Mechanistic controls of surface warming by ocean heat and carbon uptake

Lead Research Organisation: University of Liverpool
Department Name: Earth, Ocean and Ecological Sciences


We are all aware of how carbon emissions are leading to concern about a warming of the planet. In our view, the climate response to carbon emissions can be divided into the following stages:
1. Past and on going increases in atmospheric CO2 are leading to a global warming of up to 0.6C over the last 50 years. The regional variability is though much larger than this global signal.
2. Continuing emissions are increasing atmospheric CO2 and driving a heat flux into the ocean, leading to ocean warming. The amount of warming is sensitive to the carbon emission scenario, as well as the rate of carbon uptake by the ocean and terrestrial system.
3. The regional distribution of warming and carbon drawdown is sensitive to how the ocean interior takes up heat and carbon, involving the transfer of surface properties into the thermocline and deep ocean.
4. In the future, after emissions cease may be after many hundreds of years, the atmosphere and ocean will approach an equilibrium with each other. At this point, the final atmospheric CO2 and the amount of climate warming is simply related to cumulative sum of all the previously carbon emitted.

One of the key findings of the latest IPCC report is how climate model projections suggest that global warming varies nearly linearly with cumulative carbon emissions. This response is not fully explained or understood, in terms of the essential underlying mechanisms or why different climate models reveal a different amount of warming to each other.

We have established a new theory to explain how surface warming varies in time with carbon emissions.
The aim of the proposal is to investigate the climate warming in the following manner:
(i) apply our new theory of how surface warming compares to cumulative carbon emissions, modified from an equilibrium response by the transient uptake of heat and carbon by the ocean and terrestrial systems;
(ii) conduct diagnostics of how the ocean is taking up heat, examining how the ocean is ventilated in terms of volumetric changes in ocean density classes;
(iii) develop ocean ventilation experiments with a range of ocean and climate models on timescales of decades to a thousand years, designed to explore the extent that the ocean uptake of heat and carbon are similar to each other, and assess their partly compensating effects on how surface warming links to carbon emissions;
(iv) compare with and analyse diagnostics of state of the art climate models, integrated for a century, including climate models driven by emissions, terrestrial uptake of heat and carbon, and radiative forcing from non-CO2 greenhouse gases and aerosols.

Our new theoretical framework has the potential to provide
(i) improved understanding of the mechanisms controlling the relationship between surface warming and carbon emissions, particularly focusing on the role of the ocean;
(ii) traceability between different ocean and climate models, identifying clearly which factors are leading to different climate responses;
(iii) reconcile Earth System model investigations over a wider parameter regime with IPCC class climate models.

This study is relevant for policy makers interested in different energy policies, and a link to end users is provided via the collaboration with the Hadley Centre and NOAA GFDL.

The study emphases the importance of engaging with the wider public by developing 4 targeted short and accessible videos on the climate problem, emphasising our new viewpoint.

Planned Impact

Our aim is to inform the wider community about how surface warming from carbon emissions is controlled. We wish to engage with the following stakeholders:
1. Students, school children and those in the general public who wish to acquire a more informed view as to how changes in ocean warming and sea level rise are dependant on carbon emissions.
2. The ocean research community through our publications and presentations in academic meetings.
We will organise an end of programme workshop to be held in Liverpool with our project partners Drs Richard Wood, Jason Lowe and Ben Booth from the Hadley Centre, and Bob Hallberg and John Krasting from NOAA GFDL.
3. Wider scientific community interested in climate change. We have been invited by Cambridge University Press to write an accessible review of our new theory in a new online Elements series (, which are designed to provide original and concise reviews of work within the sciences and humanities.
4. Policy makers, civic leaders and the wider public through our own research activities linked to the Research Centre for Marine Sciences ( and Living with Environmental Change (see short film, research theme from the University of Liverpool; Williams is the Director of the Research Centre and one of the four University Champions for the latter theme.

In order to engage with the wider community, including school pupils, students, teachers and the general public, we want to create a series of short accessible videos (each approx. 3 minutes long) - combinations of film and animations with commentaries - to explain the key processes involved over both short and long term timescales. We have already followed this approach by providing a series Sea Level: A Liverpool View via You Tube (OceanClimateatUoL), which provides personal, historical and future perspectives on sea level and climate change drawing upon the unique history of engagement at Liverpool.

The new series will be made up of 4 short videos:
Video 1. If we emit carbon, what is the response? This video will be an introduction to the problem the research poses. We will explain the vocabulary we will use e.g. radiation, heat and warming and demonstrate how these ideas are linked.
Video 2. What is the long term response? We assume that after many centuries the atmosphere and ocean approach a global equilibrium in terms of heat and carbon transfer; draws on the relationship derived in Williams et al. [2012] GRL.
Video 3. What is the short term response? This video will discuss how atmospheric heat and carbon are taken up by the ocean; draws on the relationship derived by Goodwin et al. [2015] Nature Geoscience.
Video 4. What are the additional uncertainties? We will discuss how there is much more complexity in the real climate system. We will illustrate radiative forcing from other greenhouse gases, such as methane, and partial offsets by aerosols and cloud cover; draws upon advice from program partners at the Hadley Centre.

Distribution: the video outputs will be distributed via YouTube and through our websites, including the Research Centre for Marine Sciences and Climate Change and the National Oceanography Centre website.

