Deep decarbonisation pathways of the energy system in times of unprecedented uncertainty in the energy sector

Unprecedented investments in clean energy technology are required for a net-zero carbon energy system before temperatures breach the Paris Agreement goals. By performing a Monte-Carlo Analysis with the detailed ETSAP-TIAM Integrated Assessment Model and by generating 4000 scenarios of the world ’ s energy system, climate and economy, we find that the uncertainty surrounding technology costs, resource potentials, climate sensitivity and the level of decoupling between energy demands and economic growth influence the efficiency of climate policies and accentuate investment risks in clean energy technologies. Contrary to other studies relying on exploring the uncertainty space via model intercomparison, we find that the CO 2 emissions and CO 2 prices vary convexly and nonlinearly with the discount rate and climate sensitivity over time. Accounting for this uncertainty is important for designing climate policies and carbon prices to accelerate the transition. In 70% of the scenarios, a 1.5 ◦ C temperature overshoot was within this decade, calling for immediate policy action. Delaying this action by ten years may result in 2 ◦ C mitigation costs being similar to those required to reach the 1.5 ◦ C target if started today, with an immediate peak in emissions, a larger uncertainty in the medium-term horizon and a higher effort for net-zero emissions.


Introduction
The energy sector routinely deals with risk and uncertainty in investment decisions and will continue to do so in the face of climate policy uncertainty. While risk could lead to profits in excess of expenditures, sustained additional risk raises the energy sector's capital cost and could alter sustainable infrastructure investment decisions (OECD / IEA, 2007). Further, climate policy uncertainty arises from the uncertainty of required CO 2 taxes and prices needed to meet the Paris Agreement target under different macro-economic, demographic and technological developments, as well as from the response of the earth's climate system in terms of global average surface temperature to emissions concentrations. Such climate policy uncertainty weakens investment incentives for low-carbon technologies. It could lead to choices that appear sub-optimal or extend the existing assets' lifetimes rather than investing in new, cleaner, more efficient ones. The uncertainties in the investments in sustainable energy infrastructure arise from several contextual factors, including the potential impacts of greenhouse gases (GHG) concentrations on the temperature and the costs of reducing emissions of GHG to slow down their accumulation in the atmosphere (IPCC, 2018). Climate sensitivity is one of the most uncertain properties to control the climate system's response over several decades to GHG concentration increases (i.e., the increase in global mean temperature in response to a doubling of atmospheric concentrations) (IPCC, 2018). The cost of climate change mitigation is influenced, among others, by uncertainties surrounding energy demands, economic and population growth, the capital and operating cost of clean energy technologies, and their deployment ratewhich largely also depends on resource potentials, societal and political factors (Rogelj et al., 2013). In this regard, mitigation policy is also affected by uncertainties in climate response, economic impacts and technology costs. In the long term, there is also a direct economic impact of physical aspects of climate change.
During COP26, there was a race to inform the media of the resulting temperature rise from the Glasgow pledges to accelerate policy implementation and mitigate investment risks to clean technologies and fuels. The level of false precision to within one-tenth of a degree Celsius of temperature estimates 80 years into the future is astounding. The integrated energy-climate-economy system is complex and uncertain. Studies with Integrated Assessment Models (IAMs) representing the interactions between these three systems have shown that limiting anthropogenic temperature increase to 1.5 • C requires immediate ambitious investments in all energy sectors to enable carbon neutrality by mid-century (Rogelj et al., 2015).
However, energy and climate literature readers are well informed of the range of uncertainty in IAMs used to estimate future temperatures, policy efficacy, and the investment needs to stabilise average global temperatures. When considering a new policy, climate change and energy decision-makers need to estimate the level and type of investment that will be made under different economic, technological, societal, geophysical and political conditions and how a new policy might change this investment behaviour. Considering this uncertainty, how do policy makers know what robust and resilient decisions are and which to act upon? Or, how do investors and policymakers know what insights are a function of input data uncertainty, model mathematical structure, model or modeller biases? How does this uncertainty impact investment decisions, fuel switching and integration of the end-use sectors?
This paper explores these questions by quantifying the uncertainty of the future configuration of the energy system associated with the contextual factors mentioned before by developing an advanced methodology and applying it to the state-of-the-art integrated assessment model ETSAP TIAM based on the IEA-ETSAP TIMES modelling framework (Loulou et al., 2016). Our analysis identifies the drivers with the most impact on policy decisions to implement the Paris Agreement goals and aims to shed light on the design of robust and effective climate change mitigation policies. The study also assesses the effectiveness of climate-change mitigation targets in restricting global average surface temperature rise to below 2 • C and 1.5 • C by 2100 above the pre-industrial levels under different economic, demographic, technical and climate sensitivity contexts, as well as the associated energy systems cost and technological change needed to restructure the present energy system. Our analysis maps the uncertainty in the solution space regarding the technology mix and investment expenditures in clean energy technologies to enable deep emissions cuts. This uncertainty mapping is critical to guiding investors and policymakers toward robust mitigation pathways. However, we acknowledge that the layers of uncertainty in our study are not expected to be resolved in the next few decades, while policy decisions must be made now.
The structure of the paper is as follows. Section 2 deals with the literature review, while section 3 presents the methodology we apply to our analysis. Section 4 discusses the main findings and results. Section 5 concludes the analysis with its policy implications.

