Stable climate metrics for emissions of short and long-lived species—combining steps and pulses

Climate metrics are often criticised for over- or under-stating the importance of different species on climate, particularly for short-lived climate forcers (SLCFs) e.g. (Pierrehumbert 2014). The IPCC 4th Assessment Report (AR4) (Forster et al 2007) noted the many shortcomings in the Global Warming Potential GWP(100), but recommended its use (at least for long-lived greenhouse gases LLGHGs) as a multi-gas strategy is preferable to a CO₂-only mitigation strategy. The IPCC 5th Assessment Report (AR5) presents global warming potentials (GWP) and global temperature change potentials (GTP) for 20-year and 100 year time horizons leading to a range of values (for methane these ranged from 4 to 84) with no recommendation as to which should be used (Myhre et al 2013). Hence, for methane, policymakers have at least a scalar factor of 20 in the value of the metric they can choose; the situation is similar for all other SLCFs. This range is due both to the choice of the types of metric, chosen impact parameter (forcing, temperature, etc), endpoint (GTP) or integrated (GWP), and to the choice of time horizon. Endpoint metrics compare the relative impacts at a particular time horizon after the emission of a species; integrated metrics compare the relative impacts integrated from the time of emission up to the chosen time horizon.

The UNFCCC's Ad Hoc Working Group on the Paris Agreement is proposing (https://unfccc.int/documents/184956) that National Inventory Reports for the Paris climate agreement will use the GWP(100) from AR5 to report aggregate emissions and removals of greenhouse gases (GHGs), although other metrics such as the GTP may be used additionally. However the IPCC Expert Meeting on Short-Lived Climate Forcers (IPCC 2018) concluded that SLCF inventories should not be converted to CO₂ equivalents using GWP(100), but rather reported separately until further assessment on the use of metrics was provided by IPCC AR6. The range in possible choices of metric value causes significant problems when making policy decisions. It has been argued that the metric value that is recommended in the UNFCCC guidance (GWP(100)) is inappropriate for the goals of the Paris Agreement (Allen et al 2016, Allen et al 2018, Fuglestvedt et al 2018) , although it has been suggested (Schleussner et al 2019) that overstating the impacts of non-CO₂ forcers (for instance by use of GWP(100)) will encourage even stronger CO₂ mitigation to compensate.

The Paris Agreement specifies two clear scientific goals: to limit temperature increases (Article 2), and to achieve balance between sources and sinks of greenhouse gases (Article 4); Fuglestvedt et al (2018) discuss various interpretations of the balance concept in the agreement. One interpretation of 'balance' could be evaluated in terms of the GHG emissions that stabilize radiative forcing (RF) at some level. Both goals are related to the impact at some later time (whether the end of the century or at the time of maximum temperature rise). For such targets endpoint metrics such as the GTP are more appropriate than integrated metrics (Shine et al 2005, Shine et al 2007). These endpoints can be fixed to a particular date such that the time horizon decreases as the date is approached (Shine et al 2007). Conversely, metrics that integrate from present to a future date (GWP or integrated GTP) give an equal weighting to climate impacts that occur now as to climate impacts that will occur when a target is about to be met or exceeded (Pierrehumbert 2014); therefore they do not directly address the Paris goals. Indeed many studies have shown that an integrated climate metric such as GWP is not useful for comparing long-term temperature effects (Allen et al 2016, Allen et al 2018, Fuglestvedt et al 2018). Thus the metrics most closely aligned with the Paris Agreement are endpoint metrics (either temperature or radiative forcing), although the time horizon of the specific endpoint is not clear. It could be the time of peak warming, or if temperatures are expected to overshoot a target, then some future time by which temperature would be required to come back below the target.

Integrated metrics would be more appropriate in economic analyses (Kandlikar 1995, Kandlikar 1996) which often look to minimise an integrated damage measure; however there is no internationally agreed damage measure due to the structural uncertainty in their underlying functional form (Weitzman 2012). Endpoint sea-level rise metrics do have mathematically similar constructions to integrated radiative forcing or integrated temperature metrics (Sterner et al 2014). These would be appropriate if there were a specified sea-level rise threshold below which we agreed to attempt to stay.

