Sea-surface temperature pattern effects have slowed global warming and biased warming-based constraints on climate sensitivity

The pattern of surface warming plays a significant role in determining the Earth's response to radiative forcing. Indeed, the Earth's radiative response is intricately linked to the intensity of climate feedbacks, which, in turn, are influenced by the regional distribution of surface warming. Distinct patterns of surface warming lead to divergent equilibrium and transient responses to identical forcing, emphasizing the need to analyse this pattern effect to understand the climate responses to external forcing. While existing studies have primarily focused on assessing the influence of warming patterns on long-term warming, such as equilibrium climate sensitivity or committed warming, the role of warming patterns in shaping the transient trajectory of global warming remains poorly understood. In this study, we introduce a novel analytical method to quantify the importance of evolving warming patterns on transient global warming. Our approach involves developing a multivariate global energy budget, which provides a unified framework for interpreting the sensitivity of the radiative response of the Earth to the warming pattern. This framework explicitly separates the radiative response caused by the global mean temperature increase, from the additional response induced by changing temperature patterns. Using this new energy balance model, we assess the relative contributions of the direct radiative forcing and changing temperature patterns to the global mean temperature change in linearly increasing forcing experiments (1pctCO2) from nine CMIP6 models. We show that the pattern effect consistently dampens global warming in the first 100 years of all simulations studied. Specifically, we quantify that the transient climate response, reached after 70 years of simulations, would be 0.4±0.2K higher (equivalent to a 20±15% increase) if the warming was uniformly distributed (i.e. in the absence of changing warming patterns). Furthermore, our study demonstrates that distinct models exhibit significantly divergent transient global warming patterns solely due to variations in the pattern effect. Overall, our results highlight the importance of changing warming patterns, specifically through the pattern effect, in influencing decadal-scale transient warming. These findings notably support recent suggestions to incorporate warming pattern uncertainties in future climate projections.

Comparing statistical estimates for the long-run temperature effect of doubled CO2 with those generated by climate models begs the question, is the long-run temperature effect of doubled CO2 that is estimated from the instrumental temperature record using statistical techniques consistent with the transient climate response, the equilibrium climate sensitivity, or the effective climate sensitivity. Here, we attempt to answer the question, what do statistical analyses of the observational record measure, by using these same statistical techniques to estimate the temperature effect of a doubling in the atmospheric concentration of carbon dioxide from seventeen simulations run for the Coupled Model Intercomparison Project 2 (CMIP2). The results indicate that the temperature effect estimated by the statistical methodology is consistent with the transient climate response and that this consistency is relatively unaffected by sample size or the increase in radiative forcing in the sample.

<p>Uncertainty in cloud feedback in climate models is a major limitation in projections of future climate. We analyse cloud biases and trends in climate models relative to satellite observations, and relate them to equilibrium climate sensitivity, transient climate response and cloud feedback. For this purpose, we develop a deep convolutional artificial neural network for determination of cloud types from low-resolution daily mean top of atmosphere shortwave and longwave radiation images, corresponding to the World Meteorological Organization (WMO) cloud genera recorded by human observers in the Global Telecommunication System. We train this network on a satellite top of atmosphere radiation dataset, and apply it on the Climate Model Intercomparison Project phase 5 and 6 (CMIP5 and CMIP6) historical and abrupt-4xCO2 experiment model output and the ERA5 and Modern-Era Retrospective Analysis for Research and Applications Version 2 (MERRA-2) reanalyses. We compare these with satellite observations, link cloud type occurrence biases and trends to climate sensitivity, and compare our cloud types with an existing cloud regime classification based on the Moderate Resolution Imaging Spectroradiometer (MODIS) and International Satellite Cloud Climatology Project (ISCCP) satellite data. We show that there is a strong linear relationship between the root mean square error of cloud type occurrence and model equilibrium climate sensitivity, transient climate response and cloud feedback (Bayes factor 7×10<sup>2</sup>, 4×10<sup>2</sup> and 13, respectively). This indicates that models with a better representation of the cloud types have a more positive cloud feedback and higher climate sensitivity. Along with other studies, our results point to a choice between two explanations: either high sensitivity models are plausible, contrary to combined assessments of climate sensitivity and cloud feedback in previous review studies, or the accuracy of representation of present-day clouds in models is negatively correlated with the accuracy of representation of future projected clouds.</p>