Background and literature review
Uncertainty in technology costs, economic and population growth, energy demands, resource potential and climate sensitivity, presents a continuous challenge (IPCC, 2018) in the valuation of control policies and decision-making under uncertainty (Lempert et al., 2003). Simple scenario analysis with IAMs to perform policy impact assessment or exploration has limitations (Haikola et al., 2019), and addressing uncertainties with systematic approaches provides more robust policy insights for decision-making.
There have been recent calls for systematic investigation of the extremes of the plausible distribution of climate mitigation scenarios, particularly towards the 6th Assessment Report Cycle of the Intergovernmental Panel on Climate Change (IPCC) (Emmerling et al., 2019;Keppo et al., 2021;McCollum et al., 2020;Tavoni and Valente, 2022;van Vuuren et al., 2020). The majority of published mitigation pathways that explore transformation towards a net-zero carbon future have been developed by integrated assessment models (IAMs) -see, for example (Fragkos et al., 2015;Huppmann et al., 2018;Marcucci et al., 2017;Rogelj et al., 2015Rogelj et al., , 2016Sognnaes et al., 2021). These models represent interactions among energy systems, economy and earth systems. They are developed based on averages of a possible range of energy system dynamics regarding future trends in population, consumption of goods and services, economic growth, behaviour, technology, policies and institutions. However, most existing IAMs rely on parametric scenario analysis to explore solution spaces (Yue et al., 2018), neglecting that projecting 50 or 100 years into the future is inherently uncertain. Inaccuracy in forecasting energy supply, demand and technology improvement projections can be demonstrated with numerous examples (Cooper and Smil, 2004). The impacts of the COVID-19 pandemic on the macroeconomic and demographic drivers of IAM scenarios would not have been thought of as probable scenarios of merit only two years ago. The latest World Energy Outlook report from the International Energy Agency (IEA) is dominated by this demand uncertainty (OECD/IEA, 2021).
The Monte-Carlo method is an adequate probabilistic risk assessment approach for policy assessment related to climate change (Schneider and Mastrandrea, 2005), and it has been applied in probabilistic evaluations of deep decarbonisation pathwayssee, for example (Kouvaritakis et al., 2005;Kypreos, 2008;Labriet et al., 2008;Marcucci et al., 2019a;Zhang and Chen, 2022). This approach propagates uncertainties by simultaneously perturbing multiple uncertain input parameters represented by probability distributions (Saltelli et al., 2008).
However, we have not seen in the literature a robust diagnosis of the uncertainty impact of the dominant uncertainties from the IAMs typically used to estimate outcomes of Nationally Determined Contributions and Net-Zero pledges. Here we present a new and advanced development of Monte-Carlo analysis into the TIMES source code and an application to study the uncertainty in key climate change mitigation policy outcomes using the global multiregional ETSAP-TIAM model (Loulou, 2008;Loulou and Labriet, 2008). The present study is the first Monte-Carlo assessment of a large-scale and full process-oriented IAM coupled with a climate model. The Monte Carlo methodology described in our study is computationally efficient and suitable for reducing the complexity of uncertainty analysis when using large-scale models. It can be effectively applied to other integrated assessment modelling frameworks too. It is based on the Latin Hypercube Sampling (LHS) (Helton and Davis, 2003) of multipliers that modify base values of the input parameters, which are more intuitive and suitable to be assessed by stakeholders and experts rather than sampling absolute levels of our inputs. In this regard, the Monte Carlo Analysis remains valid even if the base values are modified, and this is very computationally efficient as we decouple the baseline scenario from the stochastic scenarios. Finally, another methodological contribution of our study, described in Appendix II, is a computationally efficient approach to solving thousands of scenarios with large-scale IAMs on high-performance computing grids by exploiting multithreading capabilities for asynchronous submission and collection of model solution tasks without significant message passing overhead.

Methodology
In accounting for uncertainty in energy and climate policy impact assessment and exploration, in particular with Integrated Assessment models, there are two major sources of uncertainty: model structure uncertainty and parametric uncertainty (Hainsch, 2022). Parametric uncertainty has, however, a larger effect on the results than the model structure uncertainty (Gillingham et al., 2015). To account for parametric uncertainty, common approaches include parametric scenario or sensitivity analysis (SA), stochastic programming (SP), robust optimisation (RO) and Monte-Carlo Analysis (MCA). A brief comparison of the advantages and disadvantages of these approaches, particularly for energy systems analysis and integrated assessment modelling, is given in Table 1.
The decisions taken by a mathematical model based on stochastic programming are based on the expectations of uncertain outcomes from known probability distributions (Birge and Louveux, 2011). In contrast, the decisions taken by robust optimisation are usually based on extreme values (e.g., minimax and maximin) or at the tails of the distributions, i. e., local or deterministic optimisation, since global (i.e. assessing all possible values of a parameter) or probabilistic optimisation (i.e. considering the entire probability distribution of a random variable) is often computationally extensive (Moret et al., 2020;Zugno and Conejo, 2015;Gorissen et al., 2015). In our analysis, each variation of the input parameters results in a different scenario and decision. Therefore probability distributions of the model outputs are produced, suitable to quantify uncertainty in the outcomes. It should be acknowledged that these probability distributions are derived from the 4000 thousand scenarios assessed in our study and should not be interpreted as the likelihood of the obtained outcomes. In this regard, the probability of an outcome described in our analysis reflects the ratio of the number of Monte Carlo experiments (or scenarios) that are favourable to this outcome to the total number of experiments performed.
We should also note that the integration of Monte Carlo Analysis in the integrated assessment model ETSAP-TIAM does not imply that we use TIAM to perform predictions. This is clearly outside the scope of the underlying mathematical framework of the model. Rather, we perform a what-if scenario-based assessment, which in our study is augmented by the uncertainty surrounding our outcomes based on the assumed uncertainty of key contextual factors that are included as inputs in our analysis and influence the configuration of the future energy system.

The ETSAP-TIAM integrated assessment model
ETSAP-TIAM (or simply TIAM) is based on the open-source TIMES energy systems modelling framework developed by the Energy Technology Systems Analysis Program of the International Energy Agency (IEA-ETSAP). TIAM is a global instance of the open-source TIMES model generator (Loulou et al., 2016). It is a bottom-up, process-oriented, technologically detailed cost-optimisation model with a detailed representation of energy supply, conversion and end-use technologies. Besides the energy sector, TIAM includes a single-sector economy submodel and a reduced-form climate model. The three systems, energy, economy and climate, interact altogether. Elasticities of energy service demands to their own prices capture a major element of feedback effects between the energy and economy systems. Stylised damage functions capture feedback effects of environmental and climate degradation on economic production by reducing the economic output level by a fraction, reflecting the worsening of natural conditions. The optimisation performed in TIAM leads to an inter-temporal dynamic partial equilibrium on energy markets driven by maximising the total global surplus, which acts as a proxy for welfare in each region of the model. For each represented world region, market equilibrium is assured at every stage of the energy-economy systems and across time. It determines investment and operating technology decisions taken by the model.
The surplus maximisation is subject to constraints such as resources availability (in the form of detailed cost-supply curves), technical constraints governing the investment, operation and decommissioning of technology, balance constraints for all energy carriers and emissions, the timing of investment payments and cash flows, energy and climate policy, etc. Non-cost decisions or short-sighted factors, like behavioural aspects of technology choice, public acceptance, or social/institutional capacity, are considered by additional constraints and appropriate cost assumptions. Future expenditures are discounted to account for time preferences and the cost of capital.
The model horizon is from 2010 to 2100, with a step length of 5 or 10 years (customisable). In this study, we use 10 years as a step length. The temporal resolution within each year is quite coarse for computational reasons, relevant when performing a Monte Carlo Analysis: the model identifies three seasons, Summer, Intermediate (Spring/Fall) and Winter, with two timeslices per season, daytime and night. Fig. 1 shows the spatial resolution of TIAM. The model is calibrated to the SSP2 storyline (Fricko et al., 2017;O'Neill et al., 2017). Baseline future energy demands are derived from the population (KC and Lutz, 2017) and  (Dellink et al., 2017;Leimbach et al., 2017) of the SSP2 scenario, as well as historical data and trends regarding the population and demographics (UNDP, 2019), GDP in purchasing power parity at different regions (Bevir, 2012), and final energy (IEA, 2016). More information about the calibration of TIAM to the SSP2 storyline is given in Appendix I of the Supplementary Material. A detailed description of the TIAM model, its vast technology database and its mathematical formulation is given in (Loulou, 2008;Loulou and Labriet, 2008).

