Quantifying both socioeconomic and climate uncertainty in coupled human–Earth systems analysis

Domain: earth_science
Published: 2025-03-19
Editorial outcome: major_revision

Abstract
Information about the likelihood of various outcomes is needed to inform discussions about climate mitigation and adaptation. Here we provide integrated, probabilistic socio-economic and climate projections, using estimates of probability distributions for key parameters in both human and Earth system components of a coupled model. We find that policy lowers the upper tail of temperature change more than the median. We also find that while human system uncertainties dominate uncertainty of radiative forcing, Earth system uncertainties contribute more than twice as much to temperature uncertainty in scenarios without fixed emissions paths, reflecting the uncertainty of translating radiative forcing into temperature. The combination of human and Earth system uncertainty is less than additive, illustrating the value of integrated modeling. Further, we find that policy costs are more uncertain in low- and middle-income economies, and that renewables are robust investments across a wide range of policies and socio-economic uncertainties.

Introduction
Addressing climate change is ultimately a challenge of risk management, recognizing that our ability to predict future climate with any precision is limited. Many coupled human-Earth systems models have been developed to explore potential future energy, emissions, climate and other outcomes of interest. However, in these models the limits to prediction are often addressed through sensitivity analysis, scenarios and model comparisons. In particular, much focus has been on the Shared Socioeconomic Pathways (SSPs) and Representative Concentration Pathways (RCPs) developed for the Intergovernmental Panel on Climate Change (IPCC), taking the ranges of outcomes from these scenarios from different models as indicative of uncertainty1–5. While these exercises provide useful insights, they limit the uncertainty space explored by focusing on a limited set of pre-defined socioeconomic and emissions concentration pathways and corresponding climate outcomes, and provide no quantitative probabilistic interpretation6,7. With just a range of scenarios or outcomes, decision makers are left to ponder whether all of the scenarios are equally probable, and whether more extreme outcomes outside the given range are possible. Thus, there are growing calls for more formal probabilistic, risk-based approaches to inform discussions about climate mitigation and adaptation8–12. In coupled human-Earth system analysis, there is value in quantifying both socioeconomic and climate uncertainty in an integrated manner to capture the cascade of uncertainty as more variables are considered along the chain from human activities to emissions to climate, in an attempt to provide insights for further analysis of climate impacts13. While there are limits to uncertainty analysis and not all uncertain aspects of our climate future can be quantified, providing transparent quantification where there is a scientific foundation can help work against well-known biases in decision making when uncertainty is present14.

There is also a need to regularly update projections of uncertainty as new information becomes available. For example, many studies continue to use the IPCC 8.5 watts per square meter (W per m2) scenario (RCP8.5) as a reference no policy baseline. However, given slower economic growth, falling costs of low-carbon energy options and government interventions worldwide directed at expanding the role of renewables and limiting emissions, many analysts now believe the RCP8.5 no policy scenario and the heavy use of fossil fuels like coal it implies to be unlikely8,15–18. There may be good reasons to still examine RCP8.5 to understand the implications of high consequence, albeit, possibly low probability outcomes. Formal uncertainty analysis can help to provide some indication of the probability of more extreme scenarios based on transparent assessments of underlying uncertainties.

To date, scenario analysis has been the most widely used approach to addressing uncertainty in projections. In general, a scenario approach limits the number of different input assumptions explored and therefore the range of possible outcomes. The set of assumptions explored via scenarios is ultimately a judgment, which may reflect biases or miss important areas of the uncertainty space19. Focusing on the results of limited tests can also lead to overconfidence that certain criteria must be met to achieve certain outcomes. Thus, while scenarios can be a helpful tool for investigating and communicating different potential futures, they can also focus attention on a narrow set of pathways, some which may be quite unlikely, which can be counterproductive.

The advantage of uncertainty quantification via a probabilistic Monte Carlo approach is that it more fully and systematically explores the uncertainty space, investigating wide ranges of values for inputs in many different combinations, helping to focus attention on more important regions and providing insight about how likely different outcomes might be19. Being transparent about the assumptions behind an uncertainty analysis allows for a clear linking of beliefs about future emissions and their underlying drivers to outcomes and subsequent climate risk analysis, and enables investigation of how differences in those beliefs might change projected outcomes and potential strategies to manage resulting risks.

Despite these benefits, probabilistic approaches also face limitations and challenges (which are discussed in more detail in Supplementary Discussion 1). Judgments must be made regarding the data used to estimate the distributions, the distributional forms, and the correlations between parameters, with the resulting distributions of outcomes depending on those assumptions19. There are also limitations related to the interpretation of relationships between outcome distributions that are separately characterized and to structural uncertainty. Scenario discovery approaches20 can address the former and multi-model analyses can address the latter. The existence of ‘deep’ uncertainties, where information or agreement is insufficient to characterize a distribution, or where processes are so poorly known that they are not represented in the underlying models, also present challenges. Some examples include unknown future carbon-free technologies or destabilization of methane hydrates in permafrost or in the ocean and resulting methane emissions and temperature feedbacks. The exclusion of such possibilities from models means uncertainty analysis conducted using those models does not capture the true tails of outcomes, necessitating complementary what-if analysis.

Even for processes that are represented in underlying models, there can be differing views about which uncertainties can be characterized with probability distributions and which are too deep to do so. However, there is room to combine a probabilistic approach with representations of deep uncertainty, for example by generating ensembles conditional on assumptions about deep uncertainties. A number of recent studies have embraced probabilistic projections, even in the presence of deep uncertainties19,21–24, in order to provide insight for decision-making.

As long as the limitations and assumptions of uncertainty quantification are made clear, the results of such analyses can provide important insights. There have been a number of valuable uncertainty analyses in the literature focused on global economic development, emissions and climate, however, they generally focus on a limited set of uncertainties or employ relatively simple models, and many are now quite dated25–36. The economic outlook, technology costs, and estimates of Earth system response have changed considerably in recent years with new data, analysis and evidence, making it useful to revisit these uncertainties. Recent work provides useful updates for a few uncertain parameters (population, total factor productivity and climate sensitivity)9 and uncertainty in long-run economic growth rates37. Other newer work has used simple models to make probabilistic projections of emissions38 or both emissions and global mean temperature change39,40.

In this work, we take a probabilistic ensemble approach to representing a comprehensive set of both socio-economic and climate uncertainties in a complex human-Earth system model to provide an updated set of probability distributions of both human and Earth system outcomes that can help inform a risk-based decision-making process. This work builds on a previous study focused on socio-economic uncertainties19 and work using an optimal fingerprint method to assess Earth system uncertainties41. We follow earlier studies29,33,34, but employ an updated version of the MIT Integrated Global System Model (IGSM), a coupled human-Earth systems model, and a reassessment of uncertainty in input parameters. Analysis of the resulting integrated, probabilistic socio-economic and climate projections shows varying contributions of human and Earth system uncertainties to different climate outcomes and finds that they are not simply additive. We also find that emissions policy lowers the upper tail of temperature change more than the median, policy costs in low- and middle-income economies42 are more uncertain than in high-income economies, and that renewables are robust investments across a wide range of uncertain futures. This type of uncertainty analysis can inform decision-making about mitigation and adaptation. Chapter 2 of Working Group III of the IPCC’s Fifth Assessment Report (AR5) presented a set of approaches, rules and tools for decision-making, many of which would be aided by uncertainty quantification43. In particular, the probability distributions from this analysis could be used in formal decision-making under uncertainty analyses that employ expected utility theory, decision analysis, robust decision making or other deliberative methods. However, they can also provide an understanding of uncertainty and risk that can aid decision-makers in more intuitive decision-making processes.

Results
Uncertainty quantification via Monte Carlo analysis
Our Monte Carlo-based approach to uncertainty quantification involves developing probability distributions for key input parameters in both the human and Earth system components of the coupled model. These include: climate sensitivity, ocean heat uptake, aerosol forcing, population, labor and capital productivity, autonomous energy efficiency improvement rate, fossil fuel resource availability, advanced technology costs, new technology penetration rates, urban pollutant initial inventories and trends, capital vintaging rate, abatement cost elasticities for methane and nitrous oxide, and elasticities of substitution (labor versus (vs.) capital, energy vs. labor/capital, energy vs. non-energy, inter-fuel substitution, and resource supply elasticities). Estimated distributions for socioeconomic parameters are based on statistical estimates using historical data where possible, published estimates of uncertainty, literature results and expert judgment, with correlations among subsets of related parameters imposed. A joint distribution for Earth system parameters is estimated using an optimal fingerprint approach41,44,45. These input distributions may be a useful result of the effort in themselves. See Supplementary Methods 1 for distributions of all input parameters.

We then sample from the distributions, using Latin Hypercube Sampling (LHS)46,47 to draw samples from each input probability distribution, and imposing a correlation structure amongst subsets of parameters, using @Risk software in Excel. Next, we generate ensembles of model runs using the sampled parameter values and develop integrated, probabilistic socio-economic and climate projections. These projections provide insight into the probability of outcomes of interest, including emissions, CO2 concentrations, radiative forcing, temperature, precipitation, Gross Domestic Product (GDP) and energy use. Global climate mitigation policy remains a ‘choice’ variable or a ‘deep uncertainty’ which we explore with four separate policy ensembles. The ensemble scenarios include a no new climate policy reference case (Reference), a case extrapolating Nationally Determined Contribution (NDC) targets of the Paris Agreement (Paris Forever), and two policy cases that achieve long-term temperature stabilization targets of 2°C and 1.5°C (Paris 2C and Paris 1.5C). Further details of our approach are described in the Methods section and Supplementary Methods 1.

The distribution of model outcomes from the ensemble of simulations for a particular scenario provides estimates of future states and their uncertainty, conditional on the model structure, the distributions of the uncertain input parameters and their assumed correlations, and the assumed scenario attributes (e.g. policy pathway). To address uncertainty in the form of the underlying input distributions, we also test an alternate setting using uniform distributions for all socioeconomic parameters. This follows the approach of robust decision making, which assumes all values are equally likely, defining only the ranges for each parameter from which to sample. We use the 1st and 99th percentiles of our original distributions for the range of the uniform distributions19. While changing the distributional form of the inputs does affect the resulting distributions of outputs, the differences are not large and the tails of distributions are affected differently depending on the outcome (see Supplementary Fig. 7). Different assumed correlations between inputs would also affect results, with missing correlations potentially widening the outcome distributions by allowing for a great variety of input sample combinations. For example, capturing regional correlation for labor and capital productivity growth results in more narrow global GDP outcomes than if regional productivity growth was uncorrelated. Correlation assumptions can have other implications for results as well. For example, uncorrelated technology costs mean that even if one fossil-based (or renewable) technology is not competitive, another might be. If these fossil or renewable costs were correlated, it could lead to overly difficult or easy energy transitions. Given the computational demands of the models we use, we limit the ensemble size to 400 members, which, with Latin Hypercube sampling has been shown to be sufficient46,47. We further test the adequacy of this sample size by creating 1000-member ensembles. We find that this does not substantially impact the outcome distributions19 (see Supplementary Fig. 8).

Emissions
The variance in emissions is greatest in the Reference scenario, with greenhouse gas (GHG) emissions in 2100 ranging from about 76 to 118 gigatonnes of CO2-equivalent (GtCO2eq) for the 5th to 95th percentile, with a median of 96 Gt. The range of Reference emissions is shifted down compared to the high end of the full range of emissions from the IPCC Sixth Assessment Report (AR6)4 (Fig. 1). While our Reference case does not include the mitigation pledges made by the countries in their submissions under the Paris Agreement, it does include policies targeting an expansion of renewables in power generation consistent with the International Energy Agency (IEA)48, which have resulted in lower renewable technology costs and a slowing rate of emissions growth over the last decade. The Economic Projection and Policy Analysis (EPPA) model (the human system component of the MIT IGSM) employed here also reflects slower prospects for long-term regional economic growth (particularly for China).

The three policy scenarios reduce or effectively eliminate emissions uncertainty as policies are implemented in the model as emissions caps that must be met. The 90th percentile range for Paris Forever 2100 emissions is 64–91 GtCO2eq, with a median of 77 Gt. NDC targets specified as reductions from reference emissions or as emissions intensity goals leave some room for uncertainty in emissions projections due to the nature of the policies imposed and the underlying uncertainty in emissions growth. In 2100, median emissions in Paris Forever are about 19% lower than median 2100 emissions in Reference. Median 2100 emissions in Paris 2C and Paris 1.5C are 13 Gt and 9 Gt, respectively, which is 87% and 91% below median 2100 Reference emissions. The emissions constraints are binding in all cases in the Paris 2C and Paris 1.5C policy ensembles, so there is effectively no uncertainty in global emissions under those scenarios.

However, there is uncertainty about how those emissions are distributed across regions, sectors and greenhouse gases since emissions trading is allowed. These distributions depend on the cost of abatement opportunities, which change with different sampled values of input parameters. The greatest variance in regional emissions is in China, and the greatest variance in sectoral emissions is in the electricity and industry sectors (see Supplementary Figs. 9-10). Sectoral results also suggest that there are limited abatement opportunities in the agricultural, residential and industrial sectors. This reflects challenges in those sectors, where good options for reducing or eliminating emissions have yet to be identified.

Due to the many unresolved issues (e.g., cost, public acceptance, ability to operate sustainably and at scale) related to negative emission technologies (NETs) such as biomass electricity with carbon capture and storage (BECCS), direct air capture (DAC) and afforestation, we did not include these technologies in this study. However, we have explored their role in other studies49–52, and if available and scalable at reasonable cost, NETs could reduce the need for near-term emissions reductions, but in turn risk exceeding temperature targets if they cannot be scaled up53,54.

There is a presumption in many policy circles that there is a need to get to net zero emissions in this century, possibly as early as 2050, and meeting this goal would require NETs in order to offset hard-to-abate emissions, such as methane from rice and ruminants and nitrous oxide from soil management. However, all of our ensemble members meet the emissions constraints imposed in the Paris 2C and Paris 1.5C ensembles without negative emissions or even achieving net zero emissions. As emphasized in the IPCC, it is the cumulative budget over the century that matters for temperature outcomes4,55. Net zero or negative emissions in the latter half of the century would provide more near-term headroom, allowing for a more gradual transition from the current fossil fuel-heavy energy system, and lower near-term costs. In particular, to meet the Paris 1.5C emissions target under our formulation (without negative emissions options) requires an almost 60% drop in emissions between 2030 and 2035. This results in very high costs even in the early years since much more abatement is needed early to balance out emissions in the 2nd half of the century.

