1. Introduction
When the Earth system is disturbed by a radiative forcing, the temperature adjusts to reach balance again. The ultimate amount of warming is set by the climate feedback parameter, which is related to the equilibrium climate sensitivity (ECS; the equilibrium surface warming in response to doubled CO2), so having an accurate estimation of the feedback parameter is critical for predicting future warming.
Climate models have been widely used to understand climate feedbacks and estimate the sensitivity of our climate system. However, phases 5 and 6 of the Coupled Model Intercomparison Project (CMIP5 and CMIP6, respectively) ensembles exhibit a large range of ECS values (Zelinka et al. 2020). Evaluating the reliability of these models and whether they are applicable to the real world is therefore an important goal of climate science.
It has been established that feedbacks are not constant in our climate system. For example, the strength of cloud feedback tends to become more positive as the climate warms (Murphy 1995; Senior and Mitchell 2000; Winton et al. 2010; Andrews et al. 2012; Armour et al. 2013; Andrews et al. 2015; Ceppi and Gregory 2017; Proistosescu and Huybers 2017). Studies also find that ECS inferred from the historical period is smaller than the one inferred from the long-term warming. This is due to the difference in surface warming patterns in two periods, particularly weak warming in the east Pacific Ocean, resulting in a more negative cloud feedback (Gregory and Andrews 2016; Marvel et al. 2018; Dessler 2020).
Unforced variability can also lead to variability in climate feedbacks inferred from the historical record (Zhou et al. 2016; Dessler et al. 2018; Dessler 2020). These variations in feedback values are related to the fact that climate feedbacks are a function not just of global average temperature, but also of the spatial pattern of temperature change (Armour et al. 2013; Andrews et al. 2015; Gregory and Andrews 2016; Zhou et al. 2016, 2017; Andrews and Webb 2018). This phenomenon is often referred to as the “pattern effect” (Stevens et al. 2016), which can then be broken into forced and unforced components (Dessler 2020). The existence of a pattern effect means that validating climate models with observational data may be more challenging than previously thought. Yet model validation remains key for building confidence in their predictions.
In this paper, we compare feedbacks derived from climate models and observations using the traditional framework and the modified energy balance framework suggested by Dessler et al. (2018). That paper showed that the impact of the pattern effect is smaller in the modified framework in a single model. In this work, we extend that work to examine the modified framework’s performance for individual feedbacks in a multimodel ensemble. Our work shows that this framework is less influenced by unforced pattern effect, allowing us to more stringently test whether models are accurately reproducing the observations. The feedbacks in response to variability and long-term climate change could be different due to the pattern effect, so we also compare feedbacks in unforced runs with 4×CO2 forced runs to determine how the feedbacks differ with external forcing.
2. Energy balance frameworks
3. Data
The observed TOA radiative flux R is taken from the Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) product, edition 4.1 (Loeb et al. 2018). Forcing F is an update of the Intergovernmental Panel on Climate Change Fifth Assessment Report (AR5) forcing time series (Myhre et al. 2013), which was obtained from Dessler and Forster (2018). The European Center for Medium-Range Weather Forecasts ERA5 reanalysis (Hersbach et al. 2020) provides the meteorological data needed for the feedback calculations, including clear-sky fluxes. As is normally done, downward fluxes are defined to be positive. The observations and reanalysis data used in this paper cover the period from March 2000 to October 2017, which was determined by the availability of the forcing data.
To calculate individual feedbacks, deseasonalized monthly anomalies of temperature, water vapor, and surface albedo are multiplied by radiative kernels, which convert them to the induced TOA fluxes (Soden et al. 2004; Shell et al. 2008). TOA flux due to cloud changes is calculated from the monthly anomaly of cloud radiative forcing, determined as the difference between CERES all-sky fluxes and ERA5 clear-sky fluxes (Dessler and Loeb 2013), and then adjusted to account for the influences of noncloud components. An ordinary least squares regression between the TOA flux and the anomaly of global average surface temperature (2-m air temperature) yields an estimate of the strength of the feedback (Dessler and Wong 2009). A complete uncertainty analysis for the observed feedbacks is provided in section S1 of the online supplemental material. Note that in this study we mainly focus on the climate feedbacks in response to interannual variability unless otherwise specified.
For the θ framework, cloud, water vapor, and albedo feedbacks are calculated the same way as the feedbacks in the λ framework, except that 500-hPa tropical temperatures are used in the regression against fluxes. The Planck and lapse rate feedbacks are referenced to the tropospheric temperature. This means that the Planck response is the radiative response to a uniform warming of the surface and atmosphere equal to the warming of the 500-hPa temperature, while the lapse rate response is the radiative response to differential warming of the surface and atmosphere relative to the 500-hPa tropical temperature. The Planck and lapse rate fluxes are then regressed against tropical atmospheric temperature to generate the feedbacks.