Design of MCA for ETSAP-TIAM
Performing MCA with a large-scale integrated assessment model like TIAM is computationally expensive. Thus, High-Performance Computing Grids are utilised for asynchronous model solutions across multiple CPUs by leveraging the Grid and Multi-threading facility of GAMS (Rosenthal ER, 2017). The updated TIMES code supporting this facility is available at https://github.com/etsap-TIMES/TIMES_model. Key algorithmic insights are provided in Appendix II of the Supplementary Material. A detailed description is given in Panos et al., 2018).
We assume probability distributions for factors significantly impacting the energy system transformation and climate change mitigation, such as the equilibrium climate sensitivity, economic and population growth, the decoupling between the energy and the economy, the discount rate, the resource potential and investment costs of renewables and biomass, oil and gas reserves, the potential for CO 2 sequestration in the land use and forestry and geological CO 2 storage for carbon dioxide capture and sequestration (CCS) in depleted oil and gas fields and depleted aquifers. These factors are translated into input parameters for the model. These parameters are initialised by sampling them from the probability distributions of the factors they represent, as described in the next paragraph.
We perturb the uncertain model parameters using Latin Hypercube Sampling (LHS) (Helton and Davis, 2003) based on their probability density functions (PDFs). The LHS method was chosen to avoid creating large samples for obtaining meaningful statistics in MCA and reduce computational complexity without losing statistical information of the obtained results. The LHS process is described in Appendix III of the Supplementary Material. The sampled value of each random variable is either directly assigned to the corresponding TIAM parameter or is applied as an adjustment factor to the "BASE" value of the corresponding TIAM parameter derived from the model calibration and the deterministic version of the BASE_SSP2 scenario (see section 3.3). Table 2 shows the analysis's main random variables and their probability distributions. By sampling these parameters, we develop uncertainty estimates across time for major output variables of TIAM, such as temperature change, GHG emissions, GHG concentrations, energy technologies investments, energy commodities, energy systems costs and marginal GHG emissions abatement costs as interrelated functions of each other.

Scenarios definition
Four scenario families (each with 1000 states of the world (SOW) cases or Monte Carlo experiments) have been analysed with TIAM, summarised in Table 3. The reference scenario family (hereafter simply "scenario"), BASE_SSP2, follows the SSP2 developments and benchmarks three climate change mitigation scenarios. All climate change mitigation scenarios allow temperature overshooting. The 2C_SSP2 scenario aims to limit the temperature increase to 2 • C in 2100 compared to pre-industrial levels. The 2DS_SSP2_DA30 scenario derives from 2C_SSP2 but assumes a delayed climate change mitigation action starting in 2030. Finally, the 1p5c_OS_SSP2 scenario aims to limit the temperature increase to below 1.5 • C by the end of the century compared to the pre-industrial levels.
Temperature overshooting during the 21st century is associated with a cost function allowing relaxation of the temperature constraint in expensive overshoot conditions in the magnitude of the climate damage functions assessed in (Burke et al., 2015). The climate damage functions increase the cost to the economy, alter the GDP and indirectly influence the energy service demands. The penalty cost for relaxing the temperature constraint is 20% of global GDP in each period for every 1 • C temperature increase beyond the temperature constraint applied (1.5 • C or 2 • C). The constraint relaxation is important to avoid infeasibilities for Monte Carlo experiments, especially in those with climate sensitivity well above the median values of 3 • C per doubling carbon in the atmosphere.
The next section discusses key findings from the scenario analysis, while additional results are provided in Appendix IV of the Supplementary Material. Extensive datasets with the key input parameters from the Latin Hypercube Sampling and numerical results of the Monte Carlo Analysis of the four scenario families shown in Table 3 can be downloaded from the Zenodo repository with DOI: 10.5281/zenodo. 8045286

The world is ready to breach the Paris Agreement targets in the next five years
Today, the global average temperature increase from the preindustrial levels is around 1.1 • C (NASA, 2022). Climate change is moving exponentially, and the currently observed incremental progress in policy-making and investment decisions is insufficient. In 2030, the temperature increases from pre-industrial levels by 1.5 • C in 75% of the BASE_SSP2 scenarios -and in the 70% of all the 4000 scenarios assessed (Fig. 2). By 2050, the global average temperature increases by 2 • C in 80% of the BASE_SSP2 scenarios.
The analysis suggests that unprecedented and far-reaching climate policies must move quickly together with investments in low-carbon technologies. Still, immediate climate change mitigation action entails an overshoot of the 2 • C temperature increase by 2050 in 15-30% of the Table 2 Key random variables, their probability distributions and how they are applied to change the internal parameters of TIAM. The distributions were adapted from (Kypreos, 2008;Rogelj et al., 2012;Kypreos et al., 2019;Marcucci et al., 2019b Direct replacement a Each energy service demand (e.g., space heating) is associated with a driver determining its evolution over time (e.g., number of households). The relationship between the change in the driver and the change in the energy service demand is determined by an elasticity.

Table 3
Overview of the four energy and climate policy scenario families assessed in the MCA with TIAM. Each scenario family has 1000 scenarios or states of the world, sampled from the probability distributions shown in Table 2. Across the four scenario families, the sampling of the different random input parameters of the ETSAP-TIAM is the same to ensure consistency, and only the climate policy differs, as indicated in the and 1p5C_OS_SSP2 cases. The figure shows that temperature change varies smoothly as a function of climate sensitivity (CS). CS measures how much the global mean temperature will rise for a doubling of global carbon dioxide concentration in the atmosphere. CS is the main driver for those base scenarios resulting in temperatures below 2 • C in 2100. The threshold CS in 2100 of the base scenarios at 2 • C is between 1.3 and 1.4. The box plots show the interquartile range (IQR) of 50% of the scenarios, the centre line being the median of the full scenario set, and the whiskers showing 1.5xIQR. The scenarios of the BASE_SSP2 family, which are below 2 • C in 2100, are less than 2.3% of the total number of the BASE_SSP2 scenarios assessed.

