The effect of climate–carbon cycle feedbacks on emission metrics

The Climate–Carbon cycle Feedback (CCF) affects emission metric values. In the Fifth Assessment Report (AR5) of the Intergovernmental Panel on Climate Change metric values for Global Warming Potentials (GWP) and Global Temperature Potentials (GTP) are reported both with and without CCF for non-CO2 climate forcers, while CCF is always included for CO2. The estimation of CCF for non-CO2 climate forcers in AR5 is based on a linear feedback analysis. This study compares that approach with an explicit approach that uses a temperature dependent carbon cycle model. The key difference in the CCF results for non-CO2 climate forcers is that, with the approach used in AR5, a fraction of the CO2 signal induced by non-CO2 forcers will persist in the atmosphere basically forever, while, with the approach based on an explicit carbon cycle model, the atmospheric CO2 signal induced by non-CO2 forcers eventually vanishes. The differences in metric values between the two model approaches are within ±10% for all well-mixed greenhouse gases when the time horizon is limited to 100 yr or less, for both GWP and GTP. However, for long time horizons, such as 500 yr, metric values are substantially lower with the explicit CCF model than with the linear feedback approach, up to 30% lower for GWP and up to 90% lower for GTP.


Introduction
Emission metrics are used to compare climate forcers that have different atmospheric adjustment times, often using carbon dioxide (CO 2 ) as a reference gas. These comparisons are helpful when trying to assess the impact on the climate of different anthropogenic activities that cause emissions of various climate forcers. For the metrics to be as relevant as possible, they need to be well-defined and consistent in their structure and calculation.
Historically, the treatment of the Climate-Carbon cycle Feedback (CCF), considered to be one of the most important positive biogeochemical feedbacks in the climate system (Arneth et al 2010, Ciais et al 2013), has been inconsistent when calculating metrics (Myhre et al 2013). Since the fourth assessment report (AR4) of the IPCC (Solomon et al 2007), the climate-carbon cycle feedback has been taken into account when estimating the Absolute Global Warming Potential (AGWP) for CO 2 but not when estimating the AGWP for the other gases. However, there have been calls for the inclusion of the CCF for non-CO 2 gases when calculating metric values (Gillett andMatthews 2010, Collins et al 2013). Gillett and Mathews (2010) find approximately a 20% increase in the GWP values for methane (CH 4 ) and nitrous oxide (N 2 O) when including the CCF for non-CO 2 forcers. Recently a task force initiated by the United Nations Environment Programme (UNEP) and the Society of Environmental Toxicology and Chemistry (SETAC) on 'Global guidance on environmental life cycle impact assessment indicators' added to the calls. The task force recommended that metrics that include the CCF effect for non-CO 2 greenhouse gases be used when conducting Life Cycle Assessments (LCAs) (Levasseur et al 2016). Hence, it is important to assess how the CCF affects emission metrics in detail since it is possible that metric values that include the CCF will be industry standard in the near future.
In the AR5, the inconsistent treatment of the CCF for CO 2 versus non-CO 2 forcers was discussed and dealt with by presenting metric values that included the CCF (Myhre et al 2013) for all but the Short-Lived Climate Forcers (SLCFs) 2 . The approach used for estimating the contribution of CCF to metric values was based on the Linear Feedback Analysis (LFA) presented in Collins et al (2013). In this approach the temperature perturbation induced by an emission pulse of a non-CO 2 forcer causes a net release of carbon to the atmosphere, without any details about from where this carbon came. Further, the carbon added to the atmosphere is assumed to be removed from the atmosphere in the same way as an emission pulse of fossil carbon.
In this study we compare metric values, for the Global Warming Potential (GWP) and Global Temperature change Potential (GTP), estimated with two different approaches to including the CCF. We contrast the LFA approach with an approach based on a Coupled Climate-Carbon cycle Model (CCCM) that models the interaction between the climate and the carbon cycle explicitly. Our prime interest lies in the difference in CCF relaxation time scales between the two model approaches and what effect this has on absolute and relative metric values.
In section 2, we introduce the CCCM, and in section 3, we present the methods used for the numerical evaluation of the metrics. section 4 contains results and analysis, and we end with conclusions in section 5. In the supplementary material available at stacks.iop.org/ERL/12/034019/mmedia (SM) we present details of the model, elaborate on the results in more detail, and show some additional results.