We present results here using the radiative kernels of Huang et al. (2017), although we have tested other radiative kernels and found that the results and conclusions are not sensitive to the choice of kernels. We use the Held and Shell (2012) feedback decomposition, in which the Planck and lapse rate feedbacks assume constant relative humidity (RH) and the water vapor feedback is the feedback due to changes in RH (λΔRH).
The focus of this study is evaluating the models’ performance in reproducing the climate feedbacks observed in the real world. Our observations of Earth’s energy balance cover the period from 2000 to 2017, during which climate variations were mainly controlled by unforced variability, but also containing an upward trend that is likely due to forced climate change (e.g., Blunden and Arndt 2020). We chose to compare the observations to feedbacks estimated from preindustrial control runs of 26 models in the CMIP5 ensemble (Taylor et al. 2012) and 26 models in the CMIP6 ensemble (Eyring et al. 2016), all of which have no forcing. In section S2 of the online supplemental material, we show that estimates of feedbacks from forced runs are very close to those from these unforced runs for data lengths equal to that of the CERES data. The unforced runs tend to estimate a slightly weaker negative total feedback, but the differences are much smaller than other sources of uncertainty of observational feedback; thus, the choice of run type is not expected to change the conclusions of this paper.
To be consistent with the observations and avoid potential problems with long-term drift in the control runs, we first divide each control run into nonoverlapping 18-yr segments (about the same length as the observational dataset). For each segment, the feedbacks are calculated using the same method as that used for the observations. Thus, for each model, we generate between 8 and 27 estimates of each feedback, depending on the length of the control run (see Tables S4 and S6 of the online supplemental material). Differences between the segments allow us to quantify the potential impact of unforced variability on feedbacks estimated from a single 18-yr observational period.
For completeness, we also compare the feedbacks from control runs with the feedbacks from abrupt-4×CO2 runs in both frameworks. The 4×CO2 climate feedbacks are calculated by linear regression of the first 150 years of annual R anomalies against annual global temperature anomalies (Gregory et al. 2004), where the anomalies are the abrupt-4×CO2 run minus the time average of the control run. The climate feedbacks during years 21–150 have also been analyzed and our results are not sensitive to the choice of the period.
4. Results
a. Unforced climate feedbacks in the λ framework
Table 1 lists the observed and ensemble-average feedbacks calculated in the λ framework, in which the regressions are against surface temperature. Figures 1a and 1b graphically show this comparison between the observations (black symbols, with 5%–95% uncertainty range) and models. To understand the results from the models, remember that, for each model, we calculate up to 27 estimates of each feedback from individual 18-yr segments of the model’s control run. We can average these to come up with an average feedback for each model, and the blue circle shows the ensemble average of these model averages, with the bars showing the approximate 90% confidence intervals, defined as ±1.645 × standard deviation of the ensemble feedbacks. We will refer to this spread as the “structural difference” since it quantifies the impact of differences in model parameterizations and other differences in the physics.
Global mean climate feedbacks (W m−2 K−1) in CERES/ERA5, CMIP5, and CMIP6 preindustrial control (ctrl) and abrupt-4×CO2 (4×CO2) runs calculated using λ and θ frameworks. For the observations, the uncertainty is the combination of uncertainty due to forcing, trend in radiative flux, clear-sky flux, temperature, and regression (discussed in section S1 of the online supplemental material). For each CMIP5 and CMIP6 model, the average of 18-yr segments for each model is first calculated. The ensemble average and 1.645 standard deviations of the model averages are shown. The feedbacks are calculated using constant-RH breakdown (Held and Shell 2012). The residual is the difference between the total feedback and the sum of the kernel-derived feedbacks. Also shown at the bottom of each section are feedbacks calculated using the breakdown in which the Planck and lapse-rate feedbacks assume fixed specific humidity (SH).
Global mean climate feedbacks from (left) CMIP5 and (right) CMIP6 models calculated using the (a),(b) λ and (c),(d) θ frameworks. Black circles denote CERES/ERA5, and the error bar represents the total uncertainty. The ensemble mean and the approximate 90% confidence intervals (±1.645 × standard deviation) are shown as blue circles and blue error bars. The orange error bars show the mean of the model spread excluding the minimum and maximum values. The model spread is the maximum minus minimum feedbacks in a model’s 18-yr segments. The green error bars show the 5%–95% range of all segments from the ensemble. The feedbacks are calculated using the constant relative humidity framework. Total refers to the feedback computed from net TOA radiative flux; the residual (Res) is the difference between the total feedback and the sum of the kernel-derived feedbacks.
