That is, ${\displaystyle \gamma }$ represents how likely a surface is to absorb some radiation that tries to pass through it; reflected energy never makes this attempt, and so does not matter here. This behavior is intuitive if we think, to begin, about the surface of the planet: while it has a non-negligible albedo (it reflects some radiation), it is effectively opaque. The planet's surface does reflect some energy outright, but virtually all of the energy it doesn't reflect is absorbed. Very little E/M radiation simply passes through the surface of the planet. We can thus set ${\displaystyle \gamma _{s}=1}$. We are interested in solving for ${\displaystyle \gamma _{a}}$—we're interested in figuring out just how opaque the atmosphere is. From all of this, we can deduce another equation: one for the energy emitted by the atmosphere (${\displaystyle F_{a}}$).
 ${\displaystyle F_{a}=\gamma _{a}\sigma T_{a}^{4}}$ (4e)
We have to include ${\displaystyle \gamma }$ in this equation, as (recall) the atmosphere is transparent (or nearly so) only with respect to incoming solar radiation. Radiation emitted both by the surface and by the atmosphere itself has a chance of being reabsorbed.
 ${\displaystyle {\tfrac {S_{o}(1-\sigma )}{4}}+\gamma _{a}\sigma T_{a}^{4}=\gamma _{s}\sigma T_{s}^{4}}$ (4f)