Shadowing by vegetation, landforms, or clouds can reduce the surface temperature relative to unshadowed portions of the same land area. This shading effect can cause azimuthal variation of the outgoing infrared radiance that is currently not taken into account in remote sensing and Earth radiation budget analyses. In this paper, multiangle longwave (LW) (5--200 ¿m) and window (WN) (8--12 ¿m) radiances taken by the Clouds and the Earth's Radiant Energy System (CERES) rotating azimuth plane scanner on the Tropical Rainfall Measuring Mission (TRMM) and Terra satellites are used to determine the azimuthal anisotropy of LW and WN fields over all solar zenith angles and surface types in clear and cloudy conditions. The azimuthal component of the anisotropy is isolated by constructing limb-darkening models for each category of surface type and topography in each solar zenith angle (SZA) bin. The viewing zenith angle dependence of WN and LW radiances in clear scenes depends on the SZA, possibly because of changes in the boundary layer temperature structure during the day. The observed mean radiances, in general, are greater when viewing the sunlit hemisphere (backscattering) than when viewing the shaded (forward scattering) hemisphere. This forward-back contrast increases with increasing terrain roughness and is stronger for surfaces with open vegetation such as shrubs and grass than for contiguous vegetation like forests. The anisotropy is less well defined for barren deserts. Maximum anisotropy occurs for SZAs between 48¿ and 70¿. This paper provides the first evidence that clouds also induce longwave azimuthal anisotropy. Strong forward-back radiance contrast is evident for partly, mostly, and overcast scenes for SZA < 48¿. The contrast disappears for overcast scenes and decreases for partly and mostly cloudy scenes at higher SZAs. The TRMM sampling is limited and causes some biases at particular angle sets but overall provides a reasonable depiction of the anisotropy at all SZAs. Terra yields a more accurate anisotropy characterization but only for SZAs between 48¿ and 70¿. A simple model constructed from the TRMM results for clear scenes reduces clear-sky temperature prediction RMS errors by 38% or more while minimizing the biases associated with azimuthal anisotropy. The model should yield similar or better reductions in the errors associated with retrievals of skin temperature or LW fluxes, especially those from geostationary satellites. In addition, future analyses of combined TRMM, Terra, and Aqua CERES data will likely provide more accurate correction models that could further reduce errors in surface skin temperature and radiative flux for both clear and cloudy scenes.