The albedo at Earth's surface helps to govern the amount of solar energy absorbed by the Earth system and is thus a relevant physical property shaping weather and climate (Cess, 1978; Hansen et al., 1984; Pielke Sr. et al., 1998). On average, Earth reflects about 30 % of the energy it receives from the sun, of which about 13 % may be attributed to the surface albedo (Stephens et al., 2015; Donohoe and Battisti, 2011). In recent years it has become the subject of increasing research interest amongst the scientific community, as measures to increase Earth's surface albedo are increasingly viewed as an integral component of climate change mitigation and adaptation, both on (Seneviratne et al., 2018) and off (Field et al., 2018; Kravitz et al., 2018) the land. Surface albedo modifications associated with large-scale carbon dioxide removal (CDR) like re-/afforestation can detract from the effectiveness of such mitigation strategies (Boysen et al., 2016), given that such modifications generally serve to increase Earth's solar radiation budget, resulting in warming. Like emissions of GHGs and aerosols, perturbations to the planetary albedo via perturbations to the surface albedo represent true external forcings of the climate system and can be measured in terms of changes to Earth's radiative balance – or radiative forcings (Houghton et al., 1995). The radiative forcing (RF) concept provides a first-order means to compare surface albedo changes (henceforth Δα) to other perturbation types, thus enabling a more comprehensive evaluation of human activities altering Earth's surface (Houghton et al., 1995; Pielke Sr. et al., 2002).

Radiative forcing is a standard measure of the effects of various emissions or perturbations on climate and can be used to compare the effect of changes between any two points in time. It is a backward-looking measure accounting for the impact up to the given point and does not express the actual temperature response to the perturbation. To enable aggregation of emissions of different gases to a common scale, the concept of CO2-equivalent emissions is commonly used in assessments, decision making, and policy frameworks. While initially introduced to illustrate the difficulties related to comparing the climate impacts of different gases, the field of emission metrics – i.e., the methods to convert non-CO2 radiative constituents into their CO2-equivalent effects – has evolved and presently includes a suite of alternative formulations, including the global warming potential (GWP) adopted by the UNFCCC (O'Neill, 2000; Fuglestvedt et al., 2003; Fuglestvedt et al., 2010). Today, CO2-equivalency metrics form an integral part of UNFCC emission reporting and climate agreements (e.g. the Kyoto Protocol) – in addition to the fields of life cycle assessment (Heijungs and Guineév, 2012) and integrated assessment modeling (O'Neill et al., 2016) – despite much debate around GWP as the metric of choice (Denison et al., 2019). As such, many researchers seek to convert RF from Δα into a CO2-equivalent effect, which is particularly useful in land use forcing research when perturbations to terrestrial carbon cycling often accompany the Δα. Although seemingly straightforward at the surface, the procedure is complicated by two key fundamental differences between Δα and CO2: additional CO2 becomes well-mixed within the atmosphere upon emission, and the resulting atmospheric perturbation persists over millennia and cannot be fully reversed by human interventions. In other words, CO2's RF is both temporally and spatially extensive, with the ensuring climate response being independent of the location of emission, whereas the RF and ensuing climate response following Δα are more localized and can be fully reversed on short timescales.

These challenges have led researchers to adapt a variety of diverging methods for converting albedo change RFs (henceforth RFΔα) into CO2 equivalence. Unlike for conventional GHGs, however, there has been little concerted effort by the climate metric science community to build consensus or formalize a standard methodology for RFΔα (as evidenced by IPCC AR4 and AR5). Here, we review existing CO2-equivalent metrics for Δα and their underlying methods based on the RF concept. To our knowledge this is the first review dedicated to the topic since the first Δα metric surfaced 20 years ago. Herein, we compare and contrast existing metrics both quantitatively and qualitatively, with the main goal of providing added clarity surrounding the context in which the proposed metrics have (de)merits. We start in Sect. 2 by providing an overview of the methods conventionally applied in the climate metric context for estimating radiative forcings following CO2 emissions and surface albedo change. We then present the reviewed Δα metrics in Sect. 3 and systematically evaluate them quantitatively in Sect. 4 and qualitatively in Sect. 5. In Sect. 6 we review and evaluate a relatively new usage of the GWP metric previously unapplied as a Δα metric – termed GWP* – while in Sect. 7 we review the interpretation challenges of a CO2-eq. measure for Δα based on the RF concept. We conclude in Sect. 8 with a discussion about the limitations and uncertainties of the reviewed metrics, while providing recommendations and guidance for future application.

