A. Governing equations of the model   d. Radiation
A.d.iv. Dust opacity The monoclomatic optical depth for wave number is represented by using the extinction coefficient per unit volume as follows. where is altitude at the top of atmosphere. is given as follows. where is the extinction cross section, is the size distribution of scattering particle (cf. Liou, 1980; Shibata, 1999). By using extinction coefficient per unit mass , (A.40) is rewritten as follows. where is atmospheric density, and is mass mixing ratio of scattering particle. Similarly, the scattering and absorption coefficient per unit volume are represented by using the scattering cross section and the absorption cross section as follows. and the single scattering albedo is given as follows. The extinction efficiency is defined as the ration of extinction cross section to geometric cross section. Similarly, the scattering efficiency and absorption efficiency are defined as follows. In present study, the dust opacity is derived from the mass mixing ratio of atmospheric dust. Given parameters are the cross section weighted mean extinction efficiency , the single scattering albedo , the size distribution function of dust , the effective (or, cross section weighted mean) radius , and the density of dust particle . , are defined as follows, respectively. Supposing that the shape of scattering particle is sphere, the extinction coefficient per unit mass is given as follows. where is the atmospheric density. Therefore, the optical depth can be represented as follows.
A numerical simulation of thermal convection in the Martian lower atmosphere.