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I wanted to see what effect CO2 levels in atmosphere would have, to I tried an experiment.
As SpaceEngineer says, calculating the greenhouse effect is very complex and not something that SE does. But if you want some intuition for how it works with varying CO2 or other greenhouse gases, then we can use a simple model. Imagine the atmosphere as being made up of some number of layers of greenhouse gas, where each layer absorbs all of the infrared radiation that passes into it (each layer is one "extinction thickness"), while the atmosphere as a whole is transparent to the star's visible light. What will the surface temperature of the planet be, if the atmosphere has 1 layer? The energy in sunlight coming in must balance the energy in infrared radiation given back out. The power per square meter in sunlight is called the "solar constant". At Earth, this is about 1370 Watts per square meter. If 1370 Watts per square meter of visible sunlight strikes the planet, then to be in equilibrium, the top of the atmosphere must emit 1370 W/m2 of infrared radiation to space. But the atmosphere emits both upward and downward, so 1370W/m2 of infrared is emitted down to the planet surface as well. So the surface absorbs twice the solar constant worth of energy, which means it must be emitting 2740W/m2 in infrared (then the atmosphere absorbs all of that, which then balances the energy we just said it must be emitting up and down.) Schematically we can visualize these energy flows with some arrows, with each arrow representing one solar constant worth of power per unit area. The rule here is that for every arrow absorbed by something, an arrow must also be emitted. (Otherwise they will not be in thermal equilibrium and the temperature somewhere would change very quickly.)
Now we use the Stefan Boltzmann Law. The power per unit area emitted by a material is proportional to its temperature to the fourth power. (P/A = σT4
where σ is the Stefan Boltzmann constant, 5.67x10-8
). According to our sketch above, adding 1 layer of greenhouse gas to the atmosphere doubles the amount of infrared energy the surface must be emitting, which means the surface temperature must be increased by a factor of 21/4
= 1.189 from what it would be without an atmosphere.
Without an atmosphere, Earth's equilibrium temperature would be 255K or -18C. One extinction thickness of greenhouse gas raises it to 303K or almost 30C! In fact Earth's surface temperature averages 288K, indicating a greenhouse effect of about 60% of one extinction thickness. Most of that is due to water vapor, while our burning of fossil fuels is increasing the CO2 concentration and increasing the surface temperature further.
What if we add another entire layer of greenhouse gas to the atmosphere? Then the diagram looks like this (remember the rule is for every arrow in there must be an arrow out).
With 2 layers, the top of the atmosphere radiates in equilibrium with the solar constant, while the surface radiates 3 times that amount, raising the surface temperature by a factor of 31/4
= 1.316. 3 layers makes it 41/4
= 1.414. Now you might be able to see the trend. In general for an atmosphere with N extinction thicknesses of greenhouse gas, the surface temperature is multiplied by a factor of (N+1)1/4
from what it would be with no atmosphere.
Venus' atmosphere is well approximated as having about 70 extinction thicknesses of CO2, raising its surface temperature from -20C to 460C.