In spite of considering myself a “climate expert” I still struggle a bit with understanding how climate sensitivity is estimated. Admittedly, part of my confusion is because the climate system has multiple definitions of sensitivity depending on the timescale of interest. That’s why a thought experiment from a recent RealClimate.org article caught my eye. The post was written by Gavin Schmidt and describes why the earth system sensitivity (ESS) cannot be estimated by regressing temperature and radiative forcing estimates across ice-age cycles.

Any measure of climate sensitivity represents how the earth will respond to a doubling of CO₂, and is expressed as a change in temperature per change in CO₂.

ΔT / ΔCO₂

For fast timescales, during the period where CO₂ is actually rising, we use the transient climate sensitivity, which has become a somewhat standard model calculation. For longer timescales where the deep ocean can reach equilibrium (~1000 years) we estimate the equilibrium climate sensitivity, sometimes referred to as the Charney climate sensitivity. There is also an intermediate climate regime where the upper ocean can reach an equilibrium, but the deep ocean cannot. For this regime we can treat the deep ocean as an infinite heat reservoir, and the rate of heat transfer can be interpreted as a negative feedback.

The earth system sensitivity (ESS) is similar to the equilibrium climate sensitivity, but is relevant to even longer timescales of 10,000-100,000 years. On these timescales ice sheets can form and the distribution of vegetation (ex. movement of boreal forests, expansion of deserts, etc.) can change dramatically in ways that feedback onto the climate.

It might seem obvious that a regression of temperature and CO₂ over ice ages would be useful for estimating ESS, since temperature and CO₂ can vary a lot during these periods. However, this thinking ignores the fact that there are changes in solar forcing (e.g. Milankovitch forcing) that affect both temperature and CO₂, therefore they are not independent.

The thought experiment that I found particularly illuminating starts like this:

“Imagine a world where the sensitivity of the climate system to carbon dioxide was zero (note this is not Planet Earth!). Then [paleo-climate data] would show a reduced amplitude cycle, but a strong correlation between CO₂ radiative forcing and temperature. This relationship would be exactly the T to CO₂ function.”

To paraphrase, CO₂ amplifies the glacial cycles, so a system that is insensitive to CO₂ is missing this feedback process. In this case, CO2 levels will still rise and fall with the global temperature due to things like ocean temperature controlling how much CO2 is dissolved. CO₂ also still imparts a radiative forcing that affects temperature, so these would still be correlated.

“To take another extreme case, assume that that carbon cycle was insensitive to climate, but climate still responded to CO₂, then we’d see no CO₂ change and zero regression.”

In this case the ESS is not zero, but since the carbon cycle is effectively fixed by an insensitivity to the orbital forcing we might be fooled otherwise by the lack of regression.

To sum up the point of this excercise,

“In neither case would the raw T/CO₂ regression tell you what the sensitivity to CO₂ alone was… 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.”