That Silly Troposphere

While I am chillin' while my new to me but very well previously used air conditioner is working to cool extract moisture from my indoor environment, I am surfing the web a bit to update my knowledge of the troposphere. Science of Doom has a lot of information and is a lot easier to read than some of the proper papers. So for those of you that have no real life, I will post a few of the links.

This first one is on Tropospheric Basics. It has the neat idealized temperature profile of the atmosphere with a nice big red circle around the Troposphere.

The next link is to Simple Atmospheric Models. Simple models make plenty of unrealistic assumptions, because they are simple models. They are not designed to get down to the nuts and bolts of what is really going on. Some of the variables used in the simple models are played with so that the output of the models somewhat better represent what is actually happening. I use to call this brute force problem solving. When digital computers first came out, you could do "what ifs", by running one number through a range, letting the computer do all the tedious calculations, then see what happened. Kinda like beating the hell out of an equation with guesses until it made sense. I tried to avoid this as much as possible. Still, sometimes by intent or accident, my programs would end up in loops that took forever to settle on something that may or may not make sense. One of the equations is E = (1-0.3)*S/4=a*T^4, the 0.3 assumes that 30% of the incoming solar radiation is reflected, S is the solar radiation trying to come in, T is the temperature in degrees Kelin and a is what I am using for the little Greek delta symbol for 5.67*10^-8 that I screwed up in my earlier spread sheet. The 0.3 change a lot with cloud cover and a little with atmospheric composition. The little Greek epsilon that is normally in front of the a is assumed to be 1 in this model. It is not and CO2 will have some impact on how much it is not. This simple model with its assumptions would say that the surface temperature is about 15 degrees warmer than it actually is.

That leads the Science of Doom to its next Simple Atmospheric Models Part II. SoD notes that in the Troposphere that heat flow is dominated by convection. That is also noted on NASA's Energy Budget cartoon. In the Troposphere heat flow is first convection, then conduction with radiative flow considered small until water vapor and density drops somewhere near the top of the Troposphere. The simple model proves it usefulness when you back calculated the temperature of the Stratosphere using the surface/Troposphere temperature as shown in figure 1 of his post. Note that in figure 1 it is assumed that the constant temperature of the Stratosphere remains constant, which is doesn't because it is warmed by incoming solar which decreases with altitude.

"You should be able to see from figure 2 that although the surface/troposphere and stratosphere are at different temperatures, an average absorptivity value for absorbing radiation at 255 K will be quite similar to the emissivity value for emitting radiation at 215K." That bold part is where my question starts. Relative to the estimated 3.7 Watts/m2 for doubled CO2, the band of Tropospheric radiation could be wider that allowed with that assumption.

First, the range of temperature in the Tropopause varies from approximately -55 C(218K) to -90C (183K), that is a considerable wider range that 255K to 215K on which the simple model assumptions are based. Second, the actual wavelengths of the radiation would change depending on the elements emitting the radiation. While the warmer stratosphere is effectively emitting about half of its radiation back to the Troposphere, water vapor has a wider absorption range than CO2, heat transferred to N2 and O2 through collisions would be emitted in their emission spectrum. The fraction of the actual infrared spectrum absorbed by CO2 in this region plus the collisional energy transferred by the CO2 to the rarer, but still relatively abundant with respect to CO2, N2 and O2 molecules can be significant enough to not be dismissed.

"Backheating", the crappy term I am using for the upper troposphere region, is due to both the energy radiated from the stratosphere and the energy radiated/transferred by collision with excited CO2, absorbed by other, non-CO2 molecules.

So while I am pretty sure that all this has been considered in the models, I have not seem how or how well it has been considered. So I will keep on pondering in air conditioned comfort for a while.