A Gray Atmosphere is the term for a model of an Atmosphere regarding its Opacity that ignores the differences in opacity at different Wavelengths. It is a simplification used when incorporating opacity in more complex models (e.g., Stellar Structure) in order to keep the entire model from becoming unwieldy. Typically it uses a determination of the Rosseland Mean Opacity.
Rosseland Mean Opacity
Equation of Radiative Transfer (RTE)