Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake

  • Philip Goodwin, Richard G. Williams, Andy Ridgwell
  • Nature Geoscience, December 2014, Nature
  • DOI: 10.1038/ngeo2304

A single equation connecting global surface warming with carbon emissions

What is it about?

Climate models reveal that global surface warming is nearly proportional to cumulative carbon emissions on multi-decadal to centennial timescales. However, this near linear dependence between warming and cumulative carbon emissions is not understood. We present a single equation connecting surface warming and carbon emissions, which is based upon a heat balance and a global carbon budget. This near linear dependence between surface warming and carbon emissions is due to partially opposing effects of ocean heat and carbon uptake.

Why is it important?

Projections from climate models differ in how much surface warming occurs for a given carbon emission. Our particular study suggests that a surface warming of 1.1 +/- 0.5 K occurs for every 1000 PgC of carbon emitted (1000 PgC is the same as a trillion tonnes of carbon). Our theory may be used to diagnose the global warming response in different climate models and mechanistically understand the differences between their projections.


Professor Richard G Williams
University of Liverpool Department of Earth Ocean and Ecological Sciences

We hope that this article provides a theoretical underpinning to understand the response of climate models. While the detailed projections of climate models are sensitive to different model choices and forcing, the overall response of the climate models is easy to understand: the more carbon we emit, the warmer it will become, and this effect may persist after carbon emissions cease. This study brought together authors with different skills and resources. For the first time, the study sets out new theory that connects surface warming and carbon emissions and then applied our theory to understand the response of a climate model (an intermediate complexity Earth system model). The climate model is forced by a pulse of carbon emitted over several hundred years and its response assessed over an integration of 5000 years.

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The following have contributed to this page: Professor Richard G Williams