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Competing Interests: Competing Interests The authors declare no competing interests.

The much awaited and intensely negotiated Paris Agreement was adopted on 12 December 2015 by the Parties to the United Nations Framework Convention on Climate Change. The agreement set out a more ambitious long-term temperature goal than many had anticipated, implying more stringent emissions reductions that have been under-explored by the research community. By its very nature a multidisciplinary challenge, filling the knowledge gap requires not only climate scientists, but the whole Earth system science community, as well as economists, engineers, lawyers, philosophers, politicians, emergency planners and others to step up. To kick start cross-disciplinary discussions, the University of Oxford's Environmental Change Institute focused its 25th anniversary conference upon meeting the challenges of the Paris Agreement for science and society. This theme issue consists of review papers, opinion pieces and original research from some of the presentations within that meeting, covering a wide range of issues underpinning the Paris Agreement.This article is part of the theme issue 'The Paris Agreement: understanding the physical and social challenges for a warming world of 1.5°C above pre-industrial levels'., (© 2018 The Author(s).)

A number of recent studies have found a strong link between peak human-induced global warming and cumulative carbon emissions from the start of the industrial revolution, while the link to emissions over shorter periods or in the years 2020 or 2050 is generally weaker. However, cumulative targets appear to conflict with the concept of a 'floor' in emissions caused by sectors such as food production. Here, we show that the introduction of emissions floors does not reduce the importance of cumulative emissions, but may make some warming targets unachievable. For pathways that give a most likely warming up to about 4°C, cumulative emissions from pre-industrial times to year 2200 correlate strongly with most likely resultant peak warming regardless of the shape of emissions floors used, providing a more natural long-term policy horizon than 2050 or 2100. The maximum rate of CO(2)-induced warming, which will affect the feasibility and cost of adapting to climate change, is not determined by cumulative emissions but is tightly aligned with peak rates of emissions. Hence, cumulative carbon emissions to 2200 and peak emission rates could provide a clear and simple framework for CO(2) mitigation policy.

More than 100 countries have adopted a global warming limit of 2 degrees C or below (relative to pre-industrial levels) as a guiding principle for mitigation efforts to reduce climate change risks, impacts and damages. However, the greenhouse gas (GHG) emissions corresponding to a specified maximum warming are poorly known owing to uncertainties in the carbon cycle and the climate response. Here we provide a comprehensive probabilistic analysis aimed at quantifying GHG emission budgets for the 2000-50 period that would limit warming throughout the twenty-first century to below 2 degrees C, based on a combination of published distributions of climate system properties and observational constraints. We show that, for the chosen class of emission scenarios, both cumulative emissions up to 2050 and emission levels in 2050 are robust indicators of the probability that twenty-first century warming will not exceed 2 degrees C relative to pre-industrial temperatures. Limiting cumulative CO(2) emissions over 2000-50 to 1,000 Gt CO(2) yields a 25% probability of warming exceeding 2 degrees C-and a limit of 1,440 Gt CO(2) yields a 50% probability-given a representative estimate of the distribution of climate system properties. As known 2000-06 CO(2) emissions were approximately 234 Gt CO(2), less than half the proven economically recoverable oil, gas and coal reserves can still be emitted up to 2050 to achieve such a goal. Recent G8 Communiqués envisage halved global GHG emissions by 2050, for which we estimate a 12-45% probability of exceeding 2 degrees C-assuming 1990 as emission base year and a range of published climate sensitivity distributions. Emissions levels in 2020 are a less robust indicator, but for the scenarios considered, the probability of exceeding 2 degrees C rises to 53-87% if global GHG emissions are still more than 25% above 2000 levels in 2020.