A coupled climate-carbon cycle model
This study utilizes an Upwelling-Diffusion Energy Balance Model (UDEBM) presented in Sterner et al (2014) and Johansson et al (2015) coupled to a carbon cycle model based on Siegenthaler and Oeschger (1987), Jain et al (1995), and Joos et al (1996. We first present the UDEBM and then the carbon cycle model (model equations are given in SM 1.1). For the greenhouse gases explicitly studied in this paper (CH 4 , N 2 O, and sulfur hexafluoride, SF 6 ), we use simple gas cycle models in line with those used in IPCC AR5 (Myhre et al 2013), while for Black Carbon (BC) we calculate a radiative forcing pulse using the specific forcing and adjustment time of Fuglestvedt et al (2010). The LFA approach utilizes the same climate model but with a different setup of the carbon cycle model (see section 3.3) that represents the CCF using a linear relationship between temperature change and the induced carbon release.

Upwelling diffusion energy balance model
The UDEBM has two surface layers, one layer for land areas and the atmosphere above it and one for the mixed-layer ocean and the atmosphere above it. The ocean below the mixed layer has been discretized into 39 layers of equal size. The structure of the UDEBM and its calibration are based on Shine et al (2005)

The carbon cycle model
The reduced-complexity carbon cycle model used in this study consists of two parts: a four-box terrestrial biosphere model (Siegenthaler and Oeschger 1987) and an upwelling-diffusion model (UDM) (Jain et al 1995, Joos et al 1996.
The box model representing the biospheric part of the carbon cycle consists of four carbon reservoirs: 'ground vegetation plus leaves,' 'wood,' 'detritus,' and 'soils' (denoted G, W, D, and S respectively). The preindustrial values of the carbon reservoirs and the fluxes between them are based on Siegenthaler and Oeschger (1987). In order to examine the CCF we assume that decomposition and respiration rates for the D and S boxes are temperature dependent with a relationship stating the change in the rates of decomposition and respiration for a ten degree increase in global mean annual land surface temperature (so-called effective Q 10 -factors) (Harvey 1989, Friedlingstein et al 2006. The strength of the effective Q 10 -factors is highly uncertain, and recent studies (Friedlingstein 2015) indicate that the CCF may be lower than found in older literature (Friedlingstein et al 2006, Ciais et al 2013. The Net Primary Production (NPP) increases with increasing atmospheric CO 2 concentration due to the CO 2 -fertilization effect. The strength of the CO 2 fertilization effect in the model is controlled with a biota growth factor, b (see SM 1.1) (Bacastow and Keeling 1973). We assume that NPP is independent of changes in the global temperature, since the effect of climate change (besides CO 2 fertilization) on NPP varies from positive to negative among various studies and models (Friedlingstein et al 2006, Meinshausen et al 2011a. For the ocean part of the carbon cycle, the model is conceptually identical to the UDEBM, but instead of modeling energy fluxes it models vertical flows of carbon (as in Jain et al 1995). The inorganic carbonchemistry of the ocean surface controlling the exchange between the ocean and the atmosphere is parameterized based on Joos et al (1996), while the temperature dependence of the partial pressure of sea surface CO 2 is from Joos et al (2001) (see SM 1.1 for more information).
Two key parameters that control fluxes of carbon in the carbon cycle model 4 are calibrated to capture the CO 2 increase in the atmosphere since 1765 (using emissions and concentrations from Meinshausen et al 2011b) and to give a similar uptake in the biosphere and the ocean as reported in AR5 (Ciais et al 2013) (see SM 1.3).
The model does not include the slow sedimentation processes and the reactions with silicate rocks that over time scales of 10 000 to 100 000 yr cause atmospheric CO 2 perturbations to relax back to zero. Further, the model does not include the hydrologic cycle, so it does not capture changes in precipitation and soil moisture that could have important effects on CCF. Hence, the climate-carbon cycle model is relatively simple. However, related simple climate models have proven to be useful for various sorts of