Uncertainty in cloud feedback in climate models is a major limitation in projections of future climate. Therefore, to ensure the accuracy of climate models, evaluation and improvement of cloud simulation is essential. We analyse cloud biases and cloud change with respect to global mean near-surface temperature (GMST) in climate models relative to satellite observations, and relate them to equilibrium climate sensitivity, transient climate response and cloud feedback. For this purpose, we develop a supervised deep convolutional artificial neural network for determination of cloud types from low-resolution (approx. 1°×1°) daily mean top of atmosphere shortwave and longwave radiation fields, corresponding to the World Meteorological Organization (WMO) cloud genera recorded by human observers in the Global Telecommunication System. We train this network on a satellite top of atmosphere radiation observed by the Clouds and the Earth’s Radiant Energy System (CERES), and apply it on the Climate Model Intercomparison Project phase 5 and 6 (CMIP5 and CMIP6) historical and abrupt-4xCO2 experiment model output and the ECMWF Reanalysis version 5 (ERA5) and the Modern-Era Retrospective Analysis for Research and Applications version 2 (MERRA-2) reanalyses. We compare these with satellite observations, link biases in cloud type occurrence derived from the neural network to change with respect to GMST to climate sensitivity, and compare our cloud types with an existing cloud regime classification based on the Moderate Resolution Imaging Spectroradiometer (MODIS) and International Satellite Cloud Climatology Project (ISCCP) satellite data. We show that there is a significant negative linear relationship between the root mean square error of cloud type occurrence derived from the neural network and model equilibrium climate sensitivity and transient climate response (Bayes factor 22 and 17, respectively). This indicates that models with a better representation of the cloud types globally have higher climate sensitivity. Factoring in results from other studies, there are two possible explanations: either high climate sensitivity models are plausible, contrary to combined assessments of climate sensitivity by previous review studies, or the accuracy of representation of present-day clouds in models is negatively correlated with the accuracy of representation of future projected clouds.

<p>There is much current debate about the way in which the earth's climate and temperature are responding to anthropogenic and natural forcing. Current forecasts are dependent on the accuracy of how Equilibrium Climate Sensitivity (ECS) is evaluated. In the recent wide-ranging ECS sensitivity review and assessments of Sherwood et al (2020, <em>Rev. Geophys.</em> <strong>58</strong>, e2019RG000678), they report a baseline ECS 5%–95% with a range of 2.3 °C to 4.7 °C. While this is an important and much needed quantification – this wide ECS uncertainty range, based largely on uncertainty around total radiative forcing (TRF), is also problematic for our geophysical based community. The ECS value as viewed by policy and global strategy negotiators is currently only understood to a 70% (= 2.4 / 3.5) physically resolved level of resolution. An open question (to discuss in this talk) is it possible to resolve this physical measurement more accurately and what are the current main issues that need to be accommodated? As part of this discussion we present the work of Young, Allen and Bruun (2021): <em>a re-evaluation of the Earth's surface temperature response to radiative forcing </em>(2021, <em>ERL</em>, <strong>16</strong>, 054068). In that paper we have re-assessed the current evidence at the globally averaged level by adopting a generic 'data-based mechanistic' modelling strategy that incorporates statistically efficient parameter estimation. This identifies a low order, differential equation model that explains how the global average surface temperature variation responds to the influences of total radiative forcing. The model response includes a novel, stochastic oscillatory component with a period of about 55 years (range 51.6–60 years) that appears to be associated with heat energy interchange between the atmosphere and the ocean. These 'quasi-cycle' oscillations, which account for the observed pauses in global temperature increase around 1880, 1940 and 2001, appear to be related to ocean dynamic responses, particularly the Atlantic multidecadal oscillation. The model explains 90% of the variance in the global average surface temperature anomaly and yields estimates of the equilibrium climate sensitivity (ECS) (2.29 °C with 5%–95% range 2.11 °C to 2.49 °C) and the transient climate response (TCR) (1.56 °C with 5%–95% range 1.43 °C to 1.68 °C), both of which are smaller than most previous estimates. When a high level of uncertainty in the TRF is taken into account, the ECS and TCR estimates are unchanged but the ranges are increased to 1.43 °C to 3.14 °C and 0.99 °C to 2.16 °C, respectively. This then gives the 70% physical resolution limit in ECS mentioned above. Current work is in progress to test this ECS re-evaluation approach using the CMIP6 models. We will discuss some on-going findings of these model signal assessments which include a specific focus on resolution of Atlantic and Pacific Ocean pentedecadal modes.  </p><p>Peter C Young, P Geoffrey Allen and John T Bruun (2021). A re-evaluation of the Earth's surface temperature response to radiative forcing, <em>Environ. Res. Lett.</em> <strong>16</strong> 054068, https://iopscience.iop.org/article/10.1088/1748-9326/abfa50.</p>

