Demonstrating GWP*: a means of reporting warming-equivalent emissions that captures the contrasting impacts of short- and long-lived climate pollutants

To illustrate the principles outlined in the introduction, we start with a simple scenario where an emission is introduced in year 0 and then sustained at the same rate for 200 years (figure 1). For methane, concentrations increase rapidly but then plateau after a few decades as natural atmospheric removals balance ongoing emissions. Radiative forcing similarly increases rapidly due to the high radiative efficiency of CH₄ (i.e. there is a large change in forcing per change in CH₄ concentration) but then largely stabilises—although there is some increase in forcing between approximately years 50 and 150 as over this period the background methane concentration in RCP4.5 is expected to decline as anthropogenic emission rates are reduced, resulting in a greater radiative efficiency of any remaining methane emissions (i.e. including those modelled here).

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This stabilising behaviour is then also reflected in the warming that results from the sustained CH₄ emission: the bulk of the temperature change occurs rapidly, and is significant, but the rate of temperature increase declines after these initial decades. There is, however, still some long-term delayed adjustment to this initial increase. In the very long term (several centuries, but subject to the large uncertainties in the slow temperature equilibration of the Earth) the warming from any biogenic methane emission would also be expected to completely stabilise and generate no additional temperature increases, becoming indistinguishable from long-standing natural methane emission rates to which the climate system has fully adjusted [16], but to anticipate near- to medium-term climate impacts this extended temperature change remains important [18].

For CO₂, modelling an equivalent (using GWP₁₀₀) emissions scenario, we see that sustained emissions do not result in stabilising concentrations. Instead, concentrations, forcing and subsequently warming continue to increase for as long as the emissions are sustained, with an approximately linear relationship between cumulative CO₂ emissions and resultant warming (as will be expanded upon later).

This simple illustration of the impacts of sustained emissions already highlights how different short- and long-lived GHGs are, and hence why metrics that attempt to treat them in the same way will fall short. These differences are even more pronounced if we consider the impacts of decreasing emission rates.

In figure 2 we demonstrate a scenario which begins in the same way as the previous example, with a step change to sustained emissions, but after 50 years these decline linearly to reach 0 over the following 50 years. For methane, as the emissions rate declines, so too do atmospheric concentrations: from the equilibrium described earlier, we start to reduce emissions while removals continue, and so atmospheric concentrations fall when they are not continuously 'topped up' by maintained emissions. These dynamics are then reflected in the change in forcing and ultimately warming, with declining emissions able to reverse a significant proportion of recent warming over relatively short timescales.

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For CO₂, reducing the emission rate merely acts to slow the rate of continued increase in concentration until emissions reach nearly 0, at which point atmospheric concentrations slowly decline as a result of short- and medium-term carbon sinks. It would take millennia for current CO₂ concentrations to return to pre-industrial levels without active intervention [9, 7]. The changes in CO₂ concentration are reflected in the change in forcing over time. Nonlinearities in forcing and warming approximately balance each other out such that the increased temperatures from CO₂ emissions are relatively fixed at this amount once emissions cease [19], maintaining the near-linearity between cumulative CO₂ emissions and warming noted earlier even without ongoing emissions.

A 'zero emissions' target will therefore have distinct impacts depending on whether the climate pollutant is long- or short-lived, and does not imply an equivalent mitigation effort or climate response.

The differing warming legacies once emissions of either gas are removed, as shown in figure 2, also applies to one-off emission pulses. Despite pulse-comparisons being commonplace in metric design (including the GWP) and individual emission offsets, trying to describe the impacts of a pulsed emission of CO₂ with a scaled individual pulsed emission of methane, and vice versa, will inherently fail to provide similar warming pathways, and so transactions based on such exchanges will not result in climatically equivalent responses.

These two scenarios also highlight a broad principle: CO₂-induced warming depends on cumulative emissions to date, but for SLCPs such as methane, their warming contribution is predominantly a function of recent emission rates [11, 25]. GWP* can capture this key difference.

