On the potential for alternative greenhouse gas equivalence metrics to influence sectoral mitigation patterns

We consider four types of equivalence metrics: integrated RF, integrated temperature change, end-point RF (derived from Shine et al 2005 and Peters et al 2011), and end-point temperature. We note that the integrated RF metric is the GWP (Shine et al 2005), the integrated temperature metric is the iGTP (Peters et al 2011, Azar and Johansson 2012), and the end-point temperature metric is the GTP (Shine et al 2005).

In constructing an end-point RF metric to describe the relative impact of gases in terms of RF at a given time horizon, the generic formula to describe the fraction of a component in the atmosphere at time t is:

$$\begin{eqnarray} &&{F}_{i}(t)=\sum _{k=0}^{K}{a}_{i,k}\exp (-t/{\tau }_{i,k}) \end{eqnarray} \tag{ 1 }$$

(Peters et al 2011). For CO₂ this formula can be populated with parameters derived from the Bern carbon cycle model, (i.e., τ₀ = ∞ in equation (1)) (Shine et al 2005, Joos et al 1996):

$$\begin{eqnarray} &&{F}_{{\mathrm{CO}}_{2}}(t)={a}_{0}+\sum _{k=1}^{4}{a}_{k}\exp (-t/{\tau }_{k}) \end{eqnarray} \tag{ 2 }$$

where coefficients a_k and the decay times τ_k are Bern constants (table 1). Parameter values for these impact response functions, which vary as atmospheric concentrations of GHGs and global mean surface temperature change, are an inherent uncertainty implicit in equivalence metrics (Joos et al 2012). Building on the work of Peters et al (2011) and Shine et al (2005) in developing an end-point RF metric, this paper uses values outlined in Shine et al (2005). For other climate forcers of interest to our discussion a single time decay constant (i.e., K = 1,a₁ = 1 in equation (1)) is adequate, such that:

$$\begin{eqnarray} &&{F}_{G}(t)=\exp (-t/{\tau }_{G}) \end{eqnarray} \tag{ 3 }$$

describes the fraction of a pulse emission of gas G with decay time constant τ_G in the atmosphere at time t (Peters et al 2011, Shine et al 2005). While over the period of our analysis background concentration of gas G or CO₂ change, altering the radiative efficiencies and lifetimes of the forcers (Reisinger et al 2011), we adopt the assumption of Peters et al (2011) that RF develops linearly in proportion to present radiative efficiency values for relatively small perturbations in total concentration. Through the analysis we used parameter values assuming a single fixed background concentration of gas G and CO₂.

An absolute end-point measure at time t of RF of a pulse emission of gas i is estimated as:

$$\begin{eqnarray} &&A{\mathrm{epGWP}}_{i}(t)={A}_{i}\times {F}_{i}(t) \end{eqnarray} \tag{ 4 }$$

where F_i(t) for gas i is defined above and A_i represents the radiative efficiency for gas i (Shine et al 2005). Following the naming convention of Peters et al (2011), who called their integrated temperature metric 'iGTP,' we name this end-point RF metric 'epGWP,' since, like GWP, it is an RF metric. Integrated RF over a given time horizon can be calculated as:

$$\begin{eqnarray} &&A{\mathrm{GWP}}_{i}(T)=\mathrm{i}A{\mathrm{epGWP}}_{i}(T)=\int \nolimits _{0}^{T}A{\mathrm{epGEP}}_{i}(t)\hspace{0.167em} \mathrm{d}t. \end{eqnarray} \tag{ 5 }$$

An end-point temperature measure can be characterized by the convolution of equation (5) and a temperature impulse response function (Peters et al 2011, Shine et al 2005). For gas i this can be written:

$$\begin{eqnarray} A{\mathrm{GTP}}_{i}(t)&=&{A}_{i}/C\times \left (\frac{1}{1/\theta -1/{\tau }_{i}}\right )\nonumber\\ &&\times ~(\exp (-t/{\tau }_{i})-\exp (-t/\theta )) \end{eqnarray} \tag{ 6 }$$

where the climate sensitivity parameter for a doubling of CO₂λ is 0.08 K (W m⁻²)⁻¹, heat capacity C is set for a global ocean mixed layer of 100 m depth (4.2 × 10⁸ J K⁻¹ m⁻²), θ is defined as λ∗C with a value of 10.7 years, and τ_i is the lifetime of gas i (Shine et al 2005). It should be noted that the approach to estimating temperature in equation (6) neglects deep ocean interactions, which leads to discrepancies between analytical and simulation temperature values (Shine et al 2005). Various combinations of parameter values have been used to populate this function; again, we use the values used by Shine et al (2005). For CO₂ the absolute GTP can be expressed as a slightly more complex expression,

