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

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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.