Defining climate change scenario characteristics with a phase space of cumulative primary energy and carbon intensity

The climate research community uses a framework for future scenarios based on four Representative Concentration Pathways (RCPs) (van Vuuren et al 2011a, 2012, O'Neill et al 2013, van Vuuren et al 2013, Moss et al 2010). RCPs are projections of greenhouse gas (GHG) concentrations that result in radiative forcing (RF) levels of 8.5, 6.0, 4.5 and 2.6 W m⁻². Initially, RCP modeling teams were assigned these four end-point RF targets and designed scenarios to attain them (van Vuuren et al 2011a, 2011b, Riahi et al 2011, Thomson et al 2011, Masui et al 2011). The RCPs are now supported by a series of more robust Shared Socioeconomic Pathway (SSP) scenarios (Riahi et al 2017).

The collection of integrated assessment model (IAM) scenarios based on five SSP narratives provide a conceptual foundation for conditions in global society that could lead to each level of RCP forcing (Kriegler et al 2017, Calvin et al 2017, Fujimori et al 2017, Fricko et al 2017, van Vuuren et al 2017). These IAM scenarios use the SSP storylines for their internal assumptions about technological change, resource availability, economic and demographic trends to the year 2100 (Bauer et al 2017, Riahi et al 2017, Leimbach et al 2017, KC and Lutz 2014). When taken together, the full suite of SSP-RCP scenarios provide a common infrastructure for the studies of global change that will inform the next IPCC assessment (O'Neill et al 2016).

However, possible trajectories for carbon dioxide (CO₂) emissions from fossil fuel combustion may be broader than the span covered by detailed IAM scenarios. Therefore, this paper proposes a method for analyzing RCP components independently from the structure of IAMs. The cumulative amount of fossil CO₂ emissions internally consistent with each RCP can be reached using a constrained set of developments in the global energy system. This constraint involves a trade-off between the total amount of energy used and its average carbon content. In other words, a lower energy demand trajectory paired with a higher average carbon intensity of energy supply will arrive at the same level of cumulative CO₂ emissions in the year 2100 (and vice-versa).

Because the SSP-RCP scenario architecture is based on year-2100 end-points, the 21st century fossil fuel and industry (FF&I) carbon budgets consistent with each RCP can be calculated based on possible combinations of two principal factors over this period: (i) total energy resource use and (ii) its average carbon intensity. Framing RCPs in terms of these two dimensions allows a phase space diagram of global energy use to describe them.

The phase space of a dynamic system represents key parameters as axes to present the full range of its physically possible states, where each coordinate describes a unique feasible scenario outcome. In this paper, we develop a future energy system phase space to describe RCPs based on analytical solutions from a decomposition analysis of cumulative emissions (Kaya 1989). This allows for display of the fossil energy system states that correspond with RCPs across a broad range, independent of any single IAM scenario.

It is important to note that IAM scenarios of future GHGs are based on more than just CO₂ emissions from the industrial energy system—and can include significant contributions from land use change and non-CO₂ GHGs. Since the RCPs are full sets of RF components, we denote the FF&I carbon budget aspect of each as RCP^⁎ for the rest of this paper. Similar phase space approaches could be readily developed for other GHGs and tailored to specific studies of global change.

Using RCPs as benchmark pathways of GHG concentrations provides distinct benefits to the research community by decoupling climate model runs from the extensive development process needed for fully integrated scenarios of their underlying drivers. Though the SSPs now present a highly-detailed foundation for RCP scenarios, a phase space approach contributes additional conceptual support for their use in scientific studies since the RCPs are independent of any single IAM scenario or model structure. Further, this method can be applied to complement IAM scenarios, ensuring they provide sufficient coverage of future energy system uncertainties within the RCP framework.

To demonstrate the RCP phase space method, we focus on fossil fuel emissions from energy system 'no policy' reference cases. Reference cases intend to understand plausible hypotheses for future developments in global energy use which could precede climate policy. Subsequently, these reference cases are applied as 'baseline scenarios' for climate impact assessments and policy analysis (Bauer et al 2017, Clarke et al 2014).

The original RCP scenarios presented RCP8.5 as the sole pathway in the absence of any climate policy, while the other RCPs depicted various interventions aimed at mitigation (IIASA 2009, van Vuuren et al 2011a). However, the range from RCP4.5–RCP8.5 was initially identified as a plausible span for future reference case scenarios (van Vuuren et al 2011a). This plausible 'no policy' range is further reinforced by the outcome of the SSP development process which also produced reference cases leading to RF within this spectrum (Riahi et al 2017, Riahi and van Vuuren 2016). Therefore, the phase space in this paper is based on RCP4.5, 6.0 and RCP8.5. RCP2.6 is excluded because it can only be achieved with explicit climate policy.

