Back Radiation and Thermodynamics
The following picture is from Kiehl and Trenberth 
The above figure shows ‘back-radiation’ of 324 W/m2. The value ~324 W/m2 would seem implausible as it is comparable in magnitude to the radiance from the sun! If it exists why cant it be used as an energy source.
If the atmosphere radiates 324 W/m2 downward it must radiate the same upward. But the Earth only receives 235 W/m2 nett radiation from the Sun (342 W/m2 – 107 W/m2 reflected).
This back-radiation is impossible – it defies the first law of thermodynamics – energy must be conserved – there can not be more energy leaving a body than what is coming in (when in equilibrium).
If this figure was true it would mean more energy is radiated from the Earth then it receives.
“Backradiation” is the heat flowing from the cold atmosphere to the warm Earth – this also defies the Second Law of Thermodynamics. Some will say that as long as the nett flow is from cold to hot all is OK. However the figure shows a flow of 324 W/m2 from cold to hot. This is purely imaginary. What the value indicates is the heat that would flow from the atmosphere to a body at a temperature of zero K (-273 deg C) if the atmosphere was a blackbody (emissivity = 1). The atmoshere is not a ‘blackbody’ and the Earth is not at zero K!
Similarly, the 350 W/m2 upward heat flow is the theoretical radiation from a blackbody at the temperature of the Earth’s surface to a body at zero K.
There is no evidence that ‘back-radiation’ exists – it has ever been detected or measured.
This is an obvious error – how did this get past the peer review process. Why is this figure still being used to explain the Earths energy balance without questioning. Why are we spending vast amounts of money solving a problem based on this flawed hypothesis?
This is basic physics. It is in error.
How much heat is lost from the Earth’s Surface by Radiation?
By subtracting this ‘backradiation’ value (324 W/m2) from the upward radiance (390 W/m2) gives a nett surface irradiance of 66 W/m2 upward. This is less then the convective heat loss from the surface of the Earth (102 W/m2).
- The Energy budget of Kiehl and Trenberth violates the laws of thermodynamics.
- The Earths surface loses more heat from convection (102 W/m2) then by radiation (66 W/m2)
 Kiehl, J. T., K. E. Trenberth, 1997: Earth’s Annual Global Mean Energy Budget. Bull. Amer. Meteor. Soc., 78, 197-208