$$\begin{eqnarray} &&\fl A{\mathrm{GTP}}_{{\mathrm{CO}}_{2}}(t)\nonumber\\ &&=~({A}_{{\mathrm{CO}}_{2}}/C)\times \biggl \lfloor \theta {a}_{0}(1-\exp (-t/\theta ))+\sum _{i=1}^{4}\nonumber\\ &&\times ~\frac{{a}_{i}}{(1/\theta -1/{\tau }_{i})}(\exp (-t/{\tau }_{i})-\exp (-t/\theta ))\biggr \rfloor \end{eqnarray} \tag{ 7 }$$

where A_CO2 is the radiative efficiency of CO₂, and τ_i and a_i are the Bern model parameters defined in table 1. While the analytical GTP derived using impulse response functions is common in policy and literature, studies using climate models have produced alternate GTP values (Shine et al 2005, Fuglestvedt et al 2010, Reisinger et al 2010). The integration of this convolution produces the AiGTP, a metric that in value relative to CO₂ is very similar to the GWP (Azar and Johansson 2012, Peters et al 2011). By convention a metric value for gas i is defined with respect to CO₂, in the form of the ratio of the absolute metric value of gas i to the absolute metric value of carbon dioxide:

$$\begin{eqnarray} &&{\mathrm{Metric}}_{i}(t)=\frac{A{\mathrm{Metric}}_{i}(t)}{A{\mathrm{Metric}}_{{\mathrm{CO}}_{2}}(t)}. \end{eqnarray} \tag{ 8 }$$

We utilize each metric in time sensitive (TS) and conventional static time-insensitive fashion. TS metrics are defined with respect to a fixed future end-point, such that their values change with time. In this application 2100 was used as the end-point of interest for all four metrics. For the static metric scheme, we calculate values for time horizons of 20, 50, and 100 years for all four metrics. This yields a total of 16 metric schemes (figure 2). Values in the analysis deviate slightly from IPCC because they were selected to align with those used in Shine et al (2005), which produced nearly identical analytical metric values for the GWP and GTP. These parameters produce GWP values very close to those in the IPCC Second Assessment Report, which are the values currently used in the Kyoto Protocol.

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To demonstrate the influence that metrics have on the sectoral distribution of emissions, we take the Representative Concentration Pathway (RCP) 8.5 as a 'business as usual' emissions pathway and apply metric-informed mitigation against that business as usual emissions profile. RCPs describe plausible, representative emissions trajectories for the 21st century. RCP 8.5 is the high emissions scenario of the coordinated scenario generating process undertaken by the integrated assessment modeling community in support of the IPCC Fifth Assessment Report (Moss et al 2010). Each RCP includes emissions of greenhouse gases including CO₂,CH₄,N₂O, and SF₆ as well as non-greenhouse gas anthropogenic climate forcers (e.g., SO₂, black carbon) from all sectors and regions, and is defined in terms of the end-point increase in RF in the year 2100 relative to the pre-industrial baseline: RCP 8.5, for example, describes an emissions path consistent with a year 2100 RF of 8.5 W m⁻². RCP 8.5 is a product of the Model for Energy Supply Strategy Alternatives and their General Environmental Impact (MESSAGE) (Riahi et al 2007). RCP data used in this paper were obtained from the IIASA online archive (www.iiasa.ac.at/web-apps/tnt/RcpDb/dsd?Action=htmlpage&page=welcome).

2.3.1. Pricing of mitigation efforts.

2.3.2. Matching mitigation opportunities.

2.3.3. CO₂-equivalent pricing of mitigation efforts.

Enkvist et al (2007) present MCAs using a GWP-100 CO₂-equivalence. With an MCA assigned to every gas-specific RCP category, to arrange mitigation efforts according to cost for the 16 metric-informed scenarios, we calculate a non-CO₂-equivalence MCA curve, and then recalculate the non-CO₂-equivalence curve into 16 CO₂-equivalence MCA curves. When the cost curve is translated from GWP-100 to any of the 15 alternative equivalence metrics considered in this study, the marginal costs of abatement of sectors change in absolute and relative terms (e.g., figure 3). Enkvist et al do not disaggregate the global cost curve to produce regional abatement cost estimates, and while our model is structured to incorporate regionally-specific cost estimates, we treat sectors across regions uniformly.

