Let us say that the atmosphere blocks all visible light wavelengths and allows only IR wavelengths to reach the earth. The Earth would then be a source of thermal radiation. To calculate the heat emitted by the earth, I would need the value of ε.
The energy emitted by a body in watts/m2 is = εσT4. In the case of a perfect black body, ε=1. If the body only emits IR light, what should be the value of ε?