Relationships between climate variability and climate sensitivity are to be expected where the damping of a climatic anomaly is due to a change in the energy balance of the planet, such that the Fluctuation-Dissipation theorem heuristically applies [Leith, 1975]. A recent attempt to relate Equilibrium Climate Sensitivity (ECS) to global temperature variability over the historical period suggested a surprisingly tight emergent constraint on ECS [Cox et al., 2018]. However, the sensitivity-variability relationship in that study was partially hidden by anthropogenic forcing over the historical period. Here we examine instead CMIP5 control runs. These runs have no external forcing and therefore provide a much cleaner test of proposed links between internal variability and sensitivity. It has been noted before that there is a positive correlation between decadal temperature variability and climate sensitivity across climate models [Colman & Power, 2018]. Questions remained however as to how robust this relationship is across different model ensembles, what mechanisms are responsible for it, and whether it can be used as an emergent constraint on climate sensitivity. We examine the relationship between decadal variability and ECS using models of varying complexity, including CMIP5 control runs and a range of conceptual energy balance models for which analytical solutions are presented. Based on these results, a general mechanism becomes apparent and the shape of the relationship is determined to be more quadratic than linear. The nonlinearity has implications for using this relationship as an emergent constraint, where an incorrect assumption of linearity might lead to biased estimates. A further surprising implication of the study is that a slowdown in global warming does not necessarily imply that climate sensitivity is lower than previously estimated. Models with a higher sensitivity, but which broadly reproduce the long-term record of global warming, are actually more likely to have slow-down periods than models with lower sensitivity.

We examine the response of the Community Earth System Model Versions 1 and 2 (CESM1 and CESM2) to abrupt quadrupling of atmospheric CO2 concentrations (4xCO2) and to 1% annually increasing CO2 concentrations (1%CO2). Different estimates of equilibrium climate sensitivity (ECS) for CESM1 and CESM2 are presented. All estimates show that the sensitivity of CESM2 has increased by 1.5 K or more over that of CESM1. At the same time the transient climate response (TCR) of CESM1 and CESM2 derived from 1%CO2 experiments has not changed significantly—2.1 K in CESM1 and 2.0 K in CESM2. Increased initial forcing as well as stronger shortwave radiation feedbacks are responsible for the increase in ECS seen in CESM2. A decomposition of regional radiation feedbacks and their contribution to global feedbacks shows that the Southern Ocean plays a key role in the overall behavior of 4xCO2 experiments, accounting for about 50% of the total shortwave feedback in both CESM1 and CESM2. The Southern Ocean is also responsible for around half of the increase in shortwave feedback between CESM1 and CESM2, with a comparable contribution arising over tropical ocean. Experiments using a thermodynamic slab‐ocean model (SOM) yield estimates of ECS that are in remarkable agreement with those from fully coupled Earth system model (ESM) experiments for the same level of CO2 increase. Finally, we show that the similarity of TCR in CESM1 and CESM2 masks significant regional differences in warming that occur in the 1%CO2 experiments for each model.

The equilibrium climate sensitivity of a climate model is usually defined as the globally averaged equilibrium surface temperature response to a doubling of carbon dioxide. This is virtually always estimated in a version with a slab model for the upper ocean. The question is whether this estimate is accurate for the full climate model version, which includes a full-depth ocean component. This question has been answered for the low-resolution version of the Community Climate System Model, version 3 (CCSM3). The answer is that the equilibrium climate sensitivity using the full-depth ocean model is 0.14°C higher than that using the slab ocean model, which is a small increase. In addition, these sensitivity estimates have a standard deviation of nearly 0.1°C because of interannual variability. These results indicate that the standard practice of using a slab ocean model does give a good estimate of the equilibrium climate sensitivity of the full CCSM3. Another question addressed is whether the effective climate sensitivity is an accurate estimate of the equilibrium climate sensitivity. Again the answer is yes, provided that at least 150 yr of data from the doubled carbon dioxide run are used.

