Atmospheric Heating and Lapse Rate
https://www.youtube.com/watch?v=Ot5n9m4whaw
TL:DR summary - more CO2 increases surface temperatures, because the radiation temperature on the "top" of the atmosphere stays the same, but there is more insulating atmosphere below that top.
Both the 300ppm atmosphere and the 400ppm atmosphere traps ALL the thermal infrared, and re-radiates it, and traps it again, until the atmosphere becomes thin and transparent enough to radiate it into space. 400ppm radiates at a higher altitude, more heat trapped below.
The important difference is that the 400ppm atmosphere becomes transparent at a higher altitude, where the atmosphere is COLDER relative to the surface, due to "thermal lapse rate", and a less effective heat radiator ... until entire atmosphere heats up enough to radiate more heat at that higher altitude.
That may be difficult to understand, if you don't live in places with snowy mountains that you can climb into the cold. I live near Mount Hood in Oregon, where I used to be able to hike up to the snow line in the summer - today the summer snow line has moved to a higher altitude.
What is "thermal lapse rate"? Heat in a gas is vibration and motion; a molecule moving upwards loses a teeny bit of velocity because it is climbing against gravity. Not much, per molecule, or over a tiny mean-free-path, but the atmosphere is a zillion mean-free-paths high.
About half the incoming solar energy is short-wavelength infrared, about 10,000 degrees Fahrenheit (for non-scientist Americans ... as an engineer I prefer 5770 Kelvins). That infrared, and the visible light, reaches the Earth's surface just fine on a clear day. Or reaches the cloud-tops, which are pretty close to the surface, compared to the entire depth of the atmosphere.
Heat is carried away from the Earth by LONG-wavelength thermal infrared, around 255 Kelvins or -15 Fahrenheit, much colder than almost all of the Earth's surface.
That's the theory, which an electronics engineer like myself works with daily - the devices we design turn electricity into heat, which will damage electronics if we do not radiate or convect it away. A 10 centigrade rise cuts transistor lifetime in half - annoying, but more tolerant than human beings and the living world.
Electronics tells the story in space as well. Satellites measure EXACTLY how much energy comes in from the Sun (about 1366 watts per square meter). The surface of a sphere is 4 times the surface of a Sun-facing disk with the same radius.
- Convert "disk to sphere" and you calculate that the Earth SHOULD emit 1366/4 or 341.5 watts per square meter, averaged over the entire surface (reflection and infrared radiation).
Earth observation satellites measure about 340.5 W/m2 radiating into space, a deficit of 1 W/m2. Energy retained from the Sun, NOT INCLUDING energy from combustion of stored chemical energy, which adds a wee bit more. Energy is conserved - it becomes heat and hotter materials. About 90% heats ocean water, which makes the water evaporate faster, "powering" more-energetic weather. The heating will continue until "outgo" matches "income", and sadly, the heating necessary to cause that is more than you might expect.
Which is annoying, ideologically - most folks would call me a cave-man conservative. But my first loyalty is to the scientific truth, not whether Heather has two (or zero or six) mommies. I'll work on technological fixes, but I'm counting on the other 8 billion of you to purchase and USE those fixes, rather than more gasoline for your SUV.
Or your private jet, if you are climate-conscious but lavishly-wasteful Bill Gates. Develop VR versions of Davos and TED, please Bill, so I can attend as well.