2. Numerical Model
2.a. Outline of model Framework of the Whole System and Assumptions The model domain consists of an atmosphere and a ground soil layer. The effect of planetary rotation is not included. The atmosphere is set to obey the ideal gas law. CO2 is only assumed to be the atmospheric constituent 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 atmospheric model are described by a 2D version of an anelastic system developed by Ogura and Phillips (1962). According to results from vertical 1D models (e.g., Flasar and Goody, 1976; Pollack et al., 1979), the thickness of the convection layer in the Martian atmosphere with dust-free conditions should be equivalent to the scale height of the Martian atmosphere calculated with a radiative equilibrium temperature (Zurek et al., 1992). The anelastic system enables convection to be properly described, whose depth is nearly equal to the scale height of the atmosphere, since the anelastic system includes the effects of density stratification of basic fields. Turbulence Model Subgrid turbulent mixing (Turbulence parameterization) is evaluated via the formula by Klemp and Wilhelmson (1978). Surface momentum and heat fluxes (Surface flux parameterization) are given by the bulk formula of Louis (1979). In the present model, the turbulent mixing coefficient and the bulk coefficient for heat transport have the same values of those for momentum. The roughness length for the bulk coefficients is set to 1 cm (Sutton et al, 1978). Previous turbulent models have been developed to simulate turbulence in the terrestrial atmosphere. In the present study, we have assumed that these turbulent models are also applicable to the turbulence of the Martian atmosphere. Dust Transport The spatial distribution of dust is calculated by an advection diffusion equation that includes the gravitational settling of dust. The representation of dust terminal velocity follows Conrath (1975). We have assumed that the radius of a dust particle is constant (0.4 μm) in calculating dust terminal velocity. The dust flux from the surface is that of a wind tunnel experiment by White et al. (1997). Radiation Radiation of CO2 is calculated by the Goody narrow band model. A 15 μm band in the infrared wavelength region and 4.3, 2.7, 2.0 μm bands in the near infrared wavelength region are included. Values of absorption line intensity and the width of 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. The locations of these bands and the values of extinction efficiency, single scattering albedo, and the asymmetry factor of each band are adapted from Forget et al. (1999). Ground and surface layer Ground temperature (i.e., subsurface temperature) is calculated by a 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 with a Two-Dimensional Anelastic Model