The carbon cycle feedback and its impact on metric values
We evaluate the metrics (A)GWP and (A)GTP with a set of climate forcers that cover the whole scale of adjustment times, from the short-lived BC to the longlived sulfur hexafluoride (SF 6 ) and CO 2 (see table SM 1). Metric values are contingent upon the background scenario used (Joos et al 2013, 2011). We use the emissions from the RCP 4.5 scenario with additional pulse emissions of 10 6 kg = 1 Kilo ton (Kt) on top of the scenario to calculate metric values. The background scenario for the climate forcers not explicitly studied here is given by the RCP 4.5 radiative forcing scenario (Meinshausen et al 2011b).
The model's time resolution is 0.1 yr. We assume that the emission pulses of the different forcers occur in the first tenth of year 2015. The atmospheric BC stock is assumed to reach its equilibrium level directly, and then it falls back to zero in the subsequent time step. We run the model both without (described in section 3.2) and with (described in section 3.3) the CCF for non-CO 2 forcers. The CCF is in turn included in two different ways: a) by calculating it with the CCCM where the warming induced by an emissions pulse of a non-CO 2 forcer explicitly affects the different carbon reservoirs (referred to as the Explicit Carbon-Climate Feedback (ECCF) approach) and b) by calculating the CCF using an LFA approach similar to the method used in IPCC AR5 (Myhre et al 2013) and Collins et al (2013).

Absolute metric values for CO 2
When studying emission pulses of CO 2 , which is the reference gas for the relative metric values, we consistently use the CCCM with the explicit temperature dependence of the carbon cycle as in the ECCF approach. To calculate AGWP CO 2 and AGTP CO 2 , we run the CCCM with an extra emission pulse of CO 2 in addition to the emissions in the background scenario and calculate the impacts on CO 2 concentration, radiative forcing, and temperature. This is in principle similar to how the Impulse Response Function (IRF) for CO 2 used for emissions metrics in IPCC AR5 was estimated (Joos et al 2013) 5 .

Metrics without CCF for non-CO 2 forcers
When calculating metric values without the CCF for non-CO 2 forcers, we first run the CCCM with emissions from the RCP4.5 scenario to establish the background concentrations for the climate forcers we explicitly consider in the analysis. In the next step, we add emission pulses for different forcers to estimate absolute metric values, i.e. AGTP and AGWP, from which GTP and GWP values can be calculated equations (1) and (2): Here X is the climate forcer studied, H is the time horizon, AGTP X is the absolute global temperature change potential and AGWP X is the absolute global warming potential of climate forcer X.
The absolute metric values are estimated differently for CO 2 and the non-CO 2 forcer since the CCF is included for AGWP H CO 2 and AGTP H CO 2 but not for AGWP H X and AGTP H X . When estimating AGWP H X and AGTP H X we only use the gas cycle model of the studied forcer along with the UDEBM to estimate the impacts on concentration, radiative forcing, and temperature of the extra emission pulse and neglect possible interactions with the carbon cycle.
In this paper we present metric values for a time horizon up to 500 yr, while in IPCC AR5 metric values were only presented for time horizons up to 100 years for reasons related to uncertainty and potential limitations of the chosen approach to calculating metrics (Myhre et al 2013).
3.3. Metrics including the CCF for all forcers 3.3.1. The ECCF approach When including CCF for non-CO 2 forcers using the ECCF approach, the full CCCM (i.e. the temperature dependent version of the CCCM) is used. The metric values for a non-CO 2 forcer are calculated by using the full CCCM with an extra emission pulse of the non-CO 2 forcer in 2015. The impacts on the concentration of both the analyzed non-CO 2 forcer and CO 2 , through the CCF, and subsequent impact on radiative forcing and temperature are assessed. From these values we can estimate the absolute metric values for the non-CO 2 forcer with the CCF included. Hence, the direct temperature impact of emissions of a non-CO 2 forcer on decomposition and respiration rates in the terrestrial biosphere model and the temperature dependence of the oceanic inorganic carbonate chemistry are explicitly modeled in the same way as they are for an emissions pulse of CO 2 .

