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The relaxation method for the inverse solution of the radiative transfer equation is applied in a dual frequency scheme for the determination of complete vertical temperature profiles in cloudy atmospheres from radiance observations alone, without any additional information related to the expected solutions. The dual-frequency principle employs to advantage a property in the Planck function of the dependence of intensity on frequency. This property leads to the formulation of a new convergence criterion for the selection of cloud-sounding frequencies to be used for reconstructing the clear column radiance from observations made in the presence of a broken cloud layer in all fields of view. The principle is applied to the case of observations in two adjacent or partially overlapping fields of view and to the case of observations in a single field of view. The solutions are illustrated by numerical examples in the dual-frequency ranges of the 4.3 and 15 µm CO2 bands of the terrestrial atmosphere. The resulting profiles can possess the same degree of vertical resolution permitted under cloudless conditions.
Moustafa T. Chahine (Tue,) studied this question.