We now show how the corresponding GWP₁₀₀ and GWP* CO₂-equivalents compare for these two emissions scenarios. Starting with a step-change to sustained methane emissions (figure 3), using conventional application of GWP₁₀₀ reports these methane emissions as equivalent to a constant rate of CO₂-e emissions over time (this is also the same CO₂ emissions scenario as shown in figure 1). Using GWP* over the first 20 years the methane emissions are represented by very high CO₂-w.e. emissions, capturing the strong weighting given to the initial change in rate [from 0 emissions], but after this $\tfrac{{\rm{\Delta }}{E}_{{\rm{SLCP}}}}{{\rm{\Delta }}t}=0$, and so only the much lower CO₂-w.e. emissions from the 'stock' behaviour of longer-term sustained methane emissions remain.

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The main difference between GWP* and static metrics such as GWP₁₀₀ is thus: with static metrics, individual emissions are directly equated by a single value that can only represent one particular impact at or over a stated time, and which cannot fully capture the temporal differences between the impacts of different gases; but for GWP*, 'equivalent' CO₂ can vary in order to decribe dynamic responses over any time-frame of interest. As this problem occurs for any static concept of equivalence, it cannot be overcome by using alternative metrics or alternative time-horizons, as illustrated in section 2 of the supplementary material, revealing similar limitations for the 20 year Global Warming Potential (GWP₂₀) and the 100-year Global Temperature change Potential (GTP₁₀₀)

As described above, there is an approximately linear relationship between cumulative CO₂ emissions and temperature. If CO₂-equivalents do indeed describe methane emissions in an equivalent manner to CO₂, a cumulative CO₂-equivalent should therefore correspond to the warming generated by the methane emissions they describe. We can illustrate this by plotting our cumulative CO₂-equivalents alongside temperature, as in figure 3(c). While GWP* provides a reasonable fit for the methane warming profile (initially rapid temperature increases followed by a longer tail of more gradual warming GWP₁₀₀ suggests) a fixed rate of temperature change from methane that does not capture the true dynamics.

Directly relating equivalent emissions to temperature responses was not an intended usage of GWP₁₀₀, and so attempting to link cumulative GWP₁₀₀ CO₂-e to global warming is arguably an inappropriate application of the metric. However, the approach provides useful insight into how the impacts of short-and long-lived gases differ, why static metrics such as the GWP₁₀₀ will always miss important dynamics, and reveals further applications that become possible when the equivalent emissions reflect the impacts of cumulative CO₂ emissions.

A simple coefficient, the TCRE (Transient Climate Response to cumulative carbon Emissions), can link cumulative CO₂ emissions and temperature as a result of their linear relationship [26, 27]. Not only can cumulative CO₂-w.e. provide an indication of the shape of the warming profile, threfore, but also suggest a direct correspondence between the scale of emissions and warming. This is represented by the alignment of the two y axes in figure 3(c) (and every figure hereafter combining temperatures and cumulative emissions), which are scaled by a TCRE of 0.4 K per Tt CO₂ (1.52 K per Tt C). This TCRE was obtained by identifying the warming response to cumulative CO₂ emissions for RCP4.5 within the same FaIR set-up described above (see supplementary material). By expressing short-lived GHGs as a CO₂-w.e. consistent with a 'cumulative carbon' framework, GWP* thus provides a means of directly linking emissions of different gases to their resulting temperature impact through the TCRE.

GWP*, as a simple metric reliant on assumptions of linearity inherent in the GWP, cannot capture the full complexities of the climate response that alternative approaches may be able to, such as CO₂-forcing-equivalents [25], the CGTP and CGWP [14], or comprehensive modelling of the climate system. Consequently, the match between cumulative CO₂-w.e. emissions (×TCRE) and warming is not exact (and in this case the underestimation of warming may reflect, among other dynamics, an increase in the radiative efficiency of methane over this period expected as wider global methane concentrations fall under RCP4.5 [28]), while a fixed GWP was used here. There will remain applications where more complex methods are preferred, but the ease of calculating GWP* will likely prove a significant advantage for many purposes.

