Greenhouse gas emission scenarios and mitigation costs are extracted from the dataset used by Working Group III (WGIII) of AR5. Temperature projections are computed from the fifth phase of the Coupled Model Inter-comparison Project (CMIP5) runs of the working group I (WGI) outcomes. Global economic impacts are generated on the basis of the impact reviews proposed in the Fifth Assessment Report, working group II (WGII). Finally, carbon budgets are selected from a set of decision rules and preferences. For more details, refer to Methods.
We propose a method for selecting climate policies which accounts for different preferences for risk, ambiguity and time. We adopt a two-stage subjective expected utility framework5 that accounts for both state and model uncertainty. In the context of this paper, ‘model uncertainty’ refers to the existence of alternative modelling paradigms relating how mitigation costs, the dynamics of the climate system, or economic damage resulting from climate change might respond to climate policies; whereas ‘state uncertainty’ refers to the probabilistic response (of mitigation costs, temperature, or climate damage) that each of these models produces given a climate policy.
Integrated assessment model data set.
The data set is issued from the AR5 scenario database, which has been created for the Integrated Assessment Modeling Consortium (IAMC) and is hosted and maintained by the International Institute for Applied Systems Analysis (IIASA). This database is publicly available and contains outcomes from several model comparison projects, reviewed in the Fifth Assessment Report (AR5) of Working Group III of the Intergovernmental Panel on Climate Change (IPCC). The full description of the database is available in the dedicated website (https://secure.iiasa.ac.at/web-apps/ene/AR5DB) and in Section A.II.10 of the IPCC AR5.
The meta-analysis is carried out with a subset of the AR5 scenario database. We select those long-term scenario-model outcomes that meet the following criteria: model time horizon goes up to the year 2100; mitigation cost estimates are provided; carbon dioxide CO2, methane CH4 and nitrous oxide N2O emissions are provided; climate policy category is ‘baseline’, ‘reference’, or ‘first best’. ‘Baseline’ scenarios imply no climate policy after 2010, ‘reference’ scenarios implement a weak policy and current pledges, and ‘first best’ scenarios have an efficient carbon policy with an immediate target adoption. This leaves us with outcomes from eight integrated assessment models and six model inter-comparisons projects: the Asian Modeling Exercise (AME; ref. 31), the Assessment of Climate Change Mitigation Pathways and Evaluation of the Robustness of Mitigation Cost Estimates (AMPERE) project32, the Energy Modeling Forum’s Climate Change Control Scenarios (EMF-22) and Global Model Comparison Exercise (EMF-27; ref. 17), the Low climate IMpact scenarios and the Implications of required Tight emissions control Strategies (LIMITS) project16 and the Roadmaps towards Sustainable Energy futures (ROSE) project33. For each scenario we extract the global emission pathway and the mitigation costs over the century.
Carbon budget.
A carbon budget is defined as the cumulative total CO2 emissions over the period 2010–2100. For each scenario, we sum up the world emissions of CO2 from fossil-fuel combustion and industry, and from land-use change. As the database provides the annual emissions every ten years from 2010 to 2100, the intermediary annual emissions are linearly interpolated (see Supplementary Fig. 1 for an overview of the emission pathways and the carbon budgets from the selected data set).
Mitigation costs.
Each scenario is associated with information on mitigation costs. ‘Baseline’ scenarios have zero mitigation costs. Owing to the different nature of the models, mitigation costs are expressed in three different, but comparable, cost metrics: gross world product (GWP) losses, area under the marginal abatement cost curve, and additional total energy system cost. These costs are converted in % GWP change from baseline scenario. Supplementary Fig. 2 reports, for each scenario-model outcome, two dimensions: carbon budget and mitigation costs. Carbon budgets are negatively correlated with mitigation costs, in a nonlinear way.
Model categorization is based on a well-documented distinction34 between two classes of integrated assessment models: top-down (TD) models, which provide a more accurate description of the macroeconomic feedback, versus bottom-up (BU) models, which better represent the set of mitigation technologies. For the purpose of mitigation costs, TD models generally show higher costs than BU models, but it is not obvious which class of models should be considered as the most accurate.
