4 Model

A full description of the new model used can be found in Selsis (2000b). We briefly summarize below the main characteristics and new developments contained, and give the references for the basic physical and astronomical input data used.

We have developed two new tools to handle respectively one-dimensional time-dependent photochemistry and radiative transfer in planetary atmospheres. The photochemical code, called PHOEBE (PHOtochemistry for ExoBiology and Exoplanets), produces from initial atmospheric conditions and for a given stellar spectrum the abundances for each chemical species as function of altitude and time. The other code, LWT (Long Wavelengths Transmissions) computes the resultant average infrared spectrum of the planet, as well as the local radiative heating and cooling atmospheric rates.

Figure 1: Model results for the present Earth's atmosphere: thermal a) and ${\rm O}_{3}$ b) profiles. These profiles (solid lines) are computed for a constant mean irradiation. They are compared with a yearly average (dashed lines) from the CIRA database (Rees et al. 1990). This database contains monthly averaged profiles for 10 $\deg$ latitude bands; the grey area represents the envelop of all these CIRA profiles. The model fits very well the ${\rm O}_{3}$ data at most altitudes; the discrepancy above 70 km is apparent and due to night/day effects (see text, part 4.3). In graph  b), the long-dashed line shows the initial temperature profile used for the photochemical and temperature retrieval modelling; after 3 iterations, the PHOEBE profile (solid line) matches very well the observations.

   
4.1 The photochemical model PHOEBE

The photochemical model extends previous modelling codes developed by the Bordeaux Planetology Group (Titan: Toublanc et al. 1995; Neptune: Dobrijevic & Parisot 1998; Jupiter: Le Flochmoen 1997; Saturn and Uranus: Ollivier et al. 2000a and b). The following basic physical phenomena are included: photodissociation, 2 and 3 bodies chemical reactions, transfer of the stellar photons (absorption and diffusion), vertical transport of the molecules (by both molecular and eddy diffusion), condensation/evaporation phenomena.

The transfer of UV light has been improved with higher resolution data (now 1 nm, formerly 5 nm) for both the solar spectrum and the cross sections. Solar data are from the SUSIM instrument (Floyd et al. 1998). The dependence of absorption and photodissociation cross-sections and branching ratios with temperature are now included when they are known. Multiple diffusion is no longer handled through Monte-Carlo methods but through the Isaksen et al. (1977) method. This method gives good results for Rayleigh diffusion, and the speed increase allows us to solve the radiative transfer for each integration step. This method is however less precise than Monte-Carlo methods when applied to Mie scattering by aerosols.

New chemical species have been included, mainly NOx compounds (and chlorine compounds for checks on modern terrestrial atmosphere). There are now 37 species and 150 reactions in our database. For 3-body reactions, we have included an empirical efficiency coefficient, depending on the nature of the third body.

   
4.2 The radiative transfer code LWT

In parallel to PHOEBE, we have developed another code for the computation of the radiative properties of the atmosphere in the infrared. This code, called LWT (for Long Wavelength Transmission) provides the radiative cooling and heating rates at each altitude, as well as the average IR spectra of the planet. It follows closely in its structure the MODTRAN code (Berk et al. 1989), covering the spectral interval 1 to 20 000 cm^-1, with a resolution of 1 cm^-1, and for any atmospheric temperature. It includes ${\rm CO}_{2}$- ${\rm CO}_{2}$ collision-induced absorption when known (see Selsis 2000b, for a discussion). LWT also permits to reconstruct the thermal profile in radiative-convective equilibrium with a given chemical composition of the atmosphere. This temperature retrieval includes radiative and chemical heating (obtained from PHOEBE), long wavelength heating and cooling, convective adjustments. The resulting equilibrium is not a local equilibrium, as it couples all the layers in the atmosphere through Curtis matrices (see Coakley 1977). In order to calculate the photochemichal and thermal equilibrium one should use PHOEBE and LWT in an iterative process (see Sect. 5.1.2 and Fig. 4)

   
4.3 Validation of the codes

The PHOEBE code has been applied to the terrestrial and martian atmospheres in order to compare its results with observations and other models. Mean thermal and ozone terrestrial profiles are well reproduced with constant irradiation mode as shown in Fig. 1. In the upper atmosphere, above 70 km, the steady-state profiles computed with a constant irradiation, are quite different from the averaged observations that mix day and night profiles. PHOEBE was also used with a time-dependant irradiation; the results for this day/night mode are consistent with diurnal variations of mesospheric ozone (>50 km) as observed by a micro-wave instrument (Lezeaux 1999). The code reproduces well the behavior of ${\rm O}_{3}$ during the day, validating the modelling at altitudes up to about 90 km.

Simulations of the martian atmosphere, comparisons with observations and previous models have been described at length by Selsis (2000b). Some of these discussions are resumed in part 5.1.1.