How does ocean warming and steric sea level rise depend on carbon emissions?

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


There is widespread concern about how climate is responding to the on going rise in atmospheric CO2 from carbon emissions and land use changes. In our view, the climate response 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 and steric sea level rise. 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 steric sea level rise is sensitive to how the ocean interior takes up heat, involving the transfer of surface properties into the thermocline and deep ocean.
4. After emissions cease, there will be a thermal adjustment of the lower atmosphere, and the net heat flux into the ocean will cease, and so ocean warming and steric sea level will eventually likewise cease.
5. As well as a thermal equilibrium being reached, the atmosphere and ocean approach a carbon equilibrium after emissions cease, on a timescale of perhaps several hundred years to a thousand years. At this equilibrium, the final atmospheric CO2 and the amount of climate warming is related to cumulative carbon emissions based on our idealised theory.

The climate warming and steric sea level rise will be investigated using diagnostics of
(i) present day temperature and salinity observations, allowing the steric sea level to be diagnosed;
(ii) thought experiments with a range of ocean and climate models on timescales of centuries to several thousand years, designed to explore how the ocean warming spreads from the sea surface into the ocean interior, which ultimately determines the steric sea level rise;
(iii) comparison with diagnostics of state of the art climate models, integrated for a century;
(iv) comparison with idealised theory, relevant for when emissions cease;
and (iv) finally a down scaling to provide bounds on the steric sea level response on a regional scale.

This combination of the theory and Earth System models of intermediate complexity will allow a wide parameter space to be explored for a range of emission scenarios, much broader than that usually employed within IPCC assessments for the next 100 years. The study has the potential to provide accessible bounds for steric sea level rise, relevant for policy makers interested in different energy policies, and a link to end users is provided via the collaboration with the Hadley Centre.

Planned Impact

Our aim is to inform the wider community about how sea level is varying, providing a historical context and some insight as to likely future projections. 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 a workshop to be held in Liverpool with our project partners Chris Jones and Andy Ridgwell, as well as researchers from the new Hadley Centre Sea Level Group.
3. 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 provide insight into how sea level varies. Here we will create a series of short accessible videos - combinations of film and, where applicable, animations with commentaries:

1. What is sea level: explaining how sea level can vary across the world using animations displaying altimetry and tide gauge records from the Permanent Service for Mean Sea Level and footage generated from Google Earth.

2. Historic sea-level trends: we will produce a short documentary style film in which Prof. Philip Woodworth MBE of the National Oceanography Centre (NOC) will document and discuss historic sea level trends. He will emphasise the role played by Liverpool in accumulating continuous records, starting in 1764 to 1793 by William Hutchinson ( and extending to modern day measurements. He will explore sea level prediction using the analogue 'Kelvin' tidal computers (used to provide tidal forecasts for the D-Day landings), and contrast this with the super-computing solutions employed today.

3. What changes sea level: this video will be made up of three filmed laboratory experiments and an animation. The first experiment will demonstrate that when floating ice melts in sea water there is no net increase in volume. The second experiment will demonstrate melt water being added to the system. The final experiment will demonstrate the thermal expansion of water by observing the change in water level with warming.

4. What are the future prospects: we will produce another short documentary style film with Prof. Woodworth addressing how sea level rise increases the probability of flooding events linked to storm surges. Prof. Woodworth has considerable experience in both filming and radio work targeted at a general audience (e.g. BBC's "Coast" programme) and we will exploit local filming locations.

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 (see letter of support).

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 councilors, and alumni; see webcasts at Our other recent climate and sea level briefings include: 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 We have discussed fundamental new relationships for the climate system on timescales of typically 1000 years:
i) atmospheric CO2 increases exponentially with cumulative carbon emissions due to a positive feedback from ocean acidity;
ii) surface warming varies linearly with cumulative carbon emissions due to surface warming varying logarithmically with atmospheric CO2;
iii) Steric sea level should increase nearly linearly with cumulative carbon emissions, subject to the distribution of heat uptake within the ocean interior.
Exploitation Route Our analytical relations provide an accessible way to assess the impact of different fossil fuel policies for long-term climate.

This activity has led to a new app being produced at
Sectors Education,Energy,Environment

Description NERC Discovery Science
Amount £498,211 (GBP)
Funding ID NE/N009789/1 
Organisation Natural Environment Research Council 
Sector Public
Country United Kingdom
Start 09/2016 
End 06/2020