The impact of additional CO2 on temperature levels off, rather than keeps increasing. This is because the CO2 molecules, which happen to oscillate at the same frequencies as infrared leaving the atmosphere, get “filled” with the resulting heat-trapping interactions, and absorb less and less of the escaping infrared over time.
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But the justification for this conclusion comes almost entirely from the fact that a few modelers, using hundreds of parameters for unknown and currently unknowable interactions, can get a decent back-fit on previous global mean temperatures when they assume a certain sensitivity of temperature to CO2 and methane levels.
