Assume at some location clear sky OLR at TOA is 270 w/sq m assuming earth surface emissivity is one. Then say emissivity is 0.92. Then there will be scattering and reflection and some of the reflection will escape. Therefore what escapes is > 0.92 x 270 w/sqm. Say fraction of 270 w/sq m observed is Fr = 0.97 (It should be between 0.92 and one).
(a) Is there a name for Fr?
(b) Is there a "best" value for Fr averaged over earth's surface?
I can answer my own question I.M.O.
Consider the publications by Feldman, et al http://www.pnas.org/content/111/46/16297.full.pdf
and by D.L. Seidel
http://eu.wiley.com/legacy/wileychi/egec/pdf/GB085-W.PDF
From these references if the average precipitable water vapor of the earth is present in the atmosphere, the specularly reflected thermal IR cannot reach the top of the atmosphere (TOA). Therefore,one can assume that if the emissivity on average is, say, 0.95 then the fraction of the incoming IR from the earth's atmosphere that is emitted from the earth's surface is also 0.95 and one does not have to worry about the fact that some of that incoming IR is reflected, as far as observations at the TOA are concerned.
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