I think you have to give an example of an experiment that would be necessary or would even work. I don't buy the idea that you can just sit a sensor somewhere in the atmosphere and determine what the warming effect would be of doubling co2.
Data for the transmission of IR in the atmosphere in different layers has comprehensively been collected for other reasons
http://cfa-www.harvard.edu/hitran/
That should be enough to model the absorption and emission of radiation in the atmosphere
HITRAN, in which serious errors were found and corrected just recently.
(Were studies done using HITRAN prior to 2005 corrected and restated with the new data? Not that I am aware of).
In the apparent lack of adequate atmospheric experiments, here is one format.
Keep in mind, as DR has pointed out, that atmospheric CO2 concentration varies considerably - in one location, over the course of a year - downwind of a major urban environment - in a year with El Nino or without.
Moreover, numerous environments hold low or negligible quantities of water vapor.
Therefore, it seems possible to look directly at various concentrations of CO2 in the air and what their effects are, instead of taking refuge in highly questionable computer modeling.
A balloon (or series of them) is launched with instrumentation to measure IR spectral emission, temperature, CO2 concentration and the like. The supposed effects of CO2 enhancing the "greenhouse effect" are at higher tropospheric altitudes.
On top of the balloon is placed a circular "fence", made perhaps of simple bubble plastic with aluminized mylar on the outer side.
Air above the balloon is now largely sheltered from IR radiation from the earth. Air on sides and below the balloon is affected by IR radiation. The hypothesis to be tested might be "there is no measurable difference in temperature of the samples of air protected from Earth's IR as compared to samples exposed to Earth's IR.
Of course "temperature" would imply that the CO2 absorbed IR and it became kinetic energy and was imparted to other air molecules in the vicinity. There is more arm waving in theory of CO2 greenhouse effects than that, some has to do with "re emission" by CO2 of photons.
Make no mistake about it, the physics gets very complex and the modeling by computers is unable to handle adequately exactly what CO2 does in the air, with other gases around it.