The carbon budgets for the Paris 2C and Paris 1.5C scenarios are somewhat larger than estimates for these temperature targets presented in the IPCC Special 1.5°C Report55–57. For the set of climate parameters used in this study, the median transient climate response to (cumulative carbon) emissions (TCRE) obtained in our ensembles of simulations of the MIT Earth System Model (MESM) component of the IGSM is nearly identical to the value used in the IPCC Special 1.5°C Report55. However, the 90% probability range of the TCRE from the estimates we use41 is narrower. As a result, the CO2-only carbon budget for achieving a given target with 50% probability as simulated by MESM is similar to that shown by IPCC Special 1.5°C Report55, while the allowable budget for the 33%/66% probability is lower/higher. However, the main reason for the difference in carbon budget is the smaller temperature change associated with non-CO2 forcing in MESM. Compared with most IPCC scenarios, we have lower non-CO2 GHG emissions and somewhat higher SO2 emissions resulting in greater negative aerosol forcing, both of which allow for more CO2 emissions. As a result, our carbon emissions (relative to 2017) are near the high end of the range reported by Rogelj et al.56. It is important to note that IPCC carbon budget studies generally make exogenous assumptions about non-CO2 GHGs and then find the resulting remaining CO2 budget. In contrast, our approach dynamically determines the most cost-effective balance of reductions across all GHGs (using global warming potentials, GWPs, as weights).

Atmosphere and climate
Over the period from 2020 to 2100, the Paris 2C and Paris 1.5C scenarios have a smaller 90% range of CO2 concentrations and of total radiative forcing (which is the sum of the effects of all long-lived greenhouse gases plus tropospheric ozone and aerosols) compared to the Reference and Paris Forever scenarios due to their fixed emissions constraints (Fig. 2a, c). The driver of uncertainty in CO2 concentrations under those scenarios is the rate of carbon uptake by the ocean and terrestrial ecosystems. When emissions are also uncertain (as in the Reference and Paris Forever scenarios), the range of concentrations is wider, with the Reference scenario having the widest range. The uncertainty in radiative forcing is driven by: (1) varying concentrations, and (2) uncertainty in the strength of sulfate aerosol forcing. Moving from Reference to Paris Forever to Paris 2C, the distributions of end-of-century concentrations and radiative forcing become increasingly asymmetric, with policy (implemented as an emissions cap achieved with certainty) trimming the upper tail more than the lower tail (Fig. 2b, d). Paris 1.5C is slightly less skewed than Paris 2C. In 2100, the 90% bounds of CO2 concentrations are 692–871 ppm for Reference, 629–747 ppm for Paris Forever, 448–497 ppm for Paris 2C and 412–451 ppm for Paris 1.5C. For total radiative forcing, those 90% bounds are 6.9–8.6 W per m2 for Reference, 6.1–7.5 W per m2 for Paris Forever, 3.2–3.8 W per m2 for Paris 2C and 2.5–3.0 W per m2 for Paris 1.5C. We find that there is a ~8% chance that emissions will be high enough to achieve 8.5 W per m2 in 2100, supporting the concern of some analysts that it no longer should be considered a central estimate in the absence of additional policy8,15–18. However, scenarios as high as this or higher are still possible in our analysis and, hence, relevant for evaluating the expected damages.

As with concentrations and radiative forcing, policy also lowers the upper tails for temperature and precipitation (Fig. 2e, f). Uncertainty in temperature outcomes are driven by varying concentrations and radiative forcing (which in turn are driven by uncertainty in carbon uptake and aerosol forcing), along with uncertainty in ocean heat uptake and overall climate sensitivity (Earth system response to higher emissions). At the end of the century, the median 2091–2100 temperature change relative to pre-industrial levels (1861–1880) is 3.5°C for Reference, 3.1°C for Paris Forever, 1.9°C for Paris 2C and 1.5°C for Paris 1.5C. The 90% range is 2.8–4.3°C for Reference, 2.4–3.8°C for Paris Forever, 1.5–2.3°C for Paris 2C and 1.2–1.9°C for Paris 1.5C. The Reference temperature change aligns well with IPCC’s AR6 projections4 for the SSP3-7.0 scenario, which yields end-of-century median and very likely (90–100%) estimates of 3.6°C and 2.8–4.6°C, respectively. Paris Forever is similar to AR6’s SSP2-4.5 scenario (median of 2.7°C; very likely range of 2.1–3.5°C), while Paris 2C is similar to SSP1-2.6 (median of 1.8°C; very likely range of 1.3–2.4°C) and Paris 1.5C is similar to SSP1-1.9 (median of 1.4°C; very likely range of 1.0–1.8°C) (see Supplementary Table 5).

However, importantly, the AR6 estimates are based on the range of estimates of different runs from different models, not an uncertainty quantification effort designed to generate probability distributions of temperature outcomes based on emissions. There are limited studies that have done the latter. Gillingham et al.9 conducted a multimodal uncertainty quantification exercise and found median temperature resulting from baseline (no climate policy) trajectories to be 3.79°C, with a 90% range of 2.53–5.48°C. A study using the Kaya Identity and IPCC’s relationship between cumulative CO2 emissions and temperature to develop a probabilistic forecast of temperature change to 2100 found a median of 3.2°C and a 90% range of 2.4–4.9°C, assuming continuation of current trends (i.e. no climate policy)39. Older studies tended to project higher temperature changes in the absence of policy—for example, a median of 5.69°C and 90% range of 4.02–7.96°C33. However, government interventions worldwide, falling costs of low-carbon technologies and slower economic growth over the last decade have reduced estimates of emissions and, in turn, temperature change under a no climate policy scenario.

At a global scale, the uncertainty in precipitation change can be directly associated to the uncertainty in average surface-air temperature change. Higher surface-air temperatures strengthen potential evapotranspiration (across ocean surfaces and land vegetation systems) and in doing so, accelerate the hydrologic cycle. Thus, at a global scale, increasing (or reducing) near-surface warming results in larger (or smaller) increases in evapotranspiration to support the associated precipitation increases. By the end of the century, global precipitation increases by 0.15–0.28 mm per day (90% range) for Reference, 0.13–0.24 mm per day for Paris Forever, 0.10–0.16 mm per day for Paris 2C and 0.08–0.13 mm per day for Paris 1.5C (Fig. 2g, h).

Importantly, an emissions cap policy lowers the upper tail of the temperature change distributions more than the median. For example, comparing Paris 2C to the Reference, the median temperature is reduced by 1.6°C (from 3.5°C to 1.9°C) and the 95th percentile is reduced by 2°C (from 4.3°C to 2.3°C). This illustrates one of the greatest roles of climate policy—to lower (or effectively eliminate) the chance of extreme temperature outcomes. This is highlighted in Table 1, which shows how the percentage of runs exceeding given temperature levels varies across the ensemble scenarios. Results indicate that even relatively modest emissions cap policies can substantially reduce the probability of dangerously high temperature outcomes. For example, the Paris Forever scenario has modest emissions reductions relative to the Reference (see Fig. 1), yet greatly reduces the chance of temperature changes above 4°C (decreasing it from 15% to <0.25%). For the Paris 2C and Paris 1.5C scenarios, temperature is essentially bound at 2.5°C and 2°C, respectively, with less than 0.25% of runs exceeding those levels. Other policy measures, such as carbon pricing or intensity targets, that do not necessarily place an absolute limit on emissions could have a more symmetric effect on the distribution. Also important are the lower tails of the temperature change distributions. As seen in Fig. 2e, under Reference and Paris Forever, the 2°C temperature target is exceeded for all ensemble members.

Another important insight from these results is that, due to uncertainties in the climate system, a given emissions constraint cannot guarantee that a particular temperature target is met. Here we have designed emission trajectories (Paris 2C and Paris 1.5C) to achieve a particular temperature target (2°C or 1.5°C) with a given probability (66% or 50%), accounting for our estimated climate system uncertainty, meaning there is still substantial probability (33–50%) that the temperature targets will be exceeded. Looked at in another way, depending on how Earth system uncertainties are resolved, we may find that we can allow somewhat higher emissions (with low climate response) or will need to cut emissions more deeply (with high climate response) if indeed we want to remain below a given temperature target. One important implication of these results is that emissions targets intended to achieve specific temperature goals would need to be adjusted over time as the uncertainty in the climate system is resolved.

Economy
For all ensemble scenarios, GDP is endogenously determined in the model and therefore uncertain. In this particular approach, the impacts of climate change on the economy are not included. For example, if climate change caused damage to the economy, energy use and emissions might be reduced, making it less likely that such large increases in temperatures were actually possible58. On the other hand, high temperatures are likely to increase the demand for air conditioning and energy, and if that energy is from fossil fuels, the result would be an increase in emissions and a positive feedback on warming. Similarly, climate damage to agricultural yields might require more land under cultivation, more fertilizer, and more livestock, and result in more deforestation and more carbon dioxide, methane, and nitrous oxide emissions. Natural feedbacks, such as increased forest growth from higher ambient CO2, or changes in forest and land productivity, and natural sources of methane and nitrous oxide due to changes in soil temperature precipitation are included in the Earth system component of the model. Including climate change impacts on the economy would also affect the relative economic impact of different policy scenarios, however, notably, the benefits of reduced damages from climate change are not included.

For the Paris 2C and Paris 1.5C scenarios, which have the same emission trajectories for all ensemble members, the GDP impact of meeting that trajectory varies because the level of abatement needed to keep emissions on the specified trajectory, and the abatement and technology costs of doing so, varies. Here we focus on GDP results through 2050. Relative to the Reference scenario, median global GDP in 2050 is 2.1% lower under Paris Forever, 6.2% lower under Paris 2C, and 18.4% lower under Paris 1.5C (Fig. 3a). This highlights the additional reduction in GDP of achieving 1.5C vs. 2C (but we caution that our analysis does not include the climate damages to GDP avoided by these stricter policies). In all scenarios, GDP is growing, with median GDP in 2050 ending up 2.2 times higher (2.2x) than 2020 levels under Reference (with a 90% range of 2–2.4×), 2.16 times higher under Paris Forever (with a 90% range of 2–2.3×), 2.16 times higher under Paris 2C (with a 90% range of 1.9–2.2×), and 1.8 times higher under Paris 1.5C (with a 90% range of 1.7–2×).

In terms of the average annual GDP growth rate from 2020–2050 (Fig. 3b), Reference has a median of 2.66% (with a 90% range of 2.36–2.96%). Paris Forever has a median of 2.6% (with a 90% range of 2.3–2.9%), Paris 2C has a median of 2.45% (with a 90% range of 2.2–2.7%), and Paris 1.5C has a median of 1.97% (with a 90% range of 1.7–2.3%). As such, even stringent climate policy allows for global economic growth. The GDP impacts of policy could be lowered further by the availability of additional mitigation options, such as negative emission technologies (NETs), which, as noted earlier, are not included in the modeling here. In particular, under the Paris 1.5C scenario, the availability of NETs in the second half of the century would provide headroom for more near-term emissions, allowing for a more gradual energy transition and lower economic impact.

We also project regional economic growth across the policies, which is conditional on assumptions about the regional emissions allocations imposed. Here, we first determined a global carbon price trajectory starting in 2030 and increasing at 4% per year that, given median socio-economic parameter values, resulted in global emissions pathways consistent with the temperature targets. Assuming a 4% discount rate, this results in a constant present value carbon price, consistent with minimizing the net present value policy cost. This approach results in regional emissions trajectories that ensure marginal abatement costs in each region are equal to the global carbon price at median values for all input parameters. The resulting regional emissions were then used to determine the initial regional allocation of emissions allowances for the Paris 2C and Paris 1.5C ensemble implemented as global emissions trading systems. This procedure implies that under the emissions caps with median parameter settings, there is no emissions trading among regions. However, uncertain economic growth, technology costs and resource availabilities across regions mean that, within a given ensemble, regions will be net allowance buyers in some simulations and net sellers in others, and their net trading position may change over the timeframe of the simulation. The neutral assumption of no net trading under median parameter settings provides a starting point from which one might consider financial transfers or mechanism designs that could achieve more equitable outcomes.

For this setting, we find wide variation in GDP growth impacts across regions under the scenarios. For some regions, like the United States and Europe, the scenarios largely overlap, meaning the policies have a relatively small impact on GDP (Fig. 4). However, for other countries, such as China and India, and even more so for regions like the Middle East and Africa, GDP under the 2C and 1.5C policies increasingly diverges from the Reference and Paris Forever scenarios, reflecting higher policy costs. For policy costs, measured as the difference in average annual GDP growth between a policy scenario and the Reference scenario (the difference between distributions in Fig. 4), uncertainty tends to be higher for low- and middle-income economies than high-income economies. For Africa, even though the GDP growth rate within each scenario is less uncertain than other regions (due to it being a large aggregated region), the policy costs are more uncertain than the United States and Europe. For example, under the 2C policy, the policy impact on the average annual GDP growth rate in the United States ranges from a growth rate increase of 0.03 percentage points (5th percentile) to a rate decrease of 0.05 percentage points (95th percentile). For Africa under 2C, the 90% range spans a growth rate decrease of 0.46–0.76 percentage points. This result highlights the very important issue of equity among countries, especially between higher-income countries where the economies are now less energy-intensive, and low-income countries still in a relatively energy-intensive stage of growth. The results show developing countries as likely to bear the greatest costs of global climate mitigation unless specific actions are taken to avoid that outcome. With a global cap and trade policy, allowance allocation can be used to facilitate financial transfers to achieve more equitable outcomes. However, with uncertainty in growth and other factors, determining an allowance allocation that would achieve a given level of transfer would be a challenge.

Energy
Not surprisingly, our results indicate that an energy transition away from fossil fuels is required in order to achieve the long-term temperature goals of the Paris Agreement. This is achieved in our scenarios by a combination of switching to low-carbon energy sources and by reducing the amount of energy used in both production and consumption (which is driven in turn by the ease of substituting energy for non-energy inputs to production and consumption). The fossil share of total global primary energy falls from 2020 levels (88%) in all scenarios, but 2100 shares are dramatically larger in Reference and Paris Forever (79% and 76% medians) compared to Paris 2C and Paris 1.5C (26% and 23% medians) (see Supplementary Fig. 11).

As fossil energy is phased down under stringent climate policy, other low-carbon energy sources take its place. Figure 5 shows the uncertainty in global primary energy by source for 2030, 2050 and 2100 under the Reference and Paris 2C scenarios. The sources of primary energy in our model are coal (with or without carbon capture and storage (CCS)), natural gas (with or without CCS), oil, bioenergy, renewables (wind and solar), nuclear and hydro (hydro is not shown in Fig. 5 as it is modeled as a fixed resource so there is virtually no uncertainty around its deployment). The amount of primary energy from each of these sources is uncertain. Notably, Reference and Paris 2C diverge substantially for coal, gas and oil without CCS. Under Reference all three fossil energy sources continue to grow throughout the century from 2015 levels. Under Paris 2C, fossil levels are only somewhat lower in 2030 than under Reference, but they decline over time, increasingly diverging from Reference levels. Under Paris 2C, there is a particularly dramatic reduction in primary energy from coal between 2030 and 2050, and from oil between 2050 and 2100. The oil use is offset by a dramatic increase in bioenergy between 2050 and 2100, largely in the form of bio-oil as a substitute for refined oil. However, even under Reference there is a large expansion of bioenergy by 2100. Coal and gas with CCS are unused under Reference as there is not an economic incentive for them, but there is some potential for CCS under Paris 2C in the second half of the century.

