The basic formalism is that one can use an energy balance approach to estimate the transient climate response (TCR) and the equilibrium climate sensitivity (ECS). Given the change in forcing, , the change in surface temperature , and the change in system heat uptake rate, , we get
where is the change in forcing due to a doubling of atmospheric CO2.
If new estimates suggests that the change in forcing is slightly higher, and the change in system heat uptake rate is slightly lower, than previously thought, then the estimates for the TCR and ECS go down, which I think is the main difference between the new paper and the old one.
As I’ve already mentioned, there are reasons to be cautious about these results. One other issue I have with the Lewis and Curry result is that they suggest a TCR-to-ECS ratio of about 0.8, which I think is probably too high. Given the heat capacity of the oceans, and the current planetary energy imbalance, a ratio below 0.8 seems likely. I have wondered if there would be a way to incorporate this into the analysis, but it may not be straightforward.
However, a key problem with the Lewis & Curry approach, which Andrew Dessler has already discussed on Twitter, is that it essentially assumes that the one-dimensional energy-balance approach exactly represents what will happen. The implication is that if there is some change in planetary energy imbalance (or change in system heat uptake rate), driven by some well-defined change in forcing, this will then lead to a very well-defined change in surface temperature.
The problem, as is discussed in this paper (Dessler, Mauritsen & Stevens) is that this isn’t correct. Internal variability confounds the relationship between changes in system heat uptake rate, and changes in surface temperature. In a sense, this is obvious. We know that the climate system is very complex and that the exact path that it follows depends on the state of the system. If you average over long enough timescales, this becomes less significant, but over periods of many decades, it can be reasonably substantial. We don’t expect that the relationship between change in surface temperature, change in forcing, and change in system heat uptake rate over a period comparable to that of the instrumental temperature record will exactly represent the long-term sensitivity of the system.
In a sense, Lewis & Curry are taking one realisation of reality and assuming that it is an exact representation of the typical response of the system. It probably isn’t. This doesn’t mean that climate sensitivity can’t be low (even mainstream estimates do not rule this out). It simply means that we should be cautious of assuming that it is low based on an estimate that can’t fully account for how internal variability may have influenced the path that we’ve actually followed.