Fig. 3. Energy System
Costs outlining increased investment needs between the base case BASE_SSP2 and the Paris Agreement cases (2C_SSP2, 2c_SSP2_DA30, and 1p5C_OS_SSP2) across the range of uncertainty within the four scenarios and 1000 states of the world. For clarity, the figure is truncated to a maximum of 80 trillion US Dollars ($Trn). Appendix IV shows the total range of the energy system cost distributions in the different scenarios. assessed scenarios (depending on aiming at 1.5 • C or 2 • C at the end of the century). However, delaying the implementation of climate policies and investments by ten years could double the risk of overshooting the goals of the Paris Agreements by 2050. These outcomes show that there is no extra time left for delaying policies that enable the energy transition on a global scale.

Getting the world on track to Paris Agreement targets is associated with a high probability of high energy system costs
The energy system costs exponentially increase with the stringency of climate change mitigation (Fig. 3). The distribution of the energy system cost in the climate change mitigation scenarios is lognormal, indicating high frequencies of high costs. On average, moving from BASE_SSP2 to the 1p5C_OS_SSP2 scenarios requires a surge in the energy system cost by 8 $Trn in 2030 and 16 $Trn in 2050. In 25% of the 1p5C_OS_SSP2 scenarios, the total energy system cost is 60% higher than the total energy system cost of BASE_SSP2 in 2030 and 85% higher by 2050. In 4% of the 1p5C_OS_SSP2 scenarios the energy system cost in 2050 is lower than in BASE_SSP2. However, these are scenarios with very low climate sensitivity (less than 1.7 o C), high decoupling between economic growth and energy consumption, large sustainable renewable energy potentials to be exploited, and accelerated technology learning.
More than two-thirds of the additional investment required to limit the temperature increase to 1.5 • C are needed in emerging and developing economies. The private sector and consumers must carry out most transition-related energy investments. In this regard, international development banks and climate finance commitments from advanced economies can act as catalysts to accelerate capital flows and allow developing economies to step into a lower emissions pathway.

4.3.
Delaying the climate action for achieving the 2 • C target would cost almost the same as acting now to meet the 1.5 • C target A delay in mitigation action to achieve the 2 • C Paris Agreement target results in energy system costs ranging from 22 to 102 $Trn per year by 2050 (2C_SSP2_DA30 scenario). This range is directly comparable with the energy system cost for the same year for meeting the 1.5 • C target if climate policy action to achieve this target starts immediately (22-98 $Trn per year by 2050 in the 1p5_OS_SSP2 scenario).
Delaying action can reduce costs in the short-run, as in 97% of the 2C_SSP2_DA30 scenarios, the energy costs are lower than 1p5_OS_SSP2 in 2030. However, on the net, delaying action to limit the effects of climate change is costly.By 2050, 15% of 2C_SSP2_DA30 scenarios have higher energy costs than 1p5_OS_SSP2. In at least the half of the simulations the costs between 2C_SSP2_DA30 and 1p5_OS_SSP2 differ by less than 7%. Moreover, a delay in the climate change mitigation action produces persistent economic damages from higher temperatures. In the long run, the climate policy, when implemented, must be more stringent than it would have been if the climate action were started earlier and thus resulting in additional financial burdens (see Fig. 4, which compares the marginal cost of carbon in 2C_SSP2 and 2C_SSP2_DA30 scenarios; the cost of carbon in the latter is equivalent with the cost of carbon of 1p5C_OS_SSP2 scenarios).

If it is to meet the Paris Agreement target, the worldwide average carbon price in 2030 needs to be equal to today's (2022) highest carbon taxes ($ 130-137 tCO 2 -1) that are observed in very few countries
Today, there is a gap between the decarbonisation policies in place and the ambition required to limit the temperature increase to below 2 • C by the end of the century from the pre-industrial levels. Carbon prices or taxes are one of the main instruments to accelerate the decarbonisation of the economy. While carbon prices have increased in the past years in several countries, they remain short of the levels needed to drive the transformative change and unlock investment essential for decarbonisation pathways (World Bank, 2022 The marginal abatement cost of CO 2 , which is the dual of the GHG emissions budget constraint imposed at the global level in ETSAP-TIAM, has in the 2C_SSP2 scenario family that limits the global temperature increase below 2 • C a statistical mean of $168 tCO 2 − 1 in 2030, $196 tCO 2 − 1 in 2050 and $ 273 tCO 2 − 1 in 2100 (Fig. 4). In the 1.5C_OS_SSP2 scenario family, the mean marginal cost to limit the temperature increase below 1.5 • C is $ 416 tCO 2 − 1 in 2030 and $ 430 tCO 2 − 1 in 2050. In 15% of the 1.5C_OS_SSP2 scenarios, the marginal CO 2 cost in 2050 is twice the mean of 2030. In the case of delayed action for achieving the 2 • C threshold, 25% of the 2C_SSP2_DA30 scenarios have a marginal CO 2 cost in 2050 equal to or higher than the cost of achieving the 1.5 • C threshold if the corresponding emissions abatement action starts today. In all scenarios, the marginal CO 2 cost increases with the stringency of temperature change and can relax after a temperature target overshoot is reversed. At the same time, it lowers with technological change (for instance, the correlation between the marginal CO 2 cost and the CAPEX of Bioenergy with CO 2 Capture and Storage is − 0.4). The need for strong near-term carbon pricing is clear in the 2030 and 2050 box plots of Fig. 4. There are ramifications for early action and risk mitigation with an indication of the impact of climate sensitivity uncertainty on the cost of mitigation. The trend begins to breakdown towards the end of the model horizon for outlier scenarios with high climate sensitivity and discount rates.