IPCC emission metrics are based on the stratospherically adjusted RF at the tropopause in which the stratosphere is allowed to relax to the thermal steady state (Myhre et al., 2013; IPCC, 2001). Estimates of the stratospheric RF for CO2 (henceforth RFCO2) are derived from atmospheric concentration changes imposed in global radiative transfer models (Myhre et al., 1998; Etminan et al., 2016). For shortwave RFs there is no evidence to suggest that the stratospheric temperature adjusts to a surface albedo change (at least for land use and land cover change, LULCC; Smith et al., 2020; Hansen et al., 2005; Huang et al. 2020), and thus the instantaneous shortwave flux change at the top of the atmosphere (TOA) is typically taken as RFΔα, consistent with Myhre et al. (2013).

One of the major critiques of the instantaneous or stratospherically adjusted RF is that it may be inadequate as a predictor of the climate response (i.e., changes to near-surface air temperatures, precipitation). The climate may respond differently to different perturbation types despite similar RF magnitudes – or in other words – feedbacks are not independent of the perturbation type (Hansen et al., 1997; Joshi et al., 2003). Alternative RF definitions that include tropospheric adjustments (Shine et al., 2003) or even land surface temperature adjustments (Hansen et al., 2005) have been proposed with the argument that such adjustments are more indicative of the type and magnitude of feedbacks underlying the climate response (Sherwood et al., 2015; Myhre et al., 2013). These alternatives – referred to as “effective radiative forcings (ERF)” – may be preferred when they differ notably from the instantaneous or stratospherically adjusted RF, in which case their use might be preferred in metric calculations. Alternatively, climate “efficacies” can be applied to adjust instantaneous or stratospherically adjusted RF – where efficacy is defined as the temperature response to some perturbation type relative to that of CO2. The implications of applying efficacies for spatially heterogenous perturbations like Δα are discussed further in Sect. 7.

Over the past 20 years, a variety of metrics and their permutations have been employed to express RFΔα as CO2 equivalence, as evidenced from the 27 studies included in this review (Table 1).

Chiefly differentiating the methods behind the metrics shown in Table 1 – described henceforth – is how time is represented with respect to both the Δα and the reference gas (i.e., CO2) perturbations. Among the most common approaches is to relate RFΔα to the RF following a CO2 emission imposed on some atmospheric CO2 concentration background, but with a fraction of the emission instantaneously removed by Earth's ocean and terrestrial CO2 sinks by an amount defined by 1 minus the so-called “airborne fraction” (AF) – or the growth in atmospheric CO2 relative to anthropogenic CO2 emissions (Forster et al., 2007).

This method – or the “emissions equivalent of shortwave forcing (EESF)” – was first introduced by Betts (2000) and may be expressed (in kgCO2-eq.m-2) as 6EESF=RFΔαkCO2AEAF, where RFΔα is the local annual mean instantaneous RF from a monthly Δα scenario (in Wm-2), kCO2 is the global mean radiative efficiency of CO2 (e.g., Eq. ; in Wm-2kg-1), AE is Earth's surface area (5.1 × 1014 m2), and AF is the airborne fraction. Because AF appears in the denominator in Eq. (), the CO2-equivalent estimate will be highly sensitive to the choice of AF. Figure 1 plots AF since 1959 which, as can be seen, can fluctuate considerably over short time periods, ranging from a high of 0.81 in 1987 to a low of 0.20 in 1992.

