see fred «'' Jeff, the 1C value for a forcing of 3.7 W / m ^ 2 (the canonical value for doubled CO2 based on radiative transfer equations and spectroscopic data) is derived by differentiating the Stefan - Boltzmann equation that equates flux (F) to a constant (sigma) x the fourth power of temperature. (judithcurry.com)
Mishchenko, M.I., 2002: Vector radiative transfer equation for arbitrarily shaped and arbitrarily oriented particles: A microphysical derivation from statistical electromagnetics. (pubs.giss.nasa.gov)
2.170) which is for blackbody radiation, they should be using the Microscopic Radiative Transfer Equation, which has terms for both spontaneous and stimulated emissions by greenhouse gases (Thomas and Stamnes [T&S], Eqn. (realclimate.org)