In this paper we use the concepts of relating the impacts of a step change in SLCF emissions with a pulse emission of CO₂ that was first introduced in Smith et al (2012). Allen et al (2016) took this considerably further, devising a metric (subsequently labelled GWP* in Allen et al (2018)) based on a scaling of GWP that approximated the relative temperature impacts of a step change in SLCF emission with a pulse emission of CO₂. Allen et al (2018) deliberately chose to retain the use of the familiar GWP (and the reported values of the GWP) in framing the GWP*, to maintain a level of continuity with existing policy and make it easy to apply. However, they recognised that by doing this, the step/pulse equivalence would only be approximate. Here we develop further the ideas of Allen et al (2016, 2018) to demonstrate that a more formal approach (less constrained by consideration for continuity and application) to providing step/pulse equivalence leads to a metric that captures the equivalence more accurately. It retains an important policy benefit of the GWP*, which is the relative lack of sensitivity to the time horizon, but still retains an explicit time dependence.

The two most common metrics GWP and GTP differ both in the impacts they represent (radiative forcing or temperature) and in whether they are integrated or endpoint based. Following Myhre et al (2013) these metrics are defined as the absolute impact measure for a pulse emission of species X divided by that for CO₂, i.e. ${{\rm{GWP}}}_{X}={{\rm{AGWP}}}_{X}/{{\rm{AGWP}}}_{{{\rm{CO}}}_{2}},$ and ${{\rm{GTP}}}_{X}={{\rm{AGTP}}}_{X}/{{\rm{AGTP}}}_{{{\rm{CO}}}_{2}},$ where these absolute metrics are defined as ${{\rm{AGWP}}}_{X}\left(H\right)=\displaystyle {\int }_{0}^{H}{\rm{\Delta }}{F}_{X}\left(t\right)dt,$ and ${{\rm{AGTP}}}_{X}\left(H\right)={\rm{\Delta }}{T}_{X}\left(H\right),$ where ${\rm{\Delta }}{F}_{X}\left(t\right)$ and ${\rm{\Delta }}{T}_{X}\left(t\right)$ are the radiative forcing and temperature changes at time t following a unit pulse emission of species X, and H the chosen time horizon. An integrated version of the AGTP can be also constructed ${{\rm{iAGTP}}}_{X}\left(H\right)=\displaystyle {\int }_{0}^{H}{\rm{\Delta }}{T}_{X}\left(t\right)dt$ (Gillett and Matthews 2010, Peters et al 2011, Azar and Johansson 2012, Olivié and Peters 2013). For completeness here we also define an endpoint version of the AGWP which we call ${{\rm{AGFP}}}_{X}\left(H\right)={\rm{\Delta }}{F}_{X}\left(H\right)$ where AGFP is the absolute global forcing potential. See appendix A.1, available online at stacks.iop.org/ERL/15/024018/mmedia, for derivations of these formulae. As before, the relative metrics can be derived by dividing by the corresponding absolute values for CO₂ (see table 1 for values for methane). For simplicity we do not incorporate carbon cycle-temperature responses for the non-CO₂ species (equivalent to 'no cc fb' in Myhre et al (2013)).

The indirect effects of methane on ozone and stratospheric water vapour are included following Myhre et al (2013) as 1.82 × 10⁻⁴ and 0.54 × 10⁻⁴ W m⁻² ppb(CH₄)⁻¹ respectively. They are added to the Etminan et al (2016) CH₄ radiative efficiency, rather than scaling it by 1.65 as in Myhre et al (2013). The indirect effects of N₂O on methane follow Myhre et al (2013). No effects of N₂O or halocarbons on stratospheric ozone destruction are included. Table 1 and appendix A.1 shows that the iGTP and GWP are very similar, indicating that the main difference between the metrics is whether one wishes to compare an integrated impact or an endpoint impact, rather than whether a radiative forcing or temperature impact is preferred. The endpoint metrics (GFP and GTP) vary much more strongly with time horizon than the integrated metrics, and differ significantly because the thermal inertia of the climate system means that the temperature response is felt for longer than the forcing itself. Thus although physically they correspond more closely with the Paris targets, for short-lived species they vary so strongly with time horizon as to be difficult to implement in policy applications where this time horizon decreases as date is approached (Shine et al 2007).