More importantly, use of AF in Eq. () means that time-dependent atmospheric CO2 removal processes following emissions are not explicitly represented. However, using the AF may be justifiable in some contexts – such as when Δα has no time dependency (on inter-annual scales). For example, the pioneering study by Betts (2000) – to which almost all CO2-eq. literature for Δα may be traced (Table 1) – made use of AF when estimating CO2 equivalence of RFΔα because the research objective was to compare an albedo contrast between a fully grown forest and a cropland (i.e, Δα) to the stock of CO2 in the forest – a stock that had been assumed to accumulate over 80 years, which is the approximate time frame over which Earth's CO2 sinks function to remove atmospheric CO2 to a level conveniently represented by the chosen AF. Had a transient or interannual Δα scenario been modeled, however, applying the EESF method at each time step of the scenario would have severely overestimated CO2-equivalent emissions.

For this reason, Bright et al. (2016) argued that for time-dependent Δα scenarios (i.e., when Δα evolves over interannual timescales), the time dependency of CO2 removal processes (atmospheric decay) following emissions should be taken explicitly into account when estimating the effect characterized in terms of CO2-equivalent emissions (or removals), thus proposing an alternate metric termed “time-dependent emissions equivalence” – or TDEE: 7TDEE=AE-1kCO2-1YCO2-1RFΔα∗, where TDEE is a column vector of CO2-equivalent emission (or removal) pulses (i.e., one-offs) with length defined by the number of time steps (e.g., years) included in the Δα time series (in kgCO2-eq.m-2yr-1), RFΔα∗ is a column vector of the local annual mean instantaneous RFΔα (in Wm-2) corresponding to the Δα time series (or RFΔα(t)), and YCO2 is a lower triangular matrix with column (row) elements being the atmospheric CO2 fraction decreasing (increasing) with time (i.e., yCO2(t)). The elements in vector TDEE thus give the CO2-equivalent series of emission (or removal) pulses in time yielding the instantaneous RFΔα time profile (RFΔα(t)) corresponding to the temporally explicit Δα scenario (Δα(t)). Summing all elements in TDEE (i.e., ∑TDEE) gives a measure of the accumulated CO2-eq. emissions (removals) over time. The TDEE approach is conceptually similar to the CO2-forcing-equivalence (CO2-fe) approach (Jenkins et al., 2018; Zickfeld et al., 2009) building on the notion of a “forcing equivalent” index (Wigley, 1998).

Time-dependent metrics like the well-known global warming potential (GWP) (Shine et al., 1990; Rogers and Stephens, 1988) have also been applied to characterize Δα(t), which accumulates RFΔα(t) over time (temporally discretized) up to some policy or metric time horizon (TH), which is then normalized to the temporally accumulated radiative forcing following a unit pulse CO2 emission over the same TH: 8GWPΔα(TH)=∑0t=THRFΔα(t)AEkCO2∑0t=THyCO2(t), where TH is the temporal accumulation or metric time horizon. Because it is a cumulative measure, studies making use of GWP often divide by the number of time steps (TH) to approximate an annual CO2 flux (e.g., Carrer et al., 2018). The result of Eq. () can be interpreted as an equivalent pulse of CO2 (in kgCO2-eq.m-2) at t = 0 giving the same time-integrated RF at TH as that following a 1 kg pulse of CO2.

The metrics presented in Sect. 3 are systematically compared quantitatively henceforth by deriving them for a set of common cases, starting first with the metrics applied to yield a series of CO2-eq. pulse emissions (or removals) in time. For all calculations, the assumed climate “efficacy” (Hansen et al., 2005) – or the global climate sensitivity of RFΔα relative to RFCO2 – is 1.

The reviewed metrics and underlying methods for converting shortwave radiative forcings from Δα (i.e., RFΔα) into their CO2-equivalent effects – summarized in Table 3 – can primarily be differentiated by the physical interpretation of the derived measure and by whether or not a time dependency (inter-annual) for Δα was defined a priori.