Equilibrium climate sensitivity (ECS) and hydrological sensitivity describe the global mean surface temperature and precipitation responses to a doubling of atmospheric CO2. Despite their connection via the Earth’s energy budget, the physical linkage between these two metrics remains controversial. Here, using a global climate model with a perturbed mean hydrological cycle, we show that ECS and hydrological sensitivity per unit warming are anti-correlated owing to the low-cloud response to surface warming. When the amount of low clouds decreases, ECS is enhanced through reductions in the reflection of shortwave radiation. In contrast, hydrological sensitivity is suppressed through weakening of atmospheric longwave cooling, necessitating weakened condensational heating by precipitation. These compensating cloud effects are also robustly found in a multi-model ensemble, and further constrained using satellite observations. Our estimates, combined with an existing constraint to clear-sky shortwave absorption, suggest that hydrological sensitivity could be lower by 30% than raw estimates from global climate models. The connections between global mean temperature and precipitation responses to CO2 doubling (equilibrium climate and hydrological sensitivity) are driven through low-cloud responses to surface warming, according to MIROC5 perturbation experiments.

Abstract. The equilibrium climate sensitivity (ECS) – the equilibrium global mean temperature response to a doubling of atmospheric CO2 – is a high-profile metric for quantifying the Earth system's response to human-induced climate change. A widely applied approach to estimating the ECS is the “Gregory method” (Gregory et al., 2004), which uses an ordinary least squares (OLS) regression between the net radiative flux, N, and surface air temperature anomalies, ΔT, from a 150 year experiment in which atmospheric CO2 concentrations are quadrupled. The ECS is determined by extrapolating the linear fit to N=0, i.e. the ΔT-intercept, indicating the point at which the system is back in equilibrium. This method has been used to compare ECS estimates across the CMIP5 and CMIP6 ensembles and will likely be a key diagnostic for CMIP7. Despite its widespread application, there is little consistency or transparency between studies in how the climate model data is processed prior to the regression, leading to potential discrepancies in ECS estimates. We identify 32 alternative data processing pathways, varying by differences in global mean weighting, net radiative flux variable, anomaly calculation method, and linear regression fit. Using 44 CMIP6 models, we systematically assess the impact of these choices on ECS estimates and calculate uncertainty ranges using two bootstrap approaches. While the inter-model ECS range is insensitive to the data processing pathway, individual outlier models exhibit notable differences. Approximating a model's native grid cell area (if irregular) with cosine of the latitude can decrease the ECS by 11 %, the choice of N-variable can change the ECS by 6 %, and some anomaly calculation methods can introduce spurious temporal correlations in the processed data. Beyond data processing choices, we also evaluate an alternative linear regression method – total least squares (TLS) – which has a more statistically robust basis than OLS. However, for consistency with previous literature, and given TLS may reduce the ECS compared to OLS (by up to 24 %), thereby making a known bias in the Gregory method worse, we do not feel there is sufficient clarity to recommend a transition to TLS in all cases. To improve reproducibility and comparability in future studies, we recommend a standardised Gregory method: weighting the global mean by cell area, using the top of the atmosphere (as opposed to the top of model) N-variable, and calculating anomalies by first applying a rolling average to the preindustrial control timeseries then subtracting from the raw CO2 quadrupling experiment. This approach accounts for model drift while reducing noise in the data to best meet the pre-conditions of the linear regression. While CMIP6 results of the multi-model mean ECS appear insensitive to these processing choices, similar assumptions may not hold for CMIP7, underscoring the need for standardised data preparation in future climate sensitivity assessments.

<p>Using the 20-year-old climate model, HadCM3, we show that it is possible to calibrate the model to multiple observations by algorithmically changing parameters in the atmospheric model.  Fourteen atmospheric parameters were modified using a state-of-the-art derivative free optimization algorithm (DFOLS). The calibration reduces model-observational difference against hemispheric scale averages of multiple observations for the 2001-2005 period and used about 90 evaluations of the atmospheric model. The observations considered were outgoing longwave and shortwave radiation, land temperature and precipitation, sea level pressure, mid-tropospheric temperature and humidity, and global-average net flux into the Earth system. A 5-member ensemble was generated by starting the calibration from different initial parameter sets.</p><p>The calibrated model simulated large scale observations better than almost all CMIP5 and CMIP6 ensemble.  Spatial patterns of variables from the calibrated ensemble except for outgoing SW, land precipitation and mid-tropospheric humidity are as well simulated as in the CMIP6 ensemble. For these variables, spatial patterns are as well simulated as the CMIP5 ensemble.   In the calibrated ensemble, uncertainty in effective climate sensitivity (ECS; relative error of 10%) and the transient climate response (TCR; relative error of 5%) is small. This is the case for the response at doubling and quadrupling of CO2 concentrations. Uncertainties in regional climate change are also small.</p><p>A linear analysis which combines observational uncertainty with the Jacobian of observational sensitivity with respect to parameter change gives a parameter covariance matrix. This is in turn can be combined with the Jacobian of climate response with respect to parameter to give a linear estimate of uncertainty in climate response. The linear uncertainty is similar to the ensemble uncertainty. By increasing individual observational uncertainty in the  linear analysis, it is possible to see which observations are providing the constraints in  transient climate response at 4 times CO2. This analysis finds that almost all the constraint comes from land precipitation, outgoing SW radiation and the net flux, suggesting these are key observations to constrain climate model behaviour.</p>

