Editing IPCC:AR6/WGI/Chapter-7 (section)

==== 7.6.1.2 Physical Indicators ====

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The basis ofall the emissions metrics is the time profile of effective radiative forcing (ERF) following the emission of a particular compound. The emissions metrics are then built up by relating the forcing to the desired physical indicators. These forcing–response relationships can either be generated from emulators (Cross-Chapter Box 7.1; [[#Tanaka--2013|Tanaka et al., 2013]] ; [[#Gasser--2017b|Gasser et al., 2017b]] ), or from analytical expressions based on parametric equations (response functions) derived from more complex models ( [[#Myhre--2013b|Myhre et al., 2013b]] ).

To illustrate the analytical approach, the ERF time evolution following a pulse of emission can be considered an absolute global forcing potential (AGFP; similar to the ‘Instantaneous Climate Impact’ of [[#Edwards--2014|Edwards and Trancik, 2014]] ). This can be transformed into an absolute global temperature-change potential (AGTP) by combining the radiative forcing with a global surface temperature response function. This temperature response is typically derived from a two-layer energy balance emulator (Supplementary Material 7.SM.5; [[#Myhre--2013b|Myhre et al., 2013b]] ). For further physical indicators further response functions are needed based on the radiative forcing or temperature, for instance. [[#Sterner--2014|Sterner et al. (2014)]] used an upwelling-diffusiveenergy balance model to derive the thermosteric component of sea level rise as response functions to radiative forcing or global surface temperature. A metric for precipitation combines both the radiative forcing (AGFP) and temperature (AGTP) responses to derive an absolute global precipitation potential (AGPP; [[#Shine--2015|Shine et al., 2015]] ). The equations relating these metrics are given in Supplementary Material 7.SM.5.

The physical emissions metrics described above are functions of time since typically the physical effects reach a peak and then decrease in the period after a pulse emission as the concentrations of the emitted compound decay. The value of the metrics can therefore be strongly dependent on the time horizon of interest. All relative metrics (GWP, GTP etc.) are also affected by the time dependence of the CO <sub>2</sub> metrics in the denominator. Instantaneous or endpoint metrics quantify the change (e.g., in radiative forcing, global surface temperature, global mean sea level) at a particular time after the emission. These can be appropriate when the goal is to not exceed a fixed target such as a temperature or global mean sea level rise at a specific time. Emissions metrics can also be integrated from the time of emission. The most common of these is the absolute global warming potential (AGWP), which is the integral of the AGFP. The physical effect is then in units of forcing-years, degree-years or metre-years for forcing, temperature, or sea level rise, respectively. These can be appropriate for trying to reduce the overall damage potential when the effect depends on how long the change occurs for, not just how large the change is. The integrated metrics still depend on the time horizon, though for the shorter-lived compounds this dependence is somewhat smoothed by the integration. The integrated version of a metric is often denoted as iAGxx, although the integral of the forcing-based metric (iAGFP) is known as the AGWP. Both the endpoint and integrated absolute metrics for non-CO <sub>2</sub> species can be divided by the equivalent for CO <sub>2</sub> to give relative emissions metrics (e.g., GWP (=iGFP), GTP, iGTP).

Each step from radiative forcing to global surface temperature to sea level rise introduces longer time scales and therefore prolongs further the contributions to climate change of short-lived GHGs ( [[#Myhre--2013b|Myhre et al., 2013b]] ). Thus, short-lived GHGs become more important (relative to CO <sub>2</sub> ) for sea level rise than for temperature or radiative forcing ( [[#Zickfeld--2017|Zickfeld et al., 2017]] ). Integrated metrics include the effects of a pulse emission from the time of emission up to the time horizon, whereas endpoint metrics only include the effects that persist out to the time horizon. Because the largest effects of short-lived GHGs occur shortly after their emission and decline towards the end of the time period, short-lived GHGs have relatively higher integrated metrics than their corresponding endpoint metrics ( [[#Peters--2011|Peters et al., 2011]] ; [[#Levasseur--2016|Levasseur et al., 2016]] ).

For species perturbations that lead to a strong regional variation in forcing pattern, the regional temperature response can be different to that for CO <sub>2</sub> . Regional equivalents to the global metrics can be derived by replacing the global surface temperature response function with a regional response matrix relating forcing changes in one region to temperature changes in another (W.J. [[#Collins--2013|]] [[#Collins--2013|Collins et al., 2013]] ; [[#Aamaas--2017|Aamaas et al., 2017]] ; [[#Lund--2017|Lund et al., 2017]] ).

For the research discussed above, metrics for several physical variables can be constructed that are linear functions of radiative forcing. Similar metrics could be devised for other climate variables provided they can be related by response functions to radiative forcing or global surface temperature change. The radiative forcing does not increase linearly with emissions for any species, but the non-linearities (for instance changes in CO <sub>2</sub> radiative efficiency) are small compared to other uncertainties.

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