In terms of energy investment decisions made today in the face of policy uncertainty, the results suggest that renewables offer the safest bet, with great future potential regardless of the level of policy and across a broad range of potential socioeconomic futures, including different assumptions about technology costs. Based on our assessment of the probability distributions of the cost of different technologies, while the scale of competing technologies (such as nuclear, CCS or bioenergy) does vary across ensemble members, a sizable role of renewables is quite robust across the different cost assumptions. In contrast to the AR64, which shows more renewables in the policy cases, in our results renewables end up somewhat lower in 2100 in Paris 2C than in Reference, although their share of energy use is higher, because energy and electricity use are lower under stringent policy due to a greater efficiency response to policy and overall economic consumption being lower. However, if the model represented more options for electrification, it is possible that total electricity consumption would increase in the Paris 2C scenario relative to the Reference scenario, and renewables would grow beyond Reference levels throughout the century. Expanding electrification opportunities is an area for further model development. Advanced nuclear generation also has the potential to play an important role under Paris 2C in the second half of the century, with the large uncertainty range largely driven by China.

Relative role of socioeconomic and Earth system uncertainties in climate projections
Efforts to partition climate projection uncertainty59,60 have found that internal variability and uncertainty in the climate system and modeling of it are the largest drivers in the near-term. However, beyond the next decade or two, uncertainty in human systems and resulting emissions becomes an increasingly important contributor to uncertainty in climate change projections. Climate system uncertainty remains important, but the influence of socioeconomic-driven scenario uncertainty grows over time, and becomes the largest source of uncertainty after 50–100 years59. However, different approaches to estimate underlying climate and socioeconomic uncertainty can give widely varying estimates of uncertainty in scenarios, leading to different assessments of how different sources of uncertainty contribute to the overall uncertainty in climate outcomes.

It is also essential to understand that different sources of uncertainty (and related risks) can interact with one another. Terms such as cascading, propagating and compounding have been used in literature to describe the interacting uncertainties and risks related to climate change61–68. If uncertainties were simply additive, it would seem that uncertainty would grow unbounded. However, in our analysis, uncertainty ranges do not grow in an unbounded fashion as more uncertainties are considered, as many of the sampled uncertainties end up offsetting one another.

Uncertainty in the global climate outcomes presented above for Reference and Paris Forever scenarios are driven by parametric uncertainties in both the socioeconomic system, which drives emissions, and the Earth system, which drives climate responses to emissions. To explore the relative contribution of socioeconomic/emissions uncertainty and climate-response uncertainty, we compare the distributions from the full ensembles (both socioeconomic/emissions and climate-response uncertainty, thick lines in Fig. 6) to those from two different ensemble variations: (1) ensembles with only Earth system uncertainty, with emissions held at the median level (ClimUnc), and (2) ensembles with only socioeconomic variables and resulting emissions uncertain, with climate-parameters held to their median values (EmiUnc). Figure 6 compares the end-of-century (2091–2100) frequency distributions. A visual comparison of the ClimUnc and EmiUnc distributions can quickly reveal the relative contribution of uncertainties in socioeconomic and Earth system response. More formally, we can compare dispersion metrics for the distributions—here we focus on the mean absolute deviation (MAD) summarized in Table 2, but also calculate the interquartile range (IQR) and the range between the 5th and 95th percentiles (see Supplementary Table 6). Figure 7 shows the ratio of MAD for the distributions with only one source of uncertainty relative to MAD for the distributions with both uncertainties over time for the Reference ensemble. These MAD ratios reflect how much of the dispersion in the full uncertainty distribution is captured by only one source of uncertainty (either emissions or climate).

For CO2 concentrations, uncertainty due to emissions is greater than uncertainty due to climate by the end of the century, especially for the Reference ensemble (Figs. 6a and 7a). However, climate uncertainty plays an important role as well—even when emissions are certain (as in ClimUnc), there is considerable uncertainty in concentrations because of uncertainty in ocean and land uptake of CO2 as well as natural sources of other gases because of their dependence on climate. When emissions are more tightly controlled (as in the Paris Forever policy scenario), then climate uncertainty becomes relatively more important. At the end of the century the MAD ratio is 0.77 for EmiUnc and 0.56 for ClimUnc under Reference. The corresponding values under Paris Forever are 0.62 and 0.72. While climate uncertainty begins as more important, the importance of emissions uncertainty to uncertainty in CO2 concentrations grows over time, surpassing climate uncertainty by 2070 in the Reference scenario (Fig. 7a).

Emissions uncertainty becomes even more important for total radiative forcing (Figs. 6b, 7b) because forcing is also affected by uncertainty in other greenhouse gases and aerosols, such as sulfates (from SO2 emissions) and black carbon. At the end of the century the MAD ratios for EmiUnc and ClimUnc, respectively, are 0.87 and 0.38 under Reference and 0.85 and 0.43 under Paris Forever. We again see climate uncertainty as more important in early decades, but the importance of emissions uncertainty to uncertainty in total radiative forcing grows quickly, surpassing climate uncertainty by 2060 (Fig. 7b).

However, that pattern is not seen for temperature (Figs. 6c, 7c) and precipitation (Figs. 6d, 7d)—for those outcomes, uncertainty due to climate is greater than uncertainty due to emissions throughout the century. For end-of-century temperature, the MAD ratios for EmiUnc and ClimUnc, respectively, are 0.40 and 0.90 under Reference and 0.36 and 0.91 under Paris Forever. For end-of-century precipitation, the role of climate uncertainty is even stronger: the MAD ratios for ClimUnc are 0.95 and 0.96 under Reference and Paris Forever, respectively. The corresponding vales for EmiUnc are 0.26 and 0.24. The greater effect of climate uncertainty on temperature and precipitation is not surprising as the uncertain climate parameters most directly relate to how temperature is affected by a given level of radiative forcing, with only a secondary effect on carbon uptake by oceans and the terrestrial biosphere in response to warming, and precipitation outcomes are heavily driven by temperature.

Importantly, we find that emissions and climate uncertainty are less than additive—for each climate outcome, the dispersion metrics for the distributions with both emissions and climate uncertainty are less than the sum of climate uncertainty alone (ClimUnc) and emissions uncertainty alone (EmiUnc) (see Table 2 and Supplementary Table 6). Focusing on uncertainty in temperature projections in Figs. 6c, 7c, for example, the combined effect of uncertainty in climate and emissions is almost identical to climate uncertainty alone—adding emissions uncertainty barely changes the overall uncertainty. However, there is still considerable temperature uncertainty resulting from emissions uncertainty alone. These results indicate that cascading uncertainties are not necessarily additive, and capturing more uncertainties does not automatically widen the uncertainty range of outcomes because uncertainties can offset one another. This illustrates the need for an integrated modeling system for uncertainty analysis as it is unclear how to combine separate analyses of Earth system uncertainty and human system uncertainty. An assumption that such analyses are additive would be misleading.

These results may appear to contradict the results of Lehner et al.59, which finds uncertainty in human systems and resulting emissions (what they call scenario uncertainty) to be the predominate driver of temperature change uncertainty by the end of the century, since Figs. 6 and 7 shows climate uncertainty as dominating the end-of-century temperature uncertainty in both of the ensembles. However, a major reason for this is that uncertainties in our analysis are conditional on policy assumptions (i.e. whether the near-term Paris targets are met or not). Results from Lehner et al.59 are not conditional on policy but are based on sets of emissions scenarios that span both scenarios with no policy and those that at least implicitly have different policy outcomes. Still, the time evolving contribution of uncertainty follows the same general pattern of Lehner et al.59—climate response uncertainty dominating at least the first few decades, but emissions scenario uncertainty generally becoming more important over time (Fig. 7).

Methods
Model
Coupled human-Earth systems models allow for consideration of both socio-economic and climate uncertainties. Here we use the MIT Integrated Global System Model (IGSM) framework, which links the Economic Projection and Policy Analysis (EPPA) model to the MIT Earth System Model (MESM). EPPA is a recursive-dynamic multi-sector, multi-region computable general equilibrium (CGE) model of the world economy69–71 (see Supplementary Fig. 12). It is designed to develop projections of economic growth, energy transitions and anthropogenic emissions of greenhouse gas and air pollutants. The model projects economic variables (GDP, energy use, sectoral output, consumption, prices, etc.) and emissions of long-lived greenhouse gases (CO2, CH4, N2O, HFCs, PFCs and SF6) and short-lived air pollutants (CO, volatile organic compounds (VOCs), NOx, SO2, NH3, and black carbon and organic carbon aerosols) from combustion of carbon-based fuels, industrial processes, waste handling, agricultural activities and land use change. MESM is an Earth system model of intermediate complexity, modeling the Earth’s physical, chemical and biological systems to project environmental conditions that result from human activity72. MESM is able to project the full spectrum of climate-relevant conditions across the Earth system, including atmospheric concentrations of greenhouse gases and aerosols, temperature, precipitation, ice and snow extent, sea level and ocean acidity and temperature among many other variables. By linking these two models, the IGSM also allows for the development of emissions pathways consistent with different 21st century temperature outcomes.

Monte Carlo simulation
Following earlier approaches33,34 we employ Monte Carlo uncertainty analysis. The basic steps are: (1) identify uncertain input parameters and develop probability distributions for each, (2) sample from these distributions to construct multiple sets of parameter values, and (3) generate large ensembles of model runs using the sampled parameter values. The distribution of model outcomes from the ensemble of simulations for a particular scenario provides estimates of future states and their uncertainty, conditional on the model structure, the distributions of the uncertain input parameters, and the assumed scenario attributes. Figure 8 depicts this approach for representing uncertainty in a coupled human-Earth systems model (the MIT IGSM), creating probabilistic, internally consistent, integrated socio-economic and climate projections. In this particular study, climatic and other environmental feedbacks on the economic system that would result from changes in the Earth system are not included. That remains an important goal for future studies.

Probability distributions for socioeconomic input parameters19 and for Earth system input parameters41,44,45 were developed. Our focus on parametric uncertainty does not account for structural uncertainty in the models, such as equations defining objective functions, consumer preferences or the form of production functions. A summary of the probability distributions for all uncertain parameters, both socioeconomic and Earth system, is provided in Supplementary Methods 1.

Estimated distributions for socioeconomic parameters were based on statistical estimates using historical data where possible (e.g. GDP growth, autonomous energy efficiency improvement, rate of technology penetration), published estimates of uncertainty (e.g. population, fossil resource availability), literature results and expert judgment (e.g. future technology costs, elasticities of substitution, urban pollutant initial inventories and trends, capital vintaging). Probability distributions are constructed for each socio-economic parameter, some by region or sector, creating a total of over 150 distributions. For a subset of related parameters, correlation structures are also imposed, and enforced in the parameter samples, based on observed correlation where possible, but often based on expert judgment.

Uncertain Earth system parameters were estimated using an optimal fingerprint approach41,44,45. This method uses historical data on surface climate, ocean heat content, and concentrations of greenhouse-relevant gases and aerosols to estimate a joint distribution of parameters representing climate sensitivity, ocean heat uptake and aerosol radiative forcing. These estimates are based on observations through 2010, whereas previous estimates73 used data only up to 1995. We also account for uncertainty in the carbon uptake by the ocean and terrestrial ecosystems72.

To reduce computational requirements when conducting Monte Carlo analysis with the relatively complex IGSM, we employ Latin Hypercube sampling (LHS)46,47. LHS divides the distribution for each variable into equal probability segments. The mid-point values for each segment of each variable are chosen randomly, without replacement. Each random selection across all input variables creates one ensemble member. The process generates an ensemble size equal to the number of probability segments. This sampling strategy assures that every equally-likely segment of the distribution, including segments in the distribution tails, is sampled exactly once. Because our models are computationally expensive to run, we use 400-member ensembles, shown to adequately approximate the limiting distribution when using LHS, whereas pure random sampling often requires thousands or tens of thousands of samples to achieve similar accuracy34. The LHS takes in the correlation matrices that were developed for subsets of socio-economic parameters and captures the correlation among climate parameters by drawing from their joint distribution.

The same set of 400 samples is used for a reference scenario and a set of climate policy scenarios. Pairwise comparisons of results are made across scenarios with identical input values for each ensemble member pair, with the only difference between the two being the introduction of a policy constraint. This procedure is designed to enable estimation of policy costs (the difference between simulated macroeconomic outcomes in a policy case and that in the reference case) for each ensemble member.

Scenarios
Climate policy is treated as a choice variable (or deep uncertainty) in our framework, explored through a set of ensemble scenarios, rather than attempting to assign a subjective probability distribution to policy measures. The ensemble scenarios include a reference case, a case extrapolating Nationally Determined Contributions (NDC) targets of the Paris Agreement, and policy cases that achieve long-term temperature stabilization targets of 2°C and 1.5°C implemented as a cap-and-trade policy fixing the emissions path over time. (See Supplementary Table 1). Morris et al.19 explore the same set of scenarios (labeled by their median temperature outcomes), focusing on technology and socio-economic outcomes. The different scenarios are achieved by implementing different limits on emissions; all other assumptions and sampled input values are the same across scenarios. The Reference case does not include the mitigation pledges made by the countries in their submissions under the Paris Agreement, but it does include policies targeting an expansion of renewables in power generation consistent with IEA48 and those policies remain in place in all scenarios. Climate and energy policies have also been responsible for reducing the costs of low-carbon technologies and otherwise shaping energy consumption patterns through building standards and codes, appliance and vehicle efficiency and other policies. While not explicitly represented, the effects of these efforts are reflected in lower renewable technology costs and a slowing rate of emissions growth over the last decade.

The Paris Forever scenario assumes the NDCs submitted under the Paris Agreement are met by all countries by 2030 and retained thereafter74,75. For countries with absolute NDC targets (e.g. emission reductions relative to a historic year), we have implemented those as emissions caps that are retained through the horizon of the simulation, keeping emissions flat after 2030. Countries with NDC targets that are relative to business-as-usual (BAU) emissions, or are in terms of emissions intensity, retain those targets through the horizon of the simulation, but since BAU emissions and GDP vary, the targets result in varying emissions for those regions (and the world total) across ensemble members.

