Those that have followed my ramblings know that this is one of my more fun "discoveries". It is a simple "bookkeeping" error, not something that involves higher level math to "prove", just one of those things where you should be able to say check your numbers again and everyone agrees and redoes the basics. Climate Science doesn't work that way. The ability to add is not a requirement for a career in climate science. To get these Prima Donnas to admit an error is like pulling teeth. You have to have a "peer reviewed" paper on the potential discrepancy that may lead to a minor over estimation of potential impact and that paper has to run the gauntlet of good old boys defending climate science. You get fired or belittled if you mention such controversial things as math errors and are limited to controversial journals like E&E which are controversial because the climate science cadre say so.
So aside from the Kimoto error in the paper and where the paper is published, is there anything to learn from this situation? Pooh pooh occurs or no one is infallible.
If you want to double check, you can use the cloud base as your "surface". Energy in still has to equal energy out and the lower the specific heat capacity of the "surface" the less you have to be concerned with lags or delays.
Energy in day equals energy out. There is a limit to the "precision" of course, but +/-17 Wm-2 for a whole planet is not bad and the All-Sky atmospheric window in the red box is still the number to watch, not 40 Wm-2 with no true indication of error provided in the K&T energy budgets. Face it if your numbers are off by 50% on the most crucial part of the budget, it is pretty much useless. At the Top of the Atmosphere (TOA) were no one lives, accuracy is nice, but who lives at the TOA?
With cloud impact being the single highest source of uncertainty, how can the cadre ignore such a major error? It all depends on the cumulative assumptions made. This is where things get extremely messy.
The first assumption is equilibrium. Earth is at best a quasi-steady state system, there is diurnal temperature range, seasonal temperature range, decadal temperature range, pick any time frame and there is some "average" temperature range. To make life simpler, the TOA, where ever that is actually defined to be, has an equilibrium requirement, Ein=Eout based on an "average" Ein of ~1361Wm-2 which varies by a little over 3 percent between winter and summer. While that is varying, the surface albedo varies seasonally and cloud albedo varies seasonally. With all this constant variation, what is "normal" or "average" is highly debatable. The one thing that remained constant in the K&T energy budget is the 40Wm-2 window energy. It is an assumption required to estimate an "equilibrium". It just happened to be a poor assumption.
So let's compare the impact of that assumption using Kimoto's equation,
OLR(K&T97)=390 + 78 + 24 + 67 - 325 = 235
OLR(Stephens)=398 + 88 + 24 + 75 - 345 = 240
From 1997 to 2012 the estimated Ein and Eout at equilibrium increased by ~ 5Wm-2, surface energy increased by 8 Wm-2, evaporation increased by 10 Wm-2, thermals/sensible stayed the same, atmospheric solar absorption increased by 8 Wm-2 and "Back Radiation" increased by 20 Wm-2. Stephens et al. specifically point out the K&T error, Kimoto's paper was published prior to Stephens et al so Dr. Kimoto's paper is irrelevant due to bad input, garbage in garbage out. Has nothing to do with the journal.
If you like, you can revise the Kimoto calculations with more current data and find that it results in a "Planck Response" of 7.05Wm-2/K, about the same value determined in the Ramathan et al. 1981 study cited in the Kimoto paper.
A 7.05 Wm-2/K Planck response would indicate that a 3.7Wm-2 CO2 equivalent forcing would produce ~0.52C of "surface" warming. This is somewhat confusing because of the latent and sensible "surface" cooling that is included in the calculation. That "surface" cooling is transferred to the atmosphere where it improves the atmospheric "insulation" efficiency which would in turn increase the surface radiant energy absorbed which K&T assume is "constant". Now Kimoto's equation has difficulties that are a little more involved.
Now how to deal with the difference in "back radiation"? Assuming half of the total impact of 7.05 Wm-2/K is "back radiation" related, adding 4Wm-2 of energy at the surface would produce 6Wm-2 of total forcing, 6/7.05=0.85 degrees impact for Wm-2 of forcing. You could assume all surface impact is reflected resulting in 8/7.05=1.13 degrees impact for 4Wm-2 of forcing. Then comparing the Stephens et al OLR and "back radiation" you have (398+88+24)/345= 510/345=1.488 implying that adding 4Wm-2 of "back radiation" would produce 5.91Wm-2 of surface forcing or approximately 1.06 degrees of warming with no increase in latent and convective cooling. Some portion of the latent and convective cooling transferred to the atmosphere would be returned to the surface, but with only a 20Wm-2 window down and a 40 Wm-2 window up, it would be less than 50 percent.
I will leave a more rigorous dissection to others, but the cascade of errors tend to always result in higher than observed climate "Sensitivity" while a little more attention to detail indicates a lower than observed "sensitivity" or in other words, more longer term natural variability than most are willing to admit given the over estimations.
I may come back to clean this up a bit, but as is it may inspire some to take a new look at Kimoto, K. 2009.