For cases when Δα's time dependency is not known or defined a priori, the EESF measure is the only applicable measure of those reviewed, although it was shown here to be highly sensitive to the value chosen to represent CO2's airborne fraction (AF; Fig. 5) – a key input variable taking on a wide range of values depending on how it was defined. In general, when AF is defined according to historical accounts of global carbon cycling, its value is prone to large fluctuations across short timescales (Fig. 1) due to natural variability in the global carbon cycle (Ciais et al., 2013). When defined as the fraction of CO2 remaining in the atmosphere following a pulse emission – as would be obtained from a simple carbon cycle model (i.e., a CO2 impulse response function) – its value depends on the time horizon chosen and underlying model representation of atmospheric removal processes (i.e., time constants). Use of the latter definition of AF affixes a forward-looking time dependency to the EESF measure, which is inconsistent with the definition of Δα and adds subjectivity (i.e., the choice in TH). Basing the AF on global carbon budget reconstructions would at least preserve some element of objectivity, although given the measure's sensitivity to AF it would be prudent to compute the measure for a range of AFs (i.e., as constrained by the observational record) in an effort to boost transparency. Forgoing the use of an AF altogether would eliminate all subjectivity, as has been suggested elsewhere (Bright et al., 2016).

For cases involving a time-dependent Δα scenario that is defined a priori, forward-looking measures are identified whose methodological differences give rise to different interpretations of CO2 equivalence (Table 3). For example, the GWP measure can be interpreted as CO2-eq. pulse emitted at present yielding the accumulated radiative forcing of the Δα scenario at TH years into the future. GWP has merit from the standpoint that it is easy to apply and conforms to established reporting methods, accounting standards, or decision-support tools such as life cycle assessment (e.g., Cherubini et al., 2012; Sieber et al., 2020). Scientifically, however, there are important limitations to GWP when the forcing (i.e., Δα) is short-lived or temporary (Allen et al., 2016; Pierrehumbert, 2014; Allen et al., 2018; Lynch et al., 2020; Cain et al., 2019). The TDEE measure, on the other hand, can be interpreted as a complete time series of CO2 emission pulses (i.e., a complete emission scenario) yielding the instantaneous radiative forcing of the Δα scenario. When summed to TH, the latter (as ΣTDEE) provides a clearer indication of the radiative impact incurred up to TH, thus having greater scientific merit as an indicator of future warming.

The permutations of GWP and EESF applied to arrive at a time series of CO2-eq. pulses – GWP(TH) / TH and EESF / TH – have little merit on the grounds that the resulting series does not reproduce RFΔα(t) (Fig. 3d). The TDEE approach was proposed to overcome this limitation, although it should be stressed that – like GWP(TH) / TH – its derivation requires that a time-dependent Δα scenario be defined a priori, which adds uncertainty and may not always be possible.

It is well known that the conventional usage of GWP does not adequately capture different behaviors of short-and long-lived climate pollutants or their impact on global mean surface temperatures (Pierrehumbert, 2014; Allen et al., 2016; Shine et al., 2003; Fuglestvedt et al., 2010). Some have proposed an alternative usage of GWP – denoted GWP* (Allen et al., 2018) – which overcomes this problem by equating an increase in the emission rate of a short-lived climate pollutant (or radiative forcing agent) with a one-off “pulse” CO2 emission. GWP* recognizes that a pulse emission of CO2 and a sudden step change in the sustained rate of emission of a short-lived climate pollutant (SLCP) both give near-constant radiative forcing. Or, alternately, that a progressive linear increase (or decrease) in the rate of an SLCP emission is approximately equivalent to a sustained step change in the emission rate of CO2. As such, GWP* is considered to have greater “environmental integrity” than the conventional GWP metric (Allen et al., 2018), as it is better fit to serve the purpose of a measure of progress towards a global temperature-oriented climate goal (i.e., limit warming to “well below 2 ∘C”). Compared to conventional GWP, cumulative CO2-eq. emissions based on GWP* provide a clearer indication of future warming, and future CO2-eq. emission rates better indicate future warming rates. GWP* thus better relates all climate pollutants in a common cumulative emission (or emission budget) framework, making it easier to formulate mitigation strategies that provide a more accurate indication of progress towards climate stabilization.

