To quantify the SR1.5 and AR6 statements quoted above, human-induced global temperature change over a multi-decade time-interval t, relative to the level of human-induced warming at the beginning of that interval (e.g. the present day or pre-industrial), can be decomposed using the framework articulated above as follows:

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

(1)

where (overline {E_C}) and (overline {F_N}) are globally aggregated average CO2 emission-rates and non-CO2 radiative forcing, respectively (so (overline {E_C} {Delta} t) is cumulative CO2 emissions), and FN is the change in decadal-average non-CO2 forcing, all evaluated over that interval (the geophysical Zero Emissions Commitment is expected to be relatively small over a multi-decade time-interval23, but this may not be the case on longer timescales). The coefficients E (the TCRE) and F (the TCRF, or fast component of the climate response to any forcing change, denoted c1 in ref. 12, or sum of fast components24: see supplementary material), are both scenario-independent in the absence of strongly non-linear carbon cycle feedbacks or climate response. The only scenario-dependent coefficient is , the fractional Rate of Adjustment to Constant Forcing (RACF), or the relatively small fractional rate at which forcing needs to decline to maintain stable temperatures. It depends on how fast and how recently FN has increased (this term represents the delayed adjustment to past forcing increases, so is larger for more recent and rapid increases). If FN varies only on multi-decadal timescales, =c2/(Fs2), where c2 is the slow (multi-century) component of the climate sensitivity, and s2 the deep ocean thermal adjustment timescale. For representative12 coefficient values, 0.3% per year, making this third term usually small.

Aggregate CO2-e100 emissions cannot be used to calculate FN if these comprise a mixture of LLCFs and SLCFs. Aggregate CO2-e100 emissions of LLCFs, EL, can, however, be combined unambiguously and have the same impact on global temperature on decade to century timescales as the corresponding quantity of CO2. Likewise, aggregate CO2-e100 emissions of SLCFs, ES, multiplied by the AGWP100 of CO2, A100, give 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 compute ES).

For emissions reported as CO2-e100 the above expression can therefore be re-written (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, using FS=A100ES on multi-decadal timescales,

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

(3)

Hence T can be estimated directly using well-known (albeit uncertain) climate system properties if, and only if, total CO2-e100 emissions of long-lived climate forcers, EL, are specified in emission targets together with total CO2-e100 emissions, EL+ES; or, equivalently, EL and ES are specified separately. T 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 as CO2-e100, on global temperature change over a multi-decade period, relative to the level of warming at the beginning of that period, calculated with a simple climate model12. Stylised cases of constant (darker shades) and step-change (+10%, lighter shades, and 50%, dotted 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 all three cases (panel b). Warming due to an ongoing constant emission of an SLCF that started decades before the beginning 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 about 4, because E4FA100): global temperatures have already partially equilibrated with this constant emission (by how much depends on how long ago these SLCF emissions began, which is why is the only scenario-dependent coefficient in these expressions). Finally, warming due to an increase in SLCF emissions (the FA100ES term, panel d, lighter blue) is 45 times greater than would be expected from the same increase in tCO2-e100 emissions of an LLCF (panel b, lighter red) over the 20 years following the increase (FA1004.5E20 years). Hence the AR6 statement expressing methane emissions as CO2 equivalent emissions using GWP100 overstates the effect of constant methane emissions on global surface temperature by a factor of 34 while understating the effect of any new methane emission source by a factor of 45 over the 20 years following the introduction of the new source26 applies to the impact of global emissions of any SLCF. Any decrease in SLCF emissions also has a much greater impact on temperatures over a multi-decade period per tCO2-e100 avoided than a corresponding decrease in LLCF emissions (red and blue dotted lines) (Fig. 1).

Darker bands in panels a and c show, respectively, constant LLCF and SLCF emissions of 1 tCO2-e100 per year starting some decades before the interval shown. Pale bands show a 10% increase one-quarter of the way through the interval shown, while dotted lines show a 50% decrease. Resulting temperature changes relative to the start of this interval shown in panels b and d, calculated using a simple climate model: vertical axes in b and d are scaled identically to illustrate smaller rate of warming due to constant SLCF emissions and much larger warming impact of any change in SLCF emissions relative to the warming due to identical CO2-e100 LLCF emissions. Vertical arrows in the right show predicted contributions to T from the individual terms in Eq. (3): three arrows in panel b show cumulative LLCF emissions over this interval multiplied by the TCRE for the three scenarios shown; the lower and upper arrows in panel d show, respectively, the predicted warming due to ongoing constant SLCF emissions and additional warming due to the 10% increase. The figure illustrates that Eq. (3) allows reliable, if approximate, prediction of multi-decade warming T if, and only if, LLCF and SLCF emissions are specified separately.

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

Temperature change T over a multi-decade period depends, to first order, only on cumulative emissions of LLCFs (overline {E_L} {Delta} t), cumulative emissions of SLCFs (overline {E_S} {Delta} t), and net change in total SLCF emission rates ES, over that period alone. As the SR1.5 and AR6 emphasised, future warming depends on future emissions. Making use of this information, however, requires both EL and ES to be specified: only specifying the sum EL+ES introduces an ambiguity in temperature outcome.

Separate specification also facilitates assessing the implications of different metrics. For example, aggregate CO2-equivalent emissions using the 20-year Global Warming Potential (GWP20) can be approximated by EL+3ES if both EL and ES are reported as CO2-e100, with a slightly higher multiplicative factor (up to 4) if ES is dominated by forcers with lifetimes of order one year (Table 8.A.1 of ref. 12 shows that GWP20 values are similar to GWP100 values for LLCFs and 3 or 4 times GWP100 values for gases with lifetimes of order a decade or a year, respectively). Finally, we re-emphasise that these expressions capture our physical understanding of how global emissions of LLCFs and SLCFs collectively determine global temperature change, and illustrate the utility of separate specification of EL and ES. How this understanding is used to inform the assessment of the adequacy of individual emission 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 being able to estimate air quality co-benefits of mitigation.

Continued here:
Indicate separate contributions of long-lived and short-lived greenhouse gases in emission targets | npj Climate and Atmospheric Science - Nature.com