We’ve all seen how well temperature proxies and CO 2 concentrations are correlated in the Antarctic ice cores – this has been known since the early 1990’s and has featured in many high-profile discussions of climate change.





EPICA Dome C ice core greenhouse gas and isotope records.



The temperature proxies are water isotope ratios that can be used to estimate Antarctic temperatures and, via a scaling, the global values. The CO 2 and CH 4 concentration changes can be converted to radiative forcing in W/m2 based on standard formulas. These two timeseries can be correlated and the regression (in ºC/(W/m2)) has the units of climate sensitivity – but what does it represent?

For obvious reasons, we are interested in how the climate system will respond to an increase in CO 2 and that depends on time-scale and what feedbacks we consider:







The “Charney” sensitivity is generally thought of as the medium-term response of the system, including all the fast feedbacks and some of the longer term ones (like the ocean). This is usually what is meant by climate sensitivity in normal conversation. On longer (multi-millennial) timescales we expect changes in vegetation and ice-sheets to occur and alter the response and that sensitivity is often described as the Earth System Sensitivity (ESS).

But let’s go back to the correlation from EPICA Dome C:





Regression between temperature and GHG radiative forcing from Masson-Delmotte et al (2010) SkepticalScience.



Using local temperatures, the straight line regression is ~3.9 ºC/(W/m2). Assuming that global temperature changes on these timescales are roughly half as large, that implies ~2 ºC/(W/m2) at the global scale, and given that 2xCO 2 forcing is about 4 W/m2, that means a ‘sensitivity’ of ~8ºC for a doubling of CO 2 . This is very much larger than any of the standard numbers that are usually discussed. So what is going on?

The first point to recognize is that the ice age/interglacial variations are being driven by Milankovitch forcings (“orbital wobbles”). These have an almost zero effect in the global mean radiative forcing but make huge differences to the seasonal and regional solar fluxes. This makes these drivers almost uniquely effective at impacting ice sheets, hence temperature, the circulation, the biosphere, and therefore the carbon cycle. Notably, these drivers don’t fit neatly into a global forcing/global response paradigm.

Second, the relationship we are seeing in the ice cores is made up of two independent factors: the sensitivity of the CO 2 to temperature over the ice age cycle – roughly ~100 ppmv/4ºC or ~25 ppmv/ºC – and the sensitivity of the climate to CO 2 , which we’d like to know.

The problem is perhaps made clearer with two thought experiments. Imagine a world where the sensitivity of the climate system to carbon dioxide was zero (note this is not Planet Earth!). Then the records discussed above would show a reduced amplitude cycle, but a strong correlation between CO 2 radiative forcing and temperature. This relationship would be exactly the T to CO 2 function. To take another extreme case, assume that that carbon cycle was insensitive to climate, but climate still responded to CO2 2 , then we’d see no CO 2 change and zero regression. In neither case would the raw T/CO 2 regression tell you what the sensitivity to CO 2 alone was.

Instead, to constrain the Charney sensitivity from the ice age cycle you need to specifically extract out those long term changes (in ice sheets, vegetation, sea level etc.) and then estimate the total radiative forcing including these changes as forcing, not responses. In most assessments of this, you end up with 2.5ºC to 3ºC in response to 2xCO 2 . To estimate the ESS from these cycles you’d need to know what the separate impacts the CO 2 and the orbital forcing had on the ice sheets, and that is not possible just from these data. Constraints on ESS have thus come from the Pliocene (3 million years ago) or even longer Cenezoic time scales – giving a range roughly 4.5ºC to 6ºC. Lunt et al (2010) and Hansen et al (2008) have good discussions of this and we discussed it here too.

The bottom line is that you can’t estimate Earth System Sensitivity solely from correlations over ice age cycles, no matter how well put together the temperature data set is.

References