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Indicate separate contributions of long-lived and short-lived greenhouse gases in emissions targets

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To quantify the SR1.5 and AR6 statements cited above, the human-induced global temperature change over a time interval of decades ∆yourelative to the level of human-induced warming at the beginning of this interval (e.g. present or pre-industrial times), can be decomposed using the articulated framework above as follows:

$${Delta} T = kappa _Eoverline {E_C} {Delta} t + kappa _Fleft( {{Delta} F_N + rho overline {F_N} {Delta} t} right ),$$

(1)

or (overline {E_C}) and (overline {F_N}) are the average global aggregated CO2 emission rate and non-CO2 radiative forcing, respectively (so (overline {E_C} {Delta} t) is the cumulative CO2 emissions) and ∆FNOT is the change in the decadal average of non-CO2 forcing, all assessed over this interval (the geophysical “zero emissions commitment” should be relatively low over a time interval of several decades23, but this may not be the case on longer time scales). The coefficients κE (the TCRE) and κF (the TCRF, or “rapid” component of the climate response to any forcing change, denoted vs1 in ref. 12or sum of fast components24: see supplementary material), are both scenario-independent in the absence of strongly nonlinear carbon cycle feedbacks or climate response. The only scenario-dependent coefficient is ρ, the constant forcing adjustment fractional rate (RACF), or the relatively low fractional rate at which forcing must decrease to maintain stable temperatures. It depends on speed and recent date FNOT increased (this term represents the delayed adjustment to past forcing increases, so it is more important for more recent and rapid increases). Yes FNOT only varies on multi-decadal time scales, ρ =vs2//( κFs2), or vs2 is the “slow” (multi-secular) component of climate sensitivity, and s2 deep ocean thermal adjustment time scale. For the representative12 coefficient values,ρ 0.3% per year, which makes this third term generally weak.

Global CO2-e100 emissions cannot be used to calculate FNOT if these include a mixture of LLCF and SLCF. Global CO2-e100 LLCF emissions, ELcan, however, be unambiguously combined and have the same impact on global temperature on a decade-to-century scale as the corresponding amount of CO2. Similarly, aggregate CO2-e100 SLCF broadcasts, ESmultiplied by the AGWP100 of CO2, A100give the SLCF radiative forcing,FS ( A100 normally includes a first order estimate of the impact of carbon cycle feedbacks25 so for consistency this should also be included in the GWP100 values ​​used to calculate ES).

For emissions reported as CO2-e100 so the above expression can be rewritten (now grouping all LLCFs with CO2):

$${Delta} T = kappa _Eoverline {E_L} {Delta} t + kappa _Fleft( {{Delta} F_S + rho overline {F_S} {Delta} t} right ),$$

(2)

or equivalently, usingFS=A100ES on multi-decadal time scales,

$${Delta} T = kappa _Eoverline {E_L} {Delta} t + kappa _FA_{100}left( {{Delta} E_S + rho overline {E_S} {Delta} t } right).$$

(3)

Hence ∆Jcan be estimated directly using well-known (though uncertain) properties of the climate system if, and only if, total CO2-e100 emissions of long-lived climate forcers, ELare specified in the emission targets with the total CO2-e100 emissions, EL+ES; or equivalent, EL and ES are specified separately. ∆J cannot be calculated from the sum of EL+ ES alone.

This is illustrated by Fig. 1, which shows the impact of LLCF and SLCF emissions, expressed in CO2-e100on the change in global temperature over a period of several decades, compared to the level of warming at the beginning of this period, calculated with a simple climate model12. Stylized cases of constant (darker shades) and gradually varying (+10%, lighter shades and −50%, dashed lines) emissions are shown in panels a and c. Warming due to LLCF emissions (the term (kappa _Eoverline {E_L} {Delta} t) in eq. (3)) increases linearly with cumulative emissions in the three cases (panel b). Warming due to continuous constant emission from an SLCF that began decades before the start of this period (the (kappa _FA_{100}rho overline {E_S} {Delta} t) term) also increases linearly (panel d, darker blue) but at a slower rate per tCO2-e100 emitted (by a factor of approximately 4, because κE≈ 4× κFA100ρ ): global temperatures have already partially equilibrated with this constant emission (by how much depends on how long ago these SLCF emissions started, which is whyρ is the only scenario-dependent coefficient in these expressions). Finally, warming due to an increase in SLCF emissions (theκFA100ES term, panel d, lighter blue) is 4-5 times higher than would be expected with the same increase in tCO2-e100 emissions of an LLCF (panel b, lighter red) over the 20 years following the increase (κFA100 ≈ 4.5×κE× 20 years). Hence the statement AR6 “express methane emissions as CO2 equivalent emissions using GWP100overestimates the effect of constant methane emissions on global surface temperature by a factor of 3 to 4… while underestimating the effect of any new sources of methane emissions by a factor of 4 to 5 on the 20 years following the introduction of the new source”26 applies to the global emissions impact of any SLCF. Any decrease in SLCF emissions also has a much larger impact on temperatures over a period of decades per tCO2 -e100avoided than a corresponding decrease in LLCF emissions (red and blue dashed lines) (Fig. 1).

