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Greater future global warming inferred from Earth’s recent energy budget


Climate models provide the principal means of projecting global warming over the remainder of the twenty-first century but modelled estimates of warming vary by a factor of approximately two even under the same radiative forcing scenarios. Across-model relationships between currently observable attributes of the climate system and the simulated magnitude of future warming have the potential to inform projections. Here we show that robust across-model relationships exist between the global spatial patterns of several fundamental attributes of Earth’s top-of-atmosphere energy budget and the magnitude of projected global warming. When we constrain the model projections with observations, we obtain greater means and narrower ranges of future global warming across the major radiative forcing scenarios, in general. In particular, we find that the observationally informed warming projection for the end of the twenty-first century for the steepest radiative forcing scenario is about 15 per cent warmer (+0.5 degrees Celsius) with a reduction of about a third in the two-standard-deviation spread (−1.2 degrees Celsius) relative to the raw model projections reported by the Intergovernmental Panel on Climate Change. Our results suggest that achieving any given global temperature stabilization target will require steeper greenhouse gas emissions reductions than previously calculated.

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Figure 1: Sensitivity of results to predictors or predictands used and to the number of PLS components used.
Figure 2: Comparison of raw unconstrained and observationally informed projections of twenty-first-century global warming.
Figure 3: Relationship between predictor fields and the magnitude of warming.
Figure 4: Difference between more and less sensitive models in their simulation of the current climate.


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We thank Z. Hausfather for discussions. This study was supported by the Fund for Innovative Climate and Energy Research and the Carnegie Institution for Science endowment. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for the Coupled Modelled Intercomparison Project (CMIP), and we thank the climate modelling groups for producing and making available their model output. For CMIP the US 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.

Author information




K.C. conceived the study. P.T.B. performed the analysis and wrote an initial draft of the manuscript. Both authors contributed to interpretation of results and refinement of the manuscript.

Corresponding author

Correspondence to Patrick T. Brown.

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The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks T. L’Ecuyer and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Across-model relationships between short-term variability in the shortwave cloud radiative effect and long-term changes between the present and the end of the twenty-first century.

The relationship between predictor and predictand depends both on the parameter chosen as the predictand and on the location used for the predictor. a, Relationship (at 20 °S, 20 °E) between the standard deviation of the climatological seasonal cycle (σ) in the downward shortwave cloud radiative effect (↓CRE-SW) over the period 2001–2015 and the long-term change (Δ) in the ↓CRE-SW (mean from 2085–2099 minus the mean from 2001–2015). b, As in a but showing the relationship with GMSAT change. Grey confidence bounds are ±2σ for the full model range, while the red confidence bounds are ±2σ using the linear relationship between the predictor and the predictand. c, Relationship (at 45° S, 131° E) between σ for ↓CRE-SW over the period 2001–2015 and GMSAT change. d, As in c but for 30° N, 10° E. The linear regression slope, Pearson’s correlation coefficient r and standard Pearson’s P-value of the correlation coefficient are shown.

Extended Data Figure 2 Size of model spread compared to observational uncertainty.

ac, Model spread (σ) of climatological OSR, OLR and ↓N (see colour scale) df, Ratio of local model spread to CERES observational uncertainty (see colour scale). The global spatial mean of each map is displayed at the top of each panel.

Extended Data Figure 3 Flow chart summarizing the statistical procedure that is conducted in order to arrive at the prediction ratio and spread ratio.

See Supplementary Video 1 for an animation of the procedure.

Extended Data Figure 4 Tests of spread ratio and prediction ratio robustness.

a, Spread ratios, as a function of the number of PLS components used, for the nine energy-budget predictor fields, each individually targeting the ΔT2090-RCP8 predictand without the use of cross-validation. b, Same as a but using fourfold cross-validation. c, Spread ratios for test data that would not be expected to result in any predictive skill between the predictor and predictand (see Methods) using hold-one-out cross-validation. The blue and magenta lines correspond to experiments where the predictand vectors have had their values randomly scrambled or reordered. d, As in c but showing prediction ratios. The 2σ ranges of the test data across all trials are shaded in c and d. For context, the test data results are compared to one particular predictor + predictand combination from our main results (the OLR predictor field targeting the ΔT2090-RCP8.5 predictand, black line).