Among one of the more distinguishing features of GWP* is that, when applied to radiative forcings rather than pulse emissions, information about the time dependency of the perturbation (i.e., the lifetimes of “climate pollutants” or forcing agents) is not required (Lee et al., 2021; Cain et al., 2019; Allen et al., 2018), making it an attractive alternative to EESF. In other words, a GWP estimate of the “short-lived” forcing agent under scope – which requires such information to be known or defined a priori – is unnecessary in its calculation. Only the rate of change of the forcing is required, scaled by TH / AGWP(TH)CO2 as follows (Lee et al., 2021; Allen et al., 2018): 9ECO2-eq.*=THAGWP(TH)CO2ΔRFΔαΔt, where TH is the time horizon, AGWP(TH)CO2 is CO2's AGWP at the same TH (i.e., 9.2 × 10-14 Wyrm-2kg-1 when TH = 100 years), Δt is the time step change, and ΔRFΔα is the time differential of RFΔα(t) over the step change. ECO2-eq.* thus represents the CO2-eq. emission pulse for the step change and will equal EESF when the AF (in Eq. 6 denominator) corresponds to the mean of yCO2(t) over the TH (i.e., TH-1∫t=0t=THyCO2(t)dt). A TH of 100 years is typically applied in Eq. (), which is justified when it exceeds the lifetime of the SLCP or when the time-integrated radiative forcing of the forcing agent (i.e, Δα) becomes a constant at this timescale, since the time-integrated radiative forcing of the reference gas (i.e., AGWPCO2) increases linearly with TH. In other words, the TH dependence cancels out in the calculation of CO2-eq.*, rendering GWP* insensitive to the choice in TH, which contrasts with the conventional GWP (Allen et al., 2016, 2018). The step change Δt for which ΔRF is calculated is typically taken as 20 years to “reduce the volatility of CO2-eq.* emissions in response to variations in SLCP emission rates” (Allen et al. 2018; Cain et al. 2019), although comprehensive investigations into the appropriateness of this choice when applied to a wide variety of time-varying SLCP emission (radiative forcing) scenarios are lacking. We note that more recent works (Cain et al., 2019; Lee et al., 2021) employed weighting-based modifications to Eq. () in an effort to better account for the longer-term temperature equilibration to past forcing changes: 10ECO2-eq.*=(1-s)THAGWP(TH)CO2ΔRFΔαΔt+sRFΔα‾AGWP(TH)CO2, where s is a factor weighting the delayed response by global mean temperature to the radiative forcing history, represented here (following Lee et al., 2021) as the mean forcing over the period Δt – or RFΔα‾. Note that s is analogous to the “α” term seen in Eq. () of Lee et al. (2021) and that the factor 1-s is analogous to the rate contribution weight denoted as “r” in Eq. (S1) of Cain et al. (2019). Like the choice of Δt, however, few investigations have been carried out to assess the appropriateness of weight sizes applied in Eq. () for different SLCP emission (radiative forcing) scenarios having widely varying temporal dynamics.

We explore the sensitivity of the choice in both Δt and s on CO2-eq. emissions (removals) estimated with the modified GWP* approach (Eq. ) for three hypothetical local RFΔα(t) scenarios presented in Fig. 7. The first scenario – or Scenario A – is identical to the forest management scenario plotted in Fig. 6 and extended by 20 years, which is characterized by a negative RF in the short term and positive RF in the longer term (Fig. 7a, blue). In the second scenario, or Scenario B, RFΔα(t) corresponds to a linearly increasing Δα trend which is loosely analogous to incremental deforestation occurring on a regional scale (Fig. 7a, red). The third scenario, or Scenario C, resembles a permanent albedo decrease, analogous to urban expansion into a cropland (Fig. 7a, yellow).