Citation: Journal of Climate 34, 24; 10.1175/JCLI-D-21-0226.1
We can also look at the spread of feedbacks across the 18-yr segments of each model. To show this, we first calculate the spread for each model (i.e., the maximum minus the minimum feedback of each model’s 18-yr segments). The orange bars show the average of the model spread excluding the maximum and minimum spreads. These orange bars therefore tell us the impact of unforced variability on the magnitude of the feedback estimated from an 18-yr segment, which Dessler (2020) referred to as the “unforced pattern effect” and we will also refer to it thusly. The comparisons of the structural differences and the unforced pattern effect of the feedbacks in the λ framework are quantified in Table 2.
Different sources of uncertainty of unforced climate feedbacks (W m−2 K−1) in λ and θ frameworks. For each model, the mean and the spread (e.g., maximum minus minimum) of 18-yr segments are identified. The structural difference is the approximate 90% confidence intervals (±1.645 × standard deviation) for the model mean feedbacks. The unforced pattern effect is quantified as the mean of the model spread excluding the minimum and maximum values. The combined uncertainty is determined by combining the individual segments from all models into a single pool and finding the 5%–95% range of the segments in this pool.
For the total feedback, 50 of 52 models have at least one segment whose best estimate value falls within the uncertainty range of the observations. Pooling all model segments together, 71% of the segments have total feedbacks whose best estimate falls within the observational range. This is consistent with previous research (e.g., Donohoe et al. 2014; Trenberth et al. 2015), including feedbacks in CMIP3 models (Colman and Hanson 2013; Dessler 2013) that showed reasonable agreement between models and observations for the Planck, lapse rate, and water vapor feedbacks.
For all of the feedbacks other than the Planck feedback, both the structural difference and the unforced pattern effect are important. It has been previously recognized that the structural difference is an important source of uncertainty, but our results demonstrate that, when comparing a short observational record with models, the unforced pattern effect is also an important factor when using the λ framework, assuming that the models accurately reproduce the variability of the real world.
The green bars show the 5%–95% range of the pool of 18-yr feedback estimates from all models in the ensemble. This range can be thought of as the combined uncertainty from the structural differences and unforced pattern effect. Overall, there is no evidence that models are missing important physical processes, such as strong stabilizing negative cloud feedbacks (e.g., Lindzen et al. 2001). That said, this comparison underscores the weakness of this conclusion. There are large differences among the models due to model parameterizations. Furthermore, some feedbacks measured over the CERES period can be significantly affected by the unforced pattern effect. This means that models produce a very wide range of potential feedbacks, so the models do not serve as strong of a constraint as we would like.
b. Model performance in reproducing the observations in the λ framework
We calculate this metric for each segment of each model, with lower values indicating better model performance. Even if a model is perfect, we would not expect every segment from a particular model to have a low value of TEAll,λ due to the impact of the unforced pattern effect. We therefore identify the segment from each model that has the lowest value of TEAll,λ and use that to represent the ability of that model to simulate the feedbacks. Figure 2 shows each model’s lowest TEAll,λ. The ensemble average of lowest TEAll,λ (with 1 standard deviation) for the CMIP5 and CMIP6 ensembles is 0.35 ± 0.09 W m−2 K−1 and 0.45 ± 0.22 W m−2 K−1, respectively. The ranking of models based on lowest TEAll,λ is provided in Tables S2 and S3 of the online supplemental material.
The TEAll (total error) metric in (a) CMIP5 and (b) CMIP6 control runs. The metric is calculated by summing over all kernel-derived λ (red circle) and θ (black triangle) feedbacks. For each model, the segment with lowest TEAll value is identified and plotted. The models are ordered by the lowest TEAll metric in the λ framework.
Citation: Journal of Climate 34, 24; 10.1175/JCLI-D-21-0226.1
It seems reasonable to assume the models with lower values of TEAll,λ are producing more accurate feedbacks. However, there are various ways that assumption could be wrong. For example, models with errors in their estimation of feedbacks could look good if there are compensating errors in the model’s simulation of unforced variability. Similarly, a model could look bad despite accurate simulation of the feedbacks if the model’s simulation of unforced variability is poor. Last, the 18-yr record of observation might reflect a truly unusual part of variability phase space that the model runs are not run long enough to sample.
c. Unforced climate feedbacks in the θ framework
As we showed in the previous section, differences between observed and modeled feedbacks using the λ framework are strongly influenced by the unforced pattern effect, and this is one of the reasons that it is difficult to robustly compare feedbacks in models with observations. In this section, we analyze feedbacks estimated using the alternative framework, in which the tropical atmospheric temperature is the controlling variable instead of the surface temperature. As pointed out by D18, this framework is less susceptible to the unforced pattern effect when evaluating the total feedback parameter.
