For inversion purposes in remote sensing applications, it is very useful to dispose of a simple, but nevertheless accurate enough, procedure for calculating brightness temperatures as received by space-borne radiometers when observing the Earth surface through the atmosphere. Starting from an idea of Grody, a contracted form of the radiative transfer equation is proposed. It has the form of the equation for an attenuating atmosphere at constant temperature, above a lossy dielectric rough surface, under the specular approximation. However, it includes corrections for the atmospheric temperature profile and for the surface diffuse scattering. This last correction is an extension of that first proposed by Wentz. The resulting form of the equation and the importance of the correction terms are discussed for the practical case of the ocean surface. This equation has been used by the authors for the retrieval of geophysical parameters of the ocean surface and of the atmosphere from combined radiometric and radar measurements. ¿ American Geophysical Union 1994