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RCP 8.5 emissions data for the decades 2000–2100 (10 decades) were recalculated in terms of each of the equivalence metrics. This yielded 16 10 × 140 matrices (E_RCP) that expressed RCP 8.5 in CO₂-equivalence terms, separated by region by gas by price level by decade—noting that for the results presented in this paper values were not allowed to vary between regions. For all 16 E_RCP matrices, corresponding 10 × 140 costs of abatement matrices (C) were calculated, where the marginal cost of abatement for each region-gas-sector was reordered in the respective CO₂-equivalence terms. This produced two matrices, each metric-dependent, representing emissions and marginal costs of abatement in the chosen CO₂-equivalence.

Each E_RCP matrix of metric-weighted emissions was then entered into a simple model, designed to simulate decadal emissions growth and mitigation, producing a 10 × 140 emissions matrix (E_MODEL). At t = 1 (2010), no abatement occurred.

Growth at each time t > 1 was calculated by taking the difference of E_RCP emissions at time t and t − 1, so that for all time periods (∀ t∈T,T = 2,3,...,10) and all gas-sector-regions (∀i∈G,G = 1,3,...,140),

$$\begin{eqnarray} &&{E}_{\mathrm{GROWTH}}(t,i)=[{E}_{\mathrm{RCP}}(t,i)-{E}_{\mathrm{RCP}}(t-1,i)]. \end{eqnarray} \tag{ 9 }$$

Mitigation at each time t > 1(E_MIT) was calculated by minimizing the global decadal cost of abatement

$$\begin{eqnarray} &&\sum _{i=1}^{1 4 0}{E}_{\mathrm{ MIT}}(t,i)\times C(t,i) \end{eqnarray} \tag{ 10a }$$

subject to

$$\begin{eqnarray} \sum _{i=1}^{1 4 0}{E}_{\mathrm{ MIT}}(t,i)&=&{r}_{a}\times \sum _{i=1}^{1 4 0}[{E}_{\mathrm{ MODEL}}(t-1,i)\nonumber\\ &&+~{E}_{\mathrm{GROWTH}}(t,i)]. \end{eqnarray} \tag{ 10b }$$

Modeled emissions (E_MODEL) are calculated as:

$$\begin{eqnarray} {E}_{\mathrm{MODEL}}(t,i)&=&[{E}_{\mathrm{MODEL}}(t-1,i)\nonumber\\ &&+~{E}_{\mathrm{GROWTH}}(t,i)]-{E}_{\mathrm{MIT}}(t,i). \end{eqnarray} \tag{ 11 }$$

2.4.1. Rates of mitigation in the mitigation-growth model.

For each metric-informed scenario, modeled emissions (E_MODEL) resulting from an initial 12% decadal rate of abatement were input to the Model for the Assessment of Greenhouse Gas Induced Climate Change (MAGICC), a simple global climate model that incorporates gas-cycles, ice melt, and aerosols (Wigley 2008). Default MAGICC parameters included mild aerosol forcing, a climate sensitivity parameter for a doubling of CO₂ of 3.0 °C, mid-level ice melt (a designation which produces similar results between MAGICC and the main sea-level rise model in AR4 Wigley 2008), and an A1T-MES emissions scenario used for all other non-modeled forcers. Modeled emissions were crafted and input iteratively, varying decadal rates of abatement, until each scenario with E_MODEL CO₂,CH₄,N₂O, and SF₆ values substituted in achieved a forcing of 5.7 W m⁻² above 1765 in 2100. (MAGICC RF output is relative to 1990 levels; all references to RF are based on MAGICC output yet relative to 1765 levels, adjusted using approximate global mean RF in 1990 from Myhre et al (2001) and global mean gas-specific RF from the IIASA database (IIASA).) A1T-MES, a scenario derived from the MESSAGE model like RCP 8.5, included all other forcers encompassing NOx, VOCs, CO, CF4, and several HFCs (Smith 2000). A forcer that is co-emitted with a GHG is not necessarily mitigated at the same time as its respective GHG. Because both scenarios are derived from the same model, the estimated 2000, 2010, and 2020 emissions are very close, and A1T-MES values smoothly merged with the E_MODEL values taken from MESSAGE based RCP 8.5. A1T has been evaluated by MAGICC successfully, as noted in the IPCC TAR. The resulting scenarios are significantly above the pathways required to meet the goal of limiting warming to 2 °C above pre-industrial temperatures with acceptable probability (e.g. Meinshausen et al 2009), and can be interpreted as a moderate to moderate-high emissions case.