Achieving the Paris Agreement targets requires electrification and energy efficiency delivering their maximum potential
Many governments have ambitious plans for reducing emissions from mainly the power sector. However, this would only reduce global emissions by one-third. Reaching the Paris Agreement targets requires more attention to the transport, industry and buildings sectors. Spreading the use of electricity into more parts of the energy system is a key contributor to reducing GHG emissions from the end-uses (see Fig. 5). Electric cooking in households increases its share to 40% on average by 2050 in the 1.5C_OS_SSP2 scenarios at a global scale, which is about three times higher than the average share of electric cooking in the 2C_SSP2 scenarios for the same yeartoday's share of electricity in cooking fuels is estimated at 2.5% at a global scale. In 20% of the 1.5C_OS_SSP2 scenarios, the share of electric cooking exceeds 80% by 2050. The increased access to clean cooking suggests a clear alignment between sustainable development goals 7 (affordable and clean energy) and 13 (climate change mitigation).
In the residential sector, electric-based space heating accounts for 65% on average of the total space heating supply by 2050 in the 1.5C_OS_SSP2 scenario family globally, which is about 6 times today's share. In the 2C_SSP2 scenarios, the share of electric heating increases to 43% on average globally by 2050. In 25% of the 2C_SSP2 scenarios, the average share of electric space heating exceeds the one of the 1.5_OS_SSP2 scenarios in 2050, further highlighting electricity's role in meeting climate change mitigation targets. A delay in the climate change mitigation action by a decade would eventually require an acceleration of the space heating electrification resulting in an average share of 56% in 2050, i.e., about 13 percentage points more than in 2C_SSP2. Moreover, in 5% of the 2C_SSP2_DA30 scenarios, the share of electric-based space heating exceeds that observed in 1.5C_OS_SSP2 by 2050. Only in less than 3% of all climate change policy scenarios the share of electric-based heating is in 2050 at today's level. District heating complements electric-based heating and sees its share rising globally to 21% on average by 2050 of the energy consumption for heating in residential sectors in the 1.5C_OS_SSP2 scenario, which is more than twice today's levels (around 8% of the global heating demand). Notably, the share of district heating in global heat consumption has remained stable in the last 20 years.
In industry, electrification of process heating, also via hightemperature heat pumps, increases globally to an average of 33% by 2050 in the 1.5C_OS_SSP2 scenarios from around 19% todayand in 35% of the 1.5C_OS_SSP2 scenarios is twice the today's share. However, when the ambition is to limit the temperature increase to 2 • C instead of 1.5 • C, the share of electricity in final energy consumption in industry is, on average on a global scale, 24% in 2050. In only 5% of the 2C_SSP2 scenarios, the industry's electrification is higher than in 1.5C_OS_SSP2. The fuel and technology switching in industry accelerate in the case of delayed action. In 20% of the 2C_SSP2_DA30 scenarios, the share of electricity in final energy consumption in industry exceeds its share in the 1.5C_OS_SSP2 scenarios by 2050.
Finally, transport undergoes a profound transformation towards alternative fuels, i.e., electricity, biofuels and hydrogen, in the context of stringent climate change mitigation policy. The share of alternative fuels in transport reaches 63% in 2050 globally in the 1.5C_OS_SSP2. In the 2C_SSP2 scenarios, the share of alternative fuels in 2050 is somewhat lower on average, 57%. Delayed climate action would require accelerating the penetration of alternative fuels in transport in the post-2030 period. In 95% of the 2C_SSP2_DA30 scenarios, the share of alternative fuels is higher than in 2C_SSP2 in 2050 -and in 20% of the 2C_SSP2_DA30 scenarios, the alternative fuels share exceeds the share attained in the 1.5C_OS_SSP2 scenarios. This outcome, combined with the similar finding in industry, suggests that a delayed climate policy action for 2 • C could significantly increase the mitigation burden for the industrial and mobility sectors, close to the levels needed to limit the temperature increase below 1.5 • C. We should note that synthetic e-fuels are not included in the alternative fuels in Fig. 5 and in the above calculations. The synthetic e-fuels account, on average accross all the 1.5C_OS_SSP2 and 2C_SSP2 scenarios, for more than one-third of the final energy consumption in transport by 2050. They are needed for international long-distance aviation and navigation and long-distance road transport in geographies with barriers (e.g., mountainous terrain) to deploy alternative fuel infrastructure.
Across all sectors, the share of electricity in total final energy consumption doubles from 16% today to 32%, on average, in 2050 in the 1.5C_OS_SSP2 scenarios. There is no case in the ensemble of scenarios assessed in which the share of electricity remains at today's levels in 2030 or 2050, and at the same time, the global average temperature increase stays below 2 • C or 1.5 • C in 2100. The share of electricity in final energy consumption increases with the climate change mitigation ambition, as 97% of the 1p5_OS_SSP2 scenarios have higher electrification than the 2C_SSP2 scenarios by 2050.
Together with electricity, energy efficiency accelerates with the climate change mitigation effort. In 2050, 10% of the 2C_SSP2  scenarios and 80% of the 1.5C_OS_SSP2 scenarios have less final energy consumption than the BASE_SSP2 scenarios. Moreover, in 85% of the 1.5C_OS_SSP2, the final energy consumption is lower than 2C_SSP2, highlighting the need for higher efficiency gains for limiting the global temperature increase to 1.5 • C instead of 2 • C. Fig. 6 shows the global electricity supply from major options across the four assessed scenario families. There is a significant increase in power generation in the Paris Agreement-compliant 2C_SSP2 scenarios, for which in 2100, its median value is 16% above the BASE_SSP2 scenario. For comparison, the 1p5C_OS_SSP2 scenario family is 51% above BASE_SSP2, highlighting the role of electrification in achieving ambitious climate change mitigation targets. The dominance of solar electricity and other non-fossil fuels needed for achieving a high degree of electrification in the end-use markets and avoiding releasing residual carbon emissions is clear.

In electricity supply, solar PV is a robust technology to invest in
Interestingly, solar, other renewables, and nuclear have achieved higher shares than fossil fuels, even in some of the BASE_SSP2 Monte Carlo experiments (see Fig. 19 in Appendix IV). This indicates the dynamics underlying the commercialisation of renewable electricity as a competitive option, i.e., that the realisation of large-scale penetration of renewable-based electricity does not require additional support measures (as of today) when a strong climate change mitigation policy is present. Therefore, solar PV is a robust technology in the power generation markets, getting market shares with or without a carbon constraint. Nuclear power is also interesting, displaying lower uncertainty in deployment towards 2100 compared to 2050, which implies nuclear is used in all cases examined. The contribution of nuclear power in electricity production increases in the long-term in the decarbonisation scenarios. This is especially pronounced after 2050/60, when the wind and other renewable potentials are fully exploited and the additional electricity supply to meet the increasing demand needs to remain carbon-free.