The LFA approach
The LFA approach to including carbon cycle feedbacks for non-CO 2 forcers is based on Collins et al (2013), with the CCF parts of AGTP and AGWP for non-CO 2 forcer X evaluated according to equations (3) and (4).
Here AGTP X Ã (t) is the AGTP X with no CCF at time t after the emission pulse, calculated as described in section 3.  (2012), we show that a linear feedback factor of 1 GtC K yr −1 is also a decent approximation of the CCF feedback strength in our CCCM. Hence, we use this value when applying the LFA approach (figure 1) in our study. Note that the feedback factor, G, estimated in Arora et al (2013) and Boer and Arora (2012) is based on Earth System Models (ESMs) that have a far more elaborate description of the global carbon cycle than our CCCM.
In the LFA approach, absolute metric values for CO 2 are still estimated using the full CCCM as described above (see section 3.1). This is analogous to the procedure followed by Collins et al (2013) and Myhre et al (2013) who use an impulse response function for CO 2 that includes the CCF (Joos et al 2013). When estimating the absolute metric for the non-CO 2 forcers using the LFA approach, we do not use an explicit impulse response function for AGTP CO 2 as in Collins et al (2013) and Myhre et al (2013). Instead, utilizing our CCCM, we evaluate the effect on concentration, radiative forcing, and temperature of the induced CO 2 release, calculated using the feedback factor approach (figure 1). These values are then added to the corresponding values for the non-CO 2 forcer as estimated for the case with no CCF (i.e. the case presented in section 3.2), see equations (5) and (6) and figure 1. The LFA approach and our ECCF approach include the same feedbacks, but in different ways. In section 4 we compare the metric values they produce.
AGWP LFA Here the AGTP ind CO 2 (AGWP ind CO 2 ) is the AGTP (AGWP) of the induced CO 2 emission release due to the emission pulse of climate forcer X calculated using the LFA approach.

Comparing the ECCF and the LFA approaches
In the ECCF approach, the CCF consists of an increase in the decomposition rate of terrestrial organic carbon and a shift towards a higher partial pressure of dissolved CO 2 for a given level of Dissolved Inorganic Carbon (DIC) in ocean surface waters. Given a fixed background level of the atmospheric carbon stock, this implies a small release of carbon from the biosphere and the ocean to the atmosphere, which results in an increased atmospheric CO 2 concentration and additional radiative forcing and warming.
In the LFA approach, however, the net CO 2 released to the atmosphere due to the CCF is calculated by using the assumption of a linear relationship between the CO 2 flux and the direct temperature perturbation caused by the non-CO 2 forcer according to equations (3) and (4). The induced atmospheric CO 2 caused by the non-CO 2 forcer is assumed to have the same characteristics, i.e. atmospheric adjustment times, as regular emissions of fossil CO 2 and will hence end up elevating the atmospheric carbon stock basically forever ( figure 3).
Environ. Res. Lett. 12 (2017) 034019 The differences in the CCCM setups for the LFA and the ECCF approaches are presented in figure 1.

Results and metrics evaluation
We first present the AGTP and AGWP values based on different assumptions for the CCF for non-CO 2 forcers, followed by an analysis of the physical mechanisms behind the atmospheric CO 2 concentration induced by non-CO 2 forcers. Finally, we present the GWP and GTP metric values obtained when including CCF for non-CO 2 forcers using the full CCCM (i.e. the ECCF) and LFA (i.e. IPCC) approaches.