Figures 1c and 1d show the ensemble feedbacks in the θ framework, and the values are also summarized in Table 1. From this, we can draw several important conclusions. First, the structural differences (i.e., the spread due to differences in model parameterizations) within the CMIP5 and CMIP6 ensembles are smaller in the θ framework, for all feedbacks other than the Planck feedback. This suggests that at least some of the structural uncertainty in the models is related to how the models connect atmospheric and surface temperatures. This may reflect the difficulties of estimating surface temperature, including the large diurnal cycle, variations over small spatial scales, and complex interactions with the surface biosphere. Clearly, more work on this is warranted.
Second, the unforced pattern effect is also much smaller in the θ framework (see also Table 2), with the impact on the cloud feedback half of that in the λ framework. This is also shown in Tables S4–S7 of the online supplemental material, where we list for individual models the standard deviation of feedbacks calculated from 18-yr segments in λ and θ framework. This is consistent with there being less of an unforced pattern effect in the θ framework, as argued by D18. It also means that comparisons between models and our observations are less likely to be confounded by unforced variability.
Like the analysis in the λ framework, we see good agreement between the observed feedbacks and the models. There is no evidence that the models are misrepresenting any important climate processes. However, because the structural differences and unforced pattern effect are smaller in this framework, this comparison provides a stronger, more robust test of the models and the conclusion that we see no problems in the models is more convincing.
d. Model performance in reproducing the observations in the θ framework
To evaluate individual model performance in the θ framework, we calculate an analogous TEAll,θ metric following Eq. (3) but using the θ feedbacks. The lowest TEAll,θ in each model is identified and used to represent the performance of that model. In comparing with λ framework, we see that the CMIP5 ensemble average of lowest TEAll,θ is 8% smaller (i.e., 0.35 vs 0.32 W m−2 K−1), while CMIP6 is 28% smaller (i.e., 0.45 vs 0.32 W m−2 K−1). We also find that 63% of the models (33 of 52 models) have lowest TEAll,θ smaller than TEAll,λ. This superiority of TEAll,θ gives us more evidence that the θ framework provides a more precise determination of model performance. It has been shown in previous research that CMIP6 models tend to produce higher ECS values than the CMIP5 models (Zelinka et al. 2020); however, we notice that such systematic differences are not reflected in the TE metric.
e. Evaluations of cloud feedbacks
In both the λ and θ frameworks, cloud feedbacks are the major contributors of model spread. To understand how well the models reproduce the observed cloud feedback, we estimate a TE metric for the cloud feedbacks by applying Eq. (3) but with i = cloud shortwave (SW) and cloud longwave (LW) feedbacks so as obtain the TE metric for just the cloud feedback (hereinafter TECloud,λ and TECloud,θ). Similar to the analysis of TETotal, the θ framework yields smaller TECloud values in the majority of the models (71%, or 37 of 52 models) (Fig. 3).
As in Fig. 2, but for the TECloud,λ and TECloud,θ metrics.
Citation: Journal of Climate 34, 24; 10.1175/JCLI-D-21-0226.1
To evaluate how well the meridional pattern of the cloud feedback agrees between models and observations, we calculate the zonal average feedback in observations and each model by regressing the zonal average flux at each grid point against temperatures (global average surface temperature for λ and 500-hPa tropical average temperature for θ) in each 18-yr segment. Figure 4 plots the segment average for each model (gray lines) as well as the combined CMIP5 and CMIP6 ensemble average. In general, the ensemble average follows the observations, with the largest differences occurring over the equatorial region.
The zonal average (left) cloud SW, (center) cloud LW, and (right) cloud feedbacks in (a)–(c) the λ framework and (d)–(f) the θ framework. The black line is the value from the observations. The gray lines are segment-average feedbacks from each model, and the colored lines are the average of model ensemble. (g)–(i) The differences between the feedbacks inferred from the observations and from the CMIP (CMIP5 and CMIP6) ensemble (blue is the difference in the λ framework, and red is the difference in the θ framework). For this plot, the CMIP5 and CMIP6 ensembles are combined into one CMIP ensemble.