We then reconstruct the global mean temperature response (ΔT) of the CO2-eq.* emission (removal) scenario under varying assumptions surrounding the size of Δt and the weighting factor s (shown in Fig. 7b legend), which is then compared to the RFΔα-based ΔT and the ΔT reconstructed using the CO2-eq. emission (removal) scenario based on the TDEE approach (Fig. 7b–d). For Scenario A (Fig. 7b), we find no obvious parameter set that outperforms any other in terms of the faithfulness by which the CO2-eq.* emission (removal) scenario reproduces ΔT across the full time horizon. There appears to be a trade-off between the near- and long-term reproduction accuracy of different parameter sets: a 20-year Δt with no weighting (Fig. 7b, solid green curve) better reproduces the ΔT response seen in the short term (≲ 20 years) as well as the ΔT seen at the end of the scenario time horizon (year 100), whereas a 10-year Δt with no weighting (Fig. 7b, solid purple curve) better reproduces the ΔT response seen in the longer term (from ∼ 60–90 years). An increase in the weighting factor s serves to dampen the amplitude between the maximum cooling and warming seen in the short and longer term, respectively (Fig. 7b, spread between like-colored curves). As for Scenario B representing a linear increase in RF, the reconstructed ΔT is insensitive to Δt and thus only results for a 1-year Δt are computed and presented in Fig. 7c. Although a weighting factor of 0.2 is most accurate for the first ∼ 50 years, a weight of 0.1 gives a more faithful ΔT reproduction for the full time period. As for Scenario C representing a step change in RF (Fig. 7d), again we find no obvious parameter set that yields a faithful ΔT reproduction across the full time period. High s weights overpredict ΔT in the medium term but reproduce ΔT best in the longer term (Fig. 7d, solid curves), while a Δt larger than 10 years appears to result in large underpredictions in the short term (i.e., ≲ 20 years; Fig. 7d, green curves).

Unsurprisingly, ΔT reconstructed using the CO2-eq. emission (removal) scenario estimated with the TDEE approach exactly reproduces the RF-based ΔT, and thus these two estimates are plotted jointly as a single curve in Fig. 7b–d (wider solid curves). Thus, when future surface albedo changes are defined a priori (i.e., when the Δα perturbation “lifetime” is known or estimated), a CO2-eq. emission (removal) time series quantified with TDEE is far superior to one based on GWP* irrespective of the choice in Δt or weight sizes applied, making it the better CO2-eq. measure of progress towards global temperature stabilization.

The climate (i.e., temperature) response to a Δα perturbation either isolated (e.g., Jacobson and Ten Hoeve, 2012) or as part of LULCC (e.g., Pongratz et al., 2010; Betts, 2001) is highly heterogeneous in space, the magnitude and extent of which depends on its location (Brovkin et al., 2013; de Noblet-Ducoudré et al., 2012). This is because the response pattern of climate feedbacks has a strong spatial dependency – feedbacks are generally larger at higher latitudes due to higher energy budget sensitivity to clouds, water vapor, and surface albedo, which generally increases the effectiveness of RF in those regions (Shindell et al., 2015). This is in contrast to CO2 emissions where both RF and the temperature response are more homogeneous in space (Hansen and Nazarenko, 2004; Hansen et al., 2005; Myhre et al., 2013). This has caused some researchers to question the utility of a CO2-eq. measure for Δα (Jones et al., 2013) or encouraged others to look for solutions or further methodological refinements. For instance, some researchers (e.g., Cherubini et al., 2012; Zhao and Jackson, 2014) have applied climate efficacies – or the climate sensitivity of a forcing agent relative to CO2 (Joshi et al., 2003; Hansen et al., 2005) – to adjust RFΔα prior to the CO2-eq. calculation. Such adjustments recognize that the temperature response to RF depends on the geographic location, extent, and type of underlying forcing associated with the Δα (e.g., land use and land cover change (LULCC), white-roofing), which can be co-associated with other perturbations (Table 4) like those arising from changes to vegetative physical properties (for the LULCC case) which can modify the partitioning of turbulent heat fluxes above and beyond the purely radiatively driven change (Davin et al., 2007; Bright et al., 2017).

Using a climate efficacy to adjust RFΔα, however, is not without its drawbacks. A first and obvious drawback is that efficacies are climate model dependent (Hansen et al., 2005; Smith et al., 2020; Richardson et al., 2019). Climate models vary in their underlying physics, which is evidenced by the large spread in CO2's climate sensitivity across CMIP6 models (Meehl et al., 2020; Zelinka et al., 2020). A second drawback is that climate sensitivities for certain forcing agents like Δα are tied to experiments that differ largely in the way forcings have been imposed in time and space. Both drawbacks contribute to large uncertainties in the choice of efficacy for Δα. The latter drawback is especially problematic since the Δα perturbation is often accompanied by perturbations to other surface properties and fluxes (Table 4) having large spatial and temporal dependencies. The turbulent heat flux perturbations that accompany a net radiative flux change at the surface affect atmospheric temperature and humidity profiles (Bala et al., 2008; Modak et al., 2016; Schmidt et al., 2012; Kravitz et al., 2013), causing the atmosphere to adjust to a new state, resulting in a net radiative flux change at TOA that extends beyond the instantaneous shortwave radiative flux change (i.e., RFΔα).

