Measuring a fair and ambitious climate agreement using cumulative emissions

Recent scientific research assessed in the IPCC AR5 highlighted the powerful near-linear relationship between increases in global average temperature and cumulative carbon dioxide emissions (IPCC 2013). This relationship allows the probability of exceeding a given temperature target to be translated into the total amount of CO₂ emitted into the atmosphere in the past and in the future. To have a 'likely' (>66%) chance of holding global warming to less than 2 °C requires that no more than about 3670 billion tonnes of carbon dioxide (GtCO₂) are emitted in total, from 1870 until well into the future (IPCC 2013). The probability associated with this statement reflects the best current knowledge of uncertainties in the climate system. The total allowable emissions can be adjusted for past and future emissions of non-CO₂ forcing agents, historical emissions from fossil-fuel combustion and industrial processes (FFI), and past and future emissions of land-use change (LUC), to give the remaining allowable FFI CO₂ emissions to stay below 2 °C (figure 1) (IPCC 2013, Friedlingstein et al 2014). The remaining allowable emissions are for CO₂ only, which has both advantages and disadvantages (see discussion). Non-CO₂ forcing agents contribute 10%–30% of the total forcing across scenarios, and affect the cumulative carbon budget by about 15% for the set of scenarios considered (Friedlingstein et al 2014).

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Our focus here is on a >66% chance of staying below a 2 °C increase in global average temperature, the goal accepted by a broad range of countries, but our framework applies equally for other temperature limits and probabilities. The allowable emissions would increase with acceptance of either a higher temperature level (e.g. 3 °C), or a lower probability of attaining that goal (e.g. >50% probability), or both (IPCC 2013). As an example, decreasing the probability of staying below 2 °C from >66% to >50% increases the allowable emissions to 4440 GtCO₂. We discuss and include results for 2 °C with a >50% chance, and 3 °C with a >66% chance in the supporting material.

To estimate the remaining allowable emissions from the total allowable emissions of 3670 GtCO₂ (figure 1) we first subtract non-CO₂ emissions of 770 GtCO₂-equivalent (IPCC 2013). We then deduct estimates of historical emission of FFI (1465 GtCO₂ ± 8%, 5%–95% range) and LUC (533 GtCO₂ ± 55%, 5%–95% range) up to 2014 from the cumulative allowance. We take historical emissions from CDIAC (Boden et al 2015), but for the years 1990–2012 we overwrite CDIAC's estimates using the official UNFCCC Annex I country CO₂ emissions from the respective national inventory reports to the UNFCCC (UNFCCC 2014b). Using the UNFCCC data ensures our analysis is consistent with national reporting, and therefore more policy relevant. Because BP data provide the most recent estimates by country, we follow Le Quéré et al (2015) by applying energy consumption growth rates by fuel type from BP to extend our time series for non-Annex I countries to 2014. Recognizing that there remains considerable uncertainty in Chinese emissions data (Liu et al 2015), in the supporting material we repeat the analysis with China's fossil-fuel emissions as estimated by BP, which are at the high end of available estimates. We finally deduct an estimate of future LUC emissions assuming they diminish linearly to zero by 2100, broadly consistent with the LUC emissions from the RCP scenarios used in the AR5 (Ciais et al 2013, Raupach et al 2014). These adjustments can be expressed as

$$\begin{eqnarray*}&&{Q}_{{\rm{avail}}}^{{{\rm{CO}}}_{{\rm{2}}}}={Q}_{{\rm{tot}}}-{Q}^{{\mathrm{non}-\mathrm{CO}}_{{\rm{2}}}}-{Q}_{{\rm{LUC}}}-{Q}_{{\rm{past}}}.\end{eqnarray*}$$

The main source of uncertainty in the allowable emissions quota for a given temperature target is the non-CO₂ adjustment (figure 1), which depends on a choice of scenarios. The IPCC AR5 WGI used the non-CO₂ emissions (hence forcing) from RCP8.5 (remaining quota 2900 GtCO₂), while Friedlingstein et al (2014) used the non-CO₂ emissions from Working Group III's scenarios (remaining quota 2900–3600 GtCO₂, 5%–95% range), and the AR5 Synthesis Report used only the subset of the WGIII scenarios that are likely to stay below 2 °C (remaining quota 2550–3150 GtCO₂, 5%–95% range) (IPCC 2014). In our analysis, we focus on the IPCC AR5 WGI value as our central value. For a given temperature level, the next largest sources of uncertainty in the allowable remaining quota are the past LUC emissions followed by the past FFI emissions.

The cumulative emission allowance provides a framework for setting a level of global ambition and thereby bounds on future emission pathways (Friedlingstein et al 2014, Raupach et al 2014). There is limited leeway to increase this number: only accepting a higher temperature level (e.g., from 2 °C to 3 °C), reducing the probability of staying below that level (e.g., from >66% to >50%), assuming a lower climate sensitivity, or lower forcing from non-CO₂ agents (at least for the near term, noting that the long-term climate depends primarily on CO₂). Negative-emission technologies would allow more CO₂ to be emitted in the near future (Fuss et al 2014), but the cumulative allowance would be unchanged.