Cloud feedback is a dominant source of uncertainty in climate model estimates of equilibrium climate sensitivity (ECS). Cloud controlling factor analysis can observationally constrain cloud feedback. For the first time, we use separate rather than unified frameworks to assess high- and low-cloud feedbacks and constrain the net cloud feedback and subsequently, the ECS. We find a robustly positive cloud feedback (i.e., a negative feedback is <0.5% probable), indicating that clouds amplify global warming. We assess the individual and combined impacts of our cloud feedback constraints on ECS using three approaches. Two indicate an upward ECS shift with reduced uncertainty, preserving ECS–feedback correlations but using cloud feedback as a single line of evidence. The third, a Bayesian framework combining multiple lines of evidence, also suggests a higher ECS but with a smaller increase and broader confidence range.

From Equilibrium Climate Sensitivity to Carbon Climate Response

Abstract. It has been shown that a theoretically derived relation between annual global mean temperature variability and climate sensitivity held in the CMIP5 climate model ensemble (Cox et al., 2018a, hereafter CHW18). This so-called emergent relationship was then used with observations to constrain the value of equilibrium climate sensitivity (ECS) to about 3 °C. Since this study was published, CMIP6, a newer ensemble of climate models has become available. Schlund et al. (2020) showed that many of the emergent constraints found in CMIP5 were much weaker in the newer ensemble, including that of CHW18. As the constraint in CHW18 was based on a relationship derived from reasonable physical principles, it is of interest to find out why it is weaker in CMIP6. Here, we look in detail at the assumptions made in deriving the emergent relationship in CHW18 and test them for CMIP5 and CMIP6 models. We show one assumption, that of low correlation and variation between ECS and the internal variability parameter, a parameter that captures chaotic internal variability and sub-annual (fast) feedbacks, that while true for CMIP5 is not true for CMIP6. When accounted for, an emergent relationship appears once again in both CMIP ensembles, implying the theoretical basis is still applicable while the original assumption in CHW18 is not. Unfortunately, however, we are unable to provide an emergent constraint in CMIP6 as observational estimates of the internal variability parameter are too uncertain.

Equilibrium climate sensitivity (ECS), defined as the response of the global mean surface temperature response to a sustained doubling of atmospheric CO2 at equilibrium, is a key metric for quantifying the Earth’s climate sensitivity to greenhouse gas emissions. Accurate ECS estimates are therefore fundamental for reliable simulations of the long-term carbon cycle. cGENIE, as an Earth system model of intermediate complexity that integrates ocean circulation, atmospheric energy balance, and global biogeochemical cycling, is widely used to investigate cross-sphere carbon cycle evolution and long-term climate feedback mechanisms. However, previous cGENIE studies have assumed a fixed climate sensitivity (with a default radiative forcing of 4 W m-2 per CO2 doubling), which often led to inaccurate surface temperature estimates compared with proxy reconstructions, limiting the model’s ability to capture state-dependent climate feedbacks. Here we use fully coupled models (e.g., HadCM3 and CESM) to derive the relationship between atmospheric CO2 concentrations and ECS throughout the Phanerozoic. These simulations are considered to closely match proxy reconstructions of temperatures. We then incorporate state-dependent climate sensitivity into cGENIE to enhance its representation of climate feedbacks across varying CO2 levels. Our results show that temperature simulations using the unmodified cGENIE model exhibit substantial discrepancies for periods of rapid cooling and warming, such as the Late Ordovician and the PETM. However, incorporating state-dependent climate sensitivity substantially reduces the discrepancy between simulated and proxy-reconstructed surface temperatures. These findings highlight the importance of accounting for state-dependent climate sensitivity in Earth system models, both for accurately reconstructing past climate extremes and for improving projections of future climate change.