Energy budget constraints on historical radiative forcing


Radiative forcing is a fundamental quantity for understanding anthropogenic and natural drivers of past and future climate change1, yet significant uncertainty remains in our quantification of radiative forcing and its model representation2,3,4. Here we use instrumental measurements of historical global mean surface temperature change and Earth’s total heat uptake, alongside estimates of the Earth’s radiative response, to provide a top-down energy budget constraint on historical (1861–1880 to near-present) effective radiative forcing of 2.3 W m−2 (1.7–3.0W m−2; 5–95% confidence interval). This represents a near 40% reduction in the 5–95% uncertainty range assessed by the IPCC Fifth Assessment Report2. Although precise estimates of effective radiative forcing in models do not widely exist, our results suggest that the effective radiative forcing may be too small in as many as one-third of climate models in the fifth phase of the Coupled Model Intercomparison Project. Improving model representation of radiative forcing should be a priority for modelling centres. This will reduce uncertainties in climate projections that have persisted for decades4,5.

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Fig. 1: Historical ERF derived from an energy budget constraint.

Data availability

The Cowtan and Way20 global annual mean temperature anomaly dataset was accessed via All other data supporting the findings of this study are provided and/or referenced within this paper.

Code availability

The code used to produce the energy budget constraint and Fig. 1 is available via the following online repository: (ref. 51).


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T.A. was supported by the Met Office Hadley Centre Climate Programme funded by BEIS and Defra. P.M.F. was supported by NERC SMURPHS project NE/N006054/1. Both T.A. and P.M.F. were supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 820829 (CONSTRAIN project). We thank M. Ringer and J. Gregory for useful discussions.

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T.A. and P.M.F. conceived the study. T.A. performed the analysis and wrote the manuscript, with comments from P.M.F.

Correspondence to Timothy Andrews.

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Andrews, T., Forster, P.M. Energy budget constraints on historical radiative forcing. Nat. Clim. Chang. (2020).

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