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I'm looking for a formula, either precise or an approximation (it's for a video game so it's ok to have somewhat rough numbers), that determines heat retained from the sun by an atmosphere, based on its density and composition (specifically CO2 composition, but bonus points if it factors other things in too).

Does such a formula exist? Or if not, are there any rule-of-thumb sort of things I could use for estimating "If an atmosphere doubles in density, its heat will rise by X percent" or "If you replace half the CO2 in the atmosphere with O2, your heat will drop by Y percent", etc?

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Earth's atmosphere is composed of a number of layers: troposphere, stratosphere, mesosphere, thermosphere and exosphere, ascending in order from the surface.

Each layer has different characteristics and within each layer the temperature profile is different. The red line in the following US standard atmosphere graph shows the temperature profile of the atmosphere.

The temperature profile is complex and is not related to air density (the amber line on the graph) above the tropopause.

There are higher temperatures on the Earth's surface and at the stratopause but low temperatures at the tropopause and mesopause.

Atmosphere Profile

As for carbon dioxide, it is fairly well mixed in the atmosphere, particularly at altitude. Concentrations of carbon dioxide vary laterally near the Earth's surface, with the concentrated regions occurring in areas of major human activity, as can be seen from the NASA produced picture below.

enter image description here

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  • $\begingroup$ Heh. That NASA plot doesn't have a scale, nor does it even mention what the colours represent (high, low, range?) on the page you linked to. Poor form, NASA. $\endgroup$
    – naught101
    Feb 25, 2016 at 0:23
  • $\begingroup$ As I understand it, those stats are for Earth's current atmosphere at varying altitudes, correct? Surely increasing the thickness of a planet's overall atmosphere (as with terraforming) would lead to greater heat retention, right? Or no? I'm trying to figure out how the surface temp would change if you, say, doubled the entire planet's atmospheric pressure, or halved the CO2 content within the current atmospheric makeup. I'm trying to calculate surface changes to a global atmosphere, rather than altitude-specific values for the current atmosphere. $\endgroup$
    – Nerrolken
    Feb 25, 2016 at 19:35

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