A Bayesian framework for emergent constraints: case studies of
climate sensitivity with PMIP

Renoult, Martin; Hargreaves, J. C.; Sagoo, Navjit; Flynn, Clare M.; Kapsch, Marie‐Luise; Mikolajewicz, Uwe; Ohgaito, Rumi; Mauritsen, Thorsten

doi:10.5194/cp-2019-162

Cited by 4 publications

(6 citation statements)

References 32 publications

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“…Model runs have been colour-coded by their TCR value, with darker red indicating models with higher TCR and darker blue indicating lower TCR. Black lines are observational global warming datasets over the same period (Morice et al, 2012;Rohde et al, 2013;Lenssen et al, 2019;Zhang et al, 2020). Models with higher TCR either show large warming at the end of the period, or portray a strong aerosol cooling over the 20th century, particularly visible as a dip around 1960-1970 (notably CNRM-ESM1, UKESM1-0-LL and EC-Earth-Veg).…”

Section: Transient Climate Responsementioning

confidence: 99%

“…4a. Observational warming (black vertical dashed line) is the mean of Had-CRUT4 (Morice et al, 2012), Berkeley Earth (Rohde et al, 2013), GISSTEMP4 (Lenssen et al, 2019) and NOAA v5 (Zhang et al, 2020). The 90 % observational confidence interval (grey shaded vertical area) is a combination of the observational uncertainty and the internal variability.…”

Section: Transient Climate Responsementioning

confidence: 99%

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Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models

2020

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Abstract. Climate sensitivity to CO2 remains the key uncertainty in projections of future climate change. Transient climate response (TCR) is the metric of temperature sensitivity that is most relevant to warming in the next few decades and contributes the biggest uncertainty to estimates of the carbon budgets consistent with the Paris targets. Equilibrium climate sensitivity (ECS) is vital for understanding longer-term climate change and stabilisation targets. In the IPCC 5th Assessment Report (AR5), the stated “likely” ranges (16 %–84 % confidence) of TCR (1.0–2.5 K) and ECS (1.5–4.5 K) were broadly consistent with the ensemble of CMIP5 Earth system models (ESMs) available at the time. However, many of the latest CMIP6 ESMs have larger climate sensitivities, with 5 of 34 models having TCR values above 2.5 K and an ensemble mean TCR of 2.0±0.4 K. Even starker, 12 of 34 models have an ECS value above 4.5 K. On the face of it, these latest ESM results suggest that the IPCC likely ranges may need revising upwards, which would cast further doubt on the feasibility of the Paris targets. Here we show that rather than increasing the uncertainty in climate sensitivity, the CMIP6 models help to constrain the likely range of TCR to 1.3–2.1 K, with a central estimate of 1.68 K. We reach this conclusion through an emergent constraint approach which relates the value of TCR linearly to the global warming from 1975 onwards. This is a period when the signal-to-noise ratio of the net radiative forcing increases strongly, so that uncertainties in aerosol forcing become progressively less problematic. We find a consistent emergent constraint on TCR when we apply the same method to CMIP5 models. Our constraints on TCR are in good agreement with other recent studies which analysed CMIP ensembles. The relationship between ECS and the post-1975 warming trend is less direct and also non-linear. However, we are able to derive a likely range of ECS of 1.9–3.4 K from the CMIP6 models by assuming an underlying emergent relationship based on a two-box energy balance model. Despite some methodological differences; this is consistent with a previously published ECS constraint derived from warming trends in CMIP5 models to 2005. Our results seem to be part of a growing consensus amongst studies that have applied the emergent constraint approach to different model ensembles and to different aspects of the record of global warming.

