How Did I Screw Up My Energy Budget Answer and What is the Thermosphere Sink?

The screw up was easy. I replicated a formula on a spread sheet and didn't "fix" a variable. Add a typo and there you go, total garbage. That took me from my standard answer, "I don't know" to thinking I might have some sudden insight. One thing about the mess up is one thing still amazes me, the upper troposphere.

The troposphere decreases in temperature with altitude. Then the temperature increases starting at the bottom of the ozone layer at about 20,000 kilometers. Between 10K and 20 K kilometers, there is a relatively uniform temperature in the neighborhood of -55C to -70C. That is all well known. My first impression was that area was a heat sink. That heat sink plus the much lower density would change the way heat and/infrared radiation flowed in that region. While infrared is emitted in all directions by any object with any temperature, downward infrared from just above the this troposphere sink, encounters increasing absorption by water vapor and the other more densely packed green house gases. Warmer to colder is the direction of flow of heat and denser to less dense is the easier path for infrared.

All of that is not earth shattering. Different layers of the atmosphere are more opaque to different wave lengths of electromagnetic radiation. The warming at the bottom of the ozone layer is due to the interaction of ozone with Ultraviolet light. Higher in the atmosphere, Gamma rays and x-rays heat the thermosphere. Each of these temperature layers are warmest where the electromagnetic radiation that interacts with the layer enters, decreasing as the radiation is absorbed. I put that in bold that because CO2 has a stronger influence where the density of water vapor decrease, the top of the troposphere. This should cause "back warming" as CO2 concentration increases.

I use "Back warming" instead of back radiation, because back radiation implies a more uniform warming that would be felt as the full impact of CO2 increase at the surface.

Arrhenius, the scientist that discovered the CO2 potential for global warming originally estimate warming due to a doubling of CO2 to be about 5C. Another scientist of the day, Angstrom, said Arrhenius over estimated the impact of CO2. Even though Angstrom's reasoning was based on a flawed experiment, Arrhenius revisited his original work and later mentioned that the magnitude of the warming due to CO2 doubling to be 1.6 plus some warming due to water vapor feedback.

Arrhenius' second estimate is used by many climate skeptics to cast doubt on the IPCC's estimated range of potential warming due to CO2 doubling. While I don't know, it interests me why Arrhenius would revise his original work and the publication not get much use. I can't even find an English translation of the paper describing the second, lower estimate. While I cannot read the mind of a famous dead scientist, I have my doubts that he would just cave in, accept Angstrom's experiment completely, and revise is estimate solely on another scientist's novel, groundbreaking work. So I wonder what he may have discovered that may have caused his 1906 change to be published as 1.6 C with 2.1C total with water vapor feedback.

That water vapor feedback is MUCH lower than his original estimate. While I can be totally wrong, I suspect the Troposphere sink is the reason for the much lower water vapor feedback he estimated. Since his time, the estimate for CO2 only has reduced a little to the range of 1 to 1.2 degree C. That means his second estimate was pretty damn good. I would suspect that his water vapor feedback is also pretty good. That is why I am inclined to believe that ~1C for CO2 with ~0.3C for water vapor feedback may be a reasonable estimate for each greenhouse gas.

If my reasoning is not flawed, it would mean that a fairly large estimate for CO2 forcing could be correct, but only a fraction of that forcing would be felt as a temperature increase at the surface. I am sure this has been considered by many climate scientists, but I have not read a paper either promoting or dismissing this possibility.

If my reasoning is somewhat correct, it would explain a few things that baffle me. One is the energy budget. The energy in from the Sun will equal the energy out of average from the Earth. While a change in CO2 forcing will change the internal energy balance, it will not appreciable change the top of the atmosphere energy balance. Water vapor will increase due to CO2 forcing, but only to the extent that the forcing impacts a layer of the atmosphere. If the majority of the impact is indeed in the upper troposphere, water vapor feedback would be limited to that region. While CO2, a fairly well mixed gas, would have uniform forcing potential at all levels of the atmosphere, the much larger concentration of water vapor in the lower region of the troposphere, near the surface, would limit its impact as is noted by climate science which agrees that most warming will be in regions of dryer air, the poles, deserts etc.

Global warming estimates that there will be warming in the upper troposphere, consistent with my thoughts. Measurements of increased water vapor as a relative constant humidity with warming, is consistent with what is expected. The amount of troposphere warming though is somewhat less that expected. This could be due to instrumentation error. The method of measuring warming in the atmosphere via satellite using microwave sounders is a cleaver adaption of instrumentation not intended for that purpose. Weather balloons used to measure temperature with altitude have also have/had issues with instrumentation because of the wide range of temperatures, icing, solar interference etc. This complicates determining how much, in what layer and how widely spread the warming may be. If for example, the warming is widely spread in the region I call the troposphere sink, then the warming could be below the accuracy of the instrumentation.

The impact of the CO2 forcing in the upper troposphere felt at the surface would increase more slowly than expected until the lapse rate, cooling with altitude, decreases enough to have a more significant impact on the troposphere sink.

So my answer to the puzzle is that the warming at the surface will be consistent with modern estimate of CO2 in dry air forcing with water vapor feedback proportional to Arrhenius' second estimate. That would mean that the radiation window will close somewhat, increasing forcing at the top of the troposphere to bottom of the ozone layer by 2 to 4 Watts/m^2. Latent heat will increase at the surface producing a additional atmospheric forcing of 0.25 to 0.5 Watts/m^2. Finally, the other absorbed radiation in the upper troposphere will vary slightly to balance the CO2/water vapor increase, with no significant net change.

Despite my face plant in the original answer, I doubt that the surface temperature will increase by 3C by 2100.