Citation: Journal of Climate 34, 24; 10.1175/JCLI-D-21-0226.1
Similar calculations have been performed for the θ framework. In comparison with the λ framework, the θcloud SW and θcloud LW show better agreement with the observations (Figs. 4d,e), especially over the middle and high latitudes. The root-mean-square difference between the observed and ensemble-averaged λcloud SW and λcloud LW are 1.56 and 1.32 W m−2 K−1, whereas the ones for θcloud SW and θcloud LW are 0.58 and 0.74 W m−2 K−1. In addition, the structural differences (differences between the models) are significantly reduced in the θ framework (see also Fig. S2 of the online supplemental material), especially in the equatorial eastern Pacific Ocean and the southern Pacific Ocean. The equatorial Pacific remains the source of much of the disagreement and intra-ensemble spread, suggesting that further study of clouds in that region is warranted.
f. Relationship between unforced and 4xCO2 climate feedbacks in the λ and θ frameworks
Given the understandable research focus on long-term climate change, one might wonder how the feedbacks estimated from unforced variability compare to those from long-term forced climate change (e.g., Colman and Hanson 2017; Colman and Power 2018). To investigate this question, we have estimated feedbacks from the model ensembles’ abrupt-4×CO2 runs in both the λ and θ frameworks (ensemble average values are in Table 1; values for individual models are in Tables S8–S11 of the online supplemental material). As with the control runs, the ensemble spread of cloud, residual, and total 4×CO2 feedbacks estimated in the θ framework is smaller than in the λ framework.
To visualize the differences between these feedbacks, for each feedback and model we have calculated the difference between the segment-average feedback from the control run and the feedback from the abrupt-4×CO2 run. Figures 5 and 6 show histograms of these differences for the CMIP5 and CMIP6 ensembles, respectively.
The distribution of the differences between feedbacks in preindustrial control and 4×CO2 runs from CMIP5 models calculated using λ (blue) and θ (orange) frameworks. The blue and red vertical dashed lines are the ensemble mean of the distributions for λ and θ frameworks, respectively. The black vertical solid line marks the value of zero. Positive values mean that feedbacks in the control runs are less negative/more positive than in the 4×CO2 runs.
Citation: Journal of Climate 34, 24; 10.1175/JCLI-D-21-0226.1
As in Fig. 5, but for CMIP6 models.
Citation: Journal of Climate 34, 24; 10.1175/JCLI-D-21-0226.1
In the λ framework, the feedbacks in the abrupt-4×CO2 run are on average similar to those in the control run. In the θ framework, the Planck feedback is larger in the control run, while the other feedbacks tend to be smaller in the control run. These differences cancel so that differences of θTotal inferred from CMIP5 and CMIP6 ensemble between the forced and unforced runs are both close to zero (i.e., 0.004 and −0.13 W m−2 K−1). More research is needed to explore the reason of differences between two experiments in individual θ feedbacks.
The correlation of segment-average feedbacks between control and abrupt-4×CO2 runs is provided in Table 3. Consistent with previous studies (e.g., Zhou et al. 2015; Colman and Hanson 2017; Liu et al. 2018), most of the feedbacks have weak correlations, with cloud feedbacks exhibiting the strongest linear relationship in the λ framework. Zhou et al. (2015) suggested that the sensitivity of low cloud cover changes to surface warming is the key to this relationship.
The correlation coefficient between segment-averaged unforced and 4×CO2 climate feedbacks in CMIP5 and CMIP6 models in the λ and θ frameworks.
Overall, most of the relations between the same feedbacks in the control and abrupt4xCO2 runs are weaker in the θ framework than in the λ framework. As a result, the correlation of total feedback drops from 0.38 to −0.05 in the CMIP5 ensemble and from 0.61 to 0.26 in the CMIP6 ensemble. It is important to reiterate that what we present here are the relationships between short-term feedbacks estimated from many 18-yr segments. In reality, we have only a single 18-yr period, which makes it even more difficult to estimate long-term feedback strength from short-term observations.
5. Conclusions
In this study, we compare feedbacks estimated from models in the CMIP5 and CMIP6 ensembles with climate feedbacks inferred from observations using two different energy-balance frameworks, the traditional (λ) framework and modified (θ) framework proposed by Dessler et al. (2018). The difference between these two frameworks is which temperature is related to the TOA flux variations: the λ framework uses global average surface temperature while the θ framework using the 500-hPa tropical temperature.
