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DB2: Actually, I said you can't use a linear regression. It was, I believe, Phil who was arguing from the linear relationship in post 45286.

The linear relation between log(atmospheric CH4 concentration) and temperature is found from the ice core record, so this is an empirically established relation. More fundamentally, a similar linear relation is found to exist between log(CO2) and temperature. Parrenin et al. (2013) showed this relation, for a 12kyr long period beginning 20 kyr ago (from around the LGM extending into the start of the Holocene) was a very tight linear relationship with an R^2=0.99. The issue I've tried to explain in this thread is what do these relationships mean?

My interpretation of the CO2-dT (temp change) relationship is that it represents the long-term radiative equilibrium (or energy balance) climate state of the Earth. Tweak the forcings a bit, and the climate varies in response, but always in such a way as to move along that empirical CO2-dT relation. The climate system behaves as a system with one degree of freedom: effectively one can imagine the climate being controlled by a single knob representing all the forcings. Turn the knob down and you get an ice age; turn it up and you get an interglacial. But the climate (ice core) record shows us that the climate always varied along this well-defined curve in (CO2,temp) parameter space.

Or I should say always did, because the present climate state is now far from that relation (which held for at least half a million years of Earth's climate history) and getting further away each passing year. My interpretation (and one of Kirchner's possibles) is the current anomalous climate position is a consequence of the extremely rapid change in forcings that we are now imposing by the large scale burning of fossil fuels. The implication is that there is a lot of change "in the pipeline" because eventually the climate system will return to the equilibrium relation it has followed for a million or more years. The warming to date is by no means all the warming we will see, even if all fossil fuel burning stops today.

However, figuring out this response is not just a simple matter of extending the linear regression. One has to estimate this response by considering the timescales needed for the system to return to equilibrium.

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