At the earth's surface, long-wave radiation received from the atmosphere in the absence of cloud may be expressed as the sum of the flux density from an isotropic source and the flux density due to anisotropy of atmospheric radiation. Separation of these components facilitates calculations of the radiative flux received by obstructed horizontal surfaces (near walls or in valleys), by sloping planes, by solid cylinders, and by spheres and prisms. Radiation received from adjacent surfaces is also considered.

As the angular distribution of radiation is the same for overcast skies as for clear skies, the relationships for clear skies may be extended to derive climatological mean values for the long-wave irradiances of slopes, solids, etc.