by Nic Lewis

Emergent constraints on climate sensitivity: their nature and assessment of validity.

There have been quite a number of papers published in recent years concerning “emergent constraints” on equilibrium climate sensitivity (ECS) in comprehensive global climate models (GCMs), of both the current (CMIP5) and previous (CMIP3) generations. The range of ECS values in GCMs has remained almost unchanged since the early days of climate modelling; in the IPCC 5th Assessment Report (AR5) it was given as 2.1-4.7°C for CMIP5 models.[i]

From the IPCC 1st Assessment Report (FAR) to AR5, the main cause of the large uncertainty as to ECS in GCMs has been the difficulty of simulating clouds and their behaviour.[ii] This has led to cloud feedback differing between GCMs even as to its sign – and to little confidence that the true level of cloud feedback lies within its range in GCMs. Progress in understanding cloud behaviour and related convective dynamics and feedbacks has been painfully slow. We shall see in this 3-part article that emergent constraint approaches have the potential to offer useful insights into cloud behaviour, however the main focus will be on to what extent they narrow the uncertainty range of ECS in GCMs.

Emergent constraint studies typically identify a quantitative measure of an aspect of GCMs’ behaviour (a metric) that is well correlated with their ECS values across an ensemble of GCMs. They then compare observational estimates of that metric with its value in each GCM. Often they use regression to fit a linear relationship between the metric and ECS values in the GCM-ensemble, and assert that the range of ECS values spanned by the segment of the regression line consistent with observational estimates of the metric is most credible. Alternatively they derive a constrained ECS range directly from the ECS values of GCMs whose behaviour is consistent with observational estimates of the metric. Sometimes more than one metric is used. In most cases, such emergent constraint studies have favoured ECS values in the upper half (3.4–4.7°C) of the CMIP5 range.

Probably the best known emergent constraints study is Sherwood et al (2014).[iii] That study has often been cited in support of arguments that ECS is unlikely to be in the lower half of the IPCC’s 1.5–4.5°C range, contrary to what is suggested by energy-budget studies that relate warming and heat uptake during the instrumental period to the estimated change radiative forcing. The abstract to Sherwood et al (2014) says this about the spread of ECS in GCMs:

The spread arises largely from differences in the feedback from low clouds, for reasons not yet understood. Here we show that differences in the simulated strength of convective mixing between the lower and middle tropical troposphere explain about half of the variance in climate sensitivity estimated by 43 climate models. The apparent mechanism is that such mixing dehydrates the low-cloud layer at a rate that increases as the climate warms, and this rate of increase depends on the initial mixing strength, linking the mixing to cloud feedback. The mixing inferred from observations appears to be sufficiently strong to imply a climate sensitivity of more than 3 degrees for a doubling of carbon dioxide.

The Sherwood emergent constraint is linked to feedback from changes in low clouds, which affect reflected shortwave (SW) solar radiation. Differences between GCMs in SW low cloud feedback are known to be the main factor behind their wide spread of ECS values, so it makes sense that an emergent constraint would involve SW cloud feedback. Indeed, a paper published earlier this year (Qu et al 2018)[iv] concluded that all useful emergent constraints on ECS work via SW low cloud feedback, saying:

Here a statistical method (including a backward selection process) is employed to achieve a better statistical understanding of the connections between four recently proposed emergent constraint metrics and individual feedbacks influencing ECS. The relationship between each metric and ECS is largely attributable to a statistical connection with shortwave low cloud feedback, the leading cause of intermodel ECS spread. This result bolsters confidence in some of the metrics, which had assumed such a connection in the first place. Additional analysis is conducted with a few thousand artificial metrics that are randomly generated, but are well correlated with ECS. The relationships between the contrived metrics and ECS can also be linked statistically to shortwave cloud feedback. Thus any proposed or forthcoming ECS constraint based on the current generation of climate models should be viewed as a potential constraint on shortwave cloud feedback, and physical links with that feedback should be investigated to verify that the constraint is real. In addition, any proposed ECS constraint should not be taken at face value, since other factors influencing ECS besides shortwave cloud feedback could be systematically biased in the models.

The key point is that, since SW low cloud feedback accounts for a large part of the overall variation in GCM ECS values, any metric that in GCMs is well correlated with ECS is almost bound to be strongly correlated with SW cloud feedback. But, as Qu et al. go on to say, the reality of the physical links between the emergent constrain metric and SW feedback must be investigated, and even where it exists other biases in GCMs may affect the validity of their ECS values. That is a very important point.

A recent paper, Caldwell et al. 2018,[v] systematically reviewed emergent constraints on ECS, analysing the 19 previously-proposed constraints detailed in Table 1. They omitted emergent constraints that were impracticable to test or had already been found not to be robust. They also omitted two emergent constraints that targeted high-latitude clouds and were poorly correlated with ECS, which they took to mean that only constraints on tropical clouds had a strong impact on ECS.