Electricity cannot decarbonise the entire system alone, and hydrogen extends electricity's reach to hard-to-electrify sectors
In the 1.5_OS_SSP2 scenarios, hydrogen emerges by 2030 first in industry (on average, 76% of the global hydrogen consumption in 2030 occurs in industrial clusters), and by 2050 it scales up to automotive applications (on average, 50% of hydrogen consumption occurs in road transport). The mean total hydrogen supply increases from 24 EJ/yr in 2030 to 38 EJ/yr in 2050, at a global scale, in the 1.5_OS_SSP2 scenarios. Interestingly, while in 80% of the 2C_SSP2 scenarios, the total hydrogen supply is lower than in 1.5_OS_SSP2 by 2050 at a global scale, within a context of a delayed climate change mitigation action towards 2 • C about 60% of the 2C_SSP2_DA30 scenarios show higher total hydrogen supply than in 1.5_OS_SSP2 (Fig. 7).
The hydrogen penetration increases with the climate change mitigation ambition: in 80% of the 1.5C_OS_SSP2 scenarios, the use of hydrogen is higher than in the 2C_SSP2. In less than 1% of the assessed 1.5C_OS_SSP2 scenarios, there was no penetration of hydrogen by 2050. The distribution of global hydrogen supply in the 1.5C_OS_SSP2 scenarios shows a bi-modality. This is triggered by climate sensitivity ,   Fig. 7. Histograms of global hydrogen supply in 2050 in the climate change mitigation scenarios, in PJ/yr. The x-axis of the histograms represents the bins of PJ/yr. and the y-axis the number of occurrences within each bin. Notice that the histograms of the hydrogen supply are bimodal, reflecting the uncertainty in realising a "hydrogen economy" by 2050. The figure also indicates that high hydrogen penetration prospects are correlated with stringent climate change mitigation policy. Fig. 8. Hydrogen supply shares in 2050 by major technology cluster (grey = fossil hydrogen, blue = fossil with CCS hydrogen, green = hydrogen from renewable sources and electrolysis). The shares are given as histograms. The x-axis represents the bins of the shares, and the y-axis the number of occurrences within each bin. A delayed climate change mitigation action would require a faster deployment of green hydrogen in the long term compared to an immediate policy action to limit the temperature increase below 2 • C. This would result in stranded assets if, due to the delay in climate change mitigation action, investments are directed to fossil-based hydrogen production. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) which affects the stringency of the climate change mitigation action. When the climate sensitivity is below 2.6, the intensity of the climate change policy is not enough to make hydrogen a cost-effective option for the future energy mix.
Hence, the analysis suggests that a) hydrogen as an energy carrier is cost-efficient mainly under stringent climate change mitigation policies; b) if green hydrogen production costs do not significantly drop, hydrogen mainly emerges in those sectors with limited alternative decarbonisation options; c) fuel cells improvements drive hydrogen demand and infrastructure deployment.

Green is the dominant hydrogen colour under stringent climate change mitigation targets
Green hydrogen, produced from electrolysis using wind or solar electricity or biomass gasification with and without CCS, is the most compatible production option to reach climate neutrality by midcentury. In the 1.5C_OS_SSP2 scenario, green hydrogen supplies, on average, about 80% of the global needs throughout 2030-2050 (Fig. 8).
In a context of a delayed climate change mitigation action, the mean share of green hydrogen is 60% on a global scaleand it is the dominant production option by 2050 in 70% of the 2C_SSP2_DA30 scenarios. In contrast, in the 2C_SSP2 scenario, there is, on average, a production mix with green and blue hydrogen attaining shares of 40% and 30% correspondingly by 2050 (the remaining 30% is grey hydrogen). Still, green hydrogen is the main production route in 45% of the 2C_SSP2 scenarios by 2050. Regarding blue hydrogen, its role in the 1.5_OS_SSP2 scenarios is limited as it emerges as the dominant production option for 2030-2050 in only 13% of the assessed scenarios. These outcomes entail a strong investment signal towards green hydrogen with the increased climate change mitigation ambition.

Bioenergy is needed everywhere in a net-zero emissions global energy system
There is a trade-off in the use of gaseous, liquid and solid modern bioenergy between the energy supply and demand sectors. In the 2C_SSP2 scenarios, the share of bioenergy in the demand sectors rises on average to 20% globally by 2050 (from about 8% today), and a similar trend is also in the 1p5_OS_SSP2 scenarios (Fig. 9). After 2030, there is a shift of bioenergy consumption from the demand sectors to the energy transformation and supply sectors which have more options to provide negative emissions via CCS. Industry is in high need of solid bioenergy as it can provide high-temperature heat and be co-fired with coal to reduce the intensity of emissions of existing generation assets. The mean share of bioenergy in industry on a global scale increases to 33% in the 1p5_OS_SSP2 scenarios and 24% in the 2C_SSP2 scenarios by 2050.

Emissions from existing assets are a key challenge towards decarbonisation
Today, power and industry account for 60% of emissions. Reaching the Paris Agreements targets will depend on tackling the emissions challenge presented by these sectors' long-lasting assets, many of which were recently built in emerging economies and could operate for several decades. While this underpins the need for hydrogen and CCS, the analysis of this study also suggests that if pure economic optimisation at a global scale is to be taken into account, negative emissions technologies are induced mainly in industrialised regions to compensate for the emerging economies with increasing CO 2 emissions as they continue to rely on fossil fuels to support their economic development (see Fig.15 in Appendix IV of the Supplementary Material regarding the regional CO 2 emissions results). Apart from that, the perfect foresight optimisation of TIAM is imposing very early carbon mitigation actions (by accounting for lock-ins and technology deployment constraints) to create sufficient conditions to stabilise the global average temperature change below 2 • C. Fig. 10 shows the emergent carbon budgets as a combined function of climate sensitivity and net carbon dioxide removals for the 2C_SSP2 scenarios, the median of which attains annual carbon dioxide removal (CDR) levels above 20 GtCO 2 in 2100. This must be seen in relation to the global carbon emissions in the BASE_SSP2 scenarios, the median of which starts with 40 GtCO 2 in 2030 and reaches values of >65 GtCO 2 in 2100, while the remaining net CO 2 emissions in the 2C_SSP2 scenarios are, on average, below 10.5 GtCO 2 in 2100. The amount of carbon removal due to afforestation is between 5 and 5.5 GtCO 2 from 2030 to 2080 and falls to 3 GtCO 2 in 2100. Most of the contributions of CDR are related to biomass for power generation, synthetic fuels and industry, followed by gas and coal for industrial uses.
By overlaying Fig. 4 on Fig. 10, it can be argued that for some scenarios, CO 2 emissions and CO 2 price do not vary smoothly or unidirectionally as a function of discount rate over time, nor do all scenarios follow similar shape trajectories over the 21st century, as is typically the case in IAM model intercomparison scenario ensembles widely performed so far in the literature (McCollum et al., 2018;Kriegler et al., 2015;Kriegler et al., 2013).
Finally, according to our results, GHG emissions neutrality is achieved between 2050 and 2060 in 50% of all assessed scenarios (Table 4). However, the net-zero GHG emissions are achieved in the 1p5_OS_SSP2 scenarios later than in the 2C_SSP2 scenarios because of the temperature Fig. 9. Share of bioenergy (i.e., bioliquids, biogases and modern solid biomass) in global total final energy consumption (in 2020, the share is around 10%). The yaxis shows the frequency of the bins of the shares of bioenergy reported at the x-axis. overshooting in 1p5OS_SSP2 (see also Fig. 2). This outcome for the 1p5_OS_SSP2 scenarios implies a steep emissions reduction trajectory between 2030 and 2040 and less steep between 2040 and 2050. Fig. 11 shows a correlation scatter plot for some of the pertinent input perturbations and highlights the correlation with energy system mitigation transitions. Climate sensitivity influences temperature, the marginal abatement cost of CO 2 , primary energy supply, primary fossil energy, renewable energy, the total installed capacity of solar PV and bioenergy carbon capture and storage (BECCS). More nuanced correlations are seen, for example, whereby bioenergy potential is a stronger driver of BECCS installed capacity than BECCS investment capital expenditure (CAPEX). In contrast, solar PV installed capacity is far more sensitive to CAPEX than solar resource potential. The decoupling of energy intensity ("Demand Driver Elasticity" in the figure) from macroeconomic drivers is a critical uncertainty, as shown by the strong correlation between the macroeconomic driver elasticities (decoupling factors) and primary energy supply. Primary energy supply in the future becomes less correlated to energy prices and more correlated to the level of decoupling from economic growth (see Fig. 11).