One way out of the above impasse was proposed by Smith et al (2012). Instead of trying to equate impacts of pulses, i.e. 1 kg emission of X with 1 kg emission of CO₂, they suggested it was more useful to compare rates of emission (in kg yr⁻¹) of short-lived species with cumulative emissions (in kg) of CO₂. This concept was introduced into metrics in Allen et al (2016) where they used a single number (GWP_X(100)×100) to equate permanent step changes in SLCF emissions to a one-off pulse emission of CO₂. Collins et al (2018) calculated the impact of methane mitigation on allowable carbon budgets. Using a simple climate model coupled to a carbon cycle model, they showed that for a fixed temperature target, a step reduction in methane emissions of 1 Gt(CH₄) yr⁻¹ was approximately equivalent to an increase in allowed cumulative CO₂ emissions of 2900–3300 Gt(CO₂). In this paper we expand on the central step-pulse distinction in Allen et al (2016) to show how combined step/pulse metrics can be derived from first principles; and we extend this logic to include an explicit time dependence.

Although metrics have generally been defined in terms of a pulse emission of 1 kg of a species, they can equivalently be defined in terms of a step change in emission of 1 kg per year as described in Fuglestvedt et al (2003) and Shine et al (2005). We will use the '^P' or '^S' superscripts to denote metrics based on pulse or step emissions. These metrics have physically equivalent outputs (so that AGTP^P and AGTP^S both describe the change in endpoint temperature and AGFP^P and AGFP^S both describe the change in endpoint forcing), it is only the form of the input (i.e. whether a pulse or step change is considered) that changes. So for a given goal (such as a temperature threshold) the AGTP^P applied to pulse emission change or the AGTP^S applied to a step emissions change are both equally valid choices of metric to assess progress towards the limit. The inputs do not even need to be the same for each species; because they both measure progress towards the same limit, it is entirely physically consistent to compare the temperature response to a step input in one species with that to a pulse input in another. We can therefore define combined metrics 'combined GWP' (CGWP_X) and 'combined GTP' (CGTP_X) as the ratio of step responses to X to pulse responses to CO₂: CGWP_X = AGFP^S_X/AGFP^P_CO2 and CGTP_X = AGTP^S_X/${{{\rm{AGTP}}}^{{\rm{P}}}}_{{{\rm{CO}}}_{2}}.$ These metrics are no longer dimensionless, but have units of time reflecting the need to compare rates (kg yr⁻¹) with pulses (kg).

In terms of the more usual metrics, an endpoint metric for a step change in emissions is equivalent to an integrated metric for a pulse emission, i.e. AGFP^S is equivalent to AGWP^P, and AGTP^S is equivalent to iAGTP^P (see section A.1 for derivations). However, in order to emphasise the preference for endpoint metrics we will not use the integrated metric notation.

Figures 1(a), (e) show the radiative forcing and temperature responses as function of time to step changes in emissions (AGFP^S and AGTP^S) for four species HFC-32, CH₄, CFC-11 and N₂O chosen to have a range of lifetimes: 5.4, 12.4, 52 and 121 years respectively. For HFC-32 and CH₄ the step responses asymptote quite quickly, whereas for CFC-11 and N₂O they are still increasing after 100 years. The combined metrics are derived by dividing these responses by those for a pulse of CO₂ (b, f). These CGWP_X and CGTP_X ratios are moderately flat for HFC-32 and CH₄ but rise steadily for CFC-11 and N₂O (figures 1(c), (g)). Conversely, the more usual pulse/pulse metrics of GFP^P and GTP^P (figures 1(d), (h)) decrease significantly with time for HFC-32 and CH₄, but are steadier for N₂O. Metrics that vary strongly with time make them less useful for policy purposes; the choice of 100 years for the GWP as applied in the Kyoto Protocol was in essence an arbitrary (or convenient) one, and not one based on scientific reasoning (Shine 2009). Figure 1 suggests that for shorter-lived species the combined metrics, (i.e. ratio of a step response with the equivalent pulse response for CO₂), vary less with time horizon. For species with a lifetime greater than the timescale of interest (e.g. N₂O) the standard pulse metrics are more useful. For species of intermediate lifetime such as CFC-11 both combined and standard metrics have a time dependence. This is a very similar conclusion to Smith et al (2012) but phrased in terms of metrics.

