Revisiting a Claim of Reduced Climate Sensitivity Uncertainty

Nature has published a Brief Communications Arising between us (Patrick Brown, Martin Stolpe, and Ken Caldeira) and Peter Cox, Femke Nijsse, Mark Williamson and Chris Huntingford; which is in regards to their paper published earlier this year titled “Emergent constraint on equilibrium climate sensitivity from global temperature variability” (Cox et al. 2018).


  • Cox et al. (2018) used historical temperature variability to argue for a large reduction in the uncertainty range of climate sensitivity (the amount of global warming that we should expect from a doubling of atmospheric carbon dioxide) and a lowering of the central estimate of climate sensitivity.
  • We show that the use of alternative methods, that we argue are better-justified theoretically, suggest that historical temperature variability provides, at best, only a small reduction in climate sensitivity uncertainty and that it does not robustly lower or raise the central estimate of climate sensitivity.



The Cox et al. (2018) paper is about reducing uncertainty in the amount of warming that we should expect the earth to experience for a given change in greenhouse gasses. Their abstract gives a nice background and summary of their findings:

Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO2) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO2. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the ‘likely’ range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5–4.5 degrees Celsius for more than 25 years. The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC ‘likely’ range) of 2.2–3.4 degrees Celsius.

Thus, the Cox et al. (2018) study found a (slight) reduction in the central estimate of climate sensitivity (2.8ºC relative to the oft-quoted central estimate of 3.0ºC) and a large reduction in the uncertainty for climate sensitivity, as they state in their press release on the paper:

While the standard ‘likely’ range of climate sensitivity has remained at 1.5-4.5ºC for the last 25 years the new study, published in leading scientific journal Nature, has reduced this range by around 60%.

Combining these two results drastically reduces the likelihood of high values of climate sensitivity. This finding was highlighted by much of the news coverage of the paper. For example, here’s the beginning of The Guardian’s story on the paper:

Earth’s surface will almost certainly not warm up four or five degrees Celsius by 2100, according to a study which, if correct, voids worst-case UN climate change predictions.

A revised calculation of how greenhouse gases drive up the planet’s temperature reduces the range of possible end-of-century outcomes by more than half, researchers said in the report, published in the journal Nature.

“Our study all but rules out very low and very high climate sensitivities,” said lead author Peter Cox, a professor at the University of Exeter.


Our Comment

I was very interested in the results of Cox et al. (2018) for a couple of reasons.

First, just a few weeks prior to the release of Cox et al. (2018) we had published a paper (coincidentally, also in Nature) which used a similar methodology but produced a different result (our study found evidence for climate sensitivity being on the higher end of the canonical range).

Second, the Cox et al. (2018) study is based on an area of research that I had some experience in: the relationship between short-term temperature variability and long-term climate sensitivity. The general idea that these two things should be related has been around for a while (for example, it’s covered in some depth in Gerard Roe’s 2009 review on climate sensitivity). But in 2015 Kevin Bowman suggested to me that “Fluctuation-Dissipation Theorem” might be useful for using short-term temperature variability to narrow uncertainty in climate sensitivity.  It just so happens that this is the same theoretical foundation that underlies the Cox et al. (2018) results. Following Bowman’s suggestion, I spent several months looking for a useful relationship but I was unable to find one.

Thus, when Cox et al. (2018) was published, I was naturally curious about the specifics of how they arrived at their conclusions both because their results diverged from that of our related study and because they used a particular theoretical underpinning that I had previously found to be ineffectual.

I worked with Martin Stolpe and Ken Caldeira to investigate the Cox et al. (2018) methodology in some detail and to conduct a number of sensitivity tests of their results. We felt that our experiments pointed to some issues with aspects of the study’s methodology and that lead us to submit the aforementioned comment to Nature.

In our comment, we raise two primary concerns.

First, we point out that most of the reported 60% reduction in climate sensitivity uncertainty originates not from the constraint itself but from the choice of the baseline that the revised uncertainty range is compared to. Specifically, the large reduction in uncertainty depends on their choice to compare their constrained uncertainty to the broad IPCC ‘likely’ range of 1.5ºC-4.5ºC rather than to the ‘likely’ range of the raw climate models used to inform the analysis. This choice would be justifiable if the climate models sampled the entire uncertainty range for climate sensitivity but this is not the case. The model ensemble happens to start with an uncertainty range that is about 45% smaller than the IPCC-suggested ‘true’ uncertainty range (which incorporates additional information from e.g., paleoclimate studies). Since the model ensemble embodies a smaller uncertainty range than the IPCC range, one could simply take the raw models, calculate the likely range of climate sensitivity using those models, and claim that this calculation alone “reduces” climate sensitivity uncertainty by about 45%. We contend that such a calculation would not tell us anything meaningful about true climate sensitivity. Instead, it would simply tell us that the current suite of climate models don’t adequately represent the full range of climate sensitivity uncertainty.

Thus, even if the other methodological choices of Cox et al. (2018) are accepted as is, close to 3/4ths of the reported 60% reduction in climate sensitivity uncertainty is attributable to starting from a situation in which the model ensemble samples only a fraction of the full uncertainty range in climate sensitivity.

The second issue that we raise has to do with the theoretical underpinnings of the Cox et al. (2018) constraint. Specifically, The emergent constraint presented by Cox et al. (2018), based on the Fluctuation-Dissipation Theorem, “relates the mean response to impulsive external forcing of a dynamical system to its natural unforced variability” (Leith, 1975).

In this context, climate sensitivity represents the mean response to external forcing, and the measure of variability should be applied to unforced (or internally generated) temperature variability. Cox et al. (2018) state that their constraint is founded on the premise that persistent non-random forcing has been removed:

If trends arising from net radiative forcing and ocean heat uptake can be successfully removed, the net radiative forcing term Q can be approximated by white noise. Under these circumstances, equation (1) … has standard solutions … for the lag-one-year autocorrelation of the temperature.

They suggest that linear detrending with a 55-year moving window may be optimal for the separation of forced trends from variability:

Figure 4a shows the best estimate and 66% confidence limits on ECS as a function of the width of the de-trending window. Our best estimate is relatively insensitive to the chosen window width, but the 66% confidence limits show a greater sensitivity, with the minimum in uncertainty at a window width of about 55 yr (as used in the analysis above). As Extended Data Fig. 3 shows, at this optimum window width the best-fit gradient of the emergent relationship between ECS and Ψ (= 12.1) is also very close to our theory-predicted value of 2 Q2×CO2/σQ (= 12.2). This might be expected if this window length optimally separates forced trend from variability.

Linearly detrending within a moving window is an unconventional way to separate forced from unforced variability and we argue in our comment that it is inadequate for this purpose. (In their reply to our comment Cox et al. agree with this but they contend that mixing forced and unforced variability does not present the problem that we claim it does.)

Using more conventional methods to remove forced variability, we find that the Cox et al. (2018) constraint produces central estimates of climate sensitivity that lack a consistent sign shift relative to their starting value (i.e., it is not clear if the constraint shifts the best estimate of climate sensitivity in the positive or negative direction).

We also find that the more complete removal of forced variability produces constrained confidence intervals on climate sensitivity that range from being no smaller than the raw model confidence intervals used to inform the analysis (Fig. 1d and 1e) to being about 11% smaller than the raw model range (Fig. 1f). This is compared to the 60% reduction in the size of the confidence interval reported in Cox et al., (2018).


Figure 1 | Comparison of central estimate and ‘likely’ range (>66%) of Equilibrium climate sensitivity over a variety of methodologies and for four observational datasets. Average changes (across the four observational datasets) in the central estimates of climate sensitivity are reported within the dashed-line range, average changes in uncertainty ranges (confidence intervals) are reported at the bottom of the figure, and r2 values of the relationship are reported at the top of the figure. Results corresponding to observations from GISTEMP, HadCRUT4, NOAA and Berkeley Earth are shown in black, red, blue and green respectively. Changes in uncertainty are reported relative to the raw model range (±0.95 standard deviations across the climate sensitivity range of CMIP5 models) used to inform the analysis (b) rather than relative to the broader IPCC range used as the baseline in Cox et al. (2018) (a).


Overall, we argue that historical temperature variability provides, at best, a weak constraint on climate sensitivity and that it is not clear if it suggests a higher or lower central estimate of climate sensitivity relative to the canonical 3ºC value.

For more details please see the original Cox et al. (2018) paper, our full comment and the reply to our comment by Cox et al.

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