Effect of crude oil carbon accounting decisions on meeting global climate budgets

The Intergovernmental Panel on Climate Change quantified a cumulative remaining carbon budget beyond which there is a high likelihood global average temperatures will increase more than 2 °C above preindustrial temperature. While there is global participation in mitigation efforts, there is little global collaboration to cooperatively mitigate emissions. Instead, countries have been acting as individual agents with independent emission reduction objectives. However, such asymmetric unilateral climate policies create the opportunity for carbon leakage resulting from the shift in embodied carbon emissions within trade networks. In this analysis, we use an optimization-based model of the global crude trade as a case study to demonstrate the importance of a cooperative, system-level approach to climate policy in order to most effectively, efficiently, and equitably achieve carbon mitigation objectives. To do this, we first characterize the cost and life cycle greenhouse gas emissions associated with the 2014 crude production and consumption system by aggregating multiple data sources and developing a balanced trade matrix. We then optimize this network to demonstrate the potential for carbon mitigation through more efficient use of crude resources. Finally, we implement a global carbon cap on total annual crude emissions. We find that such a cap would require crude consumption to drop from 4.2 gigatons (Gt) to 1.1 Gt. However, if each country had an individual carbon allocation in addition to the global cap consistent with the nationally determined contribution limits resulting from the 2015 United Nations Climate Change Conference, allowable consumption would further decrease to approximately 770 million metric tonnes. Additionally, the carbon accounting method used to assign responsibility for embodied carbon emissions associated with the traded crude further influences allowable production and consumption for each country. The simplified model presented here highlights how global cooperation and a system-level cooperative approach could guide climate policy efforts to be more cost effective and equitable, while reducing the leakage potential resulting from shifting trade patterns of embodied carbon emissions. Additionally, it demonstrates how the spatial distribution of crude consumption and production patterns change under a global carbon cap given various carbon accounting strategies.