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For the combined metrics the difference between the radiative forcing and temperature approaches is not large, the ${{\rm{CGTP}}}_{{{\rm{CH}}}_{4}}$ is around 7% smaller than the CGWP_CH4 on the longer time horizons (figure 2). The extra timescales introduced through the temperature response has more effect on the CO₂ pulse than the methane step: in figure 1 the curves in panels (a) and (e) have similar shapes, whereas the curve in (f) plateaus more quickly than (b). Fuglestvedt et al (2018) argue that the long-term climate balance goal in the Paris agreement could imply a zero net radiative forcing, for which the CGWP (for short-lived species) and GFP (for long-lived) would be appropriate.

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The time variation in the combined metrics for short-lived species is mostly due to the decrease in CO₂ concentration following a pulse. The difference between the 20 year metric and the 100 year metric is still large (roughly a factor of 1.5 for methane compared to the factor of 10 for GTP(20) versus GTP(100)), but the differences between 50 years and 100 years are much smaller (table 2)–factors of 1.2–1.3 for the combined metrics for SLCFs with a lifetime of around 20 years or less rather than the factors up to 2 for the pulse metrics (see also table 1 and appendix A.3). This means that a metric with a 75 year time horizon would be equally applicable for a climate target between (say) 2070 and 2120 within a less than 15% difference. For species with a lifetime of between 20 and 50 years, the time horizon needs to be chosen to reflect the timescale of the climate target. Even for these species the time dependence of the CGTP metric is still less than that for the GTP.

4.1. Relation to climate goals

4.2. Use of the metrics

4.3. Comparison with GWP*

The CGTP metric compares the endpoint temperatures of a step change in SLCF emissions with a pulse emission of CO₂. Allen et al (2016, 2018) show that an approximation to this metric can be derived by simply scaling the GWP by the time horizon H: GWP* = AGWP_X/(AGWP_CO2/H). They use the standard assumption of fixed TCRE (i.e. the temperature change is only dependent on the total CO₂ emitted) to make the approximation that a step change in CO₂ emissions for H years is equivalent to H one-year pulses (${{{\rm{AGTP}}}^{{\rm{S}}}}_{{{\rm{CO}}}_{2}}$ (H) ≈ H × ${{{\rm{AGTP}}}^{{\rm{P}}}}_{{{\rm{CO}}}_{2}}$(H)). They also make the approximation that GWP and GTP^S are equal (AGTP^S_X/AGTP^S_CO2 = GTP^S ≈ GWP). From this the metric CGTP_X(H) = AGTP^S_X/${{{\rm{AGTP}}}^{{\rm{P}}}}_{{{\rm{CO}}}_{2}}$ approximates to H×AGTP^S_X/${{{\rm{AGTP}}}^{{\rm{S}}}}_{{{\rm{CO}}}_{2}}$ ≈ H × GWP_X(H). Figure 3 shows the effect of these approximations; panel (a) shows that GWP underestimates GTP^S by 11% at 100 years; panel (b) shows that assumption of constant TCRE leads to an overestimate of ${{{\rm{AGTP}}}^{{\rm{P}}}}_{{{\rm{CO}}}_{2}}$ by 8% at 100 years; and panel (c) shows that GWP* therefore underestimates CGTP by up to 20%. An analogue of GWP*, GTP* (=H*GTP^S), would be a closer approximation to CGTP, within 8% for 50 < H < 100. Note that numerically ${\rm{GWP}}{* }_{{{\rm{CH}}}_{4}}\left(100\right)\approx {{\rm{CGTP}}}_{{{\rm{CH}}}_{4}}$(60) so the 100 year GWP* used in figure 2 of Allen et al (2016) gives good agreement with the expected temperature at t = 60 years in their panel (b). Therefore relaxing the constraint of trying to keep the GWP and its values for the various gases improves the physical fidelity of the step-pulse metrics from the results of Allen et al (2016, 2018). It is important to note that although the GWP* approach and the CGWP and CGTP developed here differ in their precise values, they are structurally and conceptually similar. This should be contrasted with GWP which is structurally inconsistent with the policies being addressed, giving the wrong sign of warming from a SLCF scenario in which emissions were falling (Allen et al 2018).

