The zero emission year is estimated as the first year in which the global mean temperature of a particular CMIP5 simulation exceeds 2°C. Time series of the global mean temperature are available in the Annex I of the fifth IPCC report [33], which numerically expresses the global temperature referring to the year 2005, when global warming since the pre-industrial era (1850–1900) was 0.61°C [33]. Each of the simulated global warming time series were smoothed with a 30-year moving average filter. An example of this definition is shown in Fig 1A, in which the dashed and solid lines correspond to the simulated global warming time series with respect to the pre-industrial era and the corresponding 30 years moving average time series, respectively, which with corresponds to the RCP 8.5 scenario simulated by the model CSIRO-Mk3-6-0. For this simulation, warming reaches 2°C in the year 2042, which corresponds to the zero emission year of that particular simulation. Overall, 107 out of 138 CMIP5 simulations indicate climate warming greater than or equal to 2°C; 7 of which correspond to the RCP2.6 scenarios, 36 to the RCP4.5 scenarios, 25 to the RCP6.0 scenarios, and 39 to the RCP8.5 scenarios. Fig 1B shows the frequency distribution of the zero emission year computed for the entire set of 39 simulations of the RCP 8.5 simulation, in which the shaded area in the light red colour defines the range of variation of climate warming time series of the RCP 8.5. Note that the CMIP5 simulations end in 2100 and that the 30 year moving average is not defined after 2085.

To validate the definition of the ZEY and the personal quota, the simplified climate-carbon cycle model MAGICC [30] was used. MAGICC stands for Model for the Assessment of Greenhouse Gas Induced Climate Change and solves a coupled ocean-atmosphere system and a world average carbon cycle model. MAGICC uses as its input time series of greenhouse gases emissions and gives as a result a time series of greenhouse gas concentrations in the atmosphere and global warming with respect to the pre-industrial period. Parameters involved in the model were calibrated for each of the CMIP5 models [30], and based on historical observations, a set of 600 probabilistic/historically constrained runs were included in MAGICC for quantifying uncertainty in the analysis [2,31,32].

MAGICC simulations start in 2000, and to construct the time series of greenhouse gas emissions that forces this model, the time series of CO₂ emissions from CDIAC (cdiac.ornl.gov, [37]) were used for the period between 2000 and 2015. Different scenarios of CO₂ emissions between 2016 and 2100 are built based on a uniform personal quota, and the time series of the median world population estimated by the United Nations [40]. With respect to the emissions of other greenhouse gasses, CDIAC information shows that emissions since 2005 are well represented by the RCP8.5 scenario. Consequently, the time series of emissions of other greenhouse gases in the RCP8.5 scenario was used for the period 2005–2015 in all of the simulations. Between 2016 and 2020, a linear transition between emissions of RCP8.5 and RCP2.6 is considered, and after 2020 the time series of emissions of other greenhouse gases of the RCP2.6 scenario was used. This is because the RCP2.6 scenario is the only scenario that is coherent with the 2°C target for warming. The following scenarios are considered for the CO₂ emissions as a function of representative values of the remaining global quota T:

The model MAGICC uses as its input a single text file that contains the time series of greenhouse gas emissions, with annual resolution. Input files of the simulations of this article are available in S1 Appendix.

The premise of this article is that human consumption of goods, food and transportation are the ultimate drivers of climate change. Consequently, changes in personal behaviour have a large impact on CO₂ emissions. With this, carbon footprint calculators can now have a different reading, for example, by allowing individuals to manage the personal carbon budget by summing up their annual emissions and then to evaluate the effectiveness of a particular action. The first limitation is that carbon footprint calculators are usually written in terms of an equivalent mass of CO₂, hereinafter called CO_2e (e.g., [41]), whereas the personal quota estimated here is expressed in terms of CO₂ emissions of fossil fuels, cement, and land use-related emissions. In the absence of detailed research, the bulk transformation from CO_2e to CO₂ was made based on a linear fit between the specific contributions of CO₂ radiative forcing with respect to total radiative forcing using RCP scenarios [4]. A bulk transformation factor of 0.82±0.01 kg CO₂/kg CO_2e (r² = 0.998) was obtained, and the goodness of this fit is shown in Fig 3.

The ZEY is the year in which CO₂ emissions should stop to avoid global warming greater than 2°C with respect to the pre-industrial era. By using the full set of CMIP5 simulations for the four RCP emissions scenarios [34], a distribution of the ZEY and thus the remaining global quota can be obtained, by finding the year in which each individual simulation reaches the 2°C warming limit and relating this year with accumulated CO₂ emissions. Therefore, the value is not unique and the obtained distribution is shown in Fig 4A, which shows that the RCP8.5 simulations are associated with closer zero emission years, whereas simulations of the RCP6.0 scenario provide values of the ZEY furthest away in this century. The median ZEY for scenarios RCP2.6, 4.5, 6.0 and 8.5 are 2043 (2037–2058), 2058 (2042–2069), 2062 (2047–2074), and 2043 (2033–2048), respectively. Hereinafter, numbers in brackets correspond to 84% and 16% of the ensemble of opportunity, respectively, representing the standard deviation and a 68% confidence interval. Similarly, the remaining global quota is not unique and its distribution is shown in Fig 4B, which takes into account the different climate sensitivity of the CMIP5 simulations. The median remaining global quota is 1562 Gt CO₂ (894–2061). The solid line in Fig 4B shows the ensemble of opportunity for reaching maximum warming smaller than 2°C as a function of the remaining global quota. The ensemble of opportunity for one remaining global quota is the number of simulations that have a remaining global quota greater than or equal to this value divided by the total number of simulations. The maximum remaining global quota was 3288 Gt CO₂, and the minimum was 594 Gt CO₂. Here, the minimum remaining global quota of 594 Gt CO₂ is related to the total amount of CO₂ emissions required to achieve the “well below 2°C” target. As a reference, previous studies estimated the remaining global quota since 2014 at 1500 Gt CO₂ [3], 1440 Gt CO₂ [1], and 1620 Gt CO₂ [36].

Three simulations were made using the numerical model MAGICC to validate the results for the personal quota and ZEY associated with the “well below 2°C” and 2°C targets (T = 594 Gt CO₂ and 1562, respectively). The corresponding time series of CO₂ per capita and total CO₂ are shown in Fig 7A and 7B, respectively, where the red line corresponds to the T = ∞ simulation. Black lines correspond to the simulations with a constant per capita emission until the ZEY; dashed lines in green and yellow are the subset of simulations that considers a constant personal quota until 2020, 2025, and then a linear reduction of Q as preserving the total cumulated emissions associated with 50% of the ensemble of opportunity (family of yellow dashed lines, T = 1562 Gt CO₂) and the “well below 2°C” target simulation (family of green dashed lines, T = 594 Gt CO₂). Fig 7A and 7B also show the time series of observed emissions (magenta dots) and CO₂ emissions of the RCP8.5 and RCP2.6 scenarios (red dashed line and light blue dashed line).