Given the concept of allowable global carbon emissions (referred to here as 'quota'), the question of how it could be shared among nations has been widely discussed (e.g., Meyer 2000, den Elzen et al 2005, Böhringer and Welsch 2006, Baer et al 2008, Höhne et al 2013). Here we follow the method of Raupach et al (2014), employing an 'equity' approach that divides the global quota among nations based on population, and an 'inertia' approach that divides based on the current shares of global emissions. Raupach et al (2014) find that a strict division of the global quota based on population leads to infeasible transitions in some countries (which are either close to reaching, or have already exceeded their allotted quota under such a scheme), while a strict division based on current emissions is widely seen as unfair since some countries currently emit far more per capita than others. These two alternatives act as bounds to a range of blended options, and demonstrate how national quotas can be allotted using any mix of the two alternatives, e.g. using a sharing parameter suggesting a 'middle ground'.

Raupach et al (2014) show how the national quotas obtained from the sharing parameter could be used to generate smooth pathways between countries' present emissions, f₀, to near-zero emissions in the future. This concept of the interpolation is based on a decaying exponential, with decay constant $m,$ to represent mitigation. This exponential is modified to allow a smooth transition from the current pathway (represented by recent rate of change of emissions, $r),$ resulting in an idealized composite emission pathway:

$$\begin{eqnarray}&&f\left(t\right)={f}_{0}\left(1+\left(r+m\right)t\right){{\rm{e}}}^{-mt}.\end{eqnarray} \tag{ 1 }$$

The decay parameter, $m,$ is determined such that the area under the curve is equal to the quota allocated to each country based on the sharing parameter. In the unusual situation that emissions are already decreasing at a rate faster than the required mitigation rate, no solution exists for $m$ that will produce the required quota. In such cases, Raupach et al (2014) revert to a simple exponential decay,

$$\begin{eqnarray}&&f\left(t\right)={f}_{0}{{\rm{e}}}^{-mt}.\end{eqnarray} \tag{ 2 }$$

As a result of the smooth transition, the realized mitigation rate is given by

$$\begin{eqnarray}&&{m}_{R}\left(t\right)=m-\displaystyle \frac{m+r}{1+\left(m+r\right)t}.\end{eqnarray} \tag{ 3 }$$

The realized mitigation rate is a function of time. It may be negative at the start for countries with increasing emissions (emissions continue to grow for a period), but ultimately converges over time to a mitigation rate of $m$ as the effect of the transition function diminishes.

As described above, our analysis only applies to CO₂ emissions from fossil-fuel combustion and industry (FFI). We take the EU, US, and Chinese INDC submissions directly, but supplement them with longer-term pledges from the EU and US to demonstrate a longer-term analysis.

For the EU, we take their INDC of a 40% reduction below 1990 levels, and a stated aspirational target of an 80% reduction from 1990 by 2050 (European Commission 2011). For the US, we take a 17% reduction below 2005 levels in 2020 from their Copenhagen pledge, a 26%–28% reduction below 2005 levels in 2025 from their INDC, and an aspirational 83% below 2005 levels from the Copenhagen Pledge (UNFCCC 2009). The EU and US targets are for total greenhouse gas emissions, but we assume the same reductions apply for CO₂. This weakness of the cumulative emissions approach is elaborated further in the discussion.

Rather than present an intended absolute emissions reduction, China's INDC is specified in terms of an emissions intensity reduction of 60%–65% below 2005 levels by 2030. As a result, any estimate of the future emissions pathway depends on an estimate of future growth of GDP. We use forecasts recently made by the OECD that project China's GDP growth to gradually decline from today's levels to about 3.5%/yr in 2030 (OECD 2015). The choice of interpolation method between emissions intensity now (2014) and in 2030 directly determines whether and when an estimated emissions pathway will peak before 2030. We use an exponential decay function that best fits historical data over 2005–2014 and passes through both the most recent data year and the stated target (supporting material). Using this method gives an emissions peak of about 11.4 GtCO₂ in 2026 before declining slightly to 11.3 GtCO₂ in 2030 for a 60% reduction in emissions intensity, and a peak in 2021 at 10.5 GtCO₂ before declining to 9.9 GtCO₂ in 2030 for a 65% reduction. While this approach gives smooth trajectories, the possibility of substantial deviations from the pathway are not discounted. In our analysis we use the more optimistic, lower emissions pathway in the remaining analysis.

Our analysis is of the targets expressed in the INDCs, with no assumptions about the policies that may be used by countries to achieve the stated targets. In practice, it is unclear whether the stated targets will be met, and various circumstances may influence emissions along with any particular policy decisions. For example, some of the emissions reductions that have already occurred in the EU were a consequence of the collapse of Eastern Europe (Peters et al 2013), while some of those in the US were due to the Global Financial Crisis (Feng et al 2015), and it is unclear whether the slowdown in Chinese emissions growth in 2014 was due to economic challenges or long-term structural changes. Further, countries may meet their targets by displacing emissions to other countries with the help of structural changes in international trade (Peters et al 2011). We show results in the supporting material for additional temperature targets to examine a range of future outcomes.

