The last post on climate "sensitivity" was basically a rehash with some new charts. There is no serious math involved with determining "sensitivity" from any initial condition, the newer energy balance estimates of transient climate response (TCR) are basically doing the same thing with more noisy references. The relationship between average ocean energy and DWLR just makes it ridiculously simple. That was actually one of my goals with this blog, to come up with a bullet proof back of the envelope estimate of "Climate Sensitivity". But what good is knowing "Sensitivity" is 0.8C from an average ocean temperature of about 4 C degrees?
What? You still doubt it is 0.8 C? Totally lost in all the black body cavity, radiant shell, Ein=Eout stuff?
Okay, here is the MODTRAN evidence. Using the US standard atmosphere and the 4C number which requires removing 11 degrees from the estimated 288K, the outgoing long wave radiation (OLR) at 10,000 meters looking down is 228.34 Wm-2. Now when I double the CO2 in the model the OLR value will drop. Since the system tries to maintain a constant energy balance, increasing CO2 will reduce the OLR requiring the "surface" to warm in order to restore the normal energy balance.
First, it indicates that clouds are totally independent of CO2 forcing. Any positive cloud feedback and it would be much higher. Clouds are independent because of the different responses to forcings of the liquid and gas "greenhouse effects". Clouds are not independent of various direct and indirect aerosol impacts, natural and manmade, so there can still be large changes even with a low "sensitivity" to well mixed greenhouse gases. Since CO2 forcing has no impact on clouds other than a tiny possible increase, most of the climate change "cloud positive feedback" and iris effect stuff is mathturbation. The net change will not be enough to determine anything one way or another.
Second, the "sensitivity" is based on the ocean heat capacity and a long time constant. Regionally, that low "sensitivity" can still amplify other shorter term factors, natural and manmade, possibly producing larger than expected extremes. The stronger Northern Hemisphere Sudden Stratospheric warming events for example are like relief valves releasing excess energy, figuring out how much is due to what is going to get pretty complicated. So other than CO2 didn't do "most" of it, what ever 'it' is, we are no closer to forecasting climate centuries in the future than we were before.
Third, the 4C is only the upper end of the typically bi-stable ocean temperature range. With a lower end near 2C, CO2 should reduce the overall range, at least temporarily, but not enough to prevent a major cold side swing if conditions, i.e. weak solar, larger meridional imbalance, volcanic or THC shifts, in any combination, try to drive the system to a "uniform" energy distribution. So we probably have not dodged any ice age bullets because of CO2, land use, black carbon and snow removal possibly, but CO2 nope.
Why? Because CO2 is a regulator, an important player but not the star of the show. The colder it gets the more important CO2 becomes, but it loses out to water vapor and albedo in all other cases.
The MODTRAN model is available on-line thanks to the University of Chicago. It is a model so it is a useful tool not an absolute proof, but enjoy playing around with it trying to prove or disprove anything you like.