The two-stream δ-Eddington approximation to simulate the far infrared Earth spectrum for the simultaneous atmospheric and cloud retrieval

•Introduction of a two-stream δ-Eddington approximation algorithm to simulate the Far InfraRed Earth spectrum.•Study of SACR accuracy by means of the comparison with LBLDIS (LBLRTM+DISORT) code.•Performance of the simultaneous retrieval of atmospheric and cloud parameters by using SACR algorithm. Far- to mid- infrared spectral radiances measured either from high altitude platforms or from ground can be processed to retrieve atmospheric vertical profiles and cloud parameters, variables particularly relevant in climate change studies. The retrieval requires a forward model with the capability of simulating the multiple scattering from cloud particles. The Discrete Ordinate Radiative Transfer (DISORT) offers this possibility, however, accurate simulations can be obtained only with a huge computational load. We developed a forward / retrieval model based on the two-streams δ-Eddington approximation, allowing much faster computations, while retaining good accuracy. The code, named SACR (Simultaneous Atmospheric and Clouds Retrieval), allows to retrieve simultaneously temperature and gas profiles, cloud micro-physical and geometrical parameters and surface temperature from vertical sounding observations. We illustrate the equations implemented in the SACR code, prove the self-consistency of the inversion and assess its forward model accuracy with a focus on the range from 200 to 1000 cm−1. The assessment is made by comparing the simulated spectral radiances to those computed by LBLDIS, a very accurate model integrating LBLRTM (Line By Line Radiative Transfer Model) and DISORT. For cloud particle sizes between 20 and 100 µm and optical depths between 0.1 and 10, our model shows biases smaller than 0.4 mW/(m2 sr cm−1) in upwelling radiance simulations, and biases smaller than 0.3 mW/(m2 sr cm−1) in downwelling radiance simulations. Depending on the spectral grid and on the number of atmospheric layers used, the SACR code is from 5 to 8 times faster than LBLDIS.