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

ABSTRACT 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. Access through your institution Buy or subscribe This is a preview of subscription content, access via

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subscriptions * Read our FAQs * Contact customer support SIMILAR CONTENT BEING VIEWED BY OTHERS LARGE-SCALE EMERGENCE OF REGIONAL CHANGES IN YEAR-TO-YEAR TEMPERATURE VARIABILITY BY THE END

OF THE 21ST CENTURY Article Open access 13 December 2021 DRIVERS AND MECHANISMS CONTRIBUTING TO EXCESS WARMING IN EUROPE DURING RECENT DECADES Article Open access 05 February 2025

SIGNIFICANTLY WETTER OR DRIER FUTURE CONDITIONS FOR ONE TO TWO THIRDS OF THE WORLD’S POPULATION Article Open access 11 January 2024 REFERENCES * Tebaldi, C. & Arblaster, J. M. Pattern

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between top-of-atmosphere radiation and temperatures on Earth. _J. Geophys. Res. Atmos._ 120, 3642–3659 (2015) Article  ADS  Google Scholar  Download references ACKNOWLEDGEMENTS 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 AUTHORS AND AFFILIATIONS * Department of Global

Ecology, Carnegie Institution for Science, Stanford, California, USA Patrick T. Brown, Patrick T. Brown, Ken Caldeira & Ken Caldeira Authors * Patrick T. Brown View author publications

You can also search for this author inPubMed Google Scholar * Ken Caldeira View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS 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. ETHICS DECLARATIONS COMPETING INTERESTS 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 ±2_σ_ for the full model range, while the red confidence bounds are ±2_σ_ 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. A–C, Model spread (_σ_) of climatological OSR, OLR and ↓_N_ (see colour scale) D–F, 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 Δ_T_2090-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 2_σ_ 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 Δ_T_2090-RCP8.5 predictand, black line). EXTENDED DATA FIGURE 5 HISTOGRAMS FOR THE

RAW, UNCONSTRAINED AND OBSERVATIONALLY INFORMED PROJECTIONS. A–D, Distributions for mid-century (2046–2065). E–H, 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 AA–AI correspond to the nine predictor fields’ second PLS component, panels BA–BI correspond to the third PLS component of the nine

predictor fields, panels CA–CI correspond to the fourth PLS component of the nine predictor fields and panels DA–DI correspond to the fifth PLS component of the nine predictor fields. The

number on top of each panel is the variance explained in the Δ_T_2090-RCP8.5 predictand. EXTENDED DATA FIGURE 7 OBSERVED/MODELLED PREDICTOR FIELDS AND OBSERVATIONALLY INFORMED CHANGES IN

FAST FEEDBACK MAGNITUDE. AA–AI, Model-mean value of the nine energy-budget predictor fields calculated over the period 2001–2015. Colour bars are centred on the global mean. BA–BI, CERES

satellite observations of the nine energy-budget predictor fields calculated over the period 2001–2015. Colour bars are centred on the global mean. CA–CI, 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. A–I, 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. AA–AI, Targeting the magnitude of shortwave cloud feedback. BA–BI, Targeting the magnitude of the longwave cloud feedback. CA–CI,

Targeting the magnitude of the water vapour feedback. DA–DI, 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 Δ_T_ 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 Δ_T_ predictand, respectively. EXTENDED DATA FIGURE 10 MAGNITUDE OF MONTHLY VARIABILITY RELATIONSHIP TO Δ_T_. A–C, 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). D–F, 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 Δ_T_ 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) POWERPOINT SLIDES POWERPOINT SLIDE FOR FIG. 1 POWERPOINT SLIDE FOR FIG. 2 POWERPOINT SLIDE FOR FIG. 3 POWERPOINT SLIDE FOR FIG. 4 SOURCE DATA SOURCE

DATA TO FIG. 1 SOURCE DATA TO FIG. 2 SOURCE DATA TO FIG. 3 RIGHTS AND PERMISSIONS Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Brown, P., Caldeira, K. Greater future global

warming inferred from Earth’s recent energy budget. _Nature_ 552, 45–50 (2017). https://doi.org/10.1038/nature24672 Download citation * Received: 14 July 2017 * Accepted: 23 October 2017 *

Published: 07 December 2017 * Issue Date: 07 December 2017 * DOI: https://doi.org/10.1038/nature24672 SHARE THIS ARTICLE Anyone you share the following link with will be able to read this

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