Introduction
Through international climate negotiations, such as at the Paris Climate Change Conference in 2015, policy-makers have agreed that the average global temperature rise caused by greenhouse gas emissions should not exceed 2 °C above the preindustrial average global temperature (UNFCCC 2016). In order to curb the average global temperature rise, climate models have demonstrated a limit to the cumulative emissions that can be sustained by the climate system. This limit is called the global carbon budget.
The Intergovernmental Panel on Climate Change (IPCC) reported that this budget is in the range of 870-1,240 Gt CO 2 -eq between 2011 and 2050 in order to have a 56% chance of not exceeding this 2°C temperature increase (IPCC 2014).
Limiting emissions to within the global carbon budget would require substantial greenhouse gas (GHG) mitigation efforts. McGlade and Ekins (2015) used an integrated assessment model to explore the implications of this emissions limit for fossil fuel production (McGlade and Ekins 2015). In their scenario to keep average global surface temperature rise below 2°C for all years to 2200, they found 2050 GHG emissions must be constrained to 21 Gt CO 2 -eq. This is compared to the 48 Gt CO 2 -eq emitted in 2010, and a baseline 2050 projection of 71 Gt CO 2 -eq given no emissions mitigation. This latter projection would result in almost a 5°C global average temperature rise (McGlade and Ekins 2015).
While there is general agreement on a cumulative emissions mitigation target, little policy consensus has been reached globally as to how to implement such GHG emissions reductions. Climate policy is a complex issue that involves multiple stakeholders, competing objectives, economic barriers, and issues of equity and responsibilities (IPCC 2015). As a result, the current approach has been to allow each country to determine its own contribution towards emissions reduction targets. The most recent United Nations Climate Change Conference, COP21, in Paris resulted in 188 committing to Nationally tracking mechanism affects countries differently. Tracking emissions relies on carbon accounting methods that traditionally tally only emissions sources within the country.
This has expanded in recent years to consider emissions occurring along the supply chain (i.e., carbon footprint, or embodied carbon). Some commonly discussed carbon accounting frameworks include location-based, where countries are responsible for what is emitted within their borders, production-based, where the producer would be responsible for the full life cycle emissions of what they produce, and consumptionbased, where countries are responsible for all life cycle emissions of what they consume (Steininger et al. 2015). While all methods are theoretically equivalent from a global perspective, they function differently in a fragmented climate policy regime (IPCC 2013).
For example, Jakob and Marschinski (2012) argue that the dynamics of fragmented policy regimes need to be better characterized in order to guide policies to effectively reduce global emissions (Jakob and Marschinski 2012). Gonzales-Eguino et al. (2016) define a fragmented climate regime as being characterized by different climate policies across regimes and sectors, that may lead to the relocation of production to regions with less stringent mitigation rules. Several recent studies have used integrated assessment models to demonstrate the potential for carbon leakage associated with such asymmetric climate policies (Arroyo-Currás et al. 2015;Luderer et al. 2015;Otto et al. 2015;Schaeffer et al. 2015).
Importantly, within a fragmented climate regime, the carbon accounting strategy has implications for carbon leakage given the same set of NDCs. For example, under a consumer-based method, the NDC of a net carbon exporter would largely be non-binding, and therefore provides opportunity for significant carbon leakage. Alternatively, under a producer-based method that same country's NDC could limit domestic economic activity. Therefore, when evaluating the effectiveness of NDCs, it is important to do so within the context of a given carbon accounting mechanism.
This study contributes to the literature by developing a theoretical model to explore the impact of unilateral climate goals on mitigation efficiency based on a case study of the global crude trade. Using an optimization-based approach, we develop a framework that characterizes the potential for NDCs to limit the effectiveness of climate mitigation efforts as compared to a cooperative international climate policy under a strict global carbon budget. Additionally, while under a global climate policy all carbon accounting methods should yield equivalent mitigation efficiencies (Steckel et al. 2010), the model explores how carbon accounting alternatives further interact with the fragmented climate policy-based NDCs to shift the geospatial dynamics of production and consumption.
The optimization model developed for this analysis demonstrates the influence of shifting trade patterns under different climate policies and carbon accounting strategies. While the model is simplified and theoretical, the results offer meaningful insights into potential emissions mitigation opportunities and demonstrate the importance of globally cooperative climate policies. The analysis extrapolates a simplified economy, focusing on the crude sector as a theoretical self-contained entity. Because crude is a widely traded commodity with a high degree of embodied emissions, the global crude trade is a valuable case study to demonstrate how climate policies and carbon accounting strategy interactions can incentivize or dis-incentivize cost effective carbon mitigation measures.

Methods
Throughout this study, we analyze annual international crude trade under the modeling constraint of a market approaching a stable equilibrium at a point in the future. This theoretical construct enables us to explore the potential interactions between climate policies, emissions abatement potential, cost of crude as a primary energy source, and the global distribution of consumption under a range of restrictions. While computable general equilibrium (CGE) models characterize the progression of change over time as part of a feedback loop of price, supply, and demand, we use a single year time scale to Please cite the final version of this paper: . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 7 understand how the global system would behave at its optimal configuration (i.e., future equilibrium). The analysis begins by estimating the current, baseline crude trade network. This crude network is then optimized to demonstrate how shifting trade patterns impact cost and emissions. Finally, a carbon cap is imposed to compare the outcomes of a cooperative global climate policy versus a fragmented climate policy under three carbon accounting strategies (Figure 1). The production and consumption parameters for the baseline model are from 2014. The global crude trade model in our analysis consists of 62 countries, accounting for 4 Gt of crude (29.3 billion bbls), or approximately 95% of total 2014 production. As a proxy for both price and GHG emissions, we used API gravity, which is a measure of density and is often taken as an indicator of crude quality.
All data used to develop the trade network were aggregated from 2014 data whenever possible. Exceptions to this are indicated throughout the methods section.

