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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Abstract. The 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 (Arora et al. 2019). In the IPCC 5th Assessment Report (AR5), the stated likely range of TCR was given as 1.0 to 2.5 K, with a central estimate which was broadly consistent with the ensemble mean of the CMIP5 Earth System Models (ESMs) available at the time (1.8 ± 0.4 K). Many of the latest CMIP6 ESMs have larger climate sensitivities, with 6 of 23 models having TCR values above 2.5 K, and an ensemble mean TCR of 2.1 ± 0.4 K. On the face of it, these latest ESM results suggest that the IPCC likely range of TCR 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 further constrain the likely range of TCR to 1.5–2.2 K, with a central estimate of 1.82 K. We reach this conclusion through an emergent constraint approach which relates the value of TCR to the global warming from 1970 onwards. We confirm a consistent emergent constraint on TCR when we apply the same method to CMIP5 models (Jiménez-de-la Cuesta and Mauritsen, 2019). Our emergent constraint on TCR benefits from both the large range of TCR values across the CMIP6 models, and also from the extension of the historical simulations into a period when the uncertain changes in aerosol forcing have had a far less significant impact on the trend in global warming.
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. <p>The transient climate response (TCR), transient warming for a doubling of CO2, contributes the biggest uncertainty to estimates of the carbon budgets consistent with the Paris targets. In the IPCC 5th Assessment Report (AR5), the stated ‘likely’ range of TCR was given as 1.0 to 2.5K, with a central estimate which was broadly consistent with the ensemble mean of the CMIP5 Earth System Models (ESMs) available at the time (1.8 +/- 0.4 K). Many of the latest CMIP6 ESMs have larger climate sensitivities, with 6 of 23 models having TCR values above 2.5 K, and an ensemble mean TCR of 2.1 +/- 0.4 K. On the face of it, these latest ESM results suggest that the IPCC likely range of TCRE may need revising upwards, which would cast further doubt on the feasibility of the Paris targets.</p><p>We analyse the CMIP6 models through an emergent constraint approach which relates the value of TCR to the global warming from 1970 onwards. We confirm a consistent emergent constraint on TCR when we apply the same method to CMIP5 model. Our emergent constraint on TCR benefits from both the large range of TCR values across the CMIP6 models, and also from the extension of the historical simulations into a period when the uncertain changes in aerosol forcing have had a far less significant impact on the trend in global warming.</p><p>We show that rather than increasing the uncertainty in climate sensitivity, the CMIP6 models help to further constrain the likely range of TCR to 1.5-2.2 K. In CMIP6, diagnosed emissions at carbon doubling was found to be independent of TCR, so that a constraint on TCR directly leads to a constrained estimate of TCRE, with a likely range of 1.3 – 2.0 K per EgC. </p>
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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-the-art 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.

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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One of the approaches to constrain uncertainty in climate models is the identification of emergent constraints. These are physically explainable empirical relationships between a particular simulated characteristic of the current climate and future climate change from an ensemble of climate models, which can be exploited using current observations. In this paper, we develop a theory to understand the appearance of such emergent constraints. Based on this theory, we also propose a classification for emergent constraints, and applications are shown for several idealized climate models.

There is as yet no theoretical framework to guide the search for emergent
constraints. As a result, there are significant risks that indiscriminate
data-mining of the multidimensional outputs from GCMs could lead to spurious
correlations and less than robust constraints on future changes. To mitigate
against this risk, Cox et al (hereafter CHW18) proposed a theory-motivated
emergent constraint, using the one-box Hasselmann model to identify a linear
relationship between ECS and a metric of global temperature variability
involving both temperature standard deviation and autocorrelation ($\Psi$). A
number of doubts have been raised about this approach, some concerning the
theory and the application of the one-box model to understand relationships in
complex GCMs which are known to have more than the single characteristic
timescale. We illustrate theory driven testing of emergent constraints using
this as an example, namely we demonstrate that the linear $\Psi$-ECS
proportionality is not an artifact of the one-box model and rigorously features
to a good approximation in more realistic, yet still analytically soluble
conceptual models, namely the two-box and diffusion models. Each of the
conceptual models predict different power spectra with only the diffusion
model's pink spectrum being compatible with observations and the complex CMIP5
GCMs. We also show that the theoretically predicted $\Psi$-ECS relationship
exists in the \texttt{piControl} as well as \texttt{historical} CMIP5
experiments and that the differing gradients of the proportionality are
inversely related to the effective forcing in that experiment.