Work out how that change is modified by distance (radiative power varies with
the fourth power of temperature and energy density does down with the second power of distance.
The fact is the atmosphere emits energy (EM radiation) in proportion to
the fourth power of its temperature.
The point was to show that there was little difference between using a linear function for modeling thermal emission and a function which varies as
the fourth power of the temperature.
The actual radiative heat transfer is, ideally, proportional to
the fourth power of the temperature, and the analysis must be based on this.
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.