Both GWP₁₀₀ and GWP* CO₂-equivalents and the methane temperature response approximately correspond at 100 years (previously noted in [29, 30] and [31], observing that the sustained Global Temperature change Potential (sGTP)—that is, the temperature change following sustained emissions over a given period—is close to the GWP). This means that, looking back over 100-years of an introduced then sustained emission, GWP₁₀₀ could also provide an appropriate indication of the total warming over this period; but otherwise can provide only limited inference. This correspondence is only the case for newly-introduced emissions subsequently sustained at the same rate over this period, and only at approximately 100 years: GWP₁₀₀ would understate the total warming impact of sustained emissions before this point, and increasingly overstate the impacts after it. Even within this 100-year period, given that most of the warming occurs in the first few decades of the sustained methane emission, GWP₁₀₀ will still overstate the annual contribution to warming at any point after this initial period. For example, if we are in year 30 of this scenario, the bulk of the warming that will result from this sustained methane emission is already experienced (the scale and speed of this warming greatly undervalued by GWP₁₀₀), so from this point onwards GWP₁₀₀ would provide an exaggerated estimate of how much additional warming to expect, and hence provide little insight in anticipating future temperatures increases (or associated climate impacts).

Once again, the scenario in which emissions start to decline further emphasises how differently the two gases behave (figure 4). As methane emissions decline, GWP₁₀₀ CO₂-e emissions also decline, but they stay positive (figure 4(b)), which, by comparison with the behaviour of CO₂, can only indicate a slowing of the resultant warming until emissions reach 0 (as shown in figure 2), at which point the temperature would be expected to remain at this elevated level (figure 4(c)).

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Using GWP*, the annual CO₂-w.e. emissions profile is more complex (figure 4(b)), as the 20 year reference period tracks across various transitions in the methane emissions profile, but crucially, in the period of declining methane emissions CO₂-w.e. emission are negative (i.e. representing a removal of CO₂ from the atmosphere). Figure 4(c) shows how this is essential to capture the temperature impacts of this methane emissions pathway: the automatic reversibility of most methane warming once the emissions are reduced or removed can only be described by a negative CO₂-equivalent, and so there is no real correspondence between the impact of this methane scenario and cumulative GWP₁₀₀ CO₂-e.

It must be emphasized that during the period of declining methane emissions, using GWP₁₀₀ does not even indicate the correct direction of temperature change. The improvement achieved by using GWP* is therefore not simply a slight refinement to the shape of the warming profile or a better scaling of cumulative emissions to temperature under a given TCRE: it captures the fundamentally different behaviour of short- and long-lived climate pollutants, which is essential to provide even a broad indication of the impacts of ambitious mitigation strategies [32].

To further highlight some of the important elements described by GWP*, we now explore a number of shorter-term emission scenarios.

As noted above, GWP₁₀₀ can variously over- or under-state the impact of methane emissions depending on the historic trajectory of these emissions, which may not be known. Here we show how application of GWP*, using the previous 20 years but no further, still gives a useful indication of anticipated temperature change. We also focus on a 50 year period to demonstrate that GWP* provides a much improved indication of short- and medium-term impacts, and is not relevant only for the longer (200 year) scenarios shown above.

Since most policy scenarios involve some prior methane emissions, we need to include these to show various dynamics that include decreases in emission rate, or incorporate behaviours that emerge in the longer term, and so all of the scenarios shown occur following 50 years of an introduced and then sustained methane emission, building on the examples above. We then change methane emissions to a new demonstrative trajectory, and after 25 years of this change, show the warming response and both CO₂-equivalent emissions (hence these figures start from 'year 75'). See supplementary material for further description of this approach, including an illustration in figure S4.

3.3.1. Stable and declining methane emissions

We begin by considering scenarios with stable or declining methane emissions (figure 5). For ongoing stable methane emissions (figure 5(a)), the CO₂-equivalent quantity is a constant annual emission under both GWP₁₀₀ and GWP*, but GWP* CO₂-w.e. is much less than GWP₁₀₀ CO₂-e (×0.25, following (2) with the suggested s), and cumulative CO₂-w.e. (×TCRE) a much better match for the modelled warming. Consequently, if we sought to offset the continued warming from long-term stable methane emissions by annually sequestering an appropriate amount of CO₂ derived using the GWP₁₀₀ (i.e. a 'net-zero emissions' policy using GWP₁₀₀), we would overstate the impacts of this methane and result in cooling, rather than temperature stabilisation [33, 34].

