Can 'Backradiation' warm its own source? Ok, although this question arises out of the global warming debate, this is a question purely for physicists and not intended to branch into that particular debate.
We are told that LWIR from the Earth to the atmosphere is absorbed by greenhouse gasses and then re-radiated (in the form of backradiation) partially to the surface of the planet, "...thus warming the surface...". 
My specific question is this:
How exactly can the re-radiated LWIR from a cooler atmosphere warm the original source of its absorbed energy?  
Edit:  I am editing this question as several people have stated this is a duplicate question.  I disagree.  The other question quoted three alternatives and some answers stated the 2nd Law of Thermodynamics was not compromised.  Please re-read my question:  can the backradiated energy possibly warm a surface which was the original source of that energy?  In other words, how can the surface heat itself further when there is no other energy source?  I hope this clarifies, and thanks to all that have answered.
 A: Firstly, not all parts of the atmosphere are cooler than the surface.  For example, the Thermosphere can be much hotter than Earth's surface.
More importantly, even for a cooler region of the atmosphere, yes some thermal radiation emitted from a cooler region is absorbed by a warmer region, it is just that more radition goes from warmer to cooler than cooler to warmer.
For example see this Earth-Atmosphere Energy Balance.  For every 98 units of energy the atmosphere emits to the Earth's surface, the Earth emits 104 units to the atmosphere (not including direct emission through the atmosphere to outer space and non-radiative transfer of heat to the atmosphere).     
A: Back radiation is not a good physics term. When one has many different bodies at different temperatures, they each radiate according to the black body formula for their type and temperature. In a thermally isolated   system  ( within a dewar for example) they will come to the same temperature in the end. 
The earth is not a closed system, and finally the black body radiation at the boundaries with space will escape. If it were not for the replenishment of energy by the radiation from the sun the earth would come at thermal equilibrium at the temperature of the space around it. ( well, forgetting the magma heat)
The presence in the atmosphere of so called ( bad terminology again) "green house gases" and some types of clouds, just delay the loss of radiation by reflecting  some of it back . The same effect as when one covers a hot water bottle  with a woolen cover: the woolen cover reflects a bit of the infrared heat it receives and delays the cooling of the bottle, even though it is cooler than the water in the bottle. The exact physical process of reflection depends on the material, in the case of gases it happens with absorption and re-radiation.
So in a sense, it is not heating, but delayed cooling that is the phenomenon.