The Paris 2C and Paris 1.5C scenarios are designed to achieve the long-term temperature stabilization targets of the Paris Agreement. The Paris Agreement has the long-term goal of “holding the increase in the global average temperature to well below 2°C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5°C above pre-industrial levels76.” We use the period 1861–1880 to determine preindustrial temperature. We interpret “well below” as targeting an emissions level so that the global mean surface temperature is likely to remain below 2°C. In IPCC terminology, “likely” is quantified as a 2/3 (66%) chance of occurring77. We interpret the 1.5°C aim as the median result, achieving it with a 50% probability. For both temperature-target scenarios, we assume all countries meet their NDCs by 2030, after which a global emissions price designed to achieve the long-term target is applied to all greenhouse gases, sectors and regions. Under median values of socio-economic parameters in the EPPA model and our estimates of climate uncertainty, the global emission trajectories result in a 66% probability of remaining below 2°C (Paris 2C) above pre-industrial levels or a 50% probability of remaining below 1.5°C (Paris 1.5C) above pre-industrial levels. The resulting regional emissions trajectories are then implemented in all ensemble members as emissions caps with trading among sectors, regions and greenhouse gases to ensure that the temperature targets are met in all cases. The emissions caps are binding upper limits on emissions, and assure that the global emissions path determined under median values of socio-economic inputs are also met when those inputs are uncertain. Under the emissions caps with median parameter settings, there is no emissions trading among regions, as the marginal cost of abatement across regions is already equalized. However, trading will occur as socio-economic uncertainty within the ensembles is sampled.

There are many alternative emission trajectories that could also achieve the same outcomes (66% chance of 2°C or 50% chance of 1.5°C). For the particular pathways used here, we first found an initial GHG emissions price that, when beginning in 2035 and rising at 4% per year under median values of socio-economic parameters, would achieve the temperature target with the specified probability given the uncertainty in our climate parameters. Such an optimized global emissions price policy tends to have a dramatic reduction in emissions in early years of the policy. For the Paris 2C scenario, we smoothed the global emission trajectory in early years, while maintaining the same cumulative GHG budget consistent with the temperature target, and then implemented that path as an emissions cap, requiring each ensemble member to achieve the same global emission trajectory. For the Paris 1.5C scenario, there is not room in the GHG budget to smooth the early years of the emission trajectory without employing negative emissions in later years, which we do not include. So, for Paris 1.5C, the emissions path resulting from the global emissions price policy is directly implemented as an emissions cap for the ensemble.

