What is CO2's Relationship to Temperature?

I just had a reader ask me this via email:

Hi Coby,

I'd like to know what models assume with regard to the relationship between radiation transmission through CO2 and its concentration in the atmosphere. Is it a linear decrease with ppm, exponential?

A sceptic website makes a big issue of this, on the grounds that a 10% (say) increase in CO2 will not produce a 10% decrease in transmission.

Thanks

Since I took the time to write a detailed answer I thought I would post it here as well:

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Hi Ted

This is actually correct. The relationship between CO2 and temperature rise (all other factors and feedbacks aside) is a logarithmic one not linear. This is not an assumption of model code or a parameter that is set, it is the output of model runs and is based on the laws of the physics of radiative gases as represented in the models.

The standard metric used to discuss CO2 and its effect on the climate is called "climate sensitivity" to CO2. Currently models are all clustered around a 3oC sensitivity per doubling, with figures from 2 to 4 all within the 95% probability range. So adding 280ppm to pre-industrial levels we would expect a 3oC increase in temperature. To get an additional 3oC warming (if this is the correct sensitivity figure) we would need to add 560ppm more, 3 more degrees requires 1120 more ppm etc. This relationship changes at extremely high CO2 and also at extremely low CO2 but it does apply to all conceivable contemporary scenarios.

Climate sensitivity to CO2 includes H2O feedback and sea ice albedo feedback, both positive, but it does not include ice sheet response which is considered too slow to include. Nor does it seperately include carbon cycle feedbacks. That is to say the figure is for a doubling regardless of source so if for example humankind does add an additional 280 ppm CO2 to the atmosphere and 3oC is correct we still may incur greater warming if carbon comes out of melting permafrost and/or suboceanic methane clathrates, both likely occurences.

Hope that helps!
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