The correlations with ECS given in Table 1 are for ensembles of all CMIP5 models for which the data needed to calculate the metric for the emergent constraint involved were available. The ensemble therefore varies between constraints as to both size and constituent models. Correlations shown in brackets are not significant at the 90% probability level. Because many models are related, and the likelihood of data-mining for high correlation constraints having taken place, the significance test is weak and (as Caldwell et al. say) should be regarded as just screening out constraints that are almost certainly not significant. In many cases the original study tested the constraint on CMIP3 models or a combination of CMIP3 and CMIP5 models, and may have obtained a stronger correlation. However, a valid emergent constraint should persist between model generations.

Table 1. Short description of each emergent constraint on ECS tested in Caldwell et al. 2018, per their Table 1, and their calculation of its correlation with ECS in CMIP5 models (from their Table 2). Correlations in brackets are not significant with 90% probability, assuming model independence.

The Caldwell findings are very interesting. Its abstract makes these points:

Several constraints are shown to be closely related, emphasizing the importance for careful understanding of proposed constraints. A new method is presented for decomposing correlation between an emergent constraint and ECS into terms related to physical processes and geographical regions. Using this decomposition, one can determine whether the processes and regions explaining correlation with ECS correspond to the physical explanation offered for the constraint. Shortwave cloud feedback is generally found to be the dominant contributor to correlations with ECS because it is the largest source of inter-model spread in ECS. In all cases, correlation results from interaction between a variety of terms, reflecting the complex nature of ECS and the fact that feedback terms and forcing are themselves correlated with each other. For 4 of the 19 constraints, the originally-proposed explanation for correlation is borne out by our analysis. These 4 constraints all predict relatively high climate sensitivity. The credibility of 6 other constraints is called into question due to correlation with ECS coming mainly from unexpected sources and/or lack of robustness to changes in ensembles. Another 6 constraints lack a testable explanation and hence cannot be confirmed. The fact that this study casts doubt upon more constraints than it confirms highlights the need for caution when identifying emergent constraints from small ensembles.

Caldwell et al. also point out that:

One problem with emergent constraints is that large inter-model correlations between current climate and future-climate quantities are expected by chance in multi-model databases. As a result, emergent constraints without a solid physical basis should be viewed with scepticism. Unfortunately, most emergent constraints in the published literature lack a satisfying physical explanation.

Caldwell et al. therefore regard a proposed emergent constraint as not credible if it lacks an identifiable physical mechanism; is not robust to change of model ensemble; or if its correlation with ECS is not due to its proposed physical mechanism. For the last point, they examine the decomposition of the correlation by source (types of feedback, and forcing from a doubling of CO 2 ) and the geographical location of the principal sources of correlation.

Caldwell et al.’s eventual assessments of the 19 proposed emergent constraints are shown in Table 2. In two cases they combined a pair of constraints that are similar and well correlated. They note that those two pairs (Volodin/Siler and Zhai/Brient Alb) are similar in that both assume cloud changes track SST in a climate-invariant way, but that although Volodin and Siler are both strongly correlated with Brient Alb, they are poorly correlated with Zhai.

Table 2. Assessment of proposed emergent constraints by Caldwell et al 2018. Reproduction of their Table 4

The fact that only 4 out of the 19 emergent constraints pass Caldwell’s basic tests of credibility is disturbing, and implies that results from emergent constraint studies should be treated with considerable scepticism. Some of the papers proposing failed constraints are highly cited, e.g. Trenberth (where the originally reported strong –0.73 correlation fell to a very weak –0.22 in CMIP5 models) has 219 citations.[i] Somewhat surprisingly, all three of the proposed emergent constraints that Trenberth and Fasullo formulated had insignificant correlations with ECS when tested on CMIP5 models.

In Parts 2 and 3 of this article I will examine the 4 constraints, all favouring high ECS values, that Caldwell et al find credible, and formulate conclusions.

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Nicholas Lewis March 2018

[i] Trenberth, K. E., and J. T. Fasullo, 2010: Simulation of present day and 21st century energy budgets of the southern oceans. J. Clim., 23, 440–454.

[i] Table 9.5 of AR5. The method used appears to slightly overestimate the ECS of the least sensitive CMIP5 models and to underestimate the ECS of the most sensitive models. A better estimate of the range would be from slightly under 2°C to slightly above 5 °C. This is almost identical to the 1.9–5.2°C range in the IPCC 1st Assessment Report (FAR).

[ii] See, e.g., Section 5.2.1 of the FAR. Note that I am including problems in simulating convection as part of the cloud simulation problems, as the two issues are intimately connected.

[iii] Sherwood, S.C., Bony, S. and Dufresne, J.L., 2014. Spread in model climate sensitivity traced to atmospheric convective mixing. Nature, 505(7481), p.37-42.

[iv] Qu, X., A. Hall, A. M. DeAngelis, M. D. Zelinka, S. A. Klein, H. Su, B. Tian, and C. Zhai, 2018: On the emergent constraints of climate sensitivity. Journal of Climate, 31 (2), 863–875, doi:10.1175/JCLI-D-17-0482.1.

[v] Caldwell, P, M Zelinka and S Klein, 2018. Evaluating Emergent Constraints on Equilibrium Climate Sensitivity. J. Climate. doi:10.1175/JCLI-D-17-0631.1, in press.

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