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For declining methane emissions rates (figure 5(b)), the key point is as noted above: the falling temperatures under this scenario are equivalent to a removal of atmospheric CO₂, as described using GWP* (unless the rate of decline in methane emissions is very gradual, see below). Under conventional use of GWP₁₀₀, it is only possible to equate any ongoing methane emissions at all to a positive CO₂ emission, suggesting continuing warming at odds with the real temperature response.

We can consider a special case where the decline in methane emissions rate is such that it is described by 0 GWP* CO₂-w.e. emissions (figure 5(c)). This can be achieved through an annual decline in methane emissions of approximately 0.3% per year (for the r and s values suggested above, see supplementary material for derivation). As shown (figure 5(c)-lower), this scenario results in negligible additional warming despite ongoing, relatively high, methane emissions. Meanwhile, the large ongoing GWP₁₀₀ CO₂-e emissions would lead to significant continued temperature increases. A key point emerges which is obscured by conventional use of GWP₁₀₀: to prevent further warming, it is necessary that net CO₂ emissions are reduced to zero, but this is not the case for methane, where it is possible to have climatically sustainable ongoing emissions.

Any decline in methane emissions rate faster than the 0.3% p.a. decline noted above suggests cooling relative to the current temperature (figure 5(b), see [16] for discussion of the physical origin and uncertainty in this rate of decline). This is broadly the role of methane in ambitious mitigation pathways, where significant, permanent, reductions in methane emission rates can permit the emissions of a fixed amount of extra CO₂, and hence the additional long-term warming it will cause, under a given temperature ceiling [35, 36]. This concept is explored further below when demonstrating the use of GWP* to assess alternative mitigations.

It should be noted that these stable or declining temperatures are relative to present temperatures, as already experienced; not relative to before the emission was introduced. (i.e. for individual temperature subplots in figures 5 and 6, warming and cumulative CO₂-equivalents are both from 0 in year 75, setting this as our reference point, but comparison with figure S4 (supplement) shows that this temperature is +5.3 mK relative to before the methane emission was introduced.) Long-term methane emitters therefore still have a warming legacy, and their continued emissions sustain elevated temperatures. It could thus be argued that, despite being able to achieve no additional warming through relatively small mitigations, continued methane emitters still have a responsibility to decrease emissions and mitigate climate change as much as possible, akin to holding countries responsible for their national contribution to observed global warming [37]. Where historical emissions are known, cumulative GWP* CO₂-w.e. emissions to date can be used to indicate this responsibility, while annual GWP₁₀₀ CO₂-e, the basis of most policy targets, cannot.

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But given that any CO₂ emissions yield continued warming, by communicating emissions and designing strategies based primarily on reductions to ongoing annual CO₂ emissions, there is an implicit baseline of no further CO₂ emissions and hence no additional warming (particularly in relation to a stated ambition of net-zero CO₂ emissions). Alternatively, if we considered an emissions-accounting framework that did reflect total warming contribution, and could describe responsibilities to reverse warming rather than just encourage no further temperature increases, the baseline for CO₂ emitters would not just be their current or recent annual CO₂ emission rates, but total cumulative CO₂ emissions to date, and they would have a responsibility to sequester carbon and reverse historic contributions, rather than simply reduce ongoing emissions. GWP* could provide a means to account for different gases within such a framework, setting climatically meaningful responsibilities for diverse sectors producing distinct emissions. Meanwhile, using annual GWP₁₀₀ CO₂-emission rates, as is common at present, results in a lack of clarity on the different historical warming contributions between sectors or the distinct climate outcomes of reducing emissions of different gases.

