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Detection of clouds and retrieval of their properties (top and bottom altitude, optical thickness) with satellite-based spectrometers needs the solution of radiative transfer in the atmosphere. Depending on the application needed for and instrument capabilities, a trade-off choice has to be made between accuracy and speed. This study aims to char-acterise the range of applicability of analytical asymptotic equations to real scenarios. It has been found that the errors, introduced withfatcat:mq7kv4xsufatzljld2a533ppga