Fig. 1: Stylized LLCF and SLCF emissions and resulting global temperature change ∆J over a period of several decades.

Darker bands in the panels a and vs show constant LLCF and SLCF emissions of 1 tCO respectively2 -e100per year beginning a few decades before the indicated interval. The pale bands show a 10% increase over a quarter of the indicated interval, while the dotted lines show a 50% decrease. Resulting temperature changes from the start of this interval displayed in panels b and Dcalculated using a simple climate model: vertical axes b and D are scaled identically to illustrate a lower rate of warming due to constant SLCF emissions and a much larger warming impact of any change in SLCF emissions compared to the warming due to identical CO2 -e100LLCF broadcasts. The vertical arrows on the right show the predicted contributions to ∆J from the individual terms of the equation. (3): three arrows in the panel b show the cumulative LLCF emissions over this interval multiplied by the TCRE for the three scenarios presented; the lower and upper arrows of the panel D show, respectively, the predicted warming due to constant continuous emissions of SLCF and the additional warming due to the 10% increase. The figure illustrates that Eq. (3) allows a reliable, albeit approximate, prediction of multi-decade warming ∆ Jif, and only if, LLCF and SLCF emissions are specified separately.

The temperature changes in the figure are calculated using a particular model, LLCF, SLCF and a scenario. The figure would, however, appear similar if another model, gas combination or past emissions scenario were used, provided that emissions do not change rapidly immediately before the start or end of the time period shown, as the relationship between emissions and warming expressed in Eq. (3) is generic. Individual terms in Eq. (3), assuming constant coefficients, are represented by the arrows to the right of panels b and d. These correspond to the warming calculated by the explicit simple climate model within the limits of the modeling uncertainties. The figure shows the temperature change relative to the beginning of the period rather than the absolute warming because the latter is not determined by the equation. (3) but depends on the history of LLCF and SLCF emissions (the specific scenario used to generate this figure is presented in full in the supplementary information).

Temperature change ∆ Jover a period of several decades depends, to first order, only on the cumulative emissions of LLCF (overline {E_L} {Delta} t)cumulative SLCF emissions (overline {E_S} {Delta} t)and net change in total SLCF emission rates ∆ ES, over this period alone. As SR1.5 and AR6 pointed out, future warming depends on future emissions. However, the use of this information requires both EL andES to be specified: specifying only the sumEL+ ES introduces ambiguity into the temperature result.

A separate specification also makes it easier to assess the implications of different metrics. For example, aggregate CO2-equivalent emissions using the 20-year global warming potential (GWP20 ) can be approximated by EL+3 ES if both EL and ESare reported as CO2-e100 with a slightly higher multiplication factor (up to 4) ifES is dominated by forcers with lifespans of the order of one year (Table 8.A.1 of Ref. 12 shows that GWP20 values ​​are similar to GWP100 values ​​for LLCF and 3 or 4 times GWP100values ​​for gases with lifetimes on the order of a decade or a year, respectively). Finally, we re-emphasize that these expressions capture our physical understanding of how global LLCF and SLCF emissions collectively drive global temperature change, and illustrate the usefulness of a separate specification ofEL andES. How this understanding is used to inform the assessment of the adequacy of individual emissions targets depends on other considerations listed above and cannot be argued from a physical science perspective alone. There will be several other advantages to the additional communication, such as the possibility of estimating the co-benefits of mitigation on air quality.