In reality, countries may not meet their emissions targets with certainty. Nevertheless, we represent these emissions targets as being achieved with certainty. An interesting exercise could be to conduct an assessment asking experts for their judgment of the range of emissions paths that countries may achieve over the century. Such an approach would quantify the uncertainty in policy rather than treating it as a choice variable.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I have finished reviewing \"Quantifying Both Socio-Economic and Climate Uncertainty in Coupled Human-Earth Systems\nAnalysis\" by Morris et al. The goal of the research is to explore the relative impact of emissions and climate-system\nuncertainties on socioeconomic, energy, and climate outcomes through a Monte Carlo experiment. While moving away from\nthe RCP-SSP scenarios towards probabilistic (or at least more comprehensive) representations of emissions uncertainty is\nan important area of research, I think this manuscript needs more work before it can be publishable in Nature\nCommunications.\nGeneral Comments:\nWhile I appreciate that Nature-style articles are written with the methods at the end, for this type of experiment some\ndiscussion of how the relevant probabality distributions were obtained is really needed ahead of the results. The reason for\nthis is that all of the results depend on the model structure (fixed and there is some discussion of this in Morris et al (2022)\nand other cited articles) and the input distributions. While the distributions are listed in the supplement, this organization\nmakes it difficult (if not impossible) to interpret the distributions and ranges of the outputs. It would also be useful for the\nauthors to reflect on how some of those distributions (and plausible other specifications) might result in narrative-relevant\ndifferences, such as changes to upper tails.\nThis is related to two additional concerns. First, it is not at all clear that 400 samples, even obtained using Latin Hypercubes,\nis remotely sufficient to capture the joint uncertainty of such a high-dimensional parameter space. The references justifying\nthis choice go back to the Webster et al, Sokolov et al, etc. papers from the 2000s, but given the increases in the\ndimensionality of the sample space relative to those papers, as well as the available computating power, these references\ndon't seem to be appropriate or sufficient for this article. The size of the hypercubes, for example, might be so large as to not\nadequately capture tail regions of the joint distribution, which are what really matter for climate risk. I would like to see more\njustification of this sample size, such as a sensitivity analysis showing convergence of key outcomes or an estimate of the\nMonte Carlo standard error. This is further compounded by a lack of details on how correlations are treated within the\nuncertainty quantification and sampling procedures.\nNext, about the uncertainty decomposition. I assume (or may have overlooked this detail in the text) that the distributions in\nFigure 8 were generated by using some fixed (central?) estimates of emissions (for the given scenario) and the best climate\nestimates. However, this then neglects the potentially interactions of tail-area climate parameters and higher (or lower)\nemissions scenarios which might (or might not!) complicate the key point about total uncertainty being limited by offsetting\nuncertainty. I would expect that this is the case in the bulk of the distributions, but higher emissions levels could result in\nlonger tails due to the higher forcing signal (this is the whole reason why we might want to continue using RCP 8.5, for\nexample).\nFinally, what are the implications of potential trend breaks in economic productivity? Obviously these can't be readily\nquantified, but don't they complicate the insights gained from quantification?\nThe literature review also fails to engage with some important papers on emissions uncertainty and the role of scenarios,\nincluding:\n* Morgan, M. G., & Keith, D. W. (2008). Improving the way we think about projecting future energy use and emissions of\ncarbon dioxide. Climatic Change, 90(3), 189–215. https://doi.org/10.1007/s10584-008-9458-1\n* Ritchie, J., & Dowlatabadi, H. (2017). The 1000 GtC coal question: are cases of vastly expanded future coal combustion\nstill plausible? Energy Economics, 65, 16–31. https://doi.org/10.1016/j.eneco.2017.04.015\nThat being said, the results are presented are interesting, particularly the insights about economic growth, negative\nemissions technologies, and energy mixes, and I think this article will make a useful contribution to the literature once the\nabove issues are satisfactorily addressed.\nSpecific comments:\nAuthor List: Are the affiliations of Libardoni and Forest switched?\nLine 17: This is the first occurrence, but it may be better to not use \"probability\" interchangably \"likelihood\" in the context of\nuncertainty quantification given that \"likelihood\" has a specific statistical meaning which can diverge from \"probability\" in the\nBayesian setting.\nLine 45: \"pre-defined\" instead of \"defined\"?\nLine 45: The two key papers that should be cited at the end of this sentence are Morgan & Keith (2008) and Schneider\n(2002) [Schneider, S. H. (2002). Can we estimate the likelihood of climatic changes at 2100? Climatic Change, 52(4), 441–\n451. https://doi.org/10.1023/A:1014276210717].\nLines 58-59: This sentence (\"Formal uncertainty analysis...\") needs to be made carefully. As emissions uncertainty is\ndeep/ambiguous, one needs to be careful to not overstate the value of any particular assignment of probabilities to\nscenarios. The advantage of careful uncertainty analysis is in the transparent linking of beliefs about future emissions (or\ntheir underlying drivers) to the subsequent risk analysis, and the ability to interrogate how differences in those beliefs might\nchange projected outcomes and potential strategies to manage the resulting risks. In a vacuum (or without sufficient\ntransparency), quantification can be just as dangerous (perhaps more so) as the probability-free route the IPCC chose for the\nRCPs because those distributions can become reified and take on a life of their own.\nLines 60-62: The statement about \"most studies\" is based on a largely outdated set of references (the most recent are from\n2013), and a statement this sweeping should be supported by a more up to date literature review. For example, what about:\n* Liu, P. R., & Raftery, A. E. (2021). Country-based rate of emissions reductions should increase by 80% beyond nationally\ndetermined contributions to meet the 2 °C target. Communications Earth & Environment, 2(1), 29.\nhttps://doi.org/10.1038/s43247-021-00097-8\n* Raftery, A. E., Zimmer, A., Frierson, D. M. W., Startz, R., & Liu, P. (2017). Less than 2 °C warming by 2100 unlikely. Nature\nClimate Change, 7(9), 637–641. https://doi.org/10.1038/nclimate3352 * Srikrishnan, V., Guan, Y., Tol, R. S. J., & Keller, K.\n(2022). Probabilistic projections of baseline twenty-first century CO2 emissions using a simple calibrated integrated\nassessment model. Climatic Change, 170(3), 37. https://doi.org/10.1007/s10584-021-03279-7\namong other papers which focus on individual components (e.g. Christensen, P., Gillingham, K., & Nordhaus, W. (2018).\nUncertainty in forecasts of long-run economic growth. Proceedings of the National Academy of Sciences of the United\nStates of America, 115(21), 5409–5414. https://doi.org/10.1073/pnas.1713628115)?\nLine 88: Is \"variability\" maybe more appropriate than \"uncertainty\"?\nLines 145-147: I might rephrase this sentence, it reads as though you show that the reductions/costs are not politically\nfeasible.\nLine 153: Why is the uncertainty in the TCRE lower in your study than in the IPCC report? Is that just a byproduct of the\nmodel and/or inference from Libardoni et al (2019)?\nLines 242-244/Figure 4: This figure appears to be somewhat shoehorned in. Does it add anything to this manuscript, versus\nbeing a tool for public communication?\nLines 258-259: Given the emphasis on uncertainty quantification and risk, it would be useful to include a perspective on how\nthe choice to not consider economic-environmental feedbacks (which is reasonable, this is difficult to model!) might impact\nthe results. Otherwise, there's a risk of over-interpreting the resulting distributions when e.g. the divergences between the\nreference and Paris forever cases might not be so pronounced given the potential feedbacks discussed in e.g. Woodard, D.\nL., Davis, S. J., & Randerson, J. T. (2019). Economic carbon cycle feedbacks may offset additional warming from natural\nfeedbacks. Proceedings of the National Academy of Sciences, 116(3), 759–764. https://doi.org/10.1073/pnas.1805187115. This might further reduce the projected shocks (and impacts) of those policies which are then subsequently analyzed.\nLines 394-401: See my comment above about this uncertainty decomposition and Figure 8. How much support does this\nfigure provide for the statements about how uncertainties compound and what uncertainties contribute most?\nLines 557-566: How are correlations taken into account in the LHS sampling (if not for the socioeconomic parameters, for the\nclimate parameters, per the description of the climate calibration method in the prior paragraph?)", "reviewer_2": "Decision making around climate change could be improved if the likelihood of various outcomes could be determined.\nSuch likelihoods could be embedded in traditional risk-based decision-making frameworks. Up until now, very few studies have\nattempted to provide such a uncertainty quantification, instead relying predominately on scenarios. This work attempts to fill\nthis gap through a Monte Carlo analysis using a leading integrated assessment model—the MIT Integrated Global System\nModel. The authors leverage an ensemble of 400 simulations to evaluate the distribution of important outcomes like global\nmean temperature and GDP growth, conditional on climate policy scenarios. This conditioning is important, as no single\nprobability distribution could be specified for future emissions mitigation action. The manuscript is well written, and most of\nthe points made are well supported by the results. I do have two major critiques and several minor comments, that I feel the\nauthors should consider to improve their manuscript. I believe this work makes important points, and it is my hope in making\nthese comments that the manuscript can be strengthened.\nCritique 1:\nThe authors point out that probabilistic projections could be quite useful for decision-making, and point out that the lack of\nsuch likelihoods has contributed to a fixation in some circles on extremely unlikely outcomes. For example, RCP8.5 is a very\nuseful scenario for many analyses and might serve as an extreme that should be considered, but it is often treated in\npolicy/media discussions as much more likely than it probably is. The authors point out that the scientific community has\navoided providing probabilities, and as a consequence each analyst/decision-maker is left to adopt their own. If a major,\nnovel contribution of this work is the introduction of probabilistic approaches where others have hesitated, then this point\nshould be expanded on much more in the introduction/discussion. What are some of the tradeoffs of moving away from\nscenarios? How robust are probabilistic approaches to the distributional choices? By substituting your own judgement (for\ninstance about the parameter distributions) for that of the end user, what are you gaining and what are you losing? Clearly in\nsome settings scenarios are critical, and in others this new approach would be preferred, but what are those? There is also a\ndistinction between using a probabilistic approach to focus the analysis on the most important outcomes in an exploratory\nsense and using the probabilities to compute the expected warming level and associated risk. Exploring these sorts of\nquestions more thoroughly in a thoughtful Introduction/Discussion would significantly improve the paper and would probably\nbe a larger contribution than the lengthy discussion of exact results (e.g., a 3% increase in “so and so” vs. a 5% decrease in\n“such and such”). This work is proposing to look at human-earth projections in a different way than is normally done, and\nexploring the pros and cons of the proposed approach is a significant contribution.\nCritique 2\nSome of the methodological choices should be better justified, or possibly reconsidered.\nFirst, the ensemble size of 400 is very small to search a 60-dimensional uncertainty space, even with Latin Hypercube\nsampling. On line 566 the authors cite a paper to justify using a sample size of 400 as it is deemed adequate to approximate\nthe limiting distribution. This does not seem right in an absolute sense. To declare a sample size adequate would require\nknowledge of the required precision and how noisy the statistic you’re trying to estimate is, and the required sample size\nwould also scale with the dimension of the problem. So, for example, if you’re trying to estimate the central tendency of a\nfunction of a single random variable, many fewer samples would be needed than if you’re trying to estimate the tails of a\nfunction of dozens of random variables. Latin hyper cube sampling is more efficient than random sampling, but more\njustification seems in order for such a small sample size. In the supplement of the cited paper, it appears a test was done to\nunderstand the impact of sample size on the variability in the median % 95th percentile of the temperature distribution for a\ncomparable model. Perhaps similar analyses could be considered?\nSecond, to report probability distributions conditional on policy one must be confident in the input distributions and their\ncorrelations. For Socio-Economic model parameters, it is unclear which parameters are sampled independently as the\nmanuscript states that some correlation structure is imposed. For example, it is unclear whether advanced technology costs\nfor Gas CCS, Coal CCS, and BioCCS are independent of one another. Similarly, are Wind tech costs and WindGas tech\ncosts completely independent? Missing correlation structure could be fine if the ensemble is designed to focus exploration\non the more likely regions, but seems problematic if the intention is to provide probabilistic projections. At the very least, I\nthink the authors should provide more detail about the underlying distributions and how potentially ignoring correlation might\nor might not impact the probabilistic findings.\nFurthermore, the choice of distributions aren’t justified because they are drawn on previous work. This seems fine, but one\nwonders about the robustness of the insights to alternative assumptions. It would seem appropriate that the authors address\nrobustness concerns, or point to past work where they were addressed. This point could be highlighted as a potential\ndownside of probabilistic projections, even if they provide tremendous value. So, for example, relying on probabilistic\nscenarios embed many assumptions, including ones that we suspect are wrong (no correlation) BUT they focus our attention\non important regions. Scenarios make fewer such assumptions BUT they can focus our attention on unlikely scenarios,\nwhich can be counterproductive.\nThird, I had trouble following the section titled ‘Relative Role of Socioeconomic and Earth System Uncertainties in Climate\nProjections,’ because I could not understand the core metric (the “width” of distribution A vs. the “width” of distribution B), or\nthe experimental design to derive the metric, or the figure reporting the results (Figure 8). We have statistics to report\ndispersion, like variance, CV, or IQR. Perhaps the “width” could be tied to one of those measures. If by width the authors\nrefer to the range of across all 400 ensemble members, consider the variability in such a range will be driven by the most\nextreme order statistics and would be noisy. Why did the authors use their experimental design rather than a more common\nvariance decomposition approach, like Sobol? Sobol sensitivities would report the fraction of variability attributed to different\nsources and their interactions, and might make the reviewer’s point more clearly.\nMinor Comments:\nLine 203-210: This sentence is written with climate cooling as the focus and warming as the parenthetical. If one were to\nswitch this so warming was the focus, I think it would read cleaner.\nFigure 7: Suggest breaking this figure into two panels. As it is currently designed, the reader needs to keep track of different\nenergy technologies, different policy cases, and different times. The color scheme didn’t really seem to help. I suggest\nmaking it two panels by separating the policy cases.\nLines 392-401: The explanation of the experimental set up is confusing. If the intention is to understand the contributions to\nuncertainty, why not use Sobol? One could conduct different Sobol analyses for each policy case. What is meant by ‘wider’?\nPerhaps use IQR, variance, or some other dispersion measure?\nSupplement: It would seem appropriate to provide some analysis, or point to an analysis, of the robustness of the results to\nthe choice of distributions and the correlation structure between the variates."}, "author_response": "The paper received comments from 2 reviewers. Both were generally positive, but each had two\ngeneral comments/critiques, and several specific/detailed editorial comments/suggestions that they\nbelieved would improve the paper, with much overlap between the two sets of comments. Both\nreviews were very thoughtful, from individuals who were obviously very familiar with the subject matter\nof the paper, and we have taken on board all the suggestions as best we could and believe this has\ngreatly improved the paper. A challenge we faced was remaining within the allowed word count while\nresponding to reviewers’ requests for more details and discussion. The main text ballooned to 10,000\nwords, at which point we tried to instead summarize the main points of the discussion in the main text\nand move the longer discussion to the supplementary information. The general comments/critiques and\nspecific suggestions from both reviewers are copied in full below, and our response is in included in red\nfollowing each comment.\nReviewer #1\nGeneral Comments:\n1. While I appreciate that Nature-style articles are written with the methods at the end, for this type of\nexperiment some discussion of how the relevant probabality distributions were obtained is really\nneeded ahead of the results. The reason for this is that all of the results depend on the model structure\n(fixed and there is some discussion of this in Morris et al (2022) and other cited articles) and the input\ndistributions. While the distributions are listed in the supplement, this organization makes it difficult (if\nnot impossible) to interpret the distributions and ranges of the outputs. It would also be useful for the\nauthors to reflect on how some of those distributions (and plausible other specifications) might result in\nnarrative-relevant differences, such as changes to upper tails.\nAt the beginning of the Results section we have added a description of how the probability distributions\nwere obtained to lay the context for the results that follow. Additional details remain in the Methods\nsection and the Supplementary Information (the list of distributions remains in the Supplementary\nInformation due to space constraints in the main text). However, the new text at the beginning of the\nResults section notes where to find additional details. We have also added a test using different\ndistributional forms (all uniform distributions), which we include in the Supplementary Information (and\nrefer to in the new text at the beginning of the Results section).\n2. This is related to two additional concerns. First, it is not at all clear that 400 samples, even obtained\nusing Latin Hypercubes, is remotely sufficient to capture the joint uncertainty of such a high-dimensional\nparameter space. The references justifying this choice go back to the Webster et al, Sokolov et al, etc.\npapers from the 2000s, but given the increases in the dimensionality of the sample space relative to\nthose papers, as well as the available computating power, these references don't seem to be\nappropriate or sufficient for this article. The size of the hypercubes, for example, might be so large as to\nnot adequately capture tail regions of the joint distribution, which are what really matter for climate\nrisk. I would like to see more justification of this sample size, such as a sensitivity analysis showing\nconvergence of key outcomes or an estimate of the Monte Carlo standard error. This is further\ncompounded by a lack of details on how correlations are treated within the uncertainty quantification\nand sampling procedures.\nThe main concern is whether the high dimensionality (many uncertain variables) requires a larger than\n400-member sample, also an issue raised by Reviewer 2. The developers of this method and subsequent\npapers on LHS found that a 100 member ensemble was generally adequate but recommended using a\n400 member ensemble if computational concerns were not an overriding issue. (see McKay, M.D.,\nBeckman, R. J. & Conover, W.J. (1979). A comparison of three methods for selecting values of input\nvariables in the analysis of output from a computer code. Technometrics, 21(2), 239-245; Iman, R.L.,\nDavenport, J.M. & Zeigler, D. K. (1980). Latin Hypercube Sampling (Program User's Guide). SAND79-\n1972. Sandia National Laboratories, Albuquerque, New Mexico; Iman, R.L. & Helton, J.C. (1988). An\ninvestigation of uncertainty and sensitivity analysis techniques for computer models. Risk Analysis, 8(1),\n71-90; Helton, J.C. & Davis, F.J. (2003). Latin hypercube sampling and the propagation of uncertainty in\nanalyses of complex systems. Reliability Engineering & System Safety, 81(1), 23-69.