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.

Global efforts to mitigate climate change are guided by projections of future temperatures. But the eventual equilibrium global mean temperature associated with a given stabilization level of atmospheric greenhouse gas concentrations remains uncertain, complicating the setting of stabilization targets to avoid potentially dangerous levels of global warming. Similar problems apply to the carbon cycle: observations currently provide only a weak constraint on the response to future emissions. Here we use ensemble simulations of simple climate-carbon-cycle models constrained by observations and projections from more comprehensive models to simulate the temperature response to a broad range of carbon dioxide emission pathways. We find that the peak warming caused by a given cumulative carbon dioxide emission is better constrained than the warming response to a stabilization scenario. Furthermore, the relationship between cumulative emissions and peak warming is remarkably insensitive to the emission pathway (timing of emissions or peak emission rate). Hence policy targets based on limiting cumulative emissions of carbon dioxide are likely to be more robust to scientific uncertainty than emission-rate or concentration targets. Total anthropogenic emissions of one trillion tonnes of carbon (3.67 trillion tonnes of CO(2)), about half of which has already been emitted since industrialization began, results in a most likely peak carbon-dioxide-induced warming of 2 degrees C above pre-industrial temperatures, with a 5-95% confidence interval of 1.3-3.9 degrees C.

The range of possibilities for future climate evolution needs to be taken into account when planning climate change mitigation and adaptation strategies. This requires ensembles of multi-decadal simulations to assess both chaotic climate variability and model response uncertainty. Statistical estimates of model response uncertainty, based on observations of recent climate change, admit climate sensitivities--defined as the equilibrium response of global mean temperature to doubling levels of atmospheric carbon dioxide--substantially greater than 5 K. But such strong responses are not used in ranges for future climate change because they have not been seen in general circulation models. Here we present results from the 'climateprediction.net' experiment, the first multi-thousand-member grand ensemble of simulations using a general circulation model and thereby explicitly resolving regional details. We find model versions as realistic as other state-of-the-art climate models but with climate sensitivities ranging from less than 2 K to more than 11 K. Models with such extreme sensitivities are critical for the study of the full range of possible responses of the climate system to rising greenhouse gas levels, and for assessing the risks associated with specific targets for stabilizing these levels.

The Paris Agreement has opened debate on whether limiting warming to 21 1.5°C is compatible with current emission pledges and warming of about 22 0.9°C from the mid-19 th -century to the present decade. We show that limiting 23 cumulative post-2015 CO2 emissions to about 200 GtC would limit post-2015 24 warming to less than 0.6°C in 66% of Earth System Model members of the 25 CMIP5 ensemble with no mitigation of other climate drivers, increasing to 26 240GtC with ambitious non-CO2 mitigation. We combine a simple climate-27 carbon-cycle model with estimated ranges for key climate system properties 28 from the IPCC 5 th Assessment Report. Assuming emissions peak and decline 29 to below current levels by 2030 and continue thereafter on a much steeper 30 decline, historically unprecedented but consistent with a standard ambitious 31 mitigation scenario (RCP2.6), gives a likely range of peak warming of 1.2-32 2.0°C above the mid-19 th -century. If CO2 emissions are continuously adjusted 33 over time to limit 2100 warming to 1.5°C , with ambitious non-CO2 mitigation, 34 net future cumulative CO2 emissions are unlikely to prove less than 250 GtC 35 and unlikely greater than 540GtC. Hence limiting warming to 1.5°C is not yet a 36 geophysical impossibility, but likely requires delivery on strengthened pledges 37 for 2030 followed by challengingly deep and rapid mitigation. Strengthening 38 near-term emissions reductions would hedge against a high climate response 39 or subsequent reduction-rates proving economically, technically or politically 40 unfeasible. 41 42 Main text: 43The aim of Paris Agreement is "holding the increase in global average 44 temperature to well below 2°C above pre-industrial levels and pursuing efforts 45 to limit the temperature increase to 1.5°C " 1 . The Parties also undertook to 46 achieve this goal by reducing net emissions "to achieve a balance between 47 anthropogenic sources and removals by sinks of greenhouse gases in the 48 second half of this century", and hence implicitly not by geo-engineering 49 Long-term anthropogenic warming is determined primarily by cumulative 64 emissions of CO2 7-10 : the IPCC 5 th Assessment Report (IPCC-AR5) found that 65 cumulative CO2 emissions from 1870 had to remain below 615GtC for total 66 anthropogenic warming to remain below 1.5°C in more than 66% of members 67 of the CMIP5 ensemble of Earth System Models (ESMs) 11 (see Fig. 1a). 68Accounting for the 545GtC that had been emitted by the end of 2014 12 , this 69 would indicate a remaining budget from 2015 of less than 7 years' current 70 emissions, while current commitments under the Nationally Determined 71Contributions (NDCs) indicate 2030 emissions close to current levels 13 . 72 73The scenarios and simulations on which these carbon budgets were based, 74 however, were designed to assess futures in absence of CO2 mitigation, not 75 the very ambitious mitigation scenarios and correspondingly small amounts of 76 additional warming above present that are here of interest. cumulative carbon emissions (5...

The magnitude and impact of future global warming depends on the sensitivity of the climate system to changes in greenhouse gas concentrations. The commonly accepted range for the equilibrium global mean temperature change in response to a doubling of the atmospheric carbon dioxide concentration, termed climate sensitivity, is 1.5-4.5 K (ref. 2). A number of observational studies, however, find a substantial probability of significantly higher sensitivities, yielding upper limits on climate sensitivity of 7.7 K to above 9 K (refs 3-8). Here we demonstrate that such observational estimates of climate sensitivity can be tightened if reconstructions of Northern Hemisphere temperature over the past several centuries are considered. We use large-ensemble energy balance modelling and simulate the temperature response to past solar, volcanic and greenhouse gas forcing to determine which climate sensitivities yield simulations that are in agreement with proxy reconstructions. After accounting for the uncertainty in reconstructions and estimates of past external forcing, we find an independent estimate of climate sensitivity that is very similar to those from instrumental data. If the latter are combined with the result from all proxy reconstructions, then the 5-95 per cent range shrinks to 1.5-6.2 K, thus substantially reducing the probability of very high climate sensitivity.