A. Governing equations of the model   d. Radiation
A.d.i. Radiative transfer of atmospheric CO2 Both infrared and near infrared radiative flux associated with CO2 are calculated by Goody narrow band model (c.f., Goody and Young, 1989). By using the band model, the temperature profile around 10 ∼ 15 km height which is correspond to tropopause region in the dust-free Martian atmosphere can be calculated precisely. In calculating infrared radiative flux, CO2 15 μm band is only considered. The upward and downward infrared radiative flux ( ) and the infrared radiative heating rate per unit mass are calculated as follows. is the ith narrow band width and is the Plank function which is represented as follows. where is the Plank constant, is speed of light, is the Boltzmann constant, and is temperature. is the transmission function averaged over around . is line strength, is square root of the product of line strength and line width and is the reference value of , is effective path length, and is reference pressure (= 1013 hPa). In calculating near infrared solar radiative flux, CO2 4.3 μm, 2.7 μm, and 2.0 μm band are considered. The near infrared solar radiative flux and the near infrared radiative heating rate per unit mass are calculated as follows. where , is the solar zenith angle, and is the solar radiative flux per unit wave length at the top of atmosphere which is represented as follows. where is the surface temperature of the sun (= 5760 K), is the Stefan-Boltzmann constant (= 5.67× 10-8 Wm-2K-4, is solar constant on the mean radius of Mars orbit (= 591 Wm-2), and is the radius of Mars orbit and its mean value, is solar radiative flux at the top of atmosphere. is depend on season, latitude and local time. Detail descriptions of and are shown in appendix A.d.vi. The transmission function averaged over in near infrared wavelength region is similar to that in infrared wavelength region except for the effective path length .
A numerical simulation of thermal convection in the Martian lower atmosphere.