Reference Trade Network
In order to quantify the potential for cost and emissions savings, we first characterized the existing trade network. The volume of crude traded from each country to each other country is known and is compiled in existing, proprietary datasets; however, these datasets are not publicly available and are expensive to obtain (IEA 2014). Some of these data are published in aggregate form. For example, the BP Statistical Review contains Please cite the final version of this paper: . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 8 trade data of totaled crude and petroleum products aggregated by region (BP Statistical Review of World Energy 2015), while other datasets such as the JODI-Oil Database publish total imports and exports by country but do not publish the volume of crude traded between specific country pairs (JODI-Oil World Database 2014). Other datasets have a high resolution of detail, but are only available for limited countries. For example, the EIA maintains a detailed database of crude imports to the United States by country (EIA 2015). A frequently used publicly available data source for international trade analysis is the United Nations database (UN Comtrade Database 2014). While comprehensive, these data are self-reported and therefore may be subject to reporting errors, missing data, or inconsistencies from year to year. As an example of a shortcoming of this dataset, the flows are not balanced, meaning total imports do not necessarily equal total exports; in 2014, petroleum imports totaled 14 billion bbls while exports totaled 12.6 billion bbls, a difference of ~10% (assuming a specific gravity of 0.88, or 140 kg per bbl of crude). A summary of the crude trade data sources used in this analysis is outlined in Table 1. In addition to international trade, we added domestic consumption of a country's own production to the trade matrix. To do this, we obtained 2014 production and consumption data by country from the BP Statistical Review of World Energy (BP Statistical Review of World Energy 2015), and filled in missing country production and consumption data from the JODI-Oil database (JODI-Oil World Database 2014). We assumed a country's production minus its exports represented the domestic consumption of domestically produced oil. Therefore, the complete mass balance for any given country must be that annual production plus annual imports minus annual exports is equal to total consumption (refinery inputs). Because the compiled trade partner pair data described above did not balance with the production and consumption data, we followed an iterative process to "smooth" the trade data, thereby producing a self-consistent production, trade, and consumption matrix. This smoothing was done using a linear optimization (Eq. 1). The decision variables were the trade values between partner pair countries. The optimization was constrained such that the ratio of trade among partners should be maintained as closely as possible to the trade ratios from the original compiled trade matrix. The objective of the model was therefore to minimize the sum of the absolute value of the differences between the optimized trade ratios and the original trade ratios. Rather than minimize the differences evenly across the system, however, the differences were weighted by the country's contribution to supply and consumption such that larger consumers and producers were given higher importance in achieving correct trade ratios. (1) with respect to +, -. ∈ ℝ ∀ ∈ 1, … , , ∈ 1, … , , ∈ 1, … , where +, -. is the volume of crude traded from exporter to importer ; +, 234 is the designated proportion of exporter 's product that can be traded with partner country ; KL4 is the designated proportion of importer 's total imports that can be imported from partner country ; < is the designated production volume of a given country; < is the designated consumption volume of a given country; + is the weight of the exporting country's accuracy importance; is the total number of countries in the trade network.
Equation (2) ensures each country's trade pattern balances such that its production plus its imports minus its exports is equal to its total consumption. Equation (3) ensures no country exports more crude than it produces, i.e., that no re-exports of imported product are allowed in the system (re-exports were < 0.06% of total exports in 2014 according to the UN Comtrade Database).

API estimates
In this analysis, both cost and emissions are based on the API of crude as an indicator for crude quality. The API gravity is a measure of a crude's density relative to water, and can vary from <27° (heavy crude) to >50° (very light crude). Even within a given oil field, crude API can vary as a function of location and/or age of field production. Different To determine the average API gravity of crude produced by each country as input to our analysis, we took the average of all crudes within a country in the aggregated dataset. While a production weighted average or maintaining a range of crudes for each producer would have been preferred over using the average value, specific production volume by crude type was not available for all countries. Where a country was not represented within either of these three datasets, we used the average regional API estimated by the IEA (IEA 2016).