Extended Data Figure 5 Histograms for the raw, unconstrained and observationally informed projections.

ad, Distributions for mid-century (2046–2065). eh, Distributions for the end of the century (2081–2100). Raw, unconstrained model distributions are shown in blue and observationally informed (using all nine predictor fields simultaneously) distributions are shown in orange. The blue and red dashed lines indicate distribution means. The percentage of the constrained distribution that is larger than the mean of the unconstrained distribution is displayed in the title of each panel.

Extended Data Figure 6 PLS loadings for PLS components 2–5.

Panels aaai correspond to the nine predictor fields’ second PLS component, panels babi correspond to the third PLS component of the nine predictor fields, panels caci correspond to the fourth PLS component of the nine predictor fields and panels dadi correspond to the fifth PLS component of the nine predictor fields. The number on top of each panel is the variance explained in the ΔT2090-RCP8.5 predictand.

Extended Data Figure 7 Observed/modelled predictor fields and observationally informed changes in fast feedback magnitude.

aaai, Model-mean value of the nine energy-budget predictor fields calculated over the period 2001–2015. Colour bars are centred on the global mean. babi, CERES satellite observations of the nine energy-budget predictor fields calculated over the period 2001–2015. Colour bars are centred on the global mean. caci, CERES satellite observations minus the model mean of the nine energy-budget predictor fields. d, Difference between the observationally informed and raw model-mean prediction (analogous to the prediction ratio, but taking the difference rather than the ratio) for the magnitude of six fast feedbacks (Planck, water vapour, lapse rate, shortwave cloud, longwave cloud, surface albedo) and the net feedback reported in ref. 52. Extended Data Fig. 8 shows an analogous figure but using each of the nine predictor fields separately.

Extended Data Figure 8 The association of the energy-budget predictor fields with feedback strength.

ai, Difference between the observationally informed and raw model mean for the magnitude of six fast feedbacks (Pl, Planck; WV, water vapour; LR, lapse rate; SWcl, shortwave cloud; LWcl, longwave cloud; SA, surface albedo) and the net feedback from ref. 52, corresponding to each of the nine predictor fields individually.

Extended Data Figure 9 PLS loadings for the magnitude of different feedbacks.

aaai, Targeting the magnitude of shortwave cloud feedback. babi, Targeting the magnitude of the longwave cloud feedback. caci, Targeting the magnitude of the water vapour feedback. dadi, Targeting the magnitude of the surface albedo feedback. These are the PLS loading patterns (equation (10)) associated with the first PLS component. Each panel shows the Pearson’s pattern correlation coefficient r as well as the RMSE between the given map and the associated map targeting the ΔT predictand shown in Fig. 3 and Extended Data Fig. 10a–c. The two r numbers and the two RMSE numbers correspond to each panel’s relationship with the first and second PLS loading patterns associated with the ΔT predictand, respectively.

Extended Data Figure 10 Magnitude of monthly variability relationship to ΔT.

ac, PLS loadings of the first PLS component for the predictor fields associated with the magnitude of the monthly-variability predictor. Positive loadings indicate that models with larger values tend to simulate more twenty-first century global warming and negative loadings indicate that models with smaller values tend to simulate more twenty-first-century global warming (see equation (10) in Methods). df, Cross-regression coefficients between monthly time series of components of the energy budget and surface air temperature separated by latitude bands. Solid lines represent the model mean for the more-sensitive models (models with ΔT above the model median) and dashed lines represent the model mean for the less-sensitive models (models with Δ T below the model median). Negative (positive) values on the x axis indicate variability preceding (following) surface air temperature in time. CERES observations are shown as dotted lines.

Supplementary information

Supplementary Table 1

This Supplementary Table provides details on the climate models used and which were included in which analyses. (XLSX 47 kb)

Supplementary Data

This zipped file contains the built-in MATLABTM function used to carry out PLS regression (plsregress.m), the preprocessed data saved as a MATLABTM saveset file (Preproc_Brown_PLS_delta_GMSAT.mat) and the MATLABTM code that carries out the main statistical procedure used in the study (Brown_Caldeira_PLS_delta_GMSAT.m). (ZIP 3706 kb)

Procedure Summary

Video animation summarizing the statistical procedure used to create the constrained projections. (MP4 4959 kb)

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Brown, P., Caldeira, K. Greater future global warming inferred from Earth’s recent energy budget. Nature 552, 45–50 (2017).

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