We quantify two sources of uncertainty in the feedbacks inferred from models: the structural differences and the unforced pattern effect. The structural differences are the differences in the feedbacks that can be traced to differences in the models’ parameterizations and other physics, while the unforced pattern effect are the differences in the feedbacks due to unforced variability (Dessler 2020). The unforced pattern effect can be eliminated by averaging over longer time periods, but the structural differences cannot.
In the λ framework, the structural differences and the unforced pattern effect are comparable. Overall, we see no evidence that the models are missing any important physical processes. This is not a strong confirmation of the models because of the significant spread among the models as well as the large impact on unforced variability when comparing models with a single 18-yr observational dataset.
Feedbacks estimated in the θ framework are more consistent between models and are substantially less affected by the unforced pattern effect, providing a more robust test of the ability of models to simulate the feedbacks. We also quantify individual model performance by calculating the total error (TE), which combines the error of each feedback into a single metric [Eq. (3)]. Tables S2 and S3 of the online supplemental material list our ranking of the models’ ability to simulate the observed feedbacks. The model performance in reproducing just the cloud feedback is also analyzed and yields a similar result.
We also compare feedbacks in the control runs with those in response to long-term global warming using CMIP5 and CMIP6 abrupt-4×CO2 runs. The total feedback in response to unforced variability is about equal to the 4×CO2 total feedback in both frameworks. This is not necessarily true for individual feedbacks, however. The linear relationships between climate feedbacks in the control and abrupt-4×CO2 runs are weaker in the modified energy balance framework than in the traditional framework, suggesting that while the θ framework yields more robust comparisons between observations and simulations, it has limitations in using observations of unforced variability to estimate the response to global warming.
To better predict long-term climate change, more research is needed to bridge the gap between two frameworks. If one’s interest is predicting the surface temperature in the future using θ framework, the changes in atmospheric temperature will eventually have to be converted back to surface temperature, as was done in Dessler and Forster (2018). However, if one focuses on testing the climate models, our research suggests that a better way to test model performance with recent observations is to use the θ framework.
Acknowledgments
This work was supported by National Science Foundation Grants AGS-1841308 and AGS-1661861 and by NASA FINESST Grant 80NSSC20K1606, all to Texas A&M University. We thank Mark Zelinka for providing help with our feedback calculations. We acknowledge the World Climate Research Program’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Table S12 of the online supplemental material) for producing and making available their model output. For CMIP, the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.
Data availability statement
CERES data are available at https://ceres.larc.nasa.gov/, ERA5 data are available at https://cds.climate.copernicus.eu/, and CMIP5 and CMIP6 data are available at https://esgf-node.llnl.gov/. The code is available at https://doi.org/10.5281/zenodo.5644263.
REFERENCES
Andrews, T., and M. J. Webb, 2018: The dependence of global cloud and lapse rate feedbacks on the spatial structure of tropical Pacific warming. J. Climate, 31, 641–654, https://doi.org/10.1175/JCLI-D-17-0087.1.
Andrews, T., J. M. Gregory, M. J. Webb, and K. E. Taylor, 2012: Forcing, feedbacks and climate sensitivity in CMIP5 coupled atmosphere–ocean climate models. Geophys. Res. Lett., 39, L09712, https://doi.org/10.1029/2012GL051607.
Andrews, T., J. M. Gregory, and M. J. Webb, 2015: The dependence of radiative forcing and feedback on evolving patterns of surface temperature change in climate models. J. Climate, 28, 1630–1648, https://doi.org/10.1175/JCLI-D-14-00545.1.
Armour, K. C., C. M. Bitz, and G. H. Roe, 2013: Time-varying climate sensitivity from regional feedbacks. J. Climate, 26, 4518–4534, https://doi.org/10.1175/JCLI-D-12-00544.1.
Blunden, J., and D. S. Arndt, 2020: State of the climate in 2019. Bull. Amer. Meteor. Soc., 101, S1–S429, https://doi.org/10.1175/2020BAMSStateoftheClimate.1.
Ceppi, P., and J. M. Gregory, 2017: Relationship of tropospheric stability to climate sensitivity and Earth’s observed radiation budget. Proc. Natl. Acad. Sci. USA, 114, 13 126–13 131, https://doi.org/10.1073/pnas.1714308114.
Ceppi, P., and J. M. Gregory, 2019: A refined model for the Earth’s global energy balance. Climate Dyn., 53, 4781–4797, https://doi.org/10.1007/s00382-019-04825-x.
Colman, R. A., and L. I. Hanson, 2013: On atmospheric radiative feedbacks associated with climate variability and change. Climate Dyn., 40, 475–492, https://doi.org/10.1007/s00382-012-1391-3.