On the basis of this data, we estimate three piecewise probabilistic models relating, at each time period, carbon budgets and mitigation costs. The procedure, described in the subsequent paragraph, is the same for the three estimated models; what changes are the mitigation cost data used: data coming only from TD models, data coming only from BU models, and the whole data set. First, mitigation costs are clustered in five groups spanning the range of carbon budgets. We fit each cluster data with a Weibull distribution. Second, we estimate, by means of least squares, a relationship between the Weibull distribution parameters and the budgets (the central budget of each cluster is taken as a reference in the fitting). In all cases, each scenario-model outcome is weighted equally. Supplementary Fig. 3 presents the resulting piecewise probabilistic mitigation cost function for the case of the whole data set.
Probabilistic temperature.
We use an updated version of a climate model of reduced complexity23 to emulate the CMIP5 model ensemble response. This model version is composed of a climate module DOECLIM (ref. 35) and a carbon-cycle model which includes feedbacks from the atmospheric CO2 concentration and temperature36. Key geophysical model parameters are estimated from the CMIP5 temperature projections from 2010 to 2100 using a Bayesian inversion technique based on the Markov Chain Monte Carlo (MCMC) algorithm. The estimated climate parameters are the climate sensitivity, the heat vertical diffusivity in the ocean, and the aerosol scaling factor to the total radiative forcing. The carbon-cycle estimated parameters are the carbon fertilization from living plants, the respiration sensitivity related to temperature, and the thermocline carbon transfer rate in the ocean. In addition, initial conditions of atmospheric temperature and CO2 concentration are also estimated.
To perform the MCMC, we constrain the model with the temperature projections for the four Representative Concentration Pathways (RCP2.6, RCP4.5, RCP6.0 and RCP8.5) provided by 38 climate models in the CMIP5 data set to constrain the model. We retain 5,000 equally distant combinations of parameters out of the 3,000,000 in the MCMC to avoid cross-correlation between them. The emulator is able to reproduce the spread of the temperature projections from the CMIP5 data set for the four RCPs (see Supplementary Fig. 4).
It is difficult to distinguish different classes of models from the CMIP5 ensemble as ‘there is high confidence that the model performance for global mean surface air temperature (TAS) is high’, where the level of confidence is a combination of the level of evidence and the degree of agreement (section on model evaluation in Chapter 9 of the AR5 WGI; ref. 2). Our choice is to split the model outcomes into two classes according to the extent of ocean resolution of the climate model (more or less than 50,000 horizontal grid points). For the RCP4.5 and RCP 6.0, the CMIP5 model provides good agreement, whereas for the more extreme scenario RCP2.6 and RCP8.5, the two classes of models diverge slightly after 2070. In these cases, the high-resolution models have a colder atmosphere than the low-resolution models (see Supplementary Fig. 5). Applying the two-sample Welch’s t-test37 on the two subsets of the data, the difference in yearly mean becomes highly significant after 2070 for the RCP2.6 and RCP8.5 (Supplementary Fig. 6).
Once calibrated, the emulator computes probabilistic temperature projections associated with each scenario-model outcome, given information on carbon dioxide emissions, and radiative forcing of other greenhouse gases and of aerosols. The radiative forcing for the non-CO2 greenhouse gases is taken from the database, when available, otherwise it is estimated from the emission levels and their accumulation in the atmosphere. Similarly, the radiative forcing from aerosols is taken from the data set, when available, otherwise it is inferred from the RCP database (available at http://www.iiasa.ac.at/web-apps/tnt/RcpDb). Three sets of projections are produced, one for each of the three probabilistic models (low and high ocean resolution, and the joint set).
Probabilistic impacts of climate change.