MAGICC analysis shows that the metric-informed mitigation paths, though identical in terms of 2100 mean global RF (5.7 W m⁻² above 1765) and nearly identical in temperature rise (3.14–3.21 °C above 1765), have significantly different gas-specific RF (figure 4), varying between 3.8 and 4.9 Wm⁻² for CO₂ in 2100 and between 0.4 and 1.4 W m⁻² for CH₄ in 2100, relative to 1765. The BAU run achieved a mean RF of 8.8 W m⁻² and temperature of 4.64 °C in 2100 relative to 1765.

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We note that metrics primarily affect mitigation of CO₂ and CH₄. N₂O metric values are almost invariant across time horizons, integrations, and choice of environmental impact; the N₂O metric values in table 1 have a mean of 287 with a standard deviation of only 20, in contrast to the CH₄ metric values in table 1 which have a mean of 29 with a standard deviation of 24. SF₆, with inherently larger metric values and deviations, also does not significantly affect total mitigation because it occurs in relatively trivial amounts. However, SF₆,N₂O, and other non-CO₂ non-CH₄ do rise in importance for mitigation for pricing regimes that deprioritize CH₄ relative to the long-lived gases.

Sectoral abatement tendencies highlight the ability of metrics to influence prices in CO₂-equivalence terms and abatement in a world with an ideally fluid emissions market. Trade-offs between CO₂ and CH₄ are particularly obvious. As seen in figure 4, 20-year and TS metrics, which weight the climate effects of methane heavily, led to the largest abatement of methane in both fossil fuel and land use sectors. (See table A.1 for systemic presentation of considered metrics.) The 100-year end-point metrics, in contrast, were among the most effective at encouraging mitigation of fossil fuel CO₂ emissions. TS metrics directed mitigation efforts towards short-lived forcers primarily in later decades, as the 2100 end-point nears.

Metrics that favor abatement of powerful short-lived GHGs such as CH₄ achieve the RF target at lower estimated cost within the constraints of the enforced policy structure, while allowing for relatively greater emissions of long-lived gases like CO₂. The four lowest cost, lowest CO₂ abatement trajectories are associated with integrated 20-year time horizon or evolving end-point metrics (in order of increasing cost: GWP-20, iGTP-20, GWP-TS, iGTP-TS) while the four highest cost, most aggressive CO₂ abatement trajectories are associated with long time horizon end-point metrics (in order of increasing cost: GTP-50, epGWP-50, epGWP-100, GTP-100). GWP-100, the most widely used metric in the current policy regime, falls in the middle of the spectrum. In this discussion cost considers the cost of technology, excluding interactions and flow-on effects. In this analysis, integrated costs associated with each metric must be understood as the product of choice of metric interacting with a predetermined policy structure of fixed decadal mitigation targets; absolute and relative costs associated with each metric could be quite different for policies designed to minimize total costs over the 21st century.

Over the one hundred year time horizon considered in this study, time-insensitive metrics defined over longer time scales tended to emphasize CO₂ mitigation over CH₄ mitigation (noting that the choice of a 5.7 W m⁻² (or 3.14–3.21 °C) in 2100 target constrained the total warming in all cases). This is an unsurprising result: a longer time scale emphasizes the importance of long-lived gases such as carbon dioxide relative to short-lived gases like methane. Equivalence metrics defined on long time scales therefore incentivize actions on long-lived gases rather than the powerful short-lived gases that have strongest influence on the near-term warming rate. This tendency is strongest in end-point metrics, which resulted in the highest global CH₄ contribution to RF through 2100. As the epGWP-100 and GTP-100 value methane relatively less than, for example, the GWP-100 and iGTP-100, the relative abatement cost of a metric-weighted ton of methane increases. In the end-point 100-year metric scenarios, forcing in 2100 from CO₂ was approximately 3.8 W m⁻² and CH₄ was 1.4 W m⁻², while in the integrated 100-year metric scenarios forcing in 2100 from CO₂ was approximately 4.6 W m⁻² from CO₂ and 0.7 W m⁻² from CH₄ (figure 4). In these scenarios, gases that are valued more with respect to carbon dioxide will have lower marginal costs of abatement per CO₂-equivalent emission. Conversely, under the conditions and assumptions in our analysis, metrics with shorter time horizons incentivize mitigation of short-lived species such as methane.