\nhttps://doi.org/10.1016/S0951-8320(03)00058-9) report testing it on many different types of models,\nand unlike other methods, such as random sampling where the number of runs needed rises rapidly\nwith the number of uncertain variables, found that the accuracy with which the LHS approach\napproximated a limiting distribution was quite robust to the number of samples and number of\nuncertain variables. While the approach has been tested extensively, the evidence that 400 member\nsample size is adequate is based on numerical results whose reliability depends on the nature of the\nmodel structure, and so earlier tests on different models may not necessarily apply here. To further test\nthe reliability of the method in this case, we simulated the human systems component of the IGSM 1000\ntimes and compare it to the results when simulated 400 times. These results are now reported in the\nSupplementary Information (and mentioned at the beginning of the Results section), and demonstrate\nthe adequacy of the 400-member ensemble. (The Earth system component of the IGSM has only 3\nuncertain parameters, and so it seemed unnecessary subject that part to this test as that is not “high\ndimensionality.”)\nConcern about adequately capturing the tail of the distribution, or representing the possibility of\nextreme outcomes is justified, however, this is less of a problem of the size of the Latin Hypercube\nsample in our view. The bigger problem with capturing extreme tail outcomes, is deep uncertainty\nabout various earth and economic system responses, meaning such processes are not represented well\nin our or any economic /earth system model. To address this concern, we added a discussion to the\nIntroduction about the limits of uncertainty analysis in the face of deep uncertainty, and how one might\ncomplement the analysis in this paper with scenario analysis that considered extreme outcomes that\nmight be generated by strong positive feedbacks from, for example, release of methane hydrates or\nfrom permafrost melting. This also responds to Reviewer 2’s call for more discussion in the Introduction\nof the uses and limits of formal uncertainty analysis in comparison with more traditional scenario\nanalysis methods.\n3. Next, about the uncertainty decomposition. I assume (or may have overlooked this detail in the text)\nthat the distributions in Figure 8 were generated by using some fixed (central?) estimates of emissions\n(for the given scenario) and the best climate estimates. However, this then neglects the potentially\ninteractions of tail-area climate parameters and higher (or lower) emissions scenarios which might (or\nmay not!) complicate the key point about total uncertainty being limited by offsetting uncertainty. I\nwould expect that this is the case in the bulk of the distributions, but higher emissions levels could result\nin longer tails due to the higher forcing signal (this is the whole reason why we might want to continue\nusing RCP 8.5, for example).\nIt is correct that the decomposition between earth system and socioeconomic uncertainty is done by\nsetting one or the other at central values and then varying input values for the other. There was a\nstatement to this effect in the paper. We have reviewed it and attempted to make it clearer.\nWe agree that there may well be reason to continue to use an RCP 8.5 scenario to capture the more\nextreme outcomes. We edited the passage in (new) lines 58-64 as follow with the additions/changes\nhighlighted in yellow: “However, given slower economic growth, falling costs of low-carbon energy\noptions and government interventions worldwide directed at expanding the role of renewables and\nlimiting emissions, many analysts now believe the RCP8.5 “no policy” scenario and the heavy use of\nfossil fuels like coal it implies to be unlikely. There may be good reasons to still examine RCP8.5 to\nunderstand the implications of high consequence, albeit, possibly low probability outcomes. Formal\nuncertainty analysis can help to provide some indication of the probability of more extreme scenarios\nbased on the transparent assessments of uncertainties.” Indeed, in our Figure 2 panel b, the 90%\nprobability bound in 2100 is right about at 8.5 W/m^2. So, there is every reason to consider an 8.5 or\nhigher forcing scenario, but we wouldn’t see that as a mostly likely outcome. We have edited the paper\nto more properly spell out the remaining relevance of such a scenario.\nIt is not clear to us how the decomposition approach could be misleading or, if changed, would alter the\nconclusion that the random process of picking values is going to tend to create samples of somewhat\noffsetting values. The offsetting nature of the probabilistic exercise would seem to be a fundamental\nstatistical result. Conceptually, if we ordered values of all parameters based on how they contribute to\nwarming from the highest to the lowest temperatures, it is going to be highly unlikely that a random\nprocess selects all values that create high temperatures. In most cases, some of the values will\ncontribute to relatively high temperatures and others to low temperature, thus tending to shrink both\ntails, and a lot of the results will be in the middle, reflecting the underlying distributions that give a\nhigher probability to more central values. A chance draw that gives mostly high values will produce a\nrelatively extreme high temperature outcome, but rarely will that occur, and this will be reflected in the\nestimated distributions, although we would not suggest that quantification of small tails—those below\n5% or above 95%—are highly accurate because they are based on a small number of runs. In principle,\none could set e.g. the earth system values at a high setting (high climate sensitivity, low ocean heat\nuptake, low cooling aerosol response) consistent with the joint distribution estimated for them and then\nsimulate socioeconomic uncertainty. Such a process would then generate a distribution “conditional”\non an earth system with a high response to forcing, but that distribution would need to be “discounted”\nfor the fact that the earth system values were very unlikely. It certainly is the case though that there is a\nnon-zero chance that a sample could include “all high” values, and as a sample size tended toward\ninfinity, at some point such a result would occur. The base distributions which vary both earth system\nand socioeconomic inputs allow for the tails of each to interact while also reflecting that it is highly\nunlikely that all inputs would simultaneously end up with values that drive high temperature. We have\ntaken care not to over-interpret the tails, and generally report 10 and 90% bounds, as e.g. 1 and 99%\nbounds would be based on just 4 ensemble members, and hence would not be very reliable. In table 1,\nwe report % or runs, but have taken care not to describe this as a likelihood. With the additional caveats\nin the introduction about the ability to accurately capture the distribution tails, we believe we have\naddressed the reviewer’s concerns.\n4. Finally, what are the implications of potential trend breaks in economic productivity? Obviously, these\ncan't be readily quantified, but don't they complicate the insights gained from quantification?\nOur approach to simulating uncertainty in overall economic activity (GDP) is to incorporate trend breaks\nin labor and capital productivity, the major underling drivers of GDP growth. A challenge to\nrepresenting uncertainty in long term economic growth is that we only have good data for the world\nfrom the post-World War II period, and so for most countries we have just one observation of economic\ngrowth over a ~70 year period, which obviously gives a median estimate of 70 year growth with infinite\nvariance. The approach we used was to estimate volatility in economic growth rates for 5-year periods\nusing post war GDP data, develop probability distributions of shocks to economic growth (excursions\nfrom the mean growth rate), and then sample from the distribution for each region, applying the shock\nto the underlying base trend we simulate for that 5-year period, then sample again for the next 5-year\nperiod, and so on. This random walk with drift approach was used in Webster, M., Paltsev, S., Parsons,\nJ., Reilly, J. & Jacoby, H. (2008). Uncertainty in Greenhouse Emissions and Costs of Atmospheric\nStabilization. Joint Program Report Series Report 165, 81 pages.\nhttp://globalchange.mit.edu/publication/14707, but we have re-estimated the distributions of shocks to\nGDP and the correlation of shocks among regions including more recent data. This approach produces\neconomic growth that has a trend break every 5 years, not unlike economies that have booms and\nrecessions. Note that while we use the instrument of labor and capital productivity to generate\nuncertainty in GDP, the actual rate of GDP growth in the model depends on other uncertain parameters\nsuch as resource availabilities, technology costs, population/labor force growth, etc.\nOther cited work (e.g. Gillingham et al. 2017) surveys experts on long term trends in GDP growth and\nsampled a trend rate that applied to the entire horizon of the study. Our approach is mean reverting, so\nthat the distribution of GDP is relatively wider in the near term, and widens relatively less in the long\nterm, than if one samples for a rate of growth that applies to the entire horizon of the model. Which\napproach would produce a wider distribution in any particular year (e.g. 2100) would then depend on\nthe actual distributions chosen in each case. Evidence suggests it would be inappropriate to use the\nsame distribution for both 5 year and ~100 year growth, as the statistical evidence shows less variance\nin 10 year growth than in 5 year growth rates, and still less variance in 20 year growth rates than 5 or 10\nyear growth rates, but again, limited data make it impossible to get reliable estimates for periods much\nlonger than 20 years. In principle, these approaches could be combined, simulating uncertainty in the\nbase growth rate over the entire horizon, as well as breaks in growth every 5 years to approximate\nbusiness cycle behavior, but we have not tested such a method, and it is then a further stretch to\ngenerate evidence on distributions for these two separate uncertainty processes. Of course, even with\nall of this, the post-World-War II period may be unique in some way, but we wanted to generate\ndistributions from observed data where ever possible.\n5. The literature review also fails to engage with some important papers on emissions uncertainty and\nthe role of scenarios, including:\n* Morgan, M. G., & Keith, D. W. (2008). Improving the way we think about projecting future energy use\nand emissions of carbon dioxide. Climatic Change, 90(3), 189–215. https://doi.org/10.1007/s10584-008-\n9458-1\n* Ritchie, J., & Dowlatabadi, H. (2017). The 1000 GtC coal question: are cases of vastly expanded future\ncoal combustion still plausible? Energy Economics, 65, 16–31.\nhttps://doi.org/10.1016/j.eneco.2017.04.015\nThank you for these suggestions. We agree they are relevant and important and have added reference\nto them.\nThat being said, the results are presented are interesting, particularly the insights about economic\ngrowth, negative emissions technologies, and energy mixes, and I think this article will make a useful\ncontribution to the literature once the above issues are satisfactorily addressed.\nSpecific comments:\nAuthor List: Are the affiliations of Libardoni and Forest switched?\nYes, thank you. Corrected.\nLine 17: This is the first occurrence, but it may be better to not use \"probability\" interchangably\n\"likelihood\" in the context of uncertainty quantification given that \"likelihood\" has a specific statistical\nmeaning which can diverge from \"probability\" in the Bayesian setting.\nAgreed. We went through and used more care in how we used probability, uncertainty, likelihood.\nLine 45: \"pre-defined\" instead of \"defined\"?\nWe made this change.\nLine 45: The two key papers that should be cited at the end of this sentence are Morgan & Keith (2008)\nand Schneider (2002) [Schneider, S. H. (2002). Can we estimate the likelihood of climatic changes at\n2100? Climatic Change, 52(4), 441–451. https://doi.org/10.1023/A:1014276210717].\nThese were added.\nLines 58-59: This sentence (\"Formal uncertainty analysis...\") needs to be made carefully. As emissions\nuncertainty is deep/ambiguous, one needs to be careful to not overstate the value of any particular\nassignment of probabilities to scenarios. The advantage of careful uncertainty analysis is in the\ntransparent linking of beliefs about future emissions (or their underlying drivers) to the subsequent risk\nanalysis, and the ability to interrogate how differences in those beliefs might change projected\noutcomes and potential strategies to manage the resulting risks. In a vacuum (or without sufficient\ntransparency), quantification can be just as dangerous (perhaps more so) as the probability-free route\nthe IPCC chose for the RCPs because those distributions can become reified and take on a life of their\nown.\nThe sentence was modified as follows (changes/additions highlighted):\n“Formal uncertainty analysis can help to provide some indication of the probability of more extreme\nscenarios based on transparent assessments of underlying uncertainties.”\nIn addition, in response to Reviewer 2, who wondered about the relative value of traditional scenario\nanalysis and uncertainty analysis, an extensive addition was made in the Introduction spelling out\ncaveats/limitations of uncertainty analysis. Given space limitations, a more extensive discussion was\nprovided in the supplementary information. (See response to Reviewer 2’s Critique 1).\nLines 60-62: The statement about \"most studies\" is based on a largely outdated set of references (the\nmost recent are from 2013), and a statement this sweeping should be supported by a more up to date\nliterature review. For example, what about:\n* Liu, P. R., & Raftery, A. E. (2021). Country-based rate of emissions reductions should increase by 80%\nbeyond nationally determined contributions to meet the 2 °C target. Communications Earth &\nEnvironment, 2(1), 29. https://doi.org/10.1038/s43247-021-00097-8\n* Raftery, A. E., Zimmer, A., Frierson, D. M. W., Startz, R., & Liu, P. (2017). Less than 2 °C warming by\n2100 unlikely. Nature Climate Change, 7(9), 637–641. https://doi.org/10.1038/nclimate3352\n* Srikrishnan, V., Guan, Y., Tol, R. S. J., & Keller, K. (2022). Probabilistic projections of baseline twenty-\nfirst century CO2 emissions using a simple calibrated integrated assessment model. Climatic Change,\n170(3), 37. https://doi.org/10.1007/s10584-021-03279-7\namong other papers which focus on individual components (e.g. Christensen, P., Gillingham, K., &\nNordhaus, W. (2018). Uncertainty in forecasts of long-run economic growth. Proceedings of the National\nAcademy of Sciences of the United States of America, 115(21), 5409–5414.\nhttps://doi.org/10.1073/pnas.1713628115)?\nWe have reworked this text and added reference to these more recent papers.\nLine 88: Is \"variability\" maybe more appropriate than \"uncertainty\"?\nVariance would seem to be the best term here. Edited to read: “The variance in emissions is greatest in\nthe Reference scenario….”\nLines 145-147: I might rephrase this sentence, it reads as though you show that the reductions/costs are\nnot politically feasible.\nThe sentence was deleted. On reflection it seemed to be unnecessary speculation.\nLine 153: Why is the uncertainty in the TCRE lower in your study than in the IPCC report? Is that just a\nbyproduct of the model and/or inference from Libardoni et al (2019)?\nYes, this is a statement directly about the Libardoni et al (2019) results—uncertainty in TCRE is an input\nto our uncertainty analysis. A reference to Libardoni was added here to make this clearer. The IPCC\nassesses the TCRE range independently of other uncertainties such as ocean heat uptake and response\nto aerosol forcing, resulting in a wider range of values of TCRE that appear consistent with observation.\nHowever, if you use the three independently estimated distributions, the resulting historical ensemble\nwill not be consistent with observations, because some of these uncertainties tend to offset one another\n(e.g. high TCRE, low ocean heat uptake, and a low cooling effect of aerosols produces a temperature\ntrend above the observed range, or vice versa, a low TCRE, high ocean heat uptake, and high rate of\naerosol cooling will produce to little temperature increase). Assessing the distributions of these\nparameters jointly and aligned with observations tends to narrow the distributions for individual\nuncertain parameters.\nLines 242-244/Figure 4: This figure appears to be somewhat shoehorned in. Does it add anything to this\nmanuscript, versus being a tool for public communication?\nWe have removed this figure.\nLines 258-259: Given the emphasis on uncertainty quantification and risk, it would be useful to include a\nperspective on how the choice to not consider economic-environmental feedbacks (which is reasonable,\nthis is difficult to model!) might impact the results. Otherwise, there's a risk of over-interpreting the\nresulting distributions when e.g. the divergences between the reference and Paris forever cases might\nnot be so pronounced given the potential feedbacks discussed in e.g. Woodard, D. L., Davis, S. J., &\nRanderson, J. T. (2019). Economic carbon cycle feedbacks may offset additional warming from natural\nfeedbacks. Proceedings of the National Academy of Sciences, 116(3), 759–764.\nhttps://doi.org/10.1073/pnas.1805187115. This might further reduce the projected shocks (and\nimpacts) of those policies which are then subsequently analyzed.\nYes, this can use some further explanation and discussion, and as written may be easily misinterpreted.\nThe new text reads as follows with changes and additions highlighted in yellow (and the suggested\npaper now cited).\n“For all ensemble scenarios, GDP is endogenously determined in the model and therefore uncertain. In\nthis particular approach, the impacts of climate change on the economy are not included. For example,\nif climate change caused significant damage to the economy, energy use and emissions might be\nreduced, making it somewhat less likely that such large increases in temperatures were actually\npossible. On the other hand, high temperatures are likely to increase the demand for air conditioning\nand energy, and if that energy is from fossil fuels, the result would be an increase in emissions and a\npositive feedback on warming. Similarly, climate damage to agricultural yields might require more land\nunder cultivation, more fertilizer, and more livestock, and result in more deforestation and more carbon\ndioxide, methane, and nitrous oxide emissions. Natural feedbacks, such as increased forest growth from\nhigher ambient CO2, or changes in forest and land productivity, and natural sources of methane and\nnitrous oxide due to changes in temperature precipitation are included in the earth system component\nof the model, but their feedback on the human system and economy is not included. Including climate\nchange impacts on the economy would affect the relative economic impact of different policy scenarios,\nhowever, notably, the benefits of reduced damages from climate change are not included.\nLines 394-401: See my comment above about this uncertainty decomposition and Figure 8. How much\nsupport does this figure provide for the statements about how uncertainties compound and what\nuncertainties contribute most?\nThe language was changed to hopefully make it clearer how this decomposition was accomplished. “(1)\nensembles with only earth system uncertainty, with emissions held at the median level (ClimUnc), and\n(2) ensembles with socioeconomic variables and resulting emissions uncertain, with climate-parameters\nheld to their median values (EmiUnc).”\nWe have also calculated and now report the mean absolute deviation (MAD) of the distributions (and\nalso included the interquartile range and the range between the 5th and 95th percentiles in the\nSupporting Information) and how they change depending on the uncertainties considered. This provides\nclear metrics to discuss the contributions of uncertainty and how they compound. In particular, we see\nthat these metrics for the full uncertainty distribution are lower than for the sum of the two separate\ndistributions. We have also added a new figure (new Figure 8) that shows how the ratios of MAD for the\ndistributions with only one source of uncertainty relative to MAD for the distributions with both\nuncertainties change over time for the Reference ensemble. These MAD ratios reflect how much of the\ndispersion in the full uncertainty distribution is captured by only one source of uncertainty (either\nemissions or climate).\nLines 557-566: How are correlations taken into account in the LHS sampling (if not for the\nsocioeconomic parameters, for the climate parameters, per the description of the climate calibration\nmethod in the prior paragraph?)\nThe joint distribution of uncertainty in earth system parameters is directly estimated in the optimal\nfingerprint method used to derive them. Correlation matrices among a subset of socioeconomic\nvariables were based on observed correlation where possible, but often based on expert judgement.\nThese correlation matrices were enforced in the parameter sampling using @Risk software. These\nsocioeconomic correlations are now provided in the supplementary information. The following text was\nalso added to the main text (highlighted in yellow):\n“We then sample from the distributions, using Latin Hypercube Sampling (LHS)44-45 to draw samples\nfrom each input probability distribution and imposing a correlation structure amongst subsets of\nparameters, using @Risk software in Excel.”