_The MAR model description comes from Section 2.1 from [Christoph Kittel's PhD thesis](https://orbi.uliege.be/handle/2268/258491), with some minor format changes. This is Section 2.1.3.2._
The radiative scheme is composed of two individual shortwave and infrared schemes as detailed in Morcrette (2002)[^1]. MAR uses the radiative scheme from the ECMWF ERA40 reanalyses Uppala et al. (2005)[^2].
The shortwave radiation scheme (Fouquart and Bonnel, 1980)[^3] has been updated by Morcrette (1993)[^4]. It solves the shortwave transfer equation by using a two-stream method that accounts for the scattering (due to clouds and aerosols) following a Delta-Eddington approximation (Joseph et al., 1976)[^5]. For each atmospheric layer, the transmission and reflectivity depends on 1) scatterings by molecules (Rayleigh scattering), aerosols, and clouds; 2) absorptions by gases, aerosols and clouds; 3) reflection by the surface (Morcrette, 2003)[^6]. Water vapour, uniformly-mixed gases ($CO_{2}, O_{2}$ in the original version and $CH_{4}, N_{2}O, CO$ as updated by Morcrette (1993)), and ozone (with a function of the effective zenith angle) are taken into account, as well as the temperature and the pressure. Following Morcrette (1993)[^4], the shortwave downwelling radiation (SWD) reaching the surface is particularly dependent on the aerosol concentration. Finally, the Fouquart and Bonnel's scheme determines the transmission and reflectivity for clear-sky and cloudy conditions separately assuming maximum-random cloud overlap. The scheme assumes that all cloud layers maximise their vertical overlap and that each cloud layer is treated independently (See Morcrette and Fouquart (1986)[^7] for the sensitivity of the radiative scheme to this assumption).
The shortwave radiation scheme (Fouquart and Bonnel, 1980)[^3] has been updated by Morcrette (1993)[^4]. It solves the shortwave transfer equation by using a two-stream method that accounts for the scattering (due to clouds and aerosols) following a Delta-Eddington approximation (Joseph et al., 1976)[^5]. For each atmospheric layer, the transmission and reflectivity depends on 1) scatterings by molecules (Rayleigh scattering), aerosols, and clouds; 2) absorptions by gases, aerosols and clouds; 3) reflection by the surface (Morcrette, 2003)[^6]. Water vapour, uniformly-mixed gases ($CO_{2}, O_{2}$ in the original version and $CH_{4}, N_{2}O, CO$ as updated by Morcrette (1993)[^4]), and ozone (with a function of the effective zenith angle) are taken into account, as well as the temperature and the pressure. Following Morcrette (1993)[^4], the shortwave downwelling radiation (SWD) reaching the surface is particularly dependent on the aerosol concentration. Finally, the Fouquart and Bonnel's scheme determines the transmission and reflectivity for clear-sky and cloudy conditions separately assuming maximum-random cloud overlap. The scheme assumes that all cloud layers maximise their vertical overlap and that each cloud layer is treated independently (See Morcrette and Fouquart (1986)[^7] for the sensitivity of the radiative scheme to this assumption).
For the longwave radiation scheme, MAR uses an improved version (Morcrette et al., 2003)[^6] of the Rapid Radiation Transfer Model (Mlawer et al., 1997)[^8] based on the correlated-k method. This method is an approximate technique that enables fast computations of radiative fluxes and cooling rates for nonhomogeneous atmospheres using limited approximations. The continuous infra-red spectrum is divided in several discrete bands. Each band corresponds to a small spectrum window where a limited number of gases (2 in this scheme) could strongly absorb the energy. The absorption due to these gases is modelled with a high precision, while the other gases (considered to be minor absorbers) are less rigorously taken into account. Represented species are water vapour, $CO_{2}, O_{3}, CH_{4}, N_{2}O$ and the main halocarbons (CFC-11, CFC-12, CFC-22, CCl-4) (Mlawer et al., 1997[^8]). Similarly to the shortwave scheme, the longwave scheme includes a maximum-random overlap assumption (Morcrette, 2002[^1]).