We have used similar media to disseminate our research highlights to civic leaders, such as a 'Briefing on the Science of Climate Change' on 10 February 2011 to over 200 participants including Archbishop Kelly of Liverpool, local MPs and councillors, and alumni; see webcasts at Other high-profile briefings were to Professor Tom Stocker (co-Chair of the next IPCC report) on 13 December 2011, to Lord Marland and Bishop James, 16 June 2011; and to Archbishop Kelly on 10 March 2010.


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Description Surface warming increases nearly linearly with the cumulative amount of carbon emitted to the climate system. We have explained this response using a single equation, which represents the effects of ocean heat uptake, and ocean and terrestrial carbon uptake. We have now estimated how much carbon may be emitted before meeting 1.5C or 2C global surface warming. At present carbon emission rates, we reach these warming targets in 17-18 years and 38-40 years respectively.
Exploitation Route Provides a theoretical framework to understand how surface warming in climate models is controlled. Our estimates of the maximum permitted carbon emissions to avoid 1.5C or 2C warming should be taken on board by policy makers.

Also see NERC Planet Earth article
Sectors Energy,Environment

Description Our work has been cited in the IPCC report on 1.5C warming Our work addresses how warming connects to carbon emissions, the delayed surface warming after emissions cease and how much carbon may be emitted for 2C warming is reached. In particular, these 3 papers have been cited: Goodwin, P., A. Katavouta, V.M. Roussenov, G.L. Foster, E.J. Rohling and R.G. Williams,2018. Pathways to 1.5C and 2C warming based on observational and geological constraints. Nature Geoscience, 11, 102-107, doi: 10.1038/s41561-017-0054-8. Goodwin, P., R.G. Williams and A. Ridgwell, 2015. Sensitivity of climate to cumulative carbon emissions due to compensation of ocean heat and carbon uptake. Nature Geoscience, 8, 29-34, doi:10.1038/ngeo2304. Williams, R.G., V. Roussenov, T.L. Froelicher and P. Goodwin, 2017. Drivers of continued surface warming after cessation of carbon emissions. Geophysical Research Letters, 44,
First Year Of Impact 2019
Sector Energy,Environment
Impact Types Policy & public services

Description Provides estimates of how much time left before we reach 1.5C warming
Geographic Reach Multiple continents/international 
Policy Influence Type Citation in other policy documents
Title Coupled carbon-climate Earth System Model GFDL ESM2M annual mean global surface warming response dataset (1000 year simulation) 
Description This dataset contains derived annual mean globally averaged variables to understand surface warming response in terms of changes in global carbon inventories and an empirical heat budget. The source model outputs were generated by Thomas Froelicher in 2015 using a 1000-year simulation of the global coupled carbon-climate Earth System Model developed at the Geophysical Fluid Dynamics Laboratory (GFDL ESM2M). Annual mean variables were then derived from these data as part of a Natural Environment Research Council (NERC) discovery science project "Mechanistic controls of surface warming by ocean heat and carbon uptake" standard grant reference NE/N009789/1 lead by Principal Investigator Professor Ric Williams to understand surface warming response. This was determined by calculated changes in: ocean carbon inventory; ocean carbon under saturation; saturated dissolved inorganic carbon; ocean dissolved inorganic carbon; radiative forcing from carbon dioxide; and ocean heat uptake. Additionally the dependence of radiative forcing on carbon emissions, dependence of surface warming on radiative forcing and surface warming dependence on radiative forcing were determined. Data are held in ASCII format by the British Oceanographic Data Centre. 
Type Of Material Database/Collection of data 
Year Produced 2017 
Provided To Others? Yes  
Impact No notable impact yet, but making climate model data available to everyone. 
Description Research collaborations 
Organisation Bern University of Applied Sciences
Country Switzerland 
Sector Academic/University 
PI Contribution Prof. Thomas Froelicher, Bern University, Switzerland. Author for the next IPCC report
Collaborator Contribution Collaborated on how peak surface warming may be delayed after carbon emissions cease.
Impact Output: Williams, R.G., V. Roussenov, T.L. Froelicher and P. Goodwin, 2017. Drivers of continued surface warming after cessation of carbon emissions. Geophysical Research Letters, 44, Collaboration is linked to physics and chemistry of the climate system.
Start Year 2017
Description Article for Research Feature 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Article for Research Feature, Oceans as moderators of the carbon cycle and our climate', published 29 November 2017.
Year(s) Of Engagement Activity 2017
Description Interfaith briefing 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach Regional
Primary Audience Public/other audiences
Results and Impact Discussion about climate change and likely impacts
Year(s) Of Engagement Activity 2019
Description Posters and talks at international science conferences 
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Posters at international conferences European Geophysical Union in 2017 and American Geophysical Union Ocean Sciences in 2018
Year(s) Of Engagement Activity 2016,2017
Description Press release 
Form Of Engagement Activity A press release, press conference or response to a media enquiry/interview
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Media (as a channel to the public)
Results and Impact Press release on our work showing that we only have 17 to 18 years before 1.5C warming is reached.
Year(s) Of Engagement Activity 2018
Description Web based interview 
Form Of Engagement Activity A magazine, newsletter or online publication
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Industry/Business
Results and Impact Thought piece on Global warming and Carbon Emissions, for AZO CleanTech, 31 January 2020.
Year(s) Of Engagement Activity 2020