\n“For a subset of related parameters, correlation structures are also imposed, and enforced in the\nparameter samples, based on observed correlation where possible, but often based on expert\njudgement.”\n“The LHS takes in the correlation matrices that were developed for subsets of socio-economic\nparameters and captures the correlation among climate parameters by drawing from their joint\ndistribution.”\nReviewer #2:\nCritique 1:\nThe authors point out that probabilistic projections could be quite useful for decision-making, and point\nout that the lack of such likelihoods has contributed to a fixation in some circles on extremely unlikely\noutcomes. For example, RCP8.5 is a very useful scenario for many analyses and might serve as an\nextreme that should be considered, but it is often treated in policy/media discussions as much more\nlikely than it probably is. The authors point out that the scientific community has avoided providing\nprobabilities, and as a consequence each analyst/decision-maker is left to adopt their own. If a major,\nnovel contribution of this work is the introduction of probabilistic approaches where others have\nhesitated, then this point should be expanded on much more in the introduction/discussion. What are\nsome of the tradeoffs of moving away from scenarios? How robust are probabilistic approaches to the\ndistributional choices? By substituting your own judgement (for instance about the parameter\ndistributions) for that of the end user, what are you gaining and what are you losing? Clearly in\nsome settings scenarios are critical, and in others this new approach would be preferred, but what are those?\nThere is also a distinction between using a probabilistic approach to focus the analysis on the most\nimportant outcomes in an exploratory sense and using the probabilities to compute the expected\nwarming level and associated risk. Exploring these sorts of questions more thoroughly in a thoughtful\nIntroduction/Discussion would significantly improve the paper and would probably be a larger\ncontribution than the lengthy discussion of exact results (e.g., a 3% increase in “so and so” vs. a 5%\ndecrease in “such and such”). This work is proposing to look at human-earth projections in a different\nway than is normally done, and exploring the pros and cons of the proposed approach is a significant\ncontribution.\nThis is a useful point, and is consistent with points made by Reviewer 1. We like the suggestions of\nproviding more context/caveats about probabilistic approaches, however word limits prevent us from\nexpanding on this too much. We considered moving more of the results to Supplementary Information\nto make room for more thorough discussion in the Introduction, however, Reviewer 1 thought the\nresults were interesting. In an attempt to satisfy both reviewers, we summarized main points related to\nthe uses and limitations of probabilistic approaches in an extended introduction, and then included a\nlonger discussion in the Supplementary Information. (See response to Reviewer 2’s Critique 1).\nCritique 2\nSome of the methodological choices should be better justified, or possibly reconsidered.\nFirst, the ensemble size of 400 is very small to search a 60-dimensional uncertainty space, even with\nLatin Hypercube sampling. On line 566 the authors cite a paper to justify using a sample size of 400 as it\nis deemed adequate to approximate the limiting distribution. This does not seem right in an absolute\nsense. To declare a sample size adequate would require knowledge of the required precision and how\nnoisy the statistic you’re trying to estimate is, and the required sample size would also scale with the\ndimension of the problem. So, for example, if you’re trying to estimate the central tendency of a\nfunction of a single random variable, many fewer samples would be needed than if you’re trying to\nestimate the tails of a function of dozens of random variables. Latin hyper cube sampling is more\nefficient than random sampling, but more justification seems in order for such a small sample size. In the\nsupplement of the cited paper, it appears a test was done to understand the impact of sample size on\nthe variability in the median % 95th percentile of the temperature distribution for a comparable model.\nPerhaps similar analyses could be considered?\nWe have included a test for a sample size of 1000 from the previous paper in the Supplementary\nInformation material. See response to Reviewer 1, General comment No. 2.\nSecond, to report probability distributions conditional on policy one must be confident in the input\ndistributions and their correlations. For Socio-Economic model parameters, it is unclear which\nparameters are sampled independently as the manuscript states that some correlation structure is\nimposed. For example, it is unclear whether advanced technology costs for Gas CCS, Coal CCS, and\nBioCCS are independent of one another. Similarly, are Wind tech costs and WindGas tech costs\ncompletely independent? Missing correlation structure could be fine if the ensemble is designed to\nfocus exploration on the more likely regions, but seems problematic if the intention is to provide\nprobabilistic projections. At the very least, I think the authors should provide more detail about the\nunderlying distributions and how potentially ignoring correlation might or might not impact the\nprobabilistic findings.\nThe issue of confidence in the input distributions and their correlations is important whether output\ndistributions are conditional on policy, conditional on some other assumption, or unconditional. We\nhave added a paragraph discussion of the challenges of estimating input distributions in the Introduction\nto respond to the comment in Critique 1 above on the uses and limits of uncertainty analysis. We also\nclarified how correlations are handled in the sampling in Methods section and added text to the\nbeginning of the Results section about correlations, including providing examples of how different\nassumptions about correlations could affect results. The following text was added:\n“Different assumed correlations between inputs would also affect results, with missing correlations\npotentially widening the outcome distributions by allowing for a great variety of input sample\ncombinations. For example, capturing regional correlation for labor and capital productivity growth\nresults in more narrow global GDP outcomes than if regional productivity growth was uncorrelated.\nCorrelation assumptions can have other implications for results as well. For example, uncorrelated\ntechnology costs mean that even if one fossil-based (or renewable) technology is not competitive,\nanother might be. If these fossil or renewable costs were correlated, it could lead to overly difficult or\neasy energy transitions.”\nIn the work, the joint distribution of uncertainty in earth system parameters is directly estimated in the\noptimal fingerprint method used to derive them. A correlation matrix among a subset of socioeconomic\nvariables was used and enforced in the parameter samples based on observed correlation where\npossible, but often based on expert judgement. These socioeconomic correlations are now provided in\nthe supplementary information.\nFurthermore, the choice of distributions aren’t justified because they are drawn on previous work. This\nseems fine, but one wonders about the robustness of the insights to alternative assumptions. It would\nseem appropriate that the authors address robustness concerns, or point to past work where they were\naddressed. This point could be highlighted as a potential downside of probabilistic projections, even if\nthey provide tremendous value. So, for example, relying on probabilistic scenarios embed many\nassumptions, including ones that we suspect are wrong (no correlation) BUT they focus our attention on\nimportant regions. Scenarios make fewer such assumptions BUT they can focus our attention on unlikely\nscenarios, which can be counterproductive.\nIndeed, while we apply methods used in previous work, the input distributions are themselves uncertain\nas we now discuss in the introduction in response to Critique 1. We have also now included in the\nsupplementary material a sensitivity analysis where we replace the various distributions for\nsocioeconomic variables that tend to have a strong modal value (i.e. central hump, such as normal,\nbinomial, etc.) with simple uniform distributions. Giving equal weight to the entire range of values is, we\nwould argue, a fairly strong test of the confidence one might have in the specific distributions we have\nused. Of course, it could be that the ranges estimated are too narrow (or too wide).\nThird, I had trouble following the section titled ‘Relative Role of Socioeconomic and Earth System\nUncertainties in Climate Projections,’ because I could not understand the core metric (the “width” of\ndistribution A vs. the “width” of distribution B), or the experimental design to derive the metric, or the\nfigure reporting the results (Figure 8). We have statistics to report dispersion, like variance, CV, or IQR.\nPerhaps the “width” could be tied to one of those measures. If by width the authors refer to the range\nof across all 400 ensemble members, consider the variability in such a range will be driven by the most\nextreme order statistics and would be noisy. Why did the authors use their experimental design rather\nthan a more common variance decomposition approach, like Sobol? Sobol sensitivities would report the\nfraction of variability attributed to different sources and their interactions, and might make the\nreviewer’s point more clearly.\nConducting a Sobel sensitivity analysis for this work would be extremely computationally demanding\ngiven the complexity of the models and number of uncertain variables. Here we chose to undertake a\nmore aggregated uncertainty decomposition to explore the relative role of uncertain socio-economic\ninputs collectively (which drive emissions) vs. uncertain climate inputs collectively in driving climate\noutcomes, rather than exploring the contribution of each uncertain input separately. This framing\nhighlights one of the values of this work, which is that is captures both socio-economic and climate\nuncertainty together in a complex integrated coupled human-Earth system model. This framing also\naligns with well-known work partitioning climate uncertainty into model uncertainty (i.e. climate\nuncertainty), scenario uncertainty (i.e. socioeconomic uncertainty) and internal variability (see Lehner,\nF., Deser, C., Maher, N., Marotzke, J., Fischer, E. M., Brunner, L., et al. (2020). Partitioning climate\nprojection uncertainty with multiplez large ensembles and CMIP5/6. Earth System Dynamics, 11, 491–\n508. https://doi.org/10.5194/esd-11-491-2020 and Hawkins, E. and Sutton, R., (2009). The potential to\nnarrow uncertainty in regional climate predictions, B. Am. Meteorol. Soc., 90, 1095–1107,\nhttps://doi.org/10.1175/2009BAMS2607.1).\nWe agree that switching to a specific statistical metric is appropriate and clearer. We have changed the\ntext to refer to the mean absolute deviation (MAD) of the distributions (and also included the\ninterquartile range and the range between the 5th and 95th percentiles in the Supporting Information)\nand how they change depending on the uncertainties considered. In particular, we see that these\nmetrics for the full uncertainty distribution are lower than for the sum of the two separate\ndistributions. We have also added a new figure (new Figure 8) that shows how the ratios of MAD for the\ndistributions with only one source of uncertainty relative to MAD for the distributions with both\nuncertainties change over time for the Reference ensemble. These MAD ratios reflect how much of the\ndispersion in the full uncertainty distribution is captured by only one source of uncertainty (either\nemissions or climate).\nMinor Comments:\nLine 203-210: This sentence is written with climate cooling as the focus and warming as the\nparenthetical. If one were to switch this so warming was the focus, I think it would read cleaner.\nThe wording was reversed as suggested.\nFigure 7: Suggest breaking this figure into two panels. As it is currently designed, the reader needs to\nkeep track of different energy technologies, different policy cases, and different times. The color scheme\ndidn’t really seem to help. I suggest making it two panels by separating the policy cases.\nWe wanted to retain the ability to easily compare between the Reference and Paris2C results, so we\nhave instead broken this figure into three panels by separating the time periods (2030, 2050 and 2100).\nWe believe this works well and makes for an easier interpretation.\nLines 392-401: The explanation of the experimental set up is confusing. If the intention is to understand\nthe contributions to uncertainty, why not use Sobol? One could conduct different Sobol analyses for\neach policy case. What is meant by ‘wider’? Perhaps use IQR, variance, or some other dispersion\nmeasure?\nSee response to Critique 2 above.\nSupplement: It would seem appropriate to provide some analysis, or point to an analysis, of the\nrobustness of the results to the choice of distributions and the correlation structure between the\nvariates.\nAs discussed above, we have added sensitivity of the results to a larger ensemble size and to the choice\nof distributions (by assuming that all distributions are simply uniform). We have also added text about\nthe potential implications of different correlation structures in the beginning of the Results section."}, {"round": 2, "reviewer_comments": {"reviewer_2": "This is my second time reviewing this manuscript. In my first review, I had two major critiques:\n1. That the tradeoff between probabilistic and scenario methods was not fully explored.\n2. That methodological choices, like the ensemble sample size is not fully, correlations structures and distribution choice, and the choice of dispersion statistic were not fully explained.\nThe authors have made an earnest attempt to respond to both reviewers’ comments. They have added some text to the main article and a lengthy section in the supplement discussing the pros and cons of a probabilistic approach (see comments below). They have also conducted an analysis to explore the consequences of the ensemble size and choice of parameter distribution for their findings and have added more standard dispersion metrics to their analyses.\nI have no major comments or critiques of the work at this time. My one minor comment on at this time is:\n1. In the supplement, there is a paragraph on Robust Decision Making that I think should probably be altered. The robust decision making area is active and has a variety of approaches that are commonly used. I do not think it is correct to characterize the entire area as making decisions without assigning probabilities, de-facto making every scenario equally likely, or generally focusing on minimax/maximin. For example, multi-objective robust decision-making often optimizes decisions based on the best-guess for parameters and probability distributions, and only then stress-tests those decisions based on a wider range of uncertainties [1]. It is true that those uncertainty ranges can be subjective, and this is a challenge. I do not agree that minimax approaches assume all scenarios are equally likely. I think it is more correct to say that the relative likelihood of the scenarios has no impact on the decision being made. The authors may want to consider modifying the paragraph a bit to reflect the wider range of robust methods, perhaps qualify the framing a bit, or consider removing it. Otherwise, I think the supplement is an excellent addition with a few very minor changes suggestions below.\n[1] Kasprzyk et al. Many objective robust decision making for complex environmental systems undergoing change.\nEnvironmental Modeling and Software, 42, April 2013.\nI have a few more minor comments that I do not think affect the major findings of this work, but that I hope are useful for the\nauthors in future work:\n1. Interpretation of the probabilities: In the supplement, the authors state “As long as the limitations and assumptions of\nuncertainty quantification are made clear, the results of such analyses can provide important insights.” I completely agree. I\ndo wonder whether an audience, even a sophisticated one, would be able to contextualize the probabilities. The authors\nmake a compelling case that not providing probabilities leads to a misinterpretation of extreme scenarios (e.g., RCP 8.5). At\nthe same time, one wouldn’t want to interpret the probabilities too literally (like the probability of flipping a coin), given the\nuncertainty in computing them and their conditional nature. I think the value of these probabilities is in giving the reader\nsome sense for how relatively likely different outcomes are, conditional on deep uncertainties and our current state of\nknowledge. I think the authors strike that balance here, but overinterpretation of probabilities is probably always going to be a\nproblem, as it is in other domains like weather forecasting.\n2. Use of the probabilities in a risk framework: Several times the authors suggest using the probabilities in a risk-based\ndecision framework. My only caution is that tails are often what drives decision making, and I’m not entirely convinced that\nthe tails have been pinned down. Nailing down a 90% confidence interval may not be sufficient for decision making if low-\nrisk, high-consequence scenarios are not well represented. I think this could be an area of future work, perhaps pairing with\ndeep uncertainty methods as alluded to in the Supplement.\nVery minor comments:\n1. In the supplement the authors comment that “a scenario approach limits the uncertainty space explored…” in contrasting it\nwith probabilistic methods that they claim can search a wider range. On one hand, they are absolutely right that scenario\nmethods explore relatively few scenarios, but those scenarios can represent very different worlds. The authors are correct\nthat scenario assumptions are subjective, but so too are some aspects of probabilistic methods. Perhaps it might be more\ncorrect to say that scenarios limit the search of the uncertainty space to a few narrow corridors defined by assumptions. This\nis very minor, and overall I think the section is strong.\n2. Typo (I think): In the supplement it reads “…relate to factors or processes that are so known…”. I believe it should be\nunknown.", "reviewer_3": "Review of ‘Quantifying Both Socioeconomic and Climate Uncertainty in Coupled Human-Earth Systems Analysis’\nThe above manuscript (ms) reports the results of a multivariate probability distribution propagation through an\ninterdisciplinary integrated assessment model, the MIT IGSM (‘IGSM’ hereafter). From this formal treatment, the following\nresults are obtained. (1) A quantification of changes in probability that temperature transgresses certain limits, (2) a role of\nrenewables on the same order of magnitude as for coal, if the latter is determined for the reference case, (3) heterogenous\npolicy costs across regions, (4) heterogenous fractions of human vs natural component uncertainty contributions across\noutput variables, (5) correlations in input variables lead to a reduction of output uncertainty for some instances.\nThe ms addresses a mostly neglected topic in integrated assessment modelling: a full-fledged uncertainty analysis across\nrepresented sectors. An uncertainty propagation that starts from uncertainty across multiple systems such as the human and\nthe natural, is rarely done. Attributing uncertainty in various outputs to uncertainty in the human vs the natural sphere and\nwell as the correlation analysis is novel. In that sense I support a publication in this journal.\nHowever, the ms should not be published in its present form. As main shortcomings I see\n1. An unclear setup: how exactly are the boundary conditions changed in order to generate policy cases as against the\nreference case? Does it make sense to fix emissions (and in what sense – budget constraint?) if they are uncertain\notherwise? Furthermore, in L52 the class of models is portrait to include impacts, in L322 it says that impacts are not\nincluded. That might lead to an unrealistically large emissions and temperature responses for reference case (see Woodard,\nD. L., Davis, S. J., & Randerson, J. T. (2019). Economic carbon cycle feedbacks may offset additional warming from natural\nfeedbacks. Proceedings of the National Academy of Sciences, 116(3), 759-764). Overall, I found it hard to understand: what\nis uncertain and what is kept as a fixed boundary condition? And what are the key economic assumptions of IGSM at all\n(Ramsey type, recursive-dynamic, etc).\n2. The article messes different subjects. From the title I would assume that uncertainty is in the focus. However, two main\nfindings might already hold without uncertainty treatment: heterogeneity of policy costs across regions and a role of\nrenewables in the reference case. What does uncertainty add here? If these topics are mentioned in the abstract, the link to\nuncertainty should become clear – or they should be rather treated as a secondary result. The role of renewables in the\nreference case as against the policy cases is surprising and in stark contrast to IPCC AR6 WGIII Ch3 (see Fig. 3.36). There\nmust be a reflection on this difference. That policy costs are heterogenous across regions is common wisdom in the IAM\ncommunity and does not come as a surprise from common sense. If this ms is supposed to make a point here, at the\nminimum the model’s burden sharing rules (or certificate allocation rules) must be explained.