3.3.2. Increasing methane emissions

Finally, we build on the principles and demonstrations above to provide a simple example of how GWP* can be used to better appraise GHG mitigation strategies. These mitigations are made to a baseline multi-gas scenario (figure 7), where emissions of both methane and CO₂ are introduced and then maintained at the annual emission rates used in figure 1. This scenario leads to a rapid initial increase in warming, primarily from the methane, followed by a slower temperature increase driven predominantly from the consistent rate of CO₂-induced warming. Summing the two sets of cumulative CO₂-w.e. emissions provides an approximation of this, while the two sets of cumulative CO₂e emissions suggest they have the same linear impacts, and so the total is simply a greater rate of linear increase.

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We can demonstrate the utility of multi-gas cumulative CO₂-w.e. totals in a decision making context by considering how they would describe alternative mitigation pathways, as in figure 8. In this scenario, the emissions of one gas cease in year 50, and then the emissions of the remaining gas in year 100. Stopping methane first results in a large initial reversal of recent warming, but temperatures then start to rise again due to the ongoing CO₂ emissions. Temperature then stabilises at the temperature reached in year 100 when CO₂ emissions are also stopped. Stopping CO₂ first, we see that the rate of warming declines, and then when methane emissions stop in year 100 we have a significant reversal of warming, stabilising at a lower long-term temperature than in the methane-first scenario. Cumulative CO₂-w.e. provides a clear indication of these dynamics, while cumulative CO₂e suggests either strategy would lead to the same response, but which represents neither scenario.

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These two strategies illustrate an important principle: that focussing on methane at the expense of (a GWP₁₀₀ equivalent quantity of) CO₂ is not simply a prioritisation of short- over long-term impacts, it is a trade-off. There is a large initial benefit (indeed, a significant reversal of total warming, in this scenario) from focussing on methane, but the more that action on CO₂ is postponed, the higher the temperature that we are locked in to. Consequently, reducing methane emissions, though beneficial, does not 'buy time' for delayed CO₂ mitigation in the sense that it provides an equivalent pathway to acting on CO₂. It is universally better to stop CO₂ emissions early, as the sooner they are stopped, the sooner they stop compounding and the less CO₂-induced warming we are committed to for the very long-term [38]. Rather, the negative CO₂-w.e. generated by permanently reducing methane emission rates expands the allowable space for emissions of cumulative GHGs within a total [CO₂-w.e.] emissions budget, and hence permits a greater one-off fixed quantity of CO₂ emissions under a given temperature ceiling. The inverse implication is that the longer we fail to decarbonise, and hence add to the cumulative stock of CO₂ emitted, then the smaller the permissible rate of ongoing, sustainable methane emissions within a given emissions budget (and hence also a given temperature ceiling). In this context, it is worth noting that annual fossil fuel CO₂ emissions were the highest ever in 2019 and predicted to continue increasing in 2020 [39].

We can complete the range of scenarios in this framework by adding the cases where we stop emissions of both gases earlier or later figure 9. As should be self-evident, the climatically optimum strategy is to reduce emissions of any greenhouse gases as early as possible. Stopping both gases early results in rapid cooling from the cessation of methane emissions, and also prevents the ongoing temperature increases that would occur from sustained CO₂ emissions. The scenario in which both emissions are stopped later highlights a further implication of the principles described above: while the point at which methane emissions are stopped can have an important impact on peak warming (so long as CO₂ are also stopped contemporaneously or shortly afterwards), as most of the warming impact of methane depends on the rate of emissions, it is largely time-independent. Delaying action on methane does not have as significant an impact on long-term temperature as delaying action on CO₂ emissions; the eventual temperature we remain committed to, once both emissions are stopped, is predominantly determined by the timing of CO₂ mitigation.

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The 'stock' component, respresenting the long-term temperature adjustment to methane emissions, is still important, and the scale of contemporary methane emissions is such that this element could equate to a significant increase in total allowable CO₂ emissions for warming of 1.5° C if action is taken on methane earlier rather than later [35], but by a much smaller amount than the direct GWP₁₀₀ equivalence between methane and CO₂ would suggest.