Cost Estimates
Several crude pricing models have explored relationships between crude quality parameters, socio-political issues, and crude pricing differentials (Kaufmann 2016; Kaufmann and Banerjee 2014; Reboredo 2011). These studies suggest that given the cooperative equilibrium nature of our theoretical optimization model, where price differential effects due to country risk, supply shocks, etc. are irrelevant, it is reasonable to assume the crude market is unified. Therefore, we assume the price relationship between benchmark crudes will remain consistent, and that crude API serves as a proxy for crude quality (see SI section S.4). To estimate the baseline 2014 total crude network cost, we compiled cost data from fourteen benchmark crudes, ranging in API from 13 to 38 from Deloitte's 2015 Oil and Gas Price Forecast report (Deloitte 2015). We use a line of best fit to represent the relationship between API and price. The line is fit as a differential between a crude's API/price and that of Brent crude (API 38) such that any price can be inputted for Brent to determine crude price as a function of API for the other 13 crudes. Since this study is based on 2014 data, the 2014 average price for Brent crude oil was used as the baseline.
In this model, shipping costs are estimated based on shipping distance and a oil tanker freight rate of $.004/tonne-mile. This estimate is based on the Worldscale shipping rate (WS), which is widely used as the basis for shipping price negotiations between a ship owner and a charterer. In this study shipping distances were modeled using the great circle distance based on a geographically representative subset of port locations from the World Port Index (World Port Index 2016) ( Figure S4). A circuity factor of 1.3 was applied to account for variations from the great circle path (TRB 1997). Because shipping costs and emissions were found to be marginal relative to total life cycle emissions, the results of this study are not sensitive to this simplifying assumption. Additional information regarding shipping cost and port-to-port distances is available in SI Section S.3.

Crude Life Cycle Emissions
Crude emissions can be quantified according to life cycle stages. In this model, we include upstream (extraction), shipping, midstream (refining), and downstream

Theoretical Optimized Trade Network
The linear models representing the relationship between crude API and cost/emissions can be used both to characterize the existing global system, as well as to assess the changes in cost/emissions resulting from variations in the global crude system. Because where: + b. = ( + * 0.87 + 66) * .0000073 ($/million tonnes) lm = 1.8 ($B/(million tonnes -million km)) + is the average API produced in a given country , is the target weighted average API consumed by a given country +, is the distance between exporter and importer The optimization defined above assumes any country can supply any volume of its assigned (averaged) API crude and each country can refine any API blend. This is the Please cite the final version of this paper: Abrahams, L. S., Samaras, C., . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 16 most flexible alternative and results in the upper bound cost and GHG mitigation potential. Constraints can then be added to limit the supply to that of the 2014 reference network: Supply constraint: Additionally, a second constraint can be added to limit countries to consuming crude with a blended API consistent with their refinery fleet, as determined by the 2014 reference crude network. This is representative of refinery infrastructure limitations; if a country's crude API blend changes beyond what can currently be processed by that country's refinery portfolio that country would potentially need to invest in refinery updates to reconfigure the refinery to accept the new crude blend: API blend constraint:

Theoretical Trade Network Under Climate Policies
By adding additional constraints on the total crude emissions and/or on country-specific crude emissions to the optimization, we can observe how the trade network shifts under either a global or fragmented climate policy with a carbon limit.

Global Climate Policy
To model a global climate policy scenario in which the international community cooperates to mitigate cumulative emissions to avoid the 2°C average global temperature increase, we set a global annual carbon cap across the system (refer to SI section S.2). To extrapolate a crude-specific, annual carbon cap from the global carbon budget, we considered the current portion of crude emissions; in 2014, the transportation sector contributed approximately 14% of global emissions (EPA 2016). Assuming this portion of total emissions approximately represents crude's contribution to global emissions, we attribute 14% of any global carbon budget as the carbon budget specific to the crude trade. For example, given a global annual carbon cap of 21 Gt CO 2 -eq, the associated global crude annual carbon cap would be 3 Gt CO 2 -eq. The constraint that limits total emissions to the global cap is as follows: Carbon budget constraints:

Fragmented Climate Policy
To do this, we first determined each country's allocated portion of total emissions based on the estimated 2020 GHG targets as determined by each country's nationally

Carbon Accounting Strategies
For both the global and fragmented climate policy optimization scenarios, we can implement different carbon accounting strategies in order to explore the underlying dynamics of carbon leakage and embodied carbon. In the location-based carbon accounting strategy, the upstream producing country was held accountable for upstream emissions, while the consuming country was held responsible for the shipping, midstream, and downstream emissions (Eq. 9). For simplicity, this assumes all refined products are used in that country, rather than being exported elsewhere. While in this study shipping emissions are attributed to the upstream producing country, in reality currently the responsibility for GHG emissions associated with shipping does not fall within the jurisdiction of any individual country (ICTSD 2010). In a producer based accounting framework, upstream producing countries are held responsible for all embodied emissions throughout the crude life cycle (Eq. 10). Finally, in a consumptionbased accounting framework, the consuming country is held responsible for all embodied emissions, including upstream extraction emissions (Eq. 11). The following constraints can be used to specify a carbon accounting strategy: Location-based:

Results and Discussion
In this section, we first show the reference trade network resulting from the iterative smoothing process and explore the implications of carbon accounting strategies on country-level emissions inventories. We then demonstrate the cost and emissions reduction potential achievable through shifting trade patterns and show how these patterns are influenced by global and fragmented climate policies.

Baseline Balanced 2014 Trade Matrix
The baseline 2014 global crude system developed in this analysis includes 62 countries representing 95% of total crude production. The emissions associated with these current trade flows were calculated according to the three different carbon accounting strategies and can be seen in (Figure 2), based on the estimated crude life cycle emissions (see SI section S.4). Figure 2A shows the emissions by country given producing countries are responsible for extraction emissions and consuming countries are responsible for all other life cycle emissions. In contrast, Figure 2B shows embodied life cycle carbon emissions being attributed to the upstream producer, while Figure 2C shows embodied life cycle emissions being attributed to the downstream consumer. For a more detailed look at the impact of carbon accounting method on individual country's emissions profile, see Figure   S7. Due to the asymmetric impact of carbon accounting methods on different countries, any global carbon accounting policy should carefully consider equity issues such as economic impact to developing countries. In general, many African countries would be More specifically, countries that export crude and consume very little crude, such as Algeria, a producer-based approach would result in high crude carbon emissions ( Figure   2B), while location-based (Figure 2A  When minimizing by cost, the least cost scenario for any producer country is to reduce exports and use its own crude oil first before importing crude. This allows the total global cost to drop from $3 trillion to $2.4 trillion ($590/t of oil consumed) as a result of reduced transportation, but results in a GHG emissions increase of approximately 4 Gt CO 2 -eq. Allowing supply to vary freely but constraining the weighted average consumed API gravity by country to remain the same as in the baseline 2014 network also decreases costs by ~$230B across the system to $690/t crude consumed but does not account for technical or resource constraints limiting crude extraction in each country. When minimizing total GHG emissions within the system, there are again distinct differences in cost and emissions savings across the three scenarios. When each country is allowed to supply any volume of crude to contribute to satisfying global demand rather than constraining countries to their 2014 production limits, global GHG savings of about 5.5 Gt CO 2 -eq are realized for an additional cost of about $500 billion. This translates to a relatively low cost of abatement of $90/t CO 2 -eq. When supply is constrained to 2014  production or API refining limitations, a key result is that the more flexible we can make the crude system, the more opportunity there would be for efficient consumption (low CO 2 -eq /t oil consumed). This is important because the more efficient consumption can be, the less total crude consumption would need to be reduced in order to achieve the same climate outcome, as long as minimizing emissions is the priority over minimizing cost.