Our framework can be applied to INDCs from other countries.

The cumulative emissions approach provides a powerful framework for comparing ambition and fairness, but it is not without its weaknesses. The main weakness is the treatment of non-CO₂ gases in the analysis. The IPCC showed that cumulative emissions of CO₂ largely determine global mean warming by the late 21st century and beyond (IPCC 2013), and hence cumulative carbon is critical for the long-term attainment of any selected climate target. Non-CO₂ emissions are expected to make larger contributions in the near term, and lead to increased warming for a given amount of cumulative carbon across the scenarios assessed in IPCC. We accounted for non-CO₂ forcing when estimating the remaining global quota (Rogelj et al 2015), but we did not attempt to estimate non-CO₂ pledges at the country level. However, most INDCs, or pledges in general, cover more than CO₂. Including country-level non-CO₂ into the analysis, using the cumulative emissions framework, would require some form of weighting of non-CO2 components (Myhre et al 2013). A challenge with using standard emission metrics, such as the Global Warming Potential, is that the fixed time horizon becomes less relevant when one is nearing a temperature target (Shine et al 2007). One approach could be to share the 'remaining' temperature to reach 2 °C, but then countries would be given a difficult task of how to allocate the temperature quota over time and amongst different greenhouse gases. If the cumulative emissions framework is not used, then analysis of non-CO₂ contribution is more straightforward (UNEP 2014).

We have not included LUC in our sharing, but instead removed future LUC from the remaining quota, assuming that future LUC emissions would linearly decline. While the inclusion of LUC is technically straightforward, the main challenge is country-level LUC data that is consistent over time and between countries. The EDGAR data, for example, does not have full coverage of LUC and is inconsistent with other datasets (Tubiello et al 2015). The Global Carbon Project does not provide LUC by country (Le Quéré et al 2015). The IPCC only estimated regional LUC for the five IPCC regions (Blanco et al 2014). Others have made attempts to include LUC by country (den Elzen et al 2013). Due to a lack of reliable historical data at the country level, we have not included LUC in our current analysis.

Current negotiations have focussed on country pledges of emission reductions, and the agreement between China and the US has been hailed as a major first step on a long road. Issues such as adaptation and loss and damage are particularly important to a large number of developing countries. It is clear that if 2 °C is to set the level of global ambition, commitment to deep, long-term mitigation must also be a core component of a Paris agreement, implying a radical transformation of the global energy system.

Even though the EU and US commitments are not too far removed from the inertia fairness measure, it is clear that the EU and USA would require much more ambitious targets to meet a wider range of fairness measures (e.g. equity). As an emerging economy, it will be challenging for China to balance economic growth within a 2 °C temperature limit. China accounted for 27% of global 2014 emissions and has relatively high per capita emissions, values that remain high even after adjusting China's emissions for exports and imports of goods and services (Le Quéré et al 2015). China's INDC is a long way from both measures of fairness used here. Incorporating other measures of fairness such as historical contributions would make the task for China easier, but harder for some other countries (Raupach et al 2014). Alternatively, under a higher temperature level of 3 °C with a >66% chance (supporting material) China's INDC may become fair and ambitious.

Regardless of the (implicit or explicit) method of sharing applied, the same global emission reductions are necessary if 2 °C is to be avoided. It could be argued that a push for greater ambition can reduce the credibility of pledges and erode political capital. By any measure, the global challenge is immense, requiring a technology revolution (Hoffert et al 1998, Galiana and Green 2009) and a complete decarbonization of the global economy by the second half of this century (Clarke et al 2014). The need for deep mitigation highlights the importance of zero-carbon energy sources (Hoffert et al 2002, Caldeira et al 2003, Davis et al 2013) and technologies that remove carbon from the atmosphere (Fuss et al 2014). The rapid scale up of renewable-energy technologies is critical, but the recent IPCC report highlights (Clarke et al 2014) the essential role of large-scale deployment of Carbon Capture and Storage (CCS) and bioenergy linked to CCS (BECCS). These technologies are immature (CCS) or untested (BECCS), but are the foundation of most scenarios consistent with 2 °C (Fuss et al 2014).

Our analysis suggests that a critical ingredient that is missing from current negotiations is the need for a greatly increased focus on advancing research and development on low-, zero- and negative-carbon energy sources (Barrett 2009). A limited number of countries are responsible for a large fraction of global energy innovation (Victor 2011); among these are the US, EU, and China. Pledges by those countries and others toward research and development (R&D) efforts would be a unique long-term contribution to global climate goals. Further, research indicates that a greater focus on technology development may facilitate negotiations (Schmidt 2015) and partially compensate for non-optimal climate policies (Bertram et al 2015). We believe a Paris agreement that is fair and ambitious needs to reflect deep mitigation in INDCs, strong agreements on adaptation and loss and damage in view of the high risk of exceeding 2 °C given current trends, and a companion set of pledges on technology research and innovation.