Comment on egusphere-2025-1179: Reply to Referee comment RC1

Estimates of the Earth's equilibrium climate sensitivity (ECS) from twentieth century observations predict a lower ECS than estimates from climate models, paleoclimate data, and interannual variability. Here we show that estimates of ECS from the twentieth century observations are sensitive to the assumed efficacy of aerosol and ozone forcing (efficacy for a forcer is the amount of warming per unit global average forcing divided by the warming per unit forcing from CO2). Previous estimates of ECS based on the twentieth century observations have assumed that the efficacy is unity, which in our study yields an ECS of 2.3 K (5%–95% confidence range of 1.6–4.1 K), near the bottom of the Intergovernmental Panel on Climate Change's likely range of 1.5–4.5 K. Increasing the aerosol and ozone efficacy to 1.33 increases the ECS to 3.0 K (1.9–6.8 K), a value in excellent agreement with other estimates. Forcing efficacy therefore provides a way to bridge the gap between the different estimates of ECS.

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.

We compare equilibrium climate sensitivity (ECS) estimates from pairs of long (≥800‐year) control and abruptly quadrupled CO2 simulations with shorter (150‐ and 300‐year) coupled atmosphere‐ocean simulations and slab ocean models (SOMs). Consistent with previous work, ECS estimates from shorter coupled simulations based on annual averages for years 1–150 underestimate those from SOM (−8% ± 13%) and long (−14% ± 8%) simulations. Analysis of only years 21–150 improved agreement with SOM (−2% ± 14%) and long (−8% ± 10%) estimates. Use of pentadal averages for years 51–150 results in improved agreement with long simulations (−4% ± 11%). While ECS estimates from current generation U.S. models based on SOM and coupled annual averages of years 1–150 range from 2.6°C to 5.3°C, estimates based longer simulations of the same models range from 3.2°C to 7.0°C. Such variations between methods argues for caution in comparison and interpretation of ECS estimates across models.

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.

<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.

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. 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.

On a minimal model for estimating climate sensitivity

Current climate models demonstrate large discrepancy in equilibrium climate sensitivity (ECS). The effects of cloudiness parameterization changes on the ECS of the INM‐CM4‐8 climate model were investigated. This model shows the lowest ECS among CMIP6 models. Reasonable changes in the parameterization of the degree of cloudiness yielded ECS variability of 1.8–4.1 K in INM‐CM4‐8, which was more than half of the interval for the CMIP6 models. The three principal mechanisms responsible for the increased ECS were increased cloudiness dissipation in warmer climates due to the increased water vapor deficit in the non‐cloud fraction of a cell, decreased cloudiness generation in the atmospheric boundary layer in warm climates, and the instantaneous cloud response to CO 2 increases due to stratification changes.

<strong class="journal-contentHeaderColor">Abstract.</strong> The use of paleoclimates to constrain the equilibrium climate sensitivity (ECS) has seen a growing interest. In particular, the Last Glacial Maximum (LGM) and the mid-Pliocene Warm Period have been used in emergent constraint approaches using simulations from the Paleoclimate Modelling Intercomparison Project (PMIP). Despite lower uncertainties regarding geological proxy data for the LGM in comparison with the Pliocene, the robustness of the emergent constraint between LGM temperature and ECS is weaker at both global and regional scales. Here, we investigate the climate of the LGM in models through different PMIP generations, and how various factors contribute to the spread of the model ensemble. Certain factors have large impact on an emergent constraint, such as state-dependency in climate feedbacks or model-dependency on ice sheet forcing. Other factors, such as models being out of energetic balance and sea-surface temperature not responding below -1.8 &deg;C in polar regions have a limited influence. We quantify some of the contributions and find that they mostly have extratropical origins. Contrary to what has previously been suggested, from a statistical point of view, the PMIP model generations do not differ substantially. Finally, we show that the lack of high or low ECS models in the ensembles critically limits the strength and reliability of the emergent constraints.

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.

Cloud and convective parameterizations strongly influence uncertainties in equilibrium climate sensitivity. We provide a proof‐of‐concept study to constrain these parameterizations in a perturbed parameter ensemble of the atmosphere‐only version of the Goddard Institute for Space Studies Model E2.1 simulations by evaluating model biases in the present‐day runs using multiple satellite climatologies and by comparing simulated δ18O of precipitation (δ18Op), known to be sensitive to parameterization schemes, with a global database of speleothem δ18O records covering the Last Glacial Maximum (LGM), mid‐Holocene (MH) and pre‐industrial (PI) periods. Relative to modern interannual variability, paleoclimate simulations show greater sensitivity to parameter changes, allowing for an evaluation of model uncertainties over a broader range of climate forcing and the identification of parts of the world that are parameter sensitive. Certain simulations reproduced absolute δ18Op values across all time periods, along with LGM and MH δ18Op anomalies relative to the PI, better than the default parameterization. No single set of parameterizations worked well in all climate states, likely due to the non‐stationarity of cloud feedbacks under varying boundary conditions. Future work that involves varying multiple parameter sets simultaneously with coupled ocean feedbacks will likely provide improved constraints on cloud and convective parameterizations.

Past climates provide a means for evaluating the response of the climate system to large perturbations. Our ultimate goal is to constrain climate models rigorously by paleoclimate data. For illustration, we used a conceptual climate model (a classical energy balance model) and applied the so-called “adjoint method” to minimize the misfit between our model and sea-surface temperature data for the Last Glacial Maximum (LGM, between 19,000 and 23,000 years before present). The “adjoint model” (derivative code) was generated by an “adjoint compiler.” We optimized parameters controlling the thermal diffusion and the sensitivity of the outgoing longwave radiation to changes in the zonal-mean surface temperature and the atmospheric CO2 concentration. As a result, we estimated that an equilibrium climate sensitivity between 2.2 °C and 2.5 °C was consistent with the reconstructed glacial cooling, and we were able to infer structural deficits of the simple model where the fit to current observations and paleo data was not successful.KeywordsCost FunctionOutgoing Longwave RadiationAdjoint MethodAdjoint ModelEquilibrium Climate SensitivityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.