Climate Policy Scenarios
The optimized trade network under an extrapolated crude oil global carbon limit is designed so that each country is allocated a portion of the global budget. The countryspecific apportionment is done to approximate the impact of fragmented climate policies as compared to the benefits of global cooperation. This allocation is characterized by the NDCs resulting from COP21, suggesting that the ratio of emissions contributions will remain consistent with the ratio of committed 2020 COP21 targets in the future. While in reality the NDCs do not specify how they will be achieved (i.e., how the oil industry would be affected by each country's mitigation efforts), here we highlight the implications each sector would be reduced by the committed percentage. The percentage of total carbon emissions allocated to each region is shown in Table S1. These limits can either be set as absolute limits, or the model can be run such that a country pays a penalty (i.e., carbon tax) for any emissions above its allocated budget. The latter formulation, with a global carbon budget and payments made to exceed individual country allocations, could be designed to mimic a global cap and trade policy.  Table 3, and detailed results can be found in Table S2 through Table S4.  For reference, Figure S7 shows the average API produced by each country used as input to the optimization.
Regardless of the specific carbon accounting scenario, a strict 3 Gt annual carbon cap for oil would constrain demand to at most 770 million tonnes per year (an 80% decrease over the 2014 baseline consumption) (Table 3) When considering specific accounting strategies, the different methods for carbon emissions attribution influences the total demand that can be satisfied while maintaining a global carbon budget of 3 Gt. For example, models using the location and productionbased accounting strategies enable 770 million tonnes of oil demand to be met, while the consumer-based accounting model only allows for 730 million tonnes. Therefore, the ratio of total emissions to total consumed is 4.1 tonne CO 2 -eq/tonne of oil consumed, which is higher than the 4.0 tonne CO 2 -eq/tonne of oil consumed ratio found for the baseline and 3.9 tonne CO 2 -eq/tonne of oil consumed for other two carbon accounting strategies. In other words, consumption based accounting does not allow the global system to satisfy as much demand as a production based accounting method would. This strategy also results in a 10% higher carbon intensity.
The carbon accounting strategies discussed in the previous paragraph assume each country is allocated a specific fraction of the global carbon cap based on the ratio of COP21 NDC emissions targets for 2020. However, if this allocation constraint is relaxed such that there is a global carbon cap but no country-specific carbon limits, the total demand satisfied increases to 1.1 billion tonnes for a cost of $930 billon ($850/tonne oil consumed). Therefore, without unilateral carbon limits, the volume of demand satisfied increases by over 40%, for a lower cost per unit consumed than under the consumption based carbon accounting method with country specific carbon targets. This demonstrates there may be competing influences among the interactions between NDCs and carbon accounting strategies in the long run that could inhibit the cost effectiveness of climate change mitigation efforts. For example, under a producer-based accounting strategy, a developing country with a less constrained NDC could export a significant amount of embodied carbon to countries with more constrained NDCs, resulting in less mitigation than would have occurred under a consumer-based strategy. However, the results of the scenario without NDC-based country-specific carbon budgets show the available crude is consumed by a limited number of countries; only ten countries receive crude, compared to 56 consuming product in the consumption based model. Therefore, while unilateral policies may be less efficient, they may be used as a mechanism to help ensure equitable distribution of consumption. For example, under consumption-based accounting with Please cite the final version of this paper: . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 NDCs, all countries receive a portion of demand. In contrast, with no NDCs, the optimal solution based on minimizing GHG emissions is for 10 countries to receive a portion of demand. Unilateral policies could also incentivize supply security. Under the productionbased accounting strategy with NDCs, all countries contribute to supply, but with no NDCs, the optimal solution is for a single supplier with the highest API. These results Without a globally consistent abatement strategy, it is possible that individual NDCs could be seemingly achieved with minimal real impact on global greenhouse gas mitigation efforts. Furthermore, through this study we find the NDCs and carbon accounting schemes incentivize different patterns of trade. This indicates that although COP21 NDCs might be short-term agreements (to 2025), they influence investments made in infrastructure that could potentially hinder longer-term mitigation efforts. While in the short-term NDCs may protect developing countries by shifting the mitigation responsibility to developed nations, our results show that under a strict global carbon budget, the total cost and consumption outcomes for each country are non-intuitive.
Furthermore, these are highly sensitive to the carbon accounting strategy implemented.
Therefore, while the NDCs from COP21 were an important step in committing the global community to address climate change, mitigation efforts could be more efficient and cost-effective given a system-level approach rooted in more cooperative and interactive target setting. While this analysis is primarily theoretical, it provides key insights into the dynamics of climate policy at the unilateral and globally cooperative scales. The most important sensitivities that affect these results are the crude reserves and operational supply limitations for each country, the relationship between cost and crude type, and the price elasticity of demand. These parameters could be investigated thoroughly at a technical level in the future. However, for the purposes of this scoping exercise to demonstrate the importance of a systems level approach to climate policy, the simplifying assumptions made in the analysis are appropriate and relevant. Greenhouse gas mitigation to the level at which we would remain within the globally accepted cumulative carbon budget would require extensive social, behavioral, political, and economic shifts. Global cooperation and a system-level policy approach could guide such efforts to be costeffective and equitable.
In addition to further exploring the economic interaction between crude supply and demand by incorporating price elasticities, future work could expand on this model by and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of these organizations. The authors would like to thank the anonymous reviewers for their insightful comments, which have greatly improved this work.