The 'no policy' IAM reference cases preceding mitigation in AR5 WGIII result in total emissions that correspond to the range between RCP6.0 and RCP8.5. When this set of AR5 WGIII and SSP-RCP marker scenarios are presented in total, they illustrate how IAMs collectively orient outlooks for our global energy future as the origin of cost and technology assessments for reducing future carbon emissions, and the challenges any policy goal will face in efforts to limit warming.

The following work describes the method for producing and reading an RCP phase space (section 2) and then places AR5 WGIII reference case scenarios within it (section 3). Analyzing large sets of global change scenarios with a phase space approach allows data mining techniques, such as the k-means cluster analysis we apply, to rapidly distill their key characteristics (section 3.2). This is demonstrated by mapping IAM outlooks for fossil resource use consistent with the identified clusters (section 3.3). Section 4 concludes by summarizing results of the cluster analysis in the context of mitigation cost estimates.

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The total amount of global carbon emissions (F) that could result from combustion of fossil fuels over the next century can be depicted by a two-dimensional phase space diagram (figure 1(a)). This phase space expresses the average carbon intensity of energy supply (F/E) with the horizontal axis, and total primary energy resource use (E) with the vertical axis³. The (x, y) coordinates at each point in the phase space summarize a single fossil fuel carbon emission scenario for the years 2016 through 2100. These coordinates are (F/E, E), and so when multiplied they equal a specific amount of cumulative CO₂ emissions across these 84 years.

While global energy scenarios are usually depicted as time-series lines rather than points, this phase space supresses the time dimension in order to provide a clean display and analysis of many scenarios at once. A more traditional presentation of the IPCC AR5 database (DB) scenarios as time-series is provided in supplementary online material—section I available at stacks.iop.org/ERL/13/024012/mmedia. For a ready comparison to today, the right axis of figure 1(a) shows the average level of primary energy used across the next eight decades (2016–2100)⁴.

As noted in the introduction, the RCP scenarios are designed as end-points for RF in 2100. Therefore, they could result from many different combinations of energy use and its carbon intensity. To depict the range of possible fossil CO₂ emission scenarios that could result in each RCP, the cumulative carbon emissions consistent with RCP^⁎8.5 (red), RCP^⁎6.0 (blue) and RCP^⁎4.5 (green) are plotted as lines in figure 1(a) using the methods described in supplementary information 1. This section proceeds by adding consecutive layers of detail in this RCP phase space to describe its capabilities as a tool for analyzing global change scenarios.

2.1. Placing reference points in the phase space

2.2. Phase space reference lines

Each point along the horizontal axis of figures 1(a)–(c) represents an average carbon intensity that results from a mix of fuels used to meet energy demand. The carbon intensity of each point primarily reflects various combinations of oil, gas and coal (supplementary information I). Therefore, we can denote oil as O, gas as G and coal as C, where the proportion of each fossil fuel in the primary energy mix (E_primary) is given by [Ω, γ κ]:

$$\begin{equation} \frac{O}{{{E_{{\rm{primary}}}}}} = {\rm{\Omega }},{\rm{and\,}}\frac{G}{{{E_{{\rm{primary}}}}}} = \gamma ,{\rm{and\,}}\frac{C}{{{E_{{\rm{primary}}}}}} = \kappa. \end{equation}$$

Three vertical gray lines in figure 1(b) depict values for the carbon intensity equivalent to an energy system of 100% gas [γ = 100%] (gray short-dash line), 100% oil [Ω = 100%] (gray long-dash line), and 100% coal [κ = 100%] (gray solid line).

These lines are simple markers that can be achieved through many combinations of fossil energy, renewables, nuclear or carbon capture which would result in the same coordinates.

2.3. IAM scenarios in the phase space

2.4. Mapping energy system transition in the phase space

To understand how AR5 'no policy' reference cases orient projections for fossil carbon emissions, we collect necessary inputs to each equation in supplementary information 1 from scenarios in the AR5 DB (IPCC WGIII 2014)⁵.

3.1. Populating the RCP phase space with AR5 scenarios

Each IAM reference case scenario is represented as a gray diamond in figure 2(a), with darker shading indicating overlapping scenario end-points. In figure 2(a) box plots of cumulative energy use and carbon intensity for the full series of IAM reference cases correspond with each axis. The AR5 database reference case mean scenario falls within the range of feasible solutions for CO₂ forcing between RCP^⁎6.0 and RCP^⁎8.5⁶ with a carbon intensity of 67 MtCO₂/EJ and cumulative energy use of 80 000 EJ, indicating a trend of moderate re-carbonization across the entire dataset.

