by Judith Curry

Are values of equilibrium climate sensitivity > 4.5 C plausible?

For background, see these previous posts on climate sensitivity [link]

Here are some possibilistic arguments related to climate sensitivity. I don’t think the ECS example is the best one to illustrate these ideas [see previous post], and I probably won’t include this example in anything I try to publish on this topic (my draft paper is getting too long anyways). But possibilistic thinking does point you in some different directions when pondering the upper bound of plausible ECS values.

**5. Climate sensitivity**

Equilibrium climate sensitivity (ECS) is defined as the amount of temperature change in response to a doubling of atmospheric CO_{2} concentrations, after the climate system has reached equilibrium. The issue with regards to ECS is not scenario discovery; rather, the challenge is to clarify the upper bounds of possible and plausible worst cases.

The IPCC assessments of ECS have focused on a ‘likely’ (> 66% probability) range, which has mostly been unchanged since Charney et al. (1979), to be between 1.5 and 4.5 ^{o}C. The IPCC AR4 (2007) did not provide any insight into a worst-case value of ECS, stating that values substantially higher than 4.5 ^{o}C cannot be excluded, with tail values in Figure 9.20 exceeding 10 ^{o}C. The IPCC AR5 (2013) more clearly defined the upper range, with a 10% probability of exceeding 6 ^{o}C.

Since the IPCC AR5, there has been considerable debate as to whether ECS is on the lower end of the likely range (e.g., < 3 ^{o}C) or the higher end of the likely range (for a summary, see Lewis and Curry, 2018). The analysis here bypasses that particular debate and focuses on the upper extreme values of ECS.

High-end values of ECS are of considerable interest to economists. Weitzman (2009) argued that probability density function (PDF) tails of the equilibrium climate sensitivity, fattened by structural uncertainty using a Bayesian framework, can have a large effect on the cost-benefit analysis. Proceeding in the Bayesian paradigm, Weitzman fitted a Pareto distribution to the AR4 ECS values, resulting in a fat tail that produced a probability of 0.05 of ECS exceeding 11 ^{o}C, and a 0.01% probability of exceeding 20 ^{o}C.

The range of ECS values derived from global climate models (CMIP5) that were cited by the IPCC AR5 is between 2.1 and 4.7 ^{o}C. To better constrain the values of ECS based on observational information available at the time of the AR5, Lewis and Grunwald (2018) combined instrumental period evidence with paleoclimate proxy evidence using objective Bayesian and frequentist likelihood-ratio methods. They identified a 5–95% range for ECS of 1.1–4.05 ^{o}C. Using the same analysis methods, Lewis and Curry (2018) updated the analysis for the instrumental period by extending the period and using revised estimates of forcing to determine a 5-95% range of 1.05 – 2.7 ^{o}C. The observationally-based values should be regarded as estimates of effective climate sensitivity, as they reflect feedbacks over too short a period for equilibrium to be reached.

Values of climate sensitivity exceeding 4.5 ^{o}C derived from observational analyses are arguably associated with deficiencies in the diagnostics or analysis approach (e.g. Annan and Hargreaves, 2006; Lewis and Curry, 2015). In particular, use of a non-informative prior (e.g. Jeffreys prior), or a frequentist likelihood-ratio method, narrows the upper tail considerably. However, as summarized by Frame et al. (2006), there is no observational constraint on the upper bound of ECS.

The challenges of identifying an upper bound for ECS are summarized by Stevens et al. (2016) and Knutti et al. (2017). Stevens et al. (2016) describes a systematic approach for refuting physical storylines for extreme values. Stevens et al.’s physical storyline for a very high ECS (*>*4.5 ^{o}C) is comprised of three conditions: (i) the aerosol cooling influence in recent decades would have to have been strong enough to offset most of the effect of rising greenhouse gases; (ii) tropical sea-surface temperatures at the time of the last glacial maximum would have to have been much cooler than at present; and (iii) cloud feedbacks from warming would have to be strong and positive.