\n3. This ms is not the first to quantify temperature uncertainty. A crisper summary of existing literature, in particular their\noutcomes, must be provided. Otherwise, it is not clear enough whether the findings are new or whether they are reconfirming\n– both has its role. Furthermore, the ms is virtually silent on how to potentially utilize the setup for decision-making under\nuncertainty. Only some hints to very specialized decision rules are given. However, already IPCC AR5 presented a longer\nlist of decision rules and about 60 papers with implementations (see WGIII, Ch2, 2014 – regrettably, the equivalent Chapter\ndoes not exist in AR6). Overall, to be justified in this journal, somewhat crisper statements on the relevance for decision-\nmaking should be delivered.\n4. In summarizing parts of the ms, the correlation discussion which could be a main result, should be summarized in more\nconcrete terms – why is uncertainty reduced? What is the special condition that holds here? The ms too little transcends\npure reporting of numerics; in general, more understanding of the results should be strived at.\n5. On abstract and conclusions level, summarize where human system and where natural systems uncertainty dominates –\nthese could be exciting take-home messages.\n6. L575: Why does the ms reveal to include further policy options? That is already obvious prior modelling – I do not get the\nrationale.\n7. Across the ms, avoid uncalibrated language such as ‘relatively modest’, ‘substantially’ (see abstract). Choose neutral\nterms that make clear to any reader what is meant by it.\n8. The ms lacks a differentiation between a discussion and a conclusion section."}, "author_response": "Response to Reviewers\nReviewer #2 recognized our efforts to address the comments of the original two reviewers, and had only\nminor comments on the revised version, which we have addressed. The new reviewer (Reviewer #3) was\npositive about the contributions of this paper, offering a set of comments, which we have addressed.\nWe believe the paper has been further improved as a result. The comments from both reviewers are\ncopied in full below, and our response is in included in red following each comment. The line numbers\nreferenced refer to the version of the paper with tracked changed.\nIn addition, we have followed the guidelines for the journal, updating the format of Figures/Tables,\nreferences and the Supplementary Information.\nReviewer #2:\nThis is my second time reviewing this manuscript. In my first review, I had two major critiques:\n1. That the tradeoff between probabilistic and scenario methods was not fully explored.\n2. That methodological choices, like the ensemble sample size is not fully, correlations structures and\ndistribution choice, and the choice of dispersion statistic were not fully explained.\nThe authors have made an earnest attempt to respond to both reviewers’ comments. They have added\nsome text to the main article and a lengthy section in the supplement discussing the pros and cons of a\nprobabilistic approach (see comments below). They have also conducted an analysis to explore the\nconsequences of the ensemble size and choice of parameter distribution for their findings and have\nadded more standard dispersion metrics to their analyses.\nWe thank the reviewer for the original comments and recognition of our efforts to address them. We\nbelieve the paper is much improved as a result. We also appreciate the additional comments.\nI have no major comments or critiques of the work at this time. My one minor comment on at this time\nis:\n1. In the supplement, there is a paragraph on Robust Decision Making that I think should probably be\naltered. The robust decision making area is active and has a variety of approaches that are commonly\nused. I do not think it is correct to characterize the entire area as making decisions without assigning\nprobabilities, de-facto making every scenario equally likely, or generally focusing on minimax/maximin.\nFor example, multi-objective robust decision-making often optimizes decisions based on the best-guess\nfor parameters and probability distributions, and only then stress-tests those decisions based on a wider\nrange of uncertainties [1]. It is true that those uncertainty ranges can be subjective, and this is a\nchallenge. I do not agree that minimax approaches assume all scenarios are equally likely. I think it is\nmore correct to say that the relative likelihood of the scenarios has no impact on the decision being made.\nThe authors may want to consider modifying the paragraph a bit to reflect the wider range of\nrobust methods, perhaps qualify the framing a bit, or consider removing it. Otherwise, I think the\nsupplement is an excellent addition with a few very minor changes suggestions below.\n[1] Kasprzyk et al. Many objective robust decision making for complex environmental systems\nundergoing change. Environmental Modeling and Software, 42, April 2013.\nWe have altered the paragraph mentioned in accordance this suggestion. We no longer characterize all\nrobust approaches as not assigning probabilities, and include the Kasprzyk et al. example. We also\nremoved reference to minimax/maximin.\nI have a few more minor comments that I do not think affect the major findings of this work, but that I\nhope are useful for the authors in future work:\n1. Interpretation of the probabilities: In the supplement, the authors state “As long as the limitations and assumptions of\nuncertainty quantification are made clear, the results of such analyses can provide important insights.” I completely agree. I\ndo wonder whether an audience, even a sophisticated one, would be able to contextualize the probabilities. The authors\nmake a compelling case that not providing probabilities leads to a misinterpretation of extreme scenarios (e.g., RCP 8.5). At\nthe same time, one wouldn’t want to interpret the probabilities too literally (like the probability of flipping a coin), given the\nuncertainty in computing them and their conditional nature. I think the value of these probabilities is in giving the reader\nsome sense for how relatively likely different outcomes are, conditional on deep uncertainties and our current state of\nknowledge. I think the authors strike that balance here, but overinterpretation of probabilities is probably always going to be a\nproblem, as it is in other domains like weather forecasting.\nWe agree with this point and have adjusted the text as follows:\n“As long as the limitations and assumptions of uncertainty quantification are made clear, and the\nprobabilities are not overinterpreted, the results of such analyses can provide important insights. The\nprobabilities can provide a sense of how relatively likely different outcomes are, conditional on deep\nuncertainties and our current state of knowledge.”\n2. Use of the probabilities in a risk framework: Several times the authors suggest using the probabilities\nin a risk-based decision framework. My only caution is that tails are often what drives decision making,\nand I’m not entirely convinced that the tails have been pinned down. Nailing down a 90% confidence\ninterval may not be sufficient for decision making if low-risk, high-consequence scenarios are not well\nrepresented. I think this could be an area of future work, perhaps pairing with deep uncertainty\nmethods as alluded to in the Supplement.\nThis is a good point. We have added the following to the Discussion section:\n“Importantly, further research is needed to better resolve the low-probability tails of distributions,\nincluding assessment of potentially unmodeled processes that could lead to extreme outcomes.\nCombining probabilistic and deep uncertainty methods to better understand low-risk, high-consequence\noutcomes and their implications for decision-making is an important area of future work.”\nVery minor comments:\n1. In the supplement the authors comment that “a scenario approach limits the uncertainty space\nexplored…” in contrasting it with probabilistic methods that they claim can search a wider range. On one\nhand, they are absolutely right that scenario methods explore relatively few scenarios, but those\nscenarios can represent very different worlds. The authors are correct that scenario assumptions are\nsubjective, but so too are some aspects of probabilistic methods. Perhaps it might be more\ncorrect to say that scenarios limit the search of the uncertainty space to a few narrow corridors defined by\nassumptions. This is very minor, and overall I think the section is strong.\nWe agree that the suggest tweak in wording is more accurate. We changed the text to say:\n“In general, a scenario approach limits the search of the uncertainty space to a few narrow corridors\ndefined by a limited number of different input assumptions, which in turn limits the possible outcomes.”\n2. Typo (I think): In the supplement it reads “…relate to factors or processes that are so known…”. I\nbelieve it should be unknown.\nThank you for catching this typo. We have corrected it to be “unknown”.\nReviewer #3:\nReview of ‘Quantifying Both Socioeconomic and Climate Uncertainty in Coupled Human-Earth Systems\nAnalysis’\nThe above manuscript (ms) reports the results of a multivariate probability distribution propagation\nthrough an interdisciplinary integrated assessment model, the MIT IGSM (‘IGSM’ hereafter). From this\nformal treatment, the following results are obtained. (1) A quantification of changes in probability that\ntemperature transgresses certain limits, (2) a role of renewables on the same order of magnitude as for\ncoal, if the latter is determined for the reference case, (3) heterogenous policy costs across regions, (4)\nheterogenous fractions of human vs natural component uncertainty contributions across output\nvariables, (5) correlations in input variables lead to a reduction of output uncertainty for some instances.\nThe ms addresses a mostly neglected topic in integrated assessment modelling: a full-fledged\nuncertainty analysis across represented sectors. An uncertainty propagation that starts from uncertainty\nacross multiple systems such as the human and the natural, is rarely done. Attributing uncertainty in\nvarious outputs to uncertainty in the human vs the natural sphere and well as the correlation analysis is\nnovel. In that sense I support a publication in this journal.\nThank you, we agree that this is a mostly neglected topic and believe we have made novel contributions\nin this area.\nHowever, the ms should not be published in its present form. As main shortcomings I see\n1. An unclear setup: how exactly are the boundary conditions changed in order to generate policy cases\nas against the reference case? Does it make sense to fix emissions (and in what sense – budget\nconstraint?) if they are uncertain otherwise?\nWe do not change any boundary conditions across scenarios. The different scenarios are achieved by\nimplementing different limits on emissions. We have added clarification in the Methods section as\nfollows:\nWe added to line 734 to make it clear at the beginning of the Methods section that the policies were\nimplemented as emissions caps (the implementation as emissions caps is also described in lines 404-\n419).\nWe added lines 736-738: “The different scenarios are achieved by implementing different limits on\nemissions; all other assumptions and sampled input values are the same across scenarios.”\nThe policies present in the Reference case are targeting renewables, and we have added text to make it\nclear those remain in place in all the scenarios (line 741).\nIn lines 748-749 we added clarification that we implemented the NDC targets of the Paris Agreement in\nthe ParisForever scenario as emissions caps.\nIn lines 754-773 we identify the process by which we identify the emissions paths consistent with the\ntemperature targets of 1.5C and 2C. To ensure that these emissions paths are met in all ensemble\nmembers, they are implemented as a cap-and-trade policy. We have added text to make that more\nclear.\nOne might also try to assess the uncertainty of the emissions levels that policies might achieve, rather\nthan treat policy as a choice variable as we have done. We have added lines 790-794 to make that point:\n“In reality, countries may not meet their emissions targets with certainty. Nevertheless, we represent\nthese emissions targets as being achieved with certainty. An interesting exercise could be to conduct an\nassessment asking experts for their judgement of the range of emissions paths that countries may\nachieve over the century. Such an approach would quantify the uncertainty in policy rather than treating\nit as a choice variable.”\nFurthermore, in L52 the class of models is portrait to include impacts, in L322 it says that impacts are\nnot included. That might lead to an unrealistically large emissions and temperature responses for\nreference case (see Woodard, D. L., Davis, S. J., & Randerson, J. T. (2019). Economic carbon cycle\nfeedbacks may offset additional warming from natural feedbacks. Proceedings of the National Academy\nof Sciences, 116(3), 759-764). Overall, I found it hard to understand: what is uncertain and what is kept\nas a fixed boundary condition?\nWe have adjusted the line (now line 62) to make it clear that this analysis is not going to climate impacts\nbut can provide useful insights for further climate impact analysis.\nIn lines 358-362, we have edited the text as follows:\n“In this particular approach, the impacts of climate change on the economy are not included. For\nexample, if climate change caused damage to the economy, energy use and emissions might be\nreduced, making it less likely that such large increases in temperatures were actually possible.58”\nReference 58 is included in this line and is the Woodard et al. 2019 paper mentioned.\nAnd what are the key economic assumptions of IGSM at all (Ramsey type, recursive-dynamic, etc).\nOn line 660-663, the economic model of the IGSM is described as a “recursive-dynamic multi-sector,\nmulti-region computable general equilibrium (CGE) model of the world economy69-71 (see\nSupplementary Figure 12).” Citations 69-71 are papers that provide complete documentation of the\neconomic model for readers that want more detail. We also added Supplementary Figure 12 (and\nreference it in the main text), which is an infographic of the EPPA model to provide the key features and\nassumptions at a glance.\n2. The article messes different subjects. From the title I would assume that uncertainty is in the focus.\nHowever, two main findings might already hold without uncertainty treatment: heterogeneity of policy\ncosts across regions and a role of renewables in the reference case. What does uncertainty add here? If\nthese topics are mentioned in the abstract, the link to uncertainty should become clear – or they should\nbe rather treated as a secondary result. The role of renewables in the reference case as against the\npolicy cases is surprising and in stark contrast to IPCC AR6 WGIII Ch3 (see Fig. 3.36). There must be a\nreflection on this difference. That policy costs are heterogenous across regions is common wisdom in\nthe IAM community and does not come as a surprise from common sense. If this ms is supposed to\nmake a point here, at the minimum the model’s burden sharing rules (or certificate allocation rules)\nmust be explained.\nWe agree that the abstract should focus on results directly related to the uncertainty analysis, and have\nadjusted the abstract to do so. We still include points about policy costs and renewables, but, as\nsuggested, have adjusted them to focus on points that relate to uncertainty.\nWe agree that the policy cost heterogeneity and burden sharing results are well-known and no longer\nfocus on this in the abstract. We instead highlight the greater uncertainty of policy costs among low-\nand middle- income regions compared to higher income regions. In lines 404-419 we describe how we\nachieve a neutral burden sharing allocation where under median parameter settings there is no\nincentive for trade among regions.\nFor renewables, we highlight that they robust investments across a wide range of policies and\nsocioeconomic uncertainties. While the former (robustness across policies) holds without uncertainty\ntreatment, but the latter (robustness across socio-economic uncertainties) is not as obvious a priori. For\nexample, it could have been the case that depending on the sampled technology costs, different\ntechnologies (e.g. CCS or nuclear) could have dominated, leaving only a small role for renewables.\nHowever, while the scale of competing technologies does vary across ensemble members, a sizable role\nof renewables is quite robust across the different cost assumptions- i.e. based on our assessment of the\nprobability distributions of the cost of different technologies, renewables retain a competitive edge in\nmost future pathways. We added this point to lines 473-479 of the main text.\nIn the main text on lines 479-488, we make note of the AR6 result for renewables and explain why we\nget a different result:\n“In contrast to the AR64, which shows more renewables in the policy cases, in our case renewables end\nup somewhat lower in 2100 in Paris2C than in Reference, although their share of energy use is higher,\nbecause energy and electricity use are lower under stringent policy due to a greater efficiency response\nto policy and overall economic consumption is lower. However, if the model represented more options\nfor electrification, it is possible that total electricity consumption would increase in the Paris2C scenario\nrelative to the Reference scenario, and renewables would grow beyond Reference levels throughout the\ncentury. Expanding electrification opportunities is an area for further model development.”\n3. This ms is not the first to quantify temperature uncertainty. A crisper summary of existing literature,\nin particular their outcomes, must be provided. Otherwise, it is not clear enough whether the findings\nare new or whether they are reconfirming – both has its role. Furthermore, the ms is virtually silent on\nhow to potentially utilize the setup for decision-making under uncertainty. Only some hints to very\nspecialized decision rules are given. However, already IPCC AR5 presented a longer list of decision rules\nand about 60 papers with implementations (see WGIII, Ch2, 2014 – regrettably, the equivalent Chapter\ndoes not exist in AR6). Overall, to be justified in this journal, somewhat crisper statements on the\nrelevance for decision-making should be delivered.\nWe have added reference and comparison to other temperature projections in the text (see lines 299-\n316), as well as a comparison table in the Supplementary Information (Supplementary Table 4).\nAt the end of the Introduction, we have added the following text about decision-making:\n“This type of uncertainty analysis can inform decision-making about mitigation and adaptation. Chapter\n2 of Working Group III of the IPCC’s Fifth Assessment Report (AR5) presented a set of approaches,\nrules and tools for decision-making, many of which would be aided by uncertainty quantification.43 In\nparticular, the probability distributions from this analysis could be used in formal decision-making under\nuncertainty analyses that employ expected utility theory, decision analysis, robust decision making or\nother deliberative methods. However, they can also provide an understanding of uncertainty and risk\nthat can aid decision-makers in more intuitive decision-making processes.”\n4. In summarizing parts of the ms, the correlation discussion which could be a main result, should be\nsummarized in more concrete terms – why is uncertainty reduced? What is the special condition that\nholds here? The ms too little transcends pure reporting of numerics; in general, more understanding of\nthe results should be strived at.\nWe have expanded this point in the abstract as well as in the main text (see lines 588-590) as it\nillustrates the benefits of an integrated modeling approach.\n5. On abstract and conclusions level, summarize where human system and where natural systems\nuncertainty dominates – these could be exciting take-home messages.\nWe have summarized this point in both the abstract and conclusion.\n6. L575: Why does the ms reveal to include further policy options? That is already obvious prior\nmodelling – I do not get the rationale.\nWe agree that “reveal” is the wrong word. We updated the text to provide a list of further research\nneeds.\n7. Across the ms, avoid uncalibrated language such as ‘relatively modest’, ‘substantially’ (see abstract).\nChoose neutral terms that make clear to any reader what is meant by it.\nWe removed most instances, leaving only a few where we provide numbers or Figure reference to\ncalibrate what we meant by “substantial”.\n8. The ms lacks a differentiation between a discussion and a conclusion section.\nNature Communications prescribes sections. From the author guidelines: “The main text of an Article\nshould begin with a section headed Introduction of referenced text that expands on the background of\nthe work (some overlap with the abstract is acceptable), followed by sections headed Results,\nDiscussion (if appropriate) and Methods (if appropriate). The Results and Methods sections should be\ndivided by topical subheadings; the Discussion should be succinct and may not contain subheadings.”\nLeaving no option of including a separate Conclusion section."}, {"round": 3, "reviewer_comments": {"reviewer_2": "This is my third time reviewing this manuscript. In my first review I raised major concerns, which were earnestly addressed\nby the authors. In my second review I raised minor concerns with the new text, mostly around a few claims that I felt should\nbe softened. Again, I feel the authors have done a good job addressing my concerns.\nI have no further comments for the authors at this time. In my opinion, this work is a stronger contribution now than when it\nwas first submitted because the authors have been so responsive to all three reviewers.", "reviewer_3": "I am very happy with the changes implemented by the authors. The MS significantly adds to the understanding of IAMs and\nshould be published as foreseen."}, "author_response": ""}]

Decision letter