Absolute metrics and the climate carbon feedbacks
For all non-CO 2 forcers the AGWP and AGTP values are higher when the CCF is included compared to when it is not for both approaches (figure 2). This is expected because an emission pulse of a non-CO 2 warming forcer causes a positive temperature perturbation, which, due to the CCF, causes an amount of CO 2 to enter the atmosphere (figure 3).
All climate forcers produce different temperature perturbation time profiles as a result of their different radiative efficiencies and adjustment times. This in turn causes the CCF responses to vary among the forcers (figure 3). As a consequence, the CCF effects on AGTP and AGWP differ among forcers (figure 2). Further, the differences between the two CCF approaches vary among the different forcers.
The ECCF approach results in a stronger induced atmospheric CO 2 concentration in the short run compared to the LFA approach. The time horizon over which this holds depends on the adjustment time of the non-CO 2 forcer (figure 3). This causes the AGWP and AGTP to be slightly higher for the ECCF approach than for the LFA approach over a certain time horizon, the length of which increases with the atmospheric adjustment time of the non-CO 2 forcer. The reason that the values are only slightly higher is that the effect of the differences in the induced atmospheric CO 2 concentrations are initially dwarfed by the direct RF and warming of the non-CO 2 forcers. This causes the AGWP and AGTP values, of the LFA and the ECCF approaches, to follow each other rather tightly for about 100 to 200 yr (see figure 2).
Further, with the ECCF approach the feedbackinduced atmospheric CO 2 perturbation will eventually relax back to its unperturbed state for all forcers, while the LFA approach leads to an irreversible impact on where the CCCM climate model is first used to calculate AGWP X Ã and AGTP X Ã for the studied non-CO 2 forcer X without the CCF. Then the warming-induced CO 2 release is calculated based on the estimated AGTP X Ã and the linear feedback factor G. Finally, AGTP ind CO 2 and AGWP ind CO 2 are calculated by assessing the temperature and integrated radiative forcing response of the warming-induced CO 2 release with CCCM, but now with CCF turned on. Taken together, the AGTP X Ã and AGTP ind CO 2 , and AGWP X Ã and AGWP ind CO 2 , give the AGTP and AGWP of climate forcer X for the LFA approach. Right: Our alternative approach, the ECCF approach, uses the CCCM with the CCF turned on for the emission pulse of the climate forcer studied and produces the AGTP and AGWP absolute metric values.
Environ. Res. Lett. 12 (2017) 034019 the atmospheric carbon stock ( figure 3). Hence, the LFA approach will for time horizons large enough generate higher values than the ECCF approach for both AGTP and AGWP for all forcers studied (figure 2).
The reason for the irreversible impact on the atmospheric carbon stock with the LFA approach is that it models the carbon feedback as a temperature-induced CO 2 emission, where these emissions act as 'extra emission pulses of CO 2 ' (Collins et al 2013). The irreversibility is also a model artifact since it does not include the slow geochemical processes that eventually after 10 000 to 100 000 of years would remove the anthropogenic carbon emissions from the atmosphere, a property the model shares with the IRF used for metric estimates in IPCC AR5.   Figure 2. Absolute global mean surface temperature changes (AGTP, left side) and absolute global mean cumulative radiative forcing (AGWP, right side) following 1 Kt emission pulses of BC (a) and (b), CH 4 (c) and (d), N 2 O (e) and (f), CO 2 (g) and (h), and SF 6 (i) and (j), for the three CCF assumptions studied (except for CO 2 , for which there is only the one CCF assumption). Note that the temperature scale of figure 2(a) (BC) does not encompass the peak values in the earliest time period in order to focus on the difference in evolution over time.
Environ. Res. Lett. 12 (2017) 034019 It is possible to estimate an IRF for the CCF that reflects the CCF found with the ECCF approach. Such a function could represent an accurate physical description of the carbon cycle response to the warming by non-CO 2 forcers and could avoid problems with the LFA approach presented here. In section 3 of the supplementary material we elaborate on this approach. Recently, Gasser et al (2016) also published a discussion paper on such an approach.

