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.

This is the error. Stephen's et al. produced a revised Earth Energy Budget with more realistic ranges of error and included more surface atmosphere interaction than the simplistic K&T97 budget used by Kimoto. For example surface evaporation is closer to 88Wm-2, atmospheric absorption is closer to 75 Wm-2 and "back radiation is closer to 335 to 345 Wm-2. The "back radiation" value is higher because water and ice in the atmosphere and clouds absorb close to 20Wm-2 which is directly added to the "back radiation" . Simply the "Greenhouse Effect" is about 20Wm-2 closer to saturation than previously estimated at the true surface of the Earth. K&T Budgets have gone through a number of revisions, but that ~20Wm-2 error has never been corrected so the Planck response is still over estimated by about 50%. A simple way of determining the approximate Planck response is just by comparing the more accurate "back radiation" value of ~340 Wm-2. 340Wm-2 is effective energy of a surface at 4C (277K) which would be the approximate average surface temperature of an "ideal" black body with the current "average" solar energy provided.

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.

This is an example of using an atmospheric "surface" or frame of reference. If the Night and Day values bother you, you can even do a day/night version.

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.

Equation 18 is a linear estimate of Stefan-Boltzmann Law which has to be restricted to a small range of change if it is going to be useful. That will require a good estimate of the absolute temperature of the surface being impacted. Assuming that the oceans are the more important surface. the current best estimate of the "global" sea surface temperature is 18C degrees with of course a margin of error which can be argued for decades. With a surface at 18C and no evaporation/convection, the energy flux change per degree would be 5.60Wm-2/K degrees meaning that the latent and convective cooling would have to be 7.05-5.6=1.45 Wm-2 for 7.05 Wm-2 of additional forcing to produce only one degree of warming. Since the approximate value of 4 used in equation 18 implies 4Wm-2/K for an ideal surface with no latent or convective cooling you can compare the estimated latent and convective impact by considering that 4Wm-2/K is the ideal condition and 4Wm-2 plus 1.45Wm-2 the latent and convection approximation result in an actual 5.45Wm-2/K and compare that to the actual 5.60Wm-2/K at 18C. That difference is reasonably small considering that the actual absolute surface temperature is likely more uncertain. In other words, the Kimoto approximation is in the right ballpark.

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.

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