By Andy May

Christian Freuer has translated this post to German here.

In part one we discussed various estimates of climate sensitivity (ECS, TCR, and observation-based values) and what they mean, especially those reported in the latest IPCC report, AR6. In part 2 we discussed the uncertainty in estimating cloud feedback to surface warming, and cloud feedback’s relationship with ECS. In part 3 we compared the various estimates to one another and discussed the differences between them. In this part we will discuss how Lewis and Curry convert their observation-based estimates of climate sensitivity to AR6-equivalent ECS values. Most conversions of observations to model based ECS are done in a similar way.

Lewis and Curry 2018 (LC18) matched base periods and final periods based upon volcanism records and the detrended Atlantic Multidecadal Oscillation (AMO). Other possible sources of natural variability, including solar variability, were ignored. Using these periods, an estimate of ECS was computed using the equations and values in figure 1 below.

In the table of ECS and TCR estimates, all the ECS estimates are below the AR6 likely lower bound of 2.5°C. Lewis and Curry’s TCR estimates are all below the AR6 likely lower bound of 1.4°C. This is true, even though Lewis and Curry accepted most of the assumptions made by the IPCC in AR6.

In the equations, λ is the climate feedback parameter in W/m^{2} forcing increase per degree of surface warming. LC18 assumes that λ is constant. LC18 also assume that:

Where ΔR is the radiative response to a positive change in radiative forcing (ΔF) that causes a positive change in the net downward top of the atmosphere (TOA) radiative imbalance (N). The term μ_{R }is a random, zero-mean residual term representing internal weather or climate variability that is unrelated to surface temperature changes (ΔT). In essence, R is the response to a change in surface temperature times the feedback parameter plus internal climate variability, which is assumed to be random about zero over the chosen time period. The time periods considered are listed in figure 1.

By assuming that λ is constant over all the chosen time periods, it is then independent of surface temperature, changes in climate state, and changes in radiative forcing (ΔF). Thus:

λ= (ΔF-ΔN)/ΔT

The above equation derives from the law of conservation of energy and the assumption that internal variability (μ_{R}) over the chosen period sums to zero. LC18 (and AR6) then assume that the only outside forcing is due to volcanism and the change in CO_{2}, F_{2xCO2}. This means that ECS can be calculated with the bottom equation in figure 1 if periods are chosen so that volcanism is about the same and the periods fall in the same part of the 60-70-year AMO cycle. These are the same assumptions made by the IPCC.

**Reality Check**

LC18 uses the detrended AMO, as shown in the upper graph in figure 2. Detrending emphasizes the cyclicity in the AMO, but it removes the long-term trend that is apparent in the raw undetrended data in the lower graph in figure 2.

The longer-term trend affects the base to final period comparisons identified in figure 1. The reason for the underlying secular trend in the AMO is not known but could be due to the Modern Solar Maximum identified in figure 3.

Changes in solar activity are generally small from one solar cycle to the next and from the solar cycle low to the peak. But they are cumulative over time. Extended solar maxima like the Modern Solar Maximum can have a large effect on the climate if they last long enough. The Modern Solar Maximum is the longest period of high solar activity in 600 years (Vinós, 2022, p. 210). Given this, and the apparent trend in the raw AMO, it seems likely that the differences between the LC18 base and final periods are not entirely due to the change in CO_{2} as assumed by the equations in figure 1.

**Conclusions**

The AMO trend and the solar activity trend have been up over the past 170 to 300 years, not flat as explicitly assumed in LC18 and AR6. Thus, their ECS and TCR values are maximum values and not estimates of the actual values. This is generally true of almost all observation-based and model-based estimates of ECS and TCR.

Yet nearly all observation-based estimates of ECS and TCR are below the likely lower bound reported in AR6. The problem with the new AR6 climate sensitivity estimates is not just that they are too high, it is also that they are higher than the *maximum possible* observation-based estimates. This is a point that is not made often enough.

The bibliography can be downloaded here.