Once in a while it is fun to go back through some of the realclimate.org posts just for a laugh

Once in a while it is fun to go back through some of the realclimate.org posts just for a laugh.  My favors are the Antarctic warming, not warming, warming posts when it is pretty obvious looking at the MODTRAN model of forcings that the Antarctic should be doing either nothing or cooling due to radiant physics.  It just took them a few years to figure out that any changes in the Antarctic are due to "waves" i.e. changes in ocean and atmospheric circulation.  Changes in atmospheric and oceans circulations on various time scales can be just a touch difficult to cipher, you could say they are somewhat chaotic.

Other than the extremely basic physics, there isn't much you can say one way or another and even the basic physics involve fairly large simplifications/assumptions.  "These calculations can be condensed into simplified fits to the data, such as the oft-used formula for CO2: RF = 5.35 ln(CO₂/CO₂_orig) (see Table 6.2 in IPCC TAR for the others). The logarithmic form comes from the fact that some particular lines are already saturated and that the increase in forcing depends on the ‘wings’ (see this post for more details). Forcings for lower concentration gases (such as CFCs) are linear in concentration. The calculations in Myhre et al use representative profiles for different latitudes, but different assumptions about clouds, their properties and the spatial heterogeneity mean that the global mean forcing is uncertain by about 10%. Thus the RF for a doubling of CO₂ is likely 3.7±0.4 W/m2 – the same order of magnitude as an increase of solar forcing by 2%."

That whole paragraph is a clickable link to a 2007 post at RC.  The constant 5.35 is a curve fit to available data which tries to "fit" surface temperature forcing to that elusive Effective Radiant Layer (ERL) forcing and assumes a perfect black body response by both so that the temperature of one is directly related to the other.  For absolutely childlike simplification, there is nothing wrong with this but I believe we have moved beyond that stage finally, hopefully.

Note in the quoted paragraph the "uncertain by about 10%" fairy tale.  30% skewed high is a better guess and that assumes that the "surface" is actually some relevant surface on this particular planet.  Thanks to the hiatus that sometimes does and sometimes doesn't exist, someone finally noticed that the "surface" used in climate models doesn't match the "surface" being modeled for global mean surface temperature anomaly which doesn't have any agreed upon temperature for there to be an ideal black body heat emission from, to interact with the elusive ERL.   Since another crew actually spent nearly ten years measuring CO2 forcing only to find it to be considerably less than the iconic 5.35 etc.by about 27 percent, I would expect just a bit more "back to basics" work so that the typical made for kindergarten simplifications provided to the masses reflect the huge expansion of collective climate knowledge.  Instead you have Bill Nye, the not so up to date science guy, peddling the same old same old though I have to admit even he is getting some heat from the "causers".

Try to remember that the highest range of impact assumed a 3 times amplification of the basic CO2 enhancement and when you find that the CO2 enhancement is about 30% less than expected, the amplification would also be considerably less, "all else remaining equal."

That RC post also uses the disc in space input power simplification which ignores the physical properties of the water portion (about 65% of the globe if you allow for critical angles) of the "surface" which requires a bit more specific estimate of "average" power.  Once again, a fine "simplification" for the K-9 set, but not up to snuff for serious discussion.  That issue has one paper so far but will have a few more.