Table 4
Percentage of scenarios reaching net-zero globally in different years for the different climate change mitigation scenario families assessed. The frequency of scenarios achieving net-zero before 2050 is higher in the scenario with a delayed mitigation action to avoid the economic damages from temperature overshooting. This result shows that delaying the climate change mitigation action does not mean that the effort required to achieve net-zero is smaller -not acting fast and start reducing now leads to the need to reduce more later and reach netzero emissions earlier.  Fig. 10. Uncertainty in annual CO 2 emissions, their resultant emergent cumulative CO 2 emissions (Uncertainty in carbon budgets) and the induced uncertainty in marginal abatement cost of CO 2 . The emissions are plotted against climate sensitivity. The figure highlights that the higher the climate sensitivity, the earlier and higher the uptake of negative emissions technologies to avoid temperature overshoot, which entails large GDP losses from increased climate damages.

Conclusions and policy implications
The study applied Monte Carlo Analysis to a process detailed Integrated Assessment Model, the ETSAP-TIAM model. This model is based on the open-source TIMES energy system framework developed by the Energy Technology Systems Analysis Program (ETSAP) of the International Energy Agency. The analysis examined 4000 states of the world, each with different climate sensitivity, temperature limit targets, technology costs, economic and demographic developments, resource potentials, price elasticities and other demand drivers such as the number of households, floor areas, etc. It assessed deep decarbonisation pathways under a context of unprecedented uncertainty in the energy sector.
The analysis identified key technologies for the future energy mix that help limit the average global temperature increase by the end of the century to 2 • C or 1.5 • C: hydrogen and synthetic fuels, CO 2 capture and storage (CCS), Direct Air CO 2 Capture with Sequestration (DACCS), nuclear, wind, solar and bioenergy. Many of these technologies are immature or have a low deployment rate (e.g., hydrogen and synthetic fuel pathways, electricity from CCS, or even wind turbines in several European countries where social resistance is high). To be able to realise the global investments shown in our analysis, they need to be further developed and to be supported in their early uptake stages. This outcome entails a signal to policymakers when designing energy and climate policies to accelerate the transition.
None of the 4000 Monte Carlo experiments displays reliance on one particular carbon mitigation option. This outcome suggests that a portfolio approach is suitable for achieving ambitious emissions cuts, with each alternative having different investment costs and risks. A correlation analysis of the obtained installed capacities in the different Monte Carlo experiments showed that many technologies play complementary roles in climate change mitigation. For instance, renewable and nuclear energy is deployed in all scenarios examined, without one option excluding the other. Or wind and solar energy are both deployed at high rates, and there is no energy system configuration in our analysis relying only on one of the two. Another example is in the transport sector, where electromobility co-exists with hydrogen and synthetic fuels (also of biogenic source).
However, negative correlations of some technologies' capacities indicate competition for the same resources. This is, for example, the case between bioenergy with CCS and DACCS due to the limited sequestration potential. In this regard, DACCS is deployed after the deployment of BECCS, a similar finding also noted by (Marcucci et al., 2019).
The above correlation analysis of the obtained capacities has significant policy implications. It suggests that policy designs promoting specific technologies via financial or other incentives (e.g., feed-in tariffs or priority in accessing infrastructure) or policies banning or limiting the deployment of low-carbon options identified as robust in this analysis (for example, due to social or political innacceptance of these options) are likely to entail risks to delivering the required emissions cuts and risks of high energy costs. In contrast, policies and market designs that are more technology-neutral and are based on new market design mechanisms, such as tenders and pools, could be attractive to investors because they leave options open, mitigate investment risk as they are based on market dynamics, and consider the complementarities between the different carbon emissions mitigation options.
The global investment trends we observe today lag far behind the levels required in the ensemble of the 4000 runs presented in this manuscript. The energy system configurations obtained in our analysis imply that a secure and sustainable energy supply is capital-intensive. In 20% of all scenarios examined, the energy system cost in 1p5C_OS_SSP2 by 2050 is twice the global energy system cost of the BASE_SSP2 scenario. In 5% of scenarios, the energy system cost in 1p5C_OS_SSP2 is three times higher than in BASE_SSP2 by 2050. Moreover, in more than 50% of the scenarios examined, the energy system cost in 2050 in the 1p5C_OS_SSP2 case is twice the cost of today (as calculated by the model) -see also Table 6 in the Supplementary Material. In addition, our analysis suggests that the cost of the delayed action by 10 years from now in order to limit the temperature increase by the end of the century to 2 • C from the pre-industrial levels is almost equal to the cost that would have occurred if the ambition were to limit the increase to 1.5 • C and the climate change mitigation action would have started immediately.
Such a capital-intensive energy system that realises the transition to a carbon-free economy will also call for a massive mobilisation of resources. A strong societal commitment is required in adopting new technologies such as sequestration of CO 2 or heat pumps and electromobility, even wind turbines in many countries -to mention a few examples. In this context, investors need strong long-term pricing signals. Energy markets require coordinated energy and climate legislation that do not contradict the energy and climate goals (Strambo et al., 2015), but they simplify and accelerate new projects' permitting processes and licensing. 1 Carbon prices can provide signals to investors toward clean and efficient technologies. Still, our analysis finds that the around 70 carbon pricing instruments existing today worldwide (World Bank, 2022), including taxes and emissions trading systems, are insufficient. Higher carbon prices are needed to close the gap between pledges and policies. For instance, the carbon levies of $ 130-137 tCO 2 − 1 , which are only in Sweden and Switzerland today, must be the worldwide average carbon price by 2030. By 2050 the carbon prices need to be four times higher than in 2030, on average. Such high carbon prices have social and political challenges. In cases of energy-intensive economies or when revenues from carbon taxes are not effectively recycled within the economy (e.g. if they are used to payback international debts), high carbon taxes and prices could raise inflation and energy prices (Konradt and Weder, 2021). Therefore, to realise the high carbon prices suggested in our analysis with minimum negative social impacts, tax revenue and other redistribution policies need to be implemented to alleviate the adverse effects of the increased cost of carbon on the most vulnerable.