Colman, R. A., and L. I. Hanson, 2017: On the relative strength of radiative feedbacks under climate variability and change. Climate Dyn., 49, 2115–2129, https://doi.org/10.1007/s00382-016-3441-8.
Colman, R. A., and S. B. Power, 2018: What can decadal variability tell us about climate feedbacks and sensitivity? Climate Dyn., 51, 3815–3828, https://doi.org/10.1007/s00382-018-4113-7.
Dessler, A. E., 2013: Observations of climate feedbacks over 2000–10 and comparisons to climate models. J. Climate, 26, 333–342, https://doi.org/10.1175/JCLI-D-11-00640.1.
Dessler, A. E., 2020: Potential problems measuring climate sensitivity from the historical record. J. Climate, 33, 2237–2248, https://doi.org/10.1175/JCLI-D-19-0476.1.
Dessler, A. E., and S. Wong, 2009: Estimates of the water vapor climate feedback during El Niño–Southern Oscillation. J. Climate, 22, 6404–6412, https://doi.org/10.1175/2009JCLI3052.1.
Dessler, A. E., and N. G. Loeb, 2013: Impact of dataset choice on calculations of the short-term cloud feedback. J. Geophys. Res. Atmos., 118, 2821–2826, https://doi.org/10.1002/jgrd.50199.
Dessler, A. E., and M. D. Zelinka, 2015: Climate and climate change: Climate feedbacks. Encyclopedia of Atmospheric Sciences, 2nd ed., G. R. North, J. Pyle, and F. Zhang, Eds., Academic Press, 18–25.
Dessler, A. E., and P. Forster, 2018: An estimate of equilibrium climate sensitivity from interannual variability. J. Geophys. Res. Atmos., 123, 8634–8645, https://doi.org/10.1029/2018JD028481.
Dessler, A. E., T. Mauritsen, and B. Stevens, 2018: The influence of internal variability on Earth’s energy balance framework and implications for estimating climate sensitivity. Atmos. Chem. Phys., 18, 5147–5155, https://doi.org/10.5194/acp-18-5147-2018.
Donohoe, A., K. C. Armour, A. G. Pendergrass, and D. S. Battisti, 2014: Shortwave and longwave radiative contributions to global warming under increasing CO2. Proc. Natl. Acad. Sci. USA, 111, 16 700–16 705, https://doi.org/10.1073/pnas.1412190111.
Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016: Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization. Geosci. Model Dev., 9, 1937–1958, https://doi.org/10.5194/gmd-9-1937-2016.
Fueglistaler, S., 2019: Observational evidence for two modes of coupling between sea surface temperatures, tropospheric temperature profile and shortwave cloud radiative effect in the tropics. Geophys. Res. Lett., 46, 9890–9898, https://doi.org/10.1029/2019GL083990.
Gregory, J. M., and T. Andrews, 2016: Variation in climate sensitivity and feedback parameters during the historical period. Geophys. Res. Lett., 43, 3911–3920, https://doi.org/10.1002/2016GL068406.
Gregory, J. M., and Coauthors, 2004: A new method for diagnosing radiative forcing and climate sensitivity. Geophys. Res. Lett., 31, L03205, https://doi.org/10.1029/2003GL018747.
Held, I. M., and K. M. Shell, 2012: Using relative humidity as a state variable in climate feedback analysis. J. Climate, 25, 2578–2582, https://doi.org/10.1175/JCLI-D-11-00721.1.
Hersbach, H., and Coauthors, 2020: The ERA5 global reanalysis. Quart. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803.
Huang, Y., Y. Xia, and X. Tan, 2017: On the pattern of CO2 radiative forcing and poleward energy transport. J. Geophys. Res. Atmos., 122, 10 578–10 593, https://doi.org/10.1002/2017JD027221.
Lindzen, R. S., M.-D. Chou, and A. Y. Hou, 2001: Does the Earth have an adaptive infrared iris? Bull. Amer. Meteor. Soc., 82, 417–432, https://doi.org/10.1175/1520-0477(2001)082<0417:DTEHAA>2.3.CO;2.
Liu, R., H. Su, K.-N. Liou, J. H. Jiang, Y. Gu, S. C. Liu, and C.-J. Shiu, 2018: An assessment of tropospheric water vapor feedback using radiative kernels. J. Geophys. Res. Atmos., 123, 1499–1509, https://doi.org/10.1002/2017JD027512.
Loeb, N. G., and Coauthors, 2018: Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Top-of-Atmosphere (TOA) edition-4.0 data product. J. Climate, 31, 895–918, https://doi.org/10.1175/JCLI-D-17-0208.1.