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Section: Transient Climate Responsementioning

confidence: 99%

Section: Transient Climate Responsementioning

confidence: 99%

Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models

2020

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“…In a discussion paper by Renoult et al (2020), a simple method was proposed to combine independent ECs to create a tighter estimate for Y . Where the regression is normally given as p(y|x), they propose to instead formulate the statistical model as p(x|y), allowing for a prior on π(y) to be integrated into the emergent constraint as…”

Section: Discussionmentioning

confidence: 99%

“…Much of the work on ECs has used just two scalar variables, a predictor X, and a response or predictand Y , related linearly. This could be extended to two or more predictors or predictands (Renoult et al, 2020). The predictand space to constrain will become larger however, and this might be difficult with small ESM ensembles.…”

Section: Multidimensional Ecs and Nonlinear Emergent Relationshipsmentioning

confidence: 99%

Emergent constraints on climate sensitivities

Williamson,

Thackeray,

Cox

et al. 2020

Preprint

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Despite major advances in climate science over the last 30 years, persistent uncertainties in projections of future climate change remain. Climate projections are produced with increasingly complex models which attempt to represent key processes in the Earth system, including atmospheric and oceanic circulations, convection, clouds, snow, sea-ice, vegetation and interactions with the carbon cycle. Uncertainties in the representation of these processes feed through into a range of projections from the many state-of-theart climate models now being developed and used worldwide. For example, despite major improvements in climate models, the range of equilibrium global warming due to doubling carbon dioxide still spans a range of more than three. Here we review a promising way to make use of the ensemble of climate models to reduce the uncertainties in the sensitivities of the real climate system. The emergent constraint approach uses the model ensemble to identify a relationship between an uncertain aspect of the future climate and an observable variation or trend in the contemporary climate. This review summarises previous published work on emergent constraints, and discusses the huge promise and potential dangers of the approach. Most importantly, it argues that emergent constraints should be based on well-founded physical principles such as the fluctuation-dissipation theorem. It is hoped that this review will stimulate physicists to contribute to the rapidly-developing field of emergent constraints on climate projections, bringing to it much needed rigour and physical insights.

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“…Code and data availability. The Python codes used for the different statistical methods are available from the Bolin Centre Code Repository at https://git.bolin.su.se/bolin/renoult-2020 (last access: 2 July 2020; https://doi.org/10.5281/zenodo.3928315, Renoult and Annan, 2020). The data of the PMIP2 models can be obtained by asking the corresponding modelling groups.…”

Section: Appendix A: Conjugate Prior Approachmentioning

confidence: 99%

A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

Renoult

Hargreaves²,

Sagoo

et al. 2020

Clim. Past

Self Cite

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Abstract. In this paper we introduce a Bayesian framework, which is explicit about prior assumptions, for using model ensembles and observations together to constrain future climate change. The emergent constraint approach has seen broad application in recent years, including studies constraining the equilibrium climate sensitivity (ECS) using the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period (mPWP). Most of these studies were based on ordinary least squares (OLS) fits between a variable of the climate state, such as tropical temperature, and climate sensitivity. Using our Bayesian method, and considering the LGM and mPWP separately, we obtain values of ECS of 2.7 K (0.6–5.2, 5th–95th percentiles) using the PMIP2, PMIP3, and PMIP4 datasets for the LGM and 2.3 K (0.5–4.4) with the PlioMIP1 and PlioMIP2 datasets for the mPWP. Restricting the ensembles to include only the most recent version of each model, we obtain 2.7 K (0.7–5.2) using the LGM and 2.3 K (0.4–4.5) using the mPWP. An advantage of the Bayesian framework is that it is possible to combine the two periods assuming they are independent, whereby we obtain a tighter constraint of 2.5 K (0.8–4.0) using the restricted ensemble. We have explored the sensitivity to our assumptions in the method, including considering structural uncertainty, and in the choice of models, and this leads to 95 % probability of climate sensitivity mostly below 5 K and only exceeding 6 K in a single and most uncertain case assuming a large structural uncertainty. The approach is compared with other approaches based on OLS, a Kalman filter method, and an alternative Bayesian method. An interesting implication of this work is that OLS-based emergent constraints on ECS generate tighter uncertainty estimates, in particular at the lower end, an artefact due to a flatter regression line in the case of lack of correlation. Although some fundamental challenges related to the use of emergent constraints remain, this paper provides a step towards a better foundation for their potential use in future probabilistic estimations of climate sensitivity.

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A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

Cited by 4 publications

References 32 publications

Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models

Emergent constraints on transient climate response (TCR) and equilibrium climate sensitivity (ECS) from historical warming in CMIP5 and CMIP6 models

Emergent constraints on climate sensitivities

A Bayesian framework for emergent constraints: case studies of climate sensitivity with PMIP

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