Redistribution of carbon due to non-CO 2 climate forcers
A key conceptual difference between the LFA and ECCF approaches to the CCF is that, with the LFA, the carbon added to the atmosphere is external to the linked atmosphere-biosphere-ocean system; with the ECCF, it is instead an effect of redistribution within the system. This section explores the dynamics of this redistribution following a non-CO 2 emissions pulse.
For emission pulses of all forcers the induced temperature response causes initially a flux of carbon into the atmosphere from the biosphere due to increased rates of decomposition and respiration (figure 4). The exchange between the atmosphere and the ocean is small because of the balancing of two mechanisms working in different directions, i.e. the temperature dependence of the inorganic carbon chemistry of the surface water and the increase in partial pressure of the atmosphere due to the atmospheric CO 2 increase caused by the net biosphere release of carbon.
After a number of years, depending on the atmospheric adjustment time of the climate forcer, the temperature perturbation caused by the forcing of the non-CO 2 forcer peaks and ceases (figure 2), which in turn leads to that the perturbation in all three carbon reservoirs slowly relaxes back to its unperturbed state (see figure 4).

Effects of climate carbon feedbacks on relative metric values
Our estimates of GWP and GTP give similar, but not identical, values to corresponding ones in AR5 (Myhre et al 2013). There are several reasons why we do not get an exact match to the values presented in AR5. We use a scenario with varying background concentration (based on the emission-driven RCP 4.5), while the AR5 uses a constant background. Further, we use a CCCM to estimate metric values, while AR5 uses an approach based on an impulse response function. Furthermore, we do not include the indirect effects of N 2 O emissions on its own atmospheric lifetime and on the atmospheric lifetime of CH 4 (Prather and Hsu 2010); this contributes to making the N 2 O metric values higher in this study than in AR5 where these effects are considered (Myhre et al 2013). Finally, the From table 1 it is clear that the emission metric values depend on if and how the CCF is included for non-CO 2 forcers. As expected, the metric values are lowest when the CCF is excluded for these forcers altogether, since excluding it means leaving out a positive effect on the radiative forcing and temperature change.
On short time scales (such as a 20 yr time horizon), GWP and GTP are slightly higher with the ECCF than with the LFA approach. On long time scales (GWP and GTP with a 500 yr time horizon), the results are the opposite, i.e. the LFA approach generates higher metric values than the ECCF approach because the LFA approach gives a greater AGTP and AGWP than with ECCF after a certain time horizon, see section 4.1. In general, the difference in metric values between the two approaches is greater for GTP than GWP, reaching an order of magnitude  for the short-lived forcers for GTP, for the 500 yr time horizon. This is because GWP is an integrated metric, while GTP assesses the climate effect at a certain point in time (thus disregarding everything before that). After 500 yr, the temperature signal (AGTP) from a short-lived climate forcer is virtually gone using the ECCF approach, while it has a clear positive temperature signal with LFA, causing a large relative difference between the approaches (see figures 2 and 3). However, for GWP, which integrates all past radiative forcing impacts up to the end year, the ECCF's larger CCF signal during the initial years balances to a large extent the weaker signal in the long run. Neither GTP 500 nor GWP 500 is presented in AR5 (Myhre et al 2013), a decision taken, at least in part, due to the uncertainty in long-run climate consequences of emission pulses occurring in the nearterm. However, GTP 500 can be a relevant metric for assessing long-term, and close to irreversible, climate impacts. For a 100 yr time horizon, the GWP metric values are higher with ECCF than with LFA for all forcers. For GTP, the results are mixed. The GTP metric values are higher with LFA approach than with ECCF for CH 4 and BC, while the opposite holds for the long-lived greenhouse gases (N 2 O and SF 6 ).
The metric values are sensitive to the choice of parameter values in the model. For example, increasing or decreasing the climate sensitivity value used in the model has a large impact on the absolute metric values, but a much smaller effect on relative ones. This has been shown by Karstensen et al (2015) to hold when not considering CCF. There is no reason that this general conclusion would not also hold when including CCF. In the sensitivity analysis presented in SM 2, we focus on the sensitivity with respect to Q 10 (the temperature dependence of the rates of decomposition and respiration) and b (the fertilization factor) using the ECCF approach. These are two of the most critical parameters in the carbon cycle model for its response to emissions and are directly relevant to various CO 2 -and temperature-induced feedbacks analyzed in this study. Other factors, such as NPP, preindustrial carbon content of the various carbon reservoirs, and the decomposition or respiration rates in the various reservoirs, are of course important for the general functioning of the carbon cycle model, but less directly involved in the feedback mechanisms (Bodman et al 2013). We vary Q 10 and b simultaneously in order to keep a good fit to the observed historical atmospheric CO 2 concentration (see SM 2) and estimate the sensitivity of the metric values. We find that the GWP and GTP metric values, using the ECCF approach, are relatively robust to changes in Q 10 (1.5, 2, or 2.5) and b (0.47, 0.55, or 0.62). For most relative emission metric values the changes are less than 5%, but they reach 15% in the case of GTP for a 100 yr time horizon, while absolute metric values are more sensitive.