For example, the efficacy of LULCC forcing across the six studies reviewed by Bright et al. (2015) ranged from 0.5 to 1.02 owing to differences in model set-up (e.g., fixed SST vs. slab vs. dynamic ocean), differences in the spatial extent and magnitude of the imposed LULCC forcing (e.g., historical transient vs. idealized time slice), and the LULCC definition (i.e., the type of LULCC that was included in the study such as only afforestation/deforestation vs. all LULCC). Even when controlling for differences in experimental design (e.g., CMIP protocols), the climate efficacy of historical LULCC has been found to vary considerably in both sign and magnitude (see Fig. 8, Richardson et al. 2019), which is more likely attributed to the larger spread in effective radiative forcing (ERF) for LULCC than for CO2. For instance, Smith et al. (2020) report a standard deviation of 6 % in the ERF of CO2 (4× abrupt) across 17 GCMs and Earth system models (ESMs) participating in RFMIP in contrast to 175 % for LULCC, although it should be kept in mind that the ERF is weak for LULCC and thus relative differences become large.

An additional drawback and source of uncertainty underlying efficacies is related to differences in their definition. Differences in definition can stem from either different definitions of RF itself or differences in the definition of the temperature response per unit RF (Richardson et al., 2019; Hansen et al., 2005). Regarding the latter, most base the temperature response for CO2 on the equilibrium climate sensitivity (ECS) for a CO2 doubling, although good arguments have been made for using the transient climate response (TCR) instead, particularly for short-lived forcing agents (Marvel et al., 2016; Shindell, 2014). The temperature response for the forcing agent of interest is rarely taken as the equilibrium response although there are some exceptions (e.g. “Eα” in Richardson et al., 2019, which is based on climate feedback parameters obtained from ordinary least-square regressions). Efficacies are also sensitive to the definition of RF (Richardson et al., 2019; Hansen et al., 2005). For example, the efficacy of sulfate forcing (5 × SO4) has recently been shown to vary from 0.94 to 2.97 depending on whether RF is based on the net radiative flux change at TOA from fixed SST experiments or the instantaneous shortwave flux change at the tropopause (Richardson et al., 2019).

Ideally, CO2-eq. metrics based on the RF concept should be based on an RF definition yielding efficacies approaching unity for a broad range of forcing types. Although there is currently no consensus here, strong arguments have been made for RF definitions based on the net radiative flux change at TOA resulting from fixed SST experiments with GCMs and ESMs (i.e., “Fs” in Hansen et al. 2005; “ERFSST” in Richardson et al. 2019), since such definitions yield efficacies approaching unity for a broad range of forcing types. However, for most Δα metric practitioners it is not feasible to quantify atmospheric adjustments and hence the ERF. Efficacies compatible with RFΔα (instantaneous ΔSW at TOA) could be the more feasible option for metric calculations, but broad consensus surrounding appropriate efficacy values for different forcing types associated with the Δα perturbation would need to be established first (Table 4). This is especially true for forcings involving changes to the biophysical properties of vegetation – such as LULCC, forestry, etc. – since these are constructs representing a seemingly myriad combination of perturbations acting on non-radiative controls (i.e., Δra and Δrs) of the surface energy balance. Building consensus for efficacies applicable to geoengineering-type forcings where the only physical property perturbed is the surface albedo (e.g., white roofing, sea ice brightening) would be less challenging since the confounding perturbations to Δra and Δrs and hence to the partitioning of the turbulent heat fluxes are removed. Nevertheless, irrespective of whether broad scientific consensus can be reached surrounding efficacies suitable for Δα metrics, additional responsibility would always be imposed on the metric practitioner to ensure that the chosen efficacy aligns with the forcing type underlying the RFΔα.