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3.2. k-means cluster analysis of AR5 scenarios

Describing each IAM scenario as a set of energy system coordinates in this RCP phase space allows for ready application of data mining techniques that can summarize the main characteristics of the full dataset. Accordingly, we conduct a k-means cluster analysis (supplementary information II).

K-means cluster analysis groups individual scenario data points into unique clusters with shared characteristics. This identifies groups in large data sets organically, rather than through the application of pre-specified labels or narratives. Our k-means cluster analysis identifies three distinct energy system scenarios in the AR5 WGIII database—further labeled as Groups A, B and C⁷. The cluster centers plotted in figure 2(b) summarize hundreds of IAM reference case scenarios.

Group A represents the RCP8.5 consistent scenarios of faster growth in energy demand that IAMs commonly solve through reliance on coal and consequently re-carbonization (F ≥ RCP^⁎8.5). Group B corresponds to intermediate growth in energy demand, solved with scenarios that range from decarbonization, steady-state, and re-carbonization (RCP^⁎6.0 < F < RCP^⁎8.5). Group C describes scenarios with the lowest growth in energy supply and exhibit gradual re-carbonization (F ≈ RCP^⁎6.0). In figure 2(b) dotted lines depict transition paths between the Year 2015 static case and each cluster⁸. The dotted line that tracks the 50 year baseline signal indicates gradual decarbonization while each AR5 cluster depicts transition toward re-carbonization.

Mapping scenarios with clusters provides insights into the defining characteristics of each group. We explore these further in the following section through delineating the cumulative oil, gas and coal supply scenarios of each cluster.

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Table 1. Summary of fossil energy system reference case characteristics applied by AR5 WGIII scenarios to describe RCP ranges.

					Conventional reserves and resourcesa
RCP carbon budget range	AR5 cluster	Approximate range SSP markerb	Primary energy—E [Growth]	Carbon intensity—F/E [Transition Illustrated]	Oil	Gas	Coal
F ≥ RCP⁎8.5	A	SSP5	High	Re-carbonization	1.0 x	0.7 x	3.7 x
RCP⁎6.0 < F < RCP⁎8.5	B	SSP2/SSP3/SSP4	Medium	Steady-state/Moderate Re-carbonization	1.4 x	1.0 x	1.8 x
F ≈ RCP⁎6.0	C	—	Low	Gradual Re-carbonization	1.0 x	0.7 x	1.5 x

^aCluster mean use of BGR (2015) conventional fossil energy reserves and resources (supplementary online material—section IV). ^bThese SSP marker scenarios fall into the RCP carbon budget ranges, but may not reproduce the same characteristics of each AR5 cluster (supplementary online material—section V).

3.3. AR5 reference case clusters: characteristics of oil, gas, and coal combustion

3.4. Summary of AR5 energy system reference case characteristics

This paper has offered a simple means to compare and display future scenarios of fossil carbon emissions within the SSP-RCP framework (section 2). The RCPs are end-of-century values for radiative forcing, which can be solved analytically and graphically, independent of an IAM scenario or SSP storyline. The phase space approach for RCPs provides new insights on how IAMs solve for these end-point targets. Such phase space methods offer a new approach to assessments which draw from large data sets or model outputs.

This phase space analysis shows that AR5 WGIII reference cases largely generate carbon emissions consistent with total forcings above 6 W m⁻² by departing from the 'dynamics as usual' signal of slowing primary energy demand growth and gradual decarbonisation (section 3). Achieving high re-carbonisation rates of RCP^⁎8.5 or greater leads several IAMs to exhibit near unanimity in limiting recoverable oil and gas while relying on coal production that greatly exceeds current reserve estimates (section 3.3).

Our cluster analysis indicates that AR5 no policy reference cases are collectively bullish about future coal resources, independent of RCP scenario or model (section 3.4). The IPCC AR5 WGIII DB is therefore dominated by scenarios oriented toward re-carbonization rather than the historical baseline trend which leads in the opposite direction. Recent findings on the economics of coal cast doubt on whether this outlook is still valid since recovering more than today's reserves is very unlikely, and global per-capita coal use has remained in relative steady-state since the early 20th century (Ritchie and Dowlatabadi 2017a, 2017b).

An RCP phase space also provides a clear picture of whether IAM energy system scenarios provide sufficient coverage of relevant uncertainties for robust climate policy formulation in preparation for future IPCC assessments. A full consideration of uncertain developments must undoubtedly involve scenarios that recognize the possibility of a global energy supply which evolves in steady-state, or toward re-carbonization—late 20th century trends in the global energy system may not continue. However, to remain a useful guide for policy and technology, the forthcoming IPCC AR6 and AR7 WGIII scenario database mean will need to capture the momentum of past 'business as usual', inducing a shift toward the left in the energy system phase space. The SSP2, SSP4 and SSP1 marker scenarios have provided a useful guidepost in this regard.