Conclusions
The two different approaches to including the CCF for non-CO 2 forcers give different emission metric values. The differences between the metric values obtained using the LFA approach and the ECCF approach tend to be larger for GTP than for GWP for most time horizons.
Further, in the short run, somewhat higher metric values for both GWP and GTP are obtained using the ECCF approach compared to the LFA approach because the initial CCF is stronger with the ECCF approach than with the LFA approach. However, with the ECCF approach, the elevated atmospheric CO 2 will eventually relax back to zero, while this is not the case for the LFA approach. This causes both GTP and GWP metric values to be higher with the LFA than with the ECCF approach after certain time horizons, which depend on the atmospheric adjustment times of the non-CO 2 forcers. For a 100 yr time horizon the results are mixed: for GWP the ECCF approach yields higher metric values than the LFA for all forcers, while for GTP the LFA approach yields higher metric values for BC and CH 4 , but for N 2 O and SF 6 the ECCF yields higher values.
The LFA approach treats the warming induced by the non-CO 2 forcers as if it induces extra CO 2 emissions into the combined atmosphere-biosphereocean system that with time are distributed among the carbon reservoirs similarly to a pulse emission of fossil CO 2 . Hence, use of the LFA approach will result in that a fraction of the induced CO 2 emission will remain in the atmosphere basically forever. The ECCF, on the other hand, captures the CCF in a physically consistent way as a redistribution of carbon within the atmosphere-biosphere-ocean system.
Although the LFA approach as used in IPCC AR5 has clear shortcomings for long time horizons it works reasonably well for time horizons up to~100 (~200) years for GTP (GWP). This is perhaps to be expected since the feedback factor used in the LFA approach is estimated from a climate scenario that follows a certain pathway of over a period of about 100 yr (Arora et al 2013).
Uncertainties and possible limitations of the LFA approach for time horizons beyond 100 yr were acknowledged in IPCC AR5 (Myhre et al 2013), and no metric values for time horizons beyond 100 years were presented. Hence, given the large uncertainties in the size and the dynamics of carbon cycle feedbacks, the LFA approach, as used in IPCC AR5, gives decent estimates of the carbon cycle impact of non-CO 2 greenhouse gases for time horizons limited to about a century.
However, the use of an approximate method like the LFA approach, as used in IPCC AR5, draws attention to the issue of simplicity and transparency versus accuracy and comprehensiveness when calculating emission metric values. How far simplicity can Environ. Res. Lett. 12 (2017) 034019 be stretched at the expense of comprehensiveness is up to the judgment of the scientists involved and likely depends on the context in which the metric is to be used. If and how carbon cycle feedbacks and other feedbacks within the climate system (Shindell et al 2009, Collins et al 2010, Arneth et al 2010 should be included in emission metrics is likely one of the key research issues for the development of refined emission metrics leading up to the next assessment report of the IPCC.