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Description of data sets used.

Fossil fuel CO₂ emissions, including emissions transfers associated with international trade are taken from the 2014 Carbon Budget of the Global Carbon Project¹⁶. Fossil fuel emissions were available here from 1959 to 2013, with consumption-based emissions covering the period from 1990 to 2012. To calculate per-capita emission histories, I obtained national time series of population data beginning in 1950 from the United Nations World Population Prospects¹⁷. Given the constraint on population data availability, I did not attempt to merge the Global Carbon Project fossil fuel CO₂ emissions data with other data sets that provide CO₂ emissions records before 1959, but rather focused on 1960 and 1990 as starting dates for the calculations presented here.

Regional land-use CO₂ emissions are also available from the 2014 Carbon Budget up to the year 2010 (ref. 16). To disaggregate this data to the national level, I used the methodology described in ref. 1, whereby I allocated regional data to countries within the region according to their relative changes in forest vegetation cover. In addition, I used the national estimates of land-use CO₂ emissions from the MATCH database (http://www.match-info.net)². Given some country-level differences between these two data sets, I used the average value for each country in the final calculation of land-use CO₂ carbon debts.

National emissions of CH₄, N₂O and SO₂ are available from the EDGAR database (http://edgar.jrc.ec.europa.eu) covering the period from 1970 to 2010. As in the case of land-use CO₂, I also used national CH₄ and N₂O emissions data from the MATCH database (http://www.match-info.net)², and averaged the two available data sets for CH₄ and N₂O to minimize the potential errors associated with national-level data. For consistency across data sets, as well as with the dates most commonly discussed in the climate responsibility literature^{7, 27}, I used only the data from 1990 to 2010 to calculate climate debts (see Supplementary Methods for discussion of additional uncertainties associated with historical emission estimates).

Calculation of carbon and climate debts.

For the case of fossil fuel CO₂ emissions, I calculated the ‘carbon debt’ of a country over a given window of time (t) as:

Recent analyses have shown that the climate response to CO₂ emissions can be approximated well by a constant value that does not change over time^{18, 31}. This conclusion is based on a number of recent studies that have demonstrated a linear relationship between cumulative CO₂ emissions and global temperature change in both global climate models, as well as in the observational record^{18, 31, 32, 33}. This linear relationship has been defined recently as the ‘transient climate response to cumulative carbon emissions’ (TCRE), with a best estimate of 0.4 °C per 1,000 GtCO₂ emitted and a likely (67%) uncertainty range of 0.2–0.7 °C per 1,000 GtCO₂ (0.8–2.5 °C per 1,000 Gt C; ref. 19). The TCRE has been shown to be independent of both time and emissions scenario owing to the opposing effects of: decreasing effectiveness of CO₂ radiative forcing at higher CO₂ concentrations (leading to less temperature change per unit increase in atmospheric CO₂); and decreasing strength of land and ocean carbon sinks with increasing CO₂ concentration and climate changes (leading to a larger increase in atmospheric CO₂ per unit CO₂ emission)³⁴. Consequently, the climate response to cumulative emissions can be considered to remain approximately constant for total emissions up to at least 7,300 GtCO₂ (2,000 Gt C) and until the time at which temperatures peak¹⁹. This means also that the above carbon debt calculation can be meaningfully applied to any particular historical time window (as defined by the start and end year), without any need to treat past emissions differently from current or future emissions. And as CO₂ emissions produced over time have the same per-unit effect on global temperatures, accumulated carbon debts represent a direct national contribution to climate warming in excess of (or below) a share based on their fraction of world population over time. For the limited portion of the historical period studied here, this method is a very reasonable approximation of the climate response to accumulated CO₂ emissions over time.

For the case of temperature changes caused by CO₂ emissions from fossil fuels and land-use change, in addition to non-CO₂ greenhouse gases and aerosols, I generalized the calculation of carbon debts to calculate a country’s ‘climate debt’ as:

Here, (dT(t)_country) is each country’s actual temperature contribution (shown in Fig. 3a), and the second term represents the country’s population multiplied by the global average per-capita warming over time (shown in Fig. 3b).

Calculation of national temperature contributions.

As in the case of carbon debts discussed above, I calculated the temperature contribution of fossil fuel and land-use CO₂ emissions using a linear temperature response to cumulative CO₂ emissions of 0.4 °C per 1,000 GtCO₂ (consistent with the best estimate of the Transient Climate Response to cumulative carbon Emissions from ref. 18). This resulted in the allocation of a total CO₂-induced warming from fossil fuel and land-use emissions of 0.25 °C between 1990 and 2010.

As a linear temperature-cumulative emissions relationship can be used only to estimate the CO₂-induced temperature change, a different methodology is required for non-CO₂ gases, which must also account for their variable atmospheric lifetimes. Various methods have been used previously to calculate national temperature contributions, ranging from simple calculations of historical cumulative emissions equated using CO₂-equivalence metrics such as Global Warming Potential^{2, 3, 4}, to more complex methods involving multiple model simulations using climate models of varying complexity^{2, 4, 5}. Here, I calculated the temperature contribution of non-CO₂ gases using the methodology described in ref. 1, which is both relatively simple, and also includes an explicit method to account for the more limited atmospheric lifetime of temperature changes caused by shorter-lived non-CO₂ gases. I first used the University of Victoria Earth System Climate Model^{35, 36} to simulate the temperature response to historical concentration increases followed by zero emissions of each gas, specifying a concentration decay according to the atmospheric lifetime of each gas as in ref. 37. I then used the simulated decrease of global temperatures after zero emissions as a normalized weight applied to past emissions, such that present-day emissions were assigned a full weight, and emissions in the past were assigned a weight of less than one to represent the proportion of warming from those emissions still present in the atmosphere (see Supplementary Fig. 4).

Finally, I calculated weighted cumulative emissions for each country at each year (beginning in 1990) and used these weighted emissions to allocate the total amount of warming for each gas to individual countries according to their relative portion of global weighted emissions. I allocated a total of 0.15 °C for CH₄, 0.025 °C for N₂O and –0.1 °C for SO₂ as an estimate of the approximate contribution of each gas to temperature changes between 1990 and 2010. These values were selected to be representative of the relative magnitude of radiative forcing changes between 1990 and 2010 for CH₄, N₂O and the direct effect of SO₂ (ref. 38), as well as to reflect the idea that recent emissions of short-lived gases have had a larger effect on recent temperature changes relative to earlier historical emissions, as compared to gases with longer atmospheric lifetimes. Further details of this method, as well as comparison of the resulting national climate contributions to previous studies, can be found in ref. 1.