Marvel, K., R. Pincus, G. A. Schmidt, and R. L. Miller, 2018: Internal variability and disequilibrium confound estimates of climate sensitivity from observations. Geophys. Res. Lett., 45, 1595–1601, https://doi.org/10.1002/2017GL076468.
Murphy, J., 1995: Transient response of the Hadley Centre coupled ocean–atmosphere model to increasing carbon dioxide. Part 1: Control climate and flux adjustment. J. Climate, 8, 36–56, https://doi.org/10.1175/1520-0442(1995)008<0036:TROTHC>2.0.CO;2.
Myhre, G., and Coauthors, 2013: Anthropogenic and natural radiative forcing. Climate Change 2013: The Physical Science Basis, T. F. Stocker et al., Eds., Cambridge University Press, 659–740.
North, G. R., R. F. Cahalan, and J. A. Coakley Jr., 1981: Energy balance climate models. Rev. Geophys., 19, 91–121, https://doi.org/10.1029/RG019i001p00091.
Proistosescu, C., and P. J. Huybers, 2017: Slow climate mode reconciles historical and model-based estimates of climate sensitivity. Sci. Adv., 3, e1602821, https://doi.org/10.1126/sciadv.1602821.
Senior, C. A., and J. F. Mitchell, 2000: The time-dependence of climate sensitivity. Geophys. Res. Lett., 27, 2685–2688, https://doi.org/10.1029/2000GL011373.
Shell, K. M., J. T. Kiehl, and C. A. Shields, 2008: Using the radiative kernel technique to calculate climate feedbacks in NCAR’s Community Atmospheric Model. J. Climate, 21, 2269–2282, https://doi.org/10.1175/2007JCLI2044.1.
Sherwood, S. C., S. Bony, O. Boucher, C. Bretherton, P. M. Forster, J. M. Gregory, and B. Stevens, 2015: Adjustments in the forcing-feedback framework for understanding climate change. Bull. Amer. Meteor. Soc., 96, 217–228, https://doi.org/10.1175/BAMS-D-13-00167.1.
Soden, B. J., A. J. Broccoli, and R. S. Hemler, 2004: On the use of cloud forcing to estimate cloud feedback. J. Climate, 17, 3661–3665, https://doi.org/10.1175/1520-0442(2004)017<3661:OTUOCF>2.0.CO;2.
Stevens, B., S. C. Sherwood, S. Bony, and M. J. Webb, 2016: Prospects for narrowing bounds on Earth’s equilibrium climate sensitivity. Earth’s Future, 4, 512–522, https://doi.org/10.1002/2016EF000376.
Taylor, K. E., R. J. Stouffer, and G. A. Meehl, 2012: An overview of CMIP5 and the experiment design. Bull. Amer. Meteor. Soc., 93, 485–498, https://doi.org/10.1175/BAMS-D-11-00094.1.
Trenberth, K. E., Y. Zhang, J. T. Fasullo, and S. Taguchi, 2015: Climate variability and relationships between top-of-atmosphere radiation and temperatures on Earth. J. Geophys. Res. Atmos., 120, 3642–3659, https://doi.org/10.1002/2014JD022887.
Winton, M., K. Takahashi, and I. M. Held, 2010: Importance of ocean heat uptake efficacy to transient climate change. J. Climate, 23, 2333–2344, https://doi.org/10.1175/2009JCLI3139.1.
Zelinka, M. D., T. A. Myers, D. T. McCoy, S. Po-Chedley, P. M. Caldwell, P. Ceppi, S. A. Klein, and K. E. Taylor, 2020: Causes of higher climate sensitivity in CMIP6 models. Geophys. Res. Lett., 47, e2019GL085782, https://doi.org/10.1029/2019GL085782.
Zhou, C., M. D. Zelinka, A. E. Dessler, and S. A. Klein, 2015: The relationship between interannual and long–term cloud feedbacks. Geophys. Res. Lett., 42, 10 463–10 469, https://doi.org/10.1002/2015GL066698.
Zhou, C., M. D. Zelinka, and S. A. Klein, 2016: Impact of decadal cloud variations on the Earth’s energy budget. Nat. Geosci., 9, 871–874, https://doi.org/10.1038/ngeo2828.
Zhou, C., M. D. Zelinka, and S. A. Klein, 2017: Analyzing the dependence of global cloud feedback on the spatial pattern of sea surface temperature change with a Green’s function approach. J. Adv. Model. Earth Syst., 9, 2174–2189, https://doi.org/10.1002/2017MS001096.