The environmental implications of this trade-off depend on climate policy. For a policy directed at achieving a target RF on a time scale less than the residence time of CO₂ in the atmosphere—in this example, the year 2100—through prescribed near and mid-term mitigation targets, metrics that favor relatively cheap mitigation of short-lived greenhouse gases will produce pathways that are less expensive (and, therefore, potentially easier to achieve) but that allow for higher rates of long-lived GHG emissions, primarily CO₂, throughout the 21st century, resulting in a larger long-term warming commitment. It should be noted for more stringent RF targets (e.g. 2.6 W m⁻²) CO₂ emissions are negative by 2100, somewhat negating the concept of a warming commitment. Other environmental goals are certainly possible, but the concept of the 21st century end-point RF or temperature target is most consistent with recent attention to the 2 °C goal, highlighted in the Copenhagen Accord of 2009. Metrics that favor mitigation of short-lived GHGs might also be expected to reduce the rate of near-term warming (i.e., temperature rise in the first 30–50 years of the 21st century). This tendency was not observed in the current analysis, in part because the year 2100 RF constraint led to pathways that differed in costs rather than the evolution of temperature, and in part because cost-negative CO₂ mitigation dominates near-term abatement.

Behind the CH₄–CO₂ emissions trade-off illustrated in section 4.1 lies another set of trade-offs: sectoral abatement tendencies, following the pricing scheme outlined by the Enkvist et al (2007) adjusted for different metrics. This CH₄–CO₂ metric-driven emissions trade-off is explored with regard to cost-effective responses in van Vuuren et al (2006) and with a focus on agriculture in Reisinger et al (2012). In all of our metric-informed scenarios, cost-negative emissions from commercial and residential buildings and transportation were among the first abated. In reality, many cost-negative mitigation strategies require financing and policy measures that are beyond the scope of this analysis. For cost-positive sectors, choice of metric also influenced the ordering of various mitigation actions along the marginal cost of abatement curve. Metrics that set a high value per ton of CO₂-equivalent (and therefore low per-ton cost) on methane abatement compared to GWP-100, for example, incentivized mitigation in the agriculture and forestry sectors (figure 5). Conversely, metrics that set a low value for methane abatement compared to the GWP-100 value had the effect of placing cheaper CO₂ abatement opportunities relatively lower on the cost curve, thus effecting cheaper CO₂ cost levels representing abatement opportunities such as enhanced oil recovery and cheap carbon capture and storage. N₂O and SF₆ abatement opportunities were also repositioned on the cost curve depending on their respective metric-informed prices. As each metric arranges the marginal costs of abatement with respect to its end-point goal, it determines the amount of mitigation effort placed across gases and, therefore, sectors (table 3). Comparing extreme scenarios, these mitigation shifts across gases and sectors result in a nearly 30% difference in the representation of methane in global cumulative emissions reductions. However, as seen in figure 5, in every scenario most of the GHG abatement comes from fossil fuel CO₂, which is consistent other results (e.g. Reisinger et al 2012, Fisher et al 2007).

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Our decision to apply a constant rate of emissions reduction r_a in support of an environmental goal expressed in RF in 2100 strongly constrains the results of this study. The fixed r_a was selected as a simple case of a target-driven mitigation policy, of the form that currently dominates policy discussions. Assuming a constant rate of abatement through the late 21st century is also consistent with a number of academic (e.g., Allen et al 2009) and policy (e.g., Stern 2006) studies that assume mitigation efforts that eventually achieve and maintain a constant annual percentage rate of decrease in emissions. A year 2100 RF environmental goal is consistent with the definition of RCPs used in the most recent analyses being assessed by the IPCC.

The application of decadal scale mitigation decisions in support of a century scale environmental goal is almost certainly non-optimal from a total cost perspective. This fact has been demonstrated by integrated assessment model (IAM) studies that optimize policy under a range of technological assumptions and 21st century environmental goals, and that frequently conclude that, from a cost minimization perspective, mitigation rates should vary over time and by region or sector over the course of the century (e.g., Clarke et al 2007, Fisher et al 2007, van Vuuren et al 2006). In cost optimization studies, the choice of equivalence metric can influence the rate and distribution of mitigation efforts (e.g., Smith et al 2012, Reisinger et al 2012), and such studies can be interpreted as policy optimization tools that might inform the design of mitigation policies (Tol 2006, Weyant et al 1996).

In applying a range of metrics to a fixed policy framework, the results of our study are best understood as a policy evaluation that considers how one decision—the choice of equivalence metric—might influence mitigation patterns in the context of emissions reduction commitments agreed through a political process that weighs many factors beyond cost optimization. A further constraint on our analysis is that expenditures are minimized for each decade without foresight to offset increasing costs in later decades. This can lead to some very non-optimal cost scenarios when abatement occurs regardless of what (relatively) expensive gases a metric forces mitigation upon. This is a debatable constraint that will be investigated further in future analyses, but a moving ten year cost optimization constraint seems to us to be more realistic than a 100-year holistic cost optimization constraint given the reality of political and business planning horizons in most countries and sectors.