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We conclude that combined step-pulse metrics (CGWP and CGTP) provide a useful way to compare changes in emission rates of SLCFs (lifetimes less than around 50 years—appendix A3) with cumulative emission changes in LLGHGs so that they may be included within common baskets in climate agreements. These are endpoint climate metrics which are closely tied to long-term climate goals such as the Paris Agreement. Integrated metrics such as GWP have been shown to be structurally unsuitable for such goals (both for SLCFs and LLGHGs). The standard pulse-based endpoint metrics for SLCFs vary strongly with time making them difficult to apply in a policy situation, whereas the combined metrics we propose are reasonably stable to within around 10% over the time horizons of current policy interest (around the end of the 21st century). Thus a single time horizon CGTP(75) can be used as a suitable metric for SLCFs covering the timescales relevant to the goals of the Paris Agreement. It has been suggested (Schleussner et al 2019) that because the step-pulse metrics are designed to stablise temperatures they do not encourage further temperature reductions, however such temperature reductions are not part of any formal goal.

Combined step-pulse metrics were first introduced in the GWP* approach (Allen et al 2016, 2018, Fuglestvedt et al 2018). GWP* was designed to retain the use of values of the standard GWP, for purposes of continuity, but we show that approximations inherent in doing so mean that the GWP* underestimates the contribution of SLCFs to temperature change by up to 20%, compared to a more explicit calculation of the effect of step changes in SLCF emissions relative to a pulse emission of CO₂. We emphasize that the calculation of the combined metrics proposed here need no additional inputs, or assumptions, than are already used to generate the GWP and GTP values in Myhre et al (2013); hence tabulated values can be easily constructed. Examples for halogenated species are shown in appendix A.4 table A.1.

For treaties involving multi-species baskets such as the Kyoto Protocol and as used by many countries under their NDCs for the Paris Agreement, climate metrics can be used to convert emissions of all species to a common unit. The application of CGTPs to rates of SLCF emissions and GTPs to total LLGHG emissions allows a conversion to cumulative CO₂ equivalent units which is more relevant to climate polices, such as the Paris Agreement, that are framed in terms of long-term temperature targets. This unit is the fundamental quantity in many climate pathways (Millar et al 2017, Forster et al 2018) and is approximately related to temperature rise through the TCRE.

There is evidence that these insights can inform national targets and national policies: New Zealand's recent Zero Carbon Act (New Zealand 2019) contains a split-gas target: a decrease for methane, and a net zero target for long-lived gases. This indicates that policymakers are able to respond and adapt to the insights that emerge from considering different metrics, such as those presented here and in in Allen et al (2018).

Scientifically, the main insight from this paper and Allen et al (2016, 2018) is that the step-pulse approach (such as CGTP or GWP*) represents a vital and significant improvement in the comparison of emissions of SLCFs with long-lived greenhouse gases with regard to long-term temperature goals. Although there is no perfect, universal way of comparing forcing agents across all variables and time horizons, these papers show that the conventional use of GWP is clearly not suitable for comparing the contributions of short and long-lived climate agents towards the Paris temperature goals.

W J Collins, acknowledges funding received from the European Union's Horizon 2020 research and innovation programme under grant agreement no. 641816 (CRESCENDO). The reviewers are thanked for their helpful comments.

Any data that support the findings of this study are included within the article.