Supporting Information Available
The supplementary text includes supplementary results and references.

S.1 Historical Crude Trends
United States oil production had been steadily declining from 1985 until about 2009 when production rapidly began to increase ( Figure

S.2 Projected Crude Oil Consumption
While a carbon budget generally refers to cumulative emissions over an extended period, in this study we extrapolate the carbon budget to an annual carbon cap for a single sector.
For the petroleum sector, this is a meaningful as simulations conducted for the IPCC 5 th Assessment Report across three climate models suggest the portion of crude oil serving as primary energy source remains relatively consistent through 2100 despite changes in nuclear, renewable, and natural gas contributions as primary energy sources (IPCC 2014) (see SI section S.3). The IPCC used three climate models to project primary energy sources to 2100 ( Figure S3). The model results demonstrate consistency in the proportional contribution of crude as a primary energy source. Given global climate targets and carbon budgets, each sector would have to reduce by 50-80%. If one sector, such as transportation, falls short of these goals, the other sectors must overcompensate in order to achieve global carbon targets.
The climate models used in the IPCC report incorporate assumed marginal abatement cost curves (MACCs), which orders abatement activity by increasing cost across all sectors. Additionally, these climate models include assumptions about changes in technology, price, and availability of renewable technologies. Therefore, while we do not explicitly consider MACCs and advances in renewable energy in this study, they are implicitly accounted for in our assumption that crude consumption remains stable based Supplemental Information. Please cite the final version of this paper: . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 S4 on these model projections to 2100. Global climate targets are not limited to a single sector. However, if one sector, such as transportation, falls short of cumulative emissions targets, the other sectors would have to overcompensate in order to achieve global carbon targets. Because this work is not meant to be predictive, but rather a tool to demonstrate the importance of global coordination in emissions abatement planning, isolating the crude sector in this way serves as a case study. In particular, the international interconnectedness of the trade, varying crude qualities, geospatially ranging consumption patterns, substitutability of crude types, and the predicted consistency of crude consumption over time makes the crude sector a dynamic one to isolate for illustrative purposes. In addition, assessing the theoretical limits of application of a carbon budget to crude highlights the some of the challenges and opportunities of reducing GHGs from the petroleum production and use.
Supplemental Information. Please cite the final version of this paper: . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 S5 Figure S3: Projected primary energy source contributions by fuel type through 2100 according to three climate models (IPCC 2014) Supplemental Information. Please cite the final version of this paper: . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 S6

S.3 Shipping Cost and Emissions Estimates
The estimated shipping emissions factor (0.005 kg CO 2 /t-km) was validated by estimating a shipping emissions factor; assuming residual fuel oil is used with an energy intensity of 14 kJ/t-km (Wang 2009) and emissions factor of 77.4 t CO 2 /TJ consistent with the assumption used by the IPCC (2014), the calculated shipping emissions factor is 0.00108 kg CO 2 -e/t-km. This is reasonable because it is on the same order of magnitude, and slightly lower as expected due to operational factors and vessel capacity not being taken into account.

S.4 Crude Cost and Emissions Estimates
The linear cost model representing crude cost as a function of crude API was developed from thirteen benchmark crudes ( Figure S5). It is expressed as a differential from Brent   For reference, the average API crude produced by each country used in this analysis is shown in Figure S7.

S.5 Estimated Trade Matrix Results
In the 2014 baseline balanced trade matrix, the sum of each country's production and imports equals its exports plus consumption ( Figure S8). From these balances, it is clear which countries are net importers, net exporters, or largely domestic consumers of their own crude production. These values were derived from the iterative smoothing process, used to compile the various data sources such that each country's combined production plus import volume equals its consumption plus export volume.
Supplemental Information. Please cite the final version of this paper: Abrahams, L. S., Samaras, C., . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 S11 Figure S8: Production, consumption, and trade mass balance by country. Net importers are indicated with an asterix.

