Climate sensitivity: how has the Earth responded in the past?
In debates about the change of temperature of the Earth that we can expect in the future, it is illuminating to take a backward glance at the past changes of the temperature of the Earth. How sensitive is the Earth to the buildup of greenhouse gases?
The climate sensitivity is the rise in temperature divided by the forcing (in W/m2). In the absence of any feedback, the climate sensitivity can be shown to be 1/(4 SIGMA T3), where SIGMA is the Stefan-Boltzmann constant, (SIGMA = 5.67 x 10-8 W/M2K4), and the temperature is in Kelvin.
Numerically this is a sensitivity of 0.3 K/(W/m2), meaning that if the increase in forcing is 1 W/m2, then the resulting increase in temperature is 0.3 C, in the absence of feedback, when the Earth has come to a new equilibrium with the higher greenhouse gases.
The doubling of CO2 from pre-industrial levels will produce a forcing of 4 W/m2, which implies, in the absence of any feedback, a temperature rise of
4 x 0.3 = 1.2 C (the no-feedback result).While global climate models are necessary, it is also valuable to have a model-independent estimate of the climate response to increased CO2. What climate sensitivity did the Earth show during warming that ended the last ice age? This is the large climate change that is closest to us in time (about 10 K years ago), and therefore the most valuable. Earlier times are less relevant, because of continental drift. If you go back 200 million years ago, the continents were not even close to where they are today.
The change in temperature between the ice age and post-ice age was 5 C, and the change in solar forcing was 7.1 W/m2. This implies a climate sensitivity of 5/7.1 = 0.7 K /(W/m2). Multiplying this sensitivity by the forcing expected from a doubling of CO2 from pre-industrial levels, namely 4 W/m2, yielding a predicted temperature rise of
0.7 x 4 = 2.8 C (from the Earth’s climate record).
This is consistent with the IPCC prediction of the rise in temperature (in response to a doubling of atmospheric CO2), which is an increase in the range of 1.5 to 4.5 C. This is the change between the new higher equilibrium temperature and the past equilibrium temperature.
Notice that the paleoclimate data implies that the feedback is positive, at least on the time scales of centuries to millennia. (The feedback may well be positive on a much larger time scale of millions of years, but that is not the relevant time scale for human civilization).
Reference: Seinfeld and Pandis, Atmospheric Chemistry and Physics, (Wiley, New York, 1998).pp. 1102-1103. These authors cite a difference between glacial and interglacial periods of 5 C, and a forcing of 7.1 W/m2, and a radiative forcing for doubled CO2 of 4 W/m2.
This refutes some of the arguments made at WUWT here .