An interesting challenge to identifying the plausible upper bound for ECS has been presented by a newly developed climate model, the DOE E3SM (Golaz et al. 2019), which includes numerous technical and scientific advances. The model’s value of ECS has been determined to be 5.3 ^{o}C, higher than any of the CMIP5 model values and outside the IPCC AR5 likely range. This high value of ECS is attributable to very strong shortwave cloud feedback. The DOE E3SM model’s value of shortwave cloud feedback is larger than all CMIP5 models; however, shortwave cloud feedback is weakly constrained by observations and physical understanding. A stronger argument for placing the DOE E3SM value of climate sensitivity in the ‘borderline impossible’ category is Figure 23 in Golaz et al. (2019), which shows that the global mean surface temperature simulated by the model during the period 1960-2000 is as much as 0.5 ^{o}C lower than observed, and that since the mid-1990s the simulated temperature rises far faster than the observed temperature. This case illustrates the challenge of refuting scenarios associated with a complex storyline or model, which was noted by Stevens et al. (2016).

An additional issue regarding climate model derived values of ECS was raised by recent paper by Mauritsen et al. (2019). An intermediate version of the MPI-ESM1.2 global climate model produced an ECS value of ~ 7 ^{o}C, caused by the parameterization of low-level clouds in the tropics. Since this model version produced substantially more warming than observed in the historical period, this model version was rejected and model cloud parameters were adjusted to target a value of ECS closer to 3 ^{o}C, resulting in a final ECS value of 2.77 ^{o}C. The strategy employed by Mauritsen et al. (2019) raises the issue as to what extent climate model-derived ECS values are truly emergent, rather than a result of tuning that explicitly or implicitly considers the value of ECS and the match of the model simulations with the historical temperature record.

Was Mauritsen et al. (2019) justified in rejecting the model version with an ECS value of ~ 7 ^{o}C? Is the MPI-ESM1.2 value of ECS of 5.3 ^{o}C plausible? Observationally-derived values of ECS (e.g. Lewis and Curry, 2018) are inadequate for defining the upper bounds of ECS. There are two types of constraints that in principle can be used: emergent constraints and the Transient Climate Response.

Emergent constraints in principle can help narrow uncertainties in climate model sensitivity through empirical relationships that relate a model’s response to observable metrics. These analyses have mostly focused on cloud processes. The credibility of an emergent constraint relies upon the strength of the statistical relationship, a clear understanding of the mechanisms underlying the relationship, and the accuracy of observations. Further, the most robust emergent constraints are for model parameters that are driven by a single physical process (e.g. Winsberg, 2018). Investigations of integral constraints related to cloud processes have mostly concluded that the climate models with ECS values on the high end of the IPCC AR5 *likely* range show best agreement with the integral constraints (e.g. Caldwell et al., 2018). However, Caldwell et al. (2018) and Winsberg (2018) caution that additional processes influencing the metric and other biases in the model may affect the analysis. While the robustness and utility of these emergent constraints continues to be investigated and debated, this technique is not very helpful in identifying a plausible upper bound or in rejecting high values such as obtained by Golaz et al. (2019) and Mauritzen et al. (2019).

The Transient Climate Response (TCR) in principle can be of greater utility in providing an observational constraint on climate sensitivity. TCR is the amount of warming that might occur at the time when CO_{2} doubles, having increased gradually by 1% each year over a period of 70 years. Relative to the ECS, observationally-determined values of TCR avoid the problems of uncertainties in ocean heat uptake and the fuzzy boundary in defining equilibrium owing to a range of timescales for the various feedback processes. Further, an upper limit to TCR can in principle be determined from observational analyses.

TCR values cited by the IPCC AR5 have a *likely* (>66%) upper bound of 2.5 ^{o}C and < 5% probability of exceeding 3 ^{o}C. Knutti et al. (2017; Figure 1) show several relatively recent TCR distributions whose 90 percentile value exceeds 3 ^{o}C. Observationally-derived values of TCR determined by Lewis and Curry (2018) identified the 5-95% range to be 1.0–1.9 K. As discussed by Lewis and Curry (2015) and Lewis and Grunwald (2017), use of a non-informative prior or a frequentist likelihood-ratio method narrows the upper tail considerably. While the methodological details of determining values of TCR from observations continue to be debated, in principle the upper bound of TCR can be constrained by historical observations.

How does a constraint on the upper bound of TCR help constrain the high-end values of ECS? A TCR value of 2.93 ^{o}C was determined by Golaz et al. (2019) for the MPI-ESM1.2 model, which is well above the 95% value determined by Lewis and Curry (2018), and also above the IPCC AR5 *likely* range. Table 9.5 of the IPCC AR5 lists the ECS and TCR values of each of the CMIP5 models. If a TCR value of 2 ^{o}C is used as the maximum plausible value of TCR based on the Lewis and Curry (2018) analysis, then it seems reasonable to classify climate model-derived values of ECS associated with TCR values ≤ 2.0 ^{o}C as verified possibilities.

