_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).
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]).
Both improved shortwave and longwave radiation schemes represent the interactions (absorption, attenuation, scattering, and reflection) between hydrometeors computed by the cloud-microphysical scheme and radiations. The radiative scheme uses $q_{i}, q_{w}$, and $q_{v}$ concentrations from each atmospheric layer to determine the cloud optical properties. The latests depend on the region of the solar spectrum and on the particle phase contained in the cloud. Since properties of mixed phase clouds (containing both liquid and ice particles) are the summed contribution of both phases (Morcrette, 1993[^4]), the two next paragraphs will describe the individual contribution of ice and water particles on shortwave and longwave cloud optical properties.
For shortwave radiations, the scheme uses the microphysical properties defined by Slingo (1989)[^9] for water clouds and by Fu (1996)[^10] for ice clouds. Slingo's parameterisation links water cloud properties with the cloud liquid water path (vertically-integrated water content between the cloud base and top) and equivalent droplet-radius size distribution neglecting the effect of water vapour. In the same way, the shortwave optical properties for ice clouds are defined on the ice water content and the generalised effective size that represents the ice-crystal size distribution. In a few words, smaller ice particles have a higher radiative effect resulting notably in more scattering and absorption than larger ice particles (Morcrette, 1993[^4]).
Similarly, the water cloud properties for longwave is a function of the liquid water content vertically-integrated over the layer (liquid water path) and the effective radius based on the droplet size distribution as described by Lindner and Li (2000)[^11]. This parameterisation neglects scattering interactions which makes absorption the dominant processes for longwave radiation. Optical properties for ice particles in the longwave spectrum are functions of the cloud ice water content and generalised effective size that accounts for different ice crystal distributions (Fu et al., 1998[^12]). Furthermore, the radiative scheme used by MAR also enables the use of different parameterisations to compute the cloud optical properties. Morcrette (2002)[^1] suggested a relatively low effect on longwave but a higher effect (up to 10 W m$^{-2}$) on the shortwave in cloudy conditions.
The radiative transfer relies on the effective radius which is a factor describing the distributions of the mass and volume of the particles. The ice effective radius is computed using Sun and Rikus (1999)[^13] parametrization and is a function of the ice-water content and cloud temperature. It has been adapted to Antarctic conditions using a value of $15 \mu m$ as the minimum diameter for ice particles (Walden et al., 2003[^14]). The liquid effective radius is a linear function of the liquid water content and the droplet water concentration contained in the cloud depending on the continental or oceanic origin of the air masses (Martin et al., 1994[^15]) which in MAR is simply depending on the land-sea mask.
As highlighted above, radiative cloud properties do not directly depend on $q_{s}$ concentration. The $q_{s}$ concentration is implicitly taken into account by being partially included in the $q_{i}$ concentration from each layer treated by the radiative scheme. The contribution of $q_{s}$ is expressed as an additional mass for $q_{i}$ by assuming that the total ratio of $q_{s}$ and $q_{i}$ is similar to the ratio of effective radii, i.e only $30 \%$ of $q_{s}$ is added in $q_{i}$ seen by the radiative scheme (Gallée and Gorodetskaya, 2010[^16]). The effect of rain droplets on radiations is neglected. This assumption is reasonable knowing that the fall velocity of rain droplets used in MAR (Emde and Kahlig, 1989[^17]) induces that most of them reach the surface within one time-step of the radiative scheme.
Gas concentration are provided by historical concentration, in particular the MAR radiative scheme uses the Fortuin and Langematz (1995)'s ozone climatology[^18]. Future concentration are specified by the selected emission pathway, i.e the Representative Concentration Pathway (RCP) (Moss et al., 2010[^19]) used for the latest IPCC report or the more recent Shared Socioeconomic Pathways (ssp) (O'Neill et al., 2016[^20]) that represents future emissions for different socio-economic trajectories. Note that while the cloud mycrophisical scheme uses a constant aerosol value (Meyers et al., 1992[^21]), the aerosols inputs of the radiative scheme are time-varying loads based on a monthly climatology of tropospheric aerosols (soil dust, sulfate, sea salt, black carbon, and organic) defined by Tegen et al. (1997[^22]) and daily volcanic aerosols from the Goddard Institute for Space Studies. Only the present observed aerosol-radiation interactions till 2002 are taken into account in MAR since cloud-aerosols interactions are neglected (Wyard et al., 2018[^23]).
[^1]:Morcrette, J.-J.: The Surface Downward Longwave Radiation in the ECMWF Forecast System, Journal of Climate, 15, 1875-1892, 2002.
[^2]:Uppala, S. M., Källberg, P., Simmons, A., Andrae, U., Bechtold, V. D. C., Fiorino, M., Gibson, J., Haseler, J., Hernandez, A., Kelly, G., Li, X., Onogo, K., Saarinen, S., Sokka, N., Allan, R. P., Andersson, E., Arpe, K., Balmaseda, M. A., Beljaars, A. C. M., Berg, L. V. D., Bidlot, J., Bormann, N., Caires, S., Chevallier, F., Dethof, A., Dragosavac, M., Fisher, M., Fuentes, M., Hagemann, S., Hólm, E., Hoskins, B. J., Isaksen, L., Janssen, P. A., Jenne, R., Mcnally, A. P., Mahfouf, J. F., Morcrette, J.-J., Rayner, N. A., Saunders, R. W., Simon, P., Sterl, A., Trenberth, K. E., Untch, A., Vasiljevic, D., Viterbo, P., and Woolen, J.: The ERA-40 re-analysis, Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, applied meteorology and physical oceanography, 131, 2961-3012, 2005.
[^3]:Fouquart, Y. and Bonnel, B.: Computations of solar heating of the earth's atmosphere: A new parameterization, Beitr. Phys. Atmos., 53, 35-62, 1980.
[^4]:Morcrette, J.: Revision of the clear-sky and cloud radiative properties in the ECMWF model, ECMWF newsletter, 61, 3-14, 1993.
[^5]:Joseph, J. H., Wiscombe, W., and Weinman, J.: The delta-Eddington approximation for radiative flux transfer, Journal of the Atmospheric Sciences, 33, 2452-2459, 1976.
[^6]:Morcrette, J.-J.: Ozone-radiation interactions in the ECMWF forecast system, Tech. Rep. Technical Memorandum No 375, European Centre for Medium-Range Weather Forecasts, 2003.
[^7]:Morcrette, J.-J. and Fouquart, Y.: The overlapping of cloud layers in shortwave radiation parameterizations, Journal of the atmospheric sciences, 43, 321-328, 1986.
[^8]:Mlawer, E. J., Taubman, S. J., Brown, P. D., Iacono, M. J., and Clough, S. A.: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave, Journal of Geophysical Research: Atmospheres, 102, 16663-16682, 1997.
[^9]:Slingo, A.: A GCM parameterization for the shortwave radiative properties of water clouds, Journal of the Atmospheric Sciences, 46, 1419-1427, 1989.
[^10]:Fu, Q.: An accurate parameterization of the solar radiative properties of cirrus clouds for climate models, Journal of Climate, 9, 2058-2082, 1996.
[^11]:Lindner, T. and Li, J.: Parameterization of the optical properties for water clouds in the infrared, Journal of Climate, 13, 1797-1805, 2000.
[^12]:Fu, Q., Yang, P., and Sun, W.: An accurate parameterization of the infrared radiative properties of cirrus clouds for climate models, Journal of climate, 11, 2223-2237, 1998.
[^13]:Sun, Z. and Rikus, L.: Parametrization of effective sizes of cirrus-cloud particles and its verification against observations, Quarterly Journal of the Royal Meteorological Society, 125, 3037-3055, 1999.
[^14]:Walden, V. P., Warren, S. G., and Tuttle, E.: Atmospheric ice crystals over the Antarctic Plateau in winter, Journal of Applied Meteorology, 42, 1391-1405, 2003.
[^15]:Martin, G., Johnson, D., and Spice, A.: The measurement and parameterization of effective radius of droplets in warm stratocumulus clouds, Journal of the Atmospheric Sciences, 51, 1823-1842, 1994.
[^16]:Gallée, H. and Gorodetskaya, I. V.: Validation of a limited area model over Dome C, Antarctic Plateau, during winter, Climate dynamics, 34, 61, 2010.
[^17]:Emde, K. D. and Kahlig, P.: Comparison of the observed 19th July 1981, Montana thunderstorm with results of a one-dimensional cloud model using Kessler parameterized microphysics, in: Annales geophysicae. Atmospheres, hydrospheres and space sciences, vol. 7, pp. 405-414, 1989.
[^18]:Fortuin, J. P. and Langematz, U.: Update on the global ozone climatology and on concurrent ozone and temperature trends, in: Atmospheric Sensing and Modelling, vol. 2311, pp. 207-216, International Society for Optics and Photonics, 1995.
[^19]:Moss, R. H., Edmonds, J. A., Hibbard, K. A., Manning, M. R., Rose, S. K., Van Vuuren, D. P., Carter, T. R., Emori, S., Kainuma, M., Kram, T., Meehl, G. A., Mitchell, J. F. B., Nakicenovic, N., Riahi, K., Smith, S. J., Stouffer, R. J., Thomson, A. M., Weyant, J., and Wilbanks, T. J.: The next generation of scenarios for climate change research and assessment, Nature, 463, 747-756, 2010.
[^20]:O’Neill, B. C., Tebaldi, C., van Vuuren, D., Eyring, V., Friedlingstein, P., Hurtt, G., Knutti, R., Kriegler, E., Lamarque, J.-F., Lowe, J., et al.: The Scenario Model Intercomparison Project (ScenarioMIP) for CMIP6, Geoscientific Model Development, 9, 3461-3482, 2016.
[^21]:Meyers, M. P., DeMott, P. J., and Cotton, W. R.: New primary ice-nucleation parameterizations in an explicit cloud model, Journal of Applied Meteorology, 31, 708-721, 1992.
[^22]:Tegen, I., Hollrig, P., Chin, M., Fung, I., Jacob, D., and Penner, J.: Contribution of different aerosol species to the global aerosol extinction optical thickness: Estimates from model results, Journal of Geophysical Research: Atmospheres, 102, 23895-23915, 1997.
[^23]:Wyard, C., Doutreloup, S., Belleflamme, A., Wild, M., and Fettweis, X.: Global radiative flux and cloudiness variability for the Period 1959-2010 in Belgium: a comparison between reanalyses and the regional climate model MAR, Atmosphere, 9, 262, 2018.
