[dr_lew]

The amount of geometric dilution you're talking about would occur if the solid angle at the earth was such that the energy entered the atmosphere through a pinhole of ~.0001 steradians. It doesn't.

The pinhole is namely the disk of the sun in the sky. The solar radiation falls uniformly across the disk of the earth, but is always confined to a direction emanating from the disk of the sun. "Trust me I know what I'm doing." - Sledge Hammer

[FredZarguna]

The solar radiation falls uniformly across the disk of the earth. And is emitted over the whole surface. Hence, the factor is 2.

The dilution factor you're talking about from the sun's perspective is already accounted for in the delta-S of the absorption calculation.