; Pollack et al., 1979), the thickness of the convection layer in the Martian atmosphere with dust-free condition is expected almost equal to that of the scale height of the Martian atmosphere calculated with radiative equilibrium temperature (Zurek et al., 1992). The anelastic system enables us to describe convection whose depth is almost equal to the scale height, since the anelastic system includes the effects of density stratification of the basic field. Turbulence parametarization Subgrid turbulent mixing is evaluated by the formula of Klemp and Wilhelmson (1978). Surface momentum and heat fluxes are given by the bulk formula of Louis (1979), where the bulk coefficients depend on static stability and vertical wind shear. In the present model, the turbulent mixing coefficient and the bulk coefficient for heat transport have the same values of those for momentum, respectively. The roughness length for the bulk coefficients is set to be 1 cm (Sutton et al, 1978). Those turbulent models have been developed to simulate the turbulence in the terrestrial atmosphere. In this study, we have assumed that those 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 with gravitational settling of dust. The representation of dust terminal velocity follows Conrath (1975). We have assumed that the radius of dust particle is constant (0.4 μm). The value of dust flux from the surface is that of the wind tunnel experiment by White et al. (1997). Radiation Radiation of CO2 is calculated by the Goody narrow band model. We have included 15 μm band in the infrared wavelength region and 4.3, 2.7, 2.0 μm bands in the near infrared wavelength region. The values of absorption line intensity and width in each band are adopted from Houghton (1986). Radiation of dust is calculated by the δ-Eddington approximation model. We have included two bands (5-11.6, 20-200 μm) in the infrared wavelength region and one band (0.1-5 μm) in the solar wavelength region. These locations of bands and the values of extinction efficiency, single scattering albedo, asymmetry factor of each band are adapted from Forget et al. (1999). Ground surface The ground temperature is calculated by 1D thermal conduction equation. The values of soil density, thermal conductivity and specific heat are adopted from the standard model of Kieffer et al. (1977).
A numerical simulation of thermal convection in the Martian lower atmosphere.