S12
Based on the reference trade network, Figure S9 shows the relative impact of each of these carbon accounting methods for each country. Each bar represents the ratio of producer-, location-, and consumer-based emissions inventory for a given country. In this figure, if the three accounting measures each have a third of the total (see Argentina for example), then that country's emissions are not sensitive to the accounting strategy used.
If instead, however, one color dominates the bar, that country is highly sensitive to the carbon accounting method. For example, using a production-based carbon accounting strategy would greatly affect Yemen's emissions profile.

S.6 Country-Specific Costs and Savings
As seen in Figure S10 some countries realized cost savings as a result of the optimization, while some countries experienced losses (see Table S2-S4 for additional detailed cost results). This is primarily a result of shifting crude consumption rather than shipping savings; shipping savings costs are nominal relative to crude savings for a given country.
As an example of a country with a high potential for reducing cost, the United States has the potential to save on the order of a hundred billion dollars per year. These savings arise from consuming domestically produced crude only in the optimized model, rather than importing crude. Figure S10: Cost savings from the optimized network over the 2014 network, where demand was constrained to 2014 levels, but supply by country and consumed blended API were allowed to vary freely

S.7 Multi-Objective Optimization
In addition to estimating the potential for cost and greenhouse gas savings within the 2014 crude system assumptions, we can use this optimization model to characterize the dynamics within the system resulting from various climate policies. For example, we can implement a carbon tax across the system and set the objective to minimize total cost, consisting of crude cost, shipping cost, and GHG emissions times the carbon tax. This multi-objective optimization allows for the development of a Pareto frontier describing Supplemental Information. Please cite the final version of this paper: Abrahams, L. S., Samaras, C., . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 S15 the tradeoffs in cost and emissions. As a starting point, we set the carbon tax at $13/tonne CO 2 -eq, which is consistent with the 2015 social cost of carbon ($2015, 5% discount rate) as estimated by the Interagency Working Group on the Social Cost of Carbon (Technical Update of the Social Cost of Carbon for Regulatory Impact Analysis 2014) and vary it parametrically up to $300/tonne CO 2 -eq.
In this optimization, the objective function is the sum of monetized GHG emissions (weighted by the given social cost of carbon) and the total system cost (from crude purchases and shipping). Figure S11A shows a Pareto frontier of tradeoffs between total cost and GHG emissions. The extreme end points represent the cost minimized system (SCC = $0/tonne) and the GHG minimized system, respectively. The points between these extremes illustrate the influence of parametrically varied SCC between $13/tonne (2015 SCC, 5% discount rate) to $300/tonne. This figure shows that there is a threshold between $110 and $120/tonne where there is a significant emissions reduction and cost increase. Figure S12B shows the change in cost over the savings in GHG emissions. For lower SCCs that incentivize an emissions reduction, the GHG savings are expensive. For example, at a SCC of $66/tonne, every Gt of CO 2 avoided costs $22 trillion. However, as the SCC increases, the cost of avoided emissions decreases until it reaches the limit of the GHG minimized scenario ($8.7 trillion/Gt).

A B
Supplemental Information. Please cite the final version of this paper: Abrahams, L. S., Samaras, C., . Effect of crude oil carbon accounting decisions on meeting global climate budgets. Environment Systems and Decisions, 1-15. https://doi.org/10.1007/s10669-017-9638-5 S16 Figure S11: A) Pareto frontier between total cost and total GHG emissions, and B) dollars spent per metric tonne CO 2 avoided, as a function of social cost of carbon

S.9 Detailed Results
The following tables present detailed model results across all scenarios. The baseline is the 2014 trade network.
Baseline = 2014 balanced network Cost = cost minimized, demand constraints only Cost_supply = cost minimized, supply and demand constrained Cost_API = cost minimized, demand and API constrained GHG = GHG minimized GHG_supply = GHG minimized, supply and demand constrained GHG_API = GHG minimized, demand and API constrained 3GT = 3 Gt carbon cap, no NDC constraints 3GT_Location = location based carbon accounting, 3 GT carbon cap 3GT_Producer= production based carbon accounting, 3 GT carbon cap 3GT_Consumer = consumption based carbon accounting, 3 GT carbon cap