To improve coverage of the uncertainties illustrated by the phase space developed in this paper, we propose that future sets of energy reference cases for climate research should explore additional groupings, such as: Type D (RCP^⁎4.5 < F < RCP^⁎6.0) scenarios explicitly characterizing passive decarbonisation that follows the late 20th century trend-lines for decelerating primary energy supply growth and gradual substitution of energy carriers with lower carbon intensity; and Type E reference cases (F ≤ RCP^⁎4.5) characterizing futures where renewable energy sources are more competitive than coal or unconventional oil, and energy services are provided with more efficient technologies and dematerialized demand patterns.

Type D reference cases have recently been illustrated with the fossil energy supply scenarios developed for the Shared Socioeconomic Pathway 1 (SSP1) narrative of 'green growth' and sustainable development (Bauer et al 2016, 2017, van Vuuren et al 2017). These scenarios are plotted in figure 1 (green square) and in the supplementary online material—section V. However, the SSP1 scenarios are also consistent with the IEA's reference case outlook, which intends to present the expected outcome from today's ongoing developments in the energy sector rather than an explicit storyline of green growth. Several AR5 WGIII reference cases also correspond to Type D projections but they do not register a distinct k-means cluster because the database is biased toward re-carbonization.

Further research is needed to determine if plausible high emission reference cases consistent with RCP^⁎8.5 could be developed with scenarios that do not lead to steady-state or re-carbonization. Though it is unlikely given the current understanding of energy system costs that IAM teams could construct such reference cases since these factors are generally understood to be consistent with lower total levels of future CO₂ forcing (van Vuuren et al 2017).

RCPs, SSPs and similar sets of emission pathways are often described in the literature as equally plausible: they carry no explicit probabilistic elements because any single forcing pathway can result from a diverse range of socioeconomic and technological development possibilities for which distributions are considered unknown (Grübler and Nakićenović 2001, van Vuuren et al 2011a, 2012, Riahi et al 2017, Nakicenovic et al 2000). Thus, it is interesting that the full collection of WGIII scenarios applied within this framework have illustrated each RCP range with energy policy reference cases using such tightly coupled combinations of fossil energy inputs, regardless of the IAM applied or intercomparison exercise (couplings described in table I are also plotted in supplementary online material—section IV).

Since many scenarios cluster around clear levels of oil, gas and coal combustion, this suggests the IAM community has developed a strong consensus on how to configure model reference cases to meet the end-point constraints of the SSP-RCP framework. In this context, scientific studies that present SSP5-RCP8.5 (Group A) affirm bullish expectations for coal (O'Neill et al 2016), running counter to analogous reference cases in recent global energy outlooks (EIA 2016–2017, IEA 2014–2017, IEA 2017). For comparison, supplementary online material—section V places International Energy Agency (IEA) reference case scenarios in the RCP phase space alongside AR5 DB and SSP scenarios, and contrasts their prospects for oil, gas and coal resource use.

As the phase space in this paper illustrates, the carbon emission reference cases exceeding RCP6.0 in AR5 WGIII are producing only a few of the possible trajectories for a 21st century energy system that would precede climate policy. The SSP scenarios have improved coverage of future uncertainties by presenting a broader range of plausible scenario archetypes that could shape global energy resource use (figure 1(c)). A similar phase space analysis of SSP no policy scenarios finds IAMs emphasize natural gas when depicting SSP1, in line with the IEA's reference case (supplementary online material—section V). However, the bulk of the SSP IAM reference case scenarios maintain long-run outlooks dominated by coal, regardless of underlying narrative.

Based on these results, we suggest that the IAM generated energy policy reference cases used in AR5 may be overly constrained. IPCC WGIII AR5 DB mitigation policy and technology outlooks are also shaped by this condition. For example, IAM reference cases directed toward the historical baseline signal demonstrate significantly lower carbon prices for a 2° policy goal than steady-state or re-carbonization pathways (supplementary online material—section VI).

Since the global energy system reference cases used in IPCC AR5 are collectively oriented toward re-carbonization, they may overstate the difficulty of achieving end-of-century mitigation targets. This could influence undue antagonism toward international climate policy when the four RCPs and corresponding mitigation cases are communicated as in AR5 (Rogelj et al 2016, UNFCCC 2015, Clarke et al 2014). Therefore, evidence confirming steady-state and re-carbonization scenarios as unlikely would also indicate that ambitious policy goals will be less challenging than previously considered.

This work was made possible through support from the Pacific Institute for Climate Solutions (Transition to a low GHG economy, 36170–50280); the Carnegie Mellon (CMU) Climate and Energy Decision Making Center (CEDM) under a subcontract from the US National Science Foundation (SES-1463492); and the Canada Social Sciences and Humanities Research Council.