We use 20 estimates of total economic effects of climate change from the literature reviewed in Table 10.B.1 from Chapter 10 of the IPCC WGII AR5 (ref. 3). These estimates have been calculated using a variety of methods, but they usually aggregate one by one the economic costs accruing in different sectors of both global and local impacts. Each study reports the mean estimates of the economic climate-change damage for a given increase in global mean temperature. Five of the studies also include a measure of the uncertainty surrounding these estimates in the form of the standard deviation (normal distribution) or a confidence interval (skewed distribution). In the case of the skewed distribution, we estimate the parameters of a displaced Gamma distribution matching the reported confidence interval and mean. Given the few data and given that studies only cover temperature increases of up to 4.8 °C, we fit three different probabilistic damage models over the economic climate-change damage data. Let Id be the economic impacts, expressed in % of GWP, T be the temperature increase and βj the regression coefficients, then three impact functions are defined. The first is a quadratic impact function I1(T) = β1T + β2T2, as proposed by ref. 38, which has been used in the DICE integrated assessment model13. This function can allow for positive impacts (benefits) at low temperatures. The second is an exponential impact function I2(T) = exp(−β3T2) − 1, as introduced by ref. 39, which excludes the possibility of positive damage (benefits) and which implies greater losses at high warming levels. The third is a sextic impact function I3(T) = β4T2 + β5T6, adapted from ref. 40, which implies catastrophic outcomes at extreme temperatures. The economic damage distributions generated by the three models are shown in Supplementary Fig. 7 as probabilistic functions of the temperature increase.
The procedure to estimate the probabilistic relationship between carbon budgets and damage costs is similar to that used in generating the probabilistic mitigation costs models. First, we gather the generated damage costs in five clusters spanning the range of carbon budgets, and we fit each cluster data with a log-normal distribution. Second, we estimate, by means of least squares fit, the relationships between the log-normal distribution parameters and the carbon budgets (using the central point of each cluster as a reference). However, in the case of damage, for each of the carbon budgets we have three temperature probabilistic models and, associated with each temperature level, three damage functions. Supplementary Fig. 8 presents the three resulting piecewise probabilistic damage cost functions, for three illustrative years, using temperature projections based on the whole CMIP5 data set model.
Economic projection.
We use global projections of population and economic production growth produced by the Organisation for Economic Co-operation and Development (OECD) for the second Shared Socio-economic Pathway (SSP2; ref. 41). The SSP2 describes a ‘middle of the road’ socio-economic scenario. Let
denote production per capita for each year t ∈ T = {2010, …, 2200}, gross of any mitigation or damage cost. At each time period t, given each state of the world s, and each of the mitigation and damage probabilistic models m, the overall economic impacts associated with a carbon budget c is given by the combination of the mitigation cost Mt(c; s, m) and the climate-change damage Dt(c; s, m). Both mitigation and damage are indexed on the combination of models m, and m is defined as a triplet selected within the set Ω = {{mitigation-all, mitigation-BU, mitigation-TD} × {climate-all, climate-ocean-lo, climate-ocean-hi} × {{damage-sextic}, {damage-quadratic}, {damage-exponential}}}. The classes of model are listed in Supplementary Table 1. As both mitigation and damage losses data are expressed as % of GWP, we can compute the resulting per capita world production net of mitigation and damage losses.
Given that outcomes from the data set end in 2100, we assume that post-2100 mitigation costs decrease linearly, starting from their 2100 level and reaching zero in 2200, and that post-2100 damage costs remain constant at their 2100 level over the whole twenty-second century. As an illustration, Fig. 2 shows the distributions of Yt(c; s, m) in 2100, for twelve combinations of models ({{mitigation-BU, mitigation-TD} × {climate-ocean-lo, climate-ocean-hi} × {damage-sextic, damage-quadratic, damage-exponential}}) and for two carbon budgets. Supplementary Fig. 11 provides an intertemporal view of Yt(c; s, m) for three representative budgets.
Consumption.
Not all models included in the data set report the value of global consumption. This is particularly true for BU energy model. As we want to perform our calculation using utility, which is generally a function of consumption, we need to translate GWP into consumption figures. For those models reporting both consumption and GWP, the ratio of the two measures remains constant across scenarios and presents a similar time trend, as depicted in Supplementary Fig. 9. We fit the model mean ratio with a quadratic function and extrapolate it until 2200 (Supplementary Fig. 10). The fitted ratio is 0.741 in 2020, which is consistent with the 26% world gross saving forecast for the year 2017 by the World Economic Outlook of the International Monetary Fund, slightly increasing over time (to 0.820 in 2200). This procedure allows us to express mitigation and damage losses in terms of consumption losses. In particular, to obtain consumption per capita, we apply the fitted ratio ζt to the world net production per capita at each time period.
Utility function.
To translate consumption per capita into utility, we employ the Epstein–Zin preferences formulation42. This formulation allows one to disentangle preferences over time, consumption smoothing and risk. The recursive utility function is
where Et; s′, m′ is a