The ensemble of runs analysed notes electrification as a key enabler of the energy transition. However, the suggested electricity systems become more weather dependent, as the electricity generation from wind, solar and hydro overpasses by four times, on average, the fossilbased generation by 2050. These power systems require interconnection in all grid levels, energy storage, fast-reacting grids, demand response, and flexible generation units. Security of electricity supply will be a major issue in many geographies, either in winter or summerdepending on the region. To avoid a shortage of electricity supply, policies supporting technologies that can contribute to the security of electricity supply are essential, such as the integration of the price component of ancillary services delivering flexibility provision into the electricity price 2 , incentives for renewable energy sources with small weather variability (e.g., geothermal or solar PV in the mountains), incentives for storage at different time scales, and demand response tariffs to enable load shifts and peak shaving from consumers.
Bioenergy emerged as one of the important drivers of realising the energy transition in our analysis. Still, its sustainable exploitable potential is surrounded by high uncertainty. In scaling-up bioenergy to the levels suggested by our analysis, a basket of policies would be needed that foster bioenergy projects and develop bioenergy distribution infrastructure. Among them could be policies promoting sustainable energy crop production that does not risk food insecurity and measures 1 This result is also echoed in the recent decision of the EU to accelerate action for one-year renewable project permits https://www.reuters.com/busi ness/sustainable-business/eu-plans-one-year-renewable-energy-permits-faster -green-shift-2022-05-09/.
enabling the exploitation of currently underdeveloped bioenergy sources. Especially manure, essential for the production of biogas, needs policies to lift financial obstacles related to its use for biogas, e.g., subsidies, certificates, co-fermentation with higher-energetic sources, supports for its collection from multiple and close-together farms for usage in a single facility (Burg et al., 2019). The sustainable exploitation of forest wood, which is so much needed for large-scale BECCS applications, requires policies balancing forest management, energetic-uses, and non-energetic uses and eco-services provided by the forests (e.g., soil protection, climate regulation, pollution and water control, recreational activities) (Thees et al., 2020). Blue and green hydrogen gain growing importance in our analysis after 2040 at a global scale. We find a positive correlation between the carbon price and the penetration of hydrogen in the energy mix. Still, the future success and timing of the hydrogen economy depend on technological advancements and targeted measures. The latter should prevent stranded assets in hydrogen production pathways that do not meet longterm environmental criteria. Rigid climate goals and efficiency standards, or market-based mechanisms like fossil fuel taxation, may help develop hydrogen demand. Industrial clusters may offer good opportunities for low-carbon hydrogen deployment (Reigstad et al., 2022).
In our analysis, countries with high economic development and slowly-growing energy consumption reduce carbon emissions by going into net-negative emissions and give space within the carbon budget to emerging and less developed economies to continue fuelling their economic growth using fossil fuels. The timing of negative emissions technologies depends on the climate change mitigation ambition and climate sensitivity. Meeting the Paris Agreement targets in a context of high climate sensitivity would require deploying negative emissions technologies within this decade. Currently, only DACCS is a commercially available technology. Still, it faces issues of scaling up as today it requires a cost of carbon of about $ 1200 tCO 2 − 1 to be profitable, 3 despite that all negative emissions technologies' components are known. Besides costs, the main barriers hindering the wider deployment of negative emissions technologies include the social acceptance of onshore CO 2 storage (Sutter et al., 2013), concerns related to the integrity of CO 2 storage, and the perceived risk of carbon leakage. In this regard, policies creating market pools for the deployment of CO 2 capture and storage, as well as policies promoting research and development and pilot demonstration of negative emissions technologies, are needed to be in place urgently, together with the required regulation and legislation (IEA, 2021). The discussion above implies that mitigation policies are directly affected by uncertainties in climate response, economic impacts of climate change damages and technology costs. These factors must be fed into policy-making decisions, influencing the climate change mitigation policy effectiveness. In turn, this means that the uncertainty of these three factors will affect the mitigation costs that companies and consumers face.
In evaluating our methodology, we note that this is a first-of-a-kind Monte Carlo Analysis with a large-scale process-based integrated assessment model. To achieve this, significant progress was made in linearising all non-linear functions of the macroeconomic model, allowing to perform MCA analysis within a linearised model formulation.
Other scholars can apply this method, described and provided as open-source in Appendix III. Besides the methodology we used here, probability density functions of stochastic input can also be generated via a questionnaire addressing an expert's opinion or, like in the Prometheus model (Fragkos et al., 2015), based on systematic econometric analysis. Quadratic damage functions of temperature change with stochastic coefficients can also be included, and the problem can be solved by minimising the system's cost-plus abatement plus damages in quadratic programming formulations. Moreover, elements of Robust Optimisation, e.g., for energy security issues (Babonneau et al., 2011), can also be introduced.
Limitations in our analysis include the low temporal and spatial resolution of the framework, which is particularly relevant for the integration of high shares of renewable energy and identification of local constraints in the deployment of clean technologies, the perfect foresight character of the TIMES framework that reduces the uncertainty during the evolution of the energy system within a particular Monte Carlo experiment, and the need to additionally consider in the MCA model input parameters such as deployment rates of technologies and bounds on variables that become binding in some experiments and they are often equally uncertain with the main drivers influencing the evolution of the future energy system.

Data and code availability
The TIMES code is available at IEA-ETSAP GitHub (https://github. com/etsap-TIMES/TIMES_model) as open-source. The code used in this paper to perform Monte Carlo Analysis is also available at IEA-ETSAP https://iea-etsap.org/projects/TIMES-MCA%20Final%20R eport.zip, together with extensive documentation on how to use the scripts for solving the TIMES models over High-Performance Grid Computing. Together with the scripts, we also provide a Latin Hypercube Sampling routine and the probability distributions used in this manuscript https://iea-etsap.org/projects/TIMES-MCA%20Final%20R eport.zip. A Supplementary Data File containing the input samples for the Monte Carlo Analysis and the numerical results from the 4000 scenarios (at a global scale) can be downloaded from a Zeonodo repository with DOI 10.5281/zenodo.8045286. Other data and codes needed to reproduce the current work are available by the authors upon a reasonable request.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability
A Supplementary Data File containing the input samples for the Monte Carlo Analysis and the numerical results from the 4000 scenarios (at a global scale) can be downloaded from a Zeonodo repository with DOI 10.5281/zenodo.8045286. Additional data will be made available by authors upon a reasonable request.
International Energy Agency Technology Collaboration Programme Energy Systems Technology Systems Analysis Programme (ETSAP). The authors would also like to thank the anonymous reviewers for their constructive comments in improving the quality of the manuscript during the peer-review process.