In light of the cited analyses of ECS (which are not exhaustive), consider the following classification of values of equilibrium climate sensitivity relative to the π-based classifications provided in the possibilistic post, which provides the expert judgment of one analyst (moi). Note that overlapping values in the different classifications arise from different scenario generation methods associated with different necessity-judgment rationales:

- ECS < 0: impossible
- 0 > ECS < 1
^{o}C: implies negative feedback (unverified possibility) - 0 ≤ ECS ≤ 1.2
^{o}C: no feedback climate sensitivity (strongly verified, based on theoretical analysis and empirical observations). - 1.05 ≤ ECS ≤ 2.7
^{o}C: empirically-derived values based on energy balance models from the instrumental period with verified statistical and uncertainty analysis methods (Lewis and Curry, 2018) (corroborated possibilities) - 1.15 ≤ ECS ≤ 4.05
^{o}C: empirically-derived values including paleoclimate estimates (Lewis and Grunwald, 2018) (verified possibilities) - 2.1 ≤ ECS ≤ 4.1
^{o}C: derived from climate model simulations whose values of TCR do not exceed 2.0^{o}C. (Table 9.5, IPCC AR5) (verified possibilities) - 4.5 < ECS ≤ 6
^{ o}C: borderline impossible - ECS > 6
^{o}C: impossible

In evaluating the justification of the high-end values of ECS, it is useful to employ the logic of partial positions for an ordered scale of events. It is rational to believe with high confidence a *partial position *that equilibrium climate sensitivity is at least 1 ^{o}C and between 1 and 2.7 ^{o}C, which encompasses the strongly verified and corroborated possibilities. This partial position with a high degree of justification is relatively immune to falsification. It is also rational to provisionally extend one’s position to believe values of equilibrium climate sensitivity up to 4.1 ^{o}C – the range simulated by climate models whose TCR values do not exceed 2.0 ^{o}C — although these values are vulnerable to improvements to climate models and our observational estimates of TCR, whereby portions of this extended position may prove to be false. High degree of justification ensures that a partial position is highly immune to falsification and can be flexibly extended in many different ways when constructing a complete position.

The conceivable worst case for ECS is arguably ill-defined; there is no obvious way to positively infer this, and such inferences are hampered by timescale fuzziness between equilibrium climate sensitivity and the larger earth system sensitivity. However, one can refute estimates of extreme values of ECS from fat-tailed distributions > 10 ^{o}C (e.g. Weitzman, 2009) as arguably impossible – these reflect the statistical manufacture of extreme values that are unjustified by either observations or theoretical understanding, and extend well beyond any conceivable uncertainty or possible ignorance about the subject.

The possible worst case for ECS is judged here to be 6.0 ^{o}C, although this boundary is weakly justified. The only evidence for very high values of ECS comes from climate model simulations with very strong positive cloud feedback (e.g. Mauritzen et al. 2019; Golaz et al. 2019) and statistical analyses that use informative priors. Further examination of the CMIP6 models is needed to assess the causes, outcomes and plausibility of parameters and feedbacks in these models with very high values of ECS before rejecting them as impossible.

With regards to the plausible worst case (lower bound of borderline impossible values) of ECS, consideration was given to the upper bound of verified possibilities (4.1 ^{o}C) and also the time-honored value of 4.5 ^{o}C as the upper bound as the ‘likely’ range for ECS. Consideration of the model’s value of TCR in comparison to observationally-derived values of TCR seems to be a useful constraint for assessing the plausibility of a model’s ECS value. However, further investigation is needed to understand the methodological differences in the varying estimates of TCR and the causes of varying relations between TCR and ECS values among different models. This seems to be a more fruitful way forward than the emergent constraints approach.

Given that 4.5 ^{o}C was specified by the IPCC AR5 as the upper bound of the likely range (> 66% probability), the judgment here that specifies 4.5 ^{o}C as the maximum plausible value of ECS will undoubtedly be controversial. Other analysts may make different judgments and draw a different conclusion on this. Consideration of different rationales for making judgments on the maximum plausible value of ECS would illuminate the underlying issues and rationales for judgments.

Because of the central role that ECS plays in Integrated Assessment Models used to determine the social cost of carbon that is largely driven by tail values of ECS, the issue of clarifying the plausible and possible values of ECS is not without consequence.

via Climate Etc.

April 1, 2019 at 08:37AM