The MAMA Algorithm for Fast Computations of Upwelling Far- and Mid-Infrared Radiances in the Presence of Clouds

Abstract

A methodology for the computation of spectrally resolved upwelling radiances in the presence of atmospheric diffusive layers is presented. The algorithm, called MAMA (Martinazzo–Maestri), provides fast simulations over the whole longwave spectrum, with high accuracy, particularly for optically thin scattering layers like cirrus clouds. The solution is obtained through a simplification of the multiple-scattering term in the general equation of the radiative transfer in a plane-parallel assumption. The scattering contribution is interpreted as a linear combination of the mean ambient radiances involved in the forward and back-scatter processes, which are multiplied by factors derived from the diffusive features of the layer. For this purpose, a fundamental property of the layer is introduced, named the angular back-scattering coefficient, which describes the fraction of radiation coming from a hemisphere and back-scattered into a specific direction (the observer in our case). This property, easily derived from the phase function of the particle size distribution, can be calculated from any generic single-scattering properties database, which allows for simple upgrades of the reference optical properties within the code. The paper discusses the solutions for mean upward and downward ambient radiances and their use in the simplification of the general radiative transfer equation for thermal infrared. To assess the algorithm performance, the results obtained with the MAMA code are compared with those derived with a discrete ordinate-based radiative transfer model for a large range of physical and optical properties of ice and liquid water clouds and for multiple atmospheric conditions. It is demonstrated that, for liquid water clouds, the MAMA code accuracy is mostly within 0.4 mW/(m2cm−1sr) with respect to the reference code both at far- and mid-infrared wavelengths. Ice cloud spectra are also accurately simulated at mid-infrared for all realistic cloud cases, which makes the MAMA code suitable for the analysis of any spectral measurements of current satellite infrared sounders. At far infrared, the MAMA accuracy is excellent when ice clouds with an optical depth of less than 2 are considered, which is particularly valuable since cirrus clouds are one of the main targets of the future mission FORUM (Far-infrared Outgoing Radiation Understanding and Monitoring) of the European Space Agency. In summary, the MAMA method allows computations of cloudy sky high-resolution radiances over the full longwave spectrum (4–100 μm) in less than a second (for pre-computed gas optical depths and on a standard personal computer). The algorithm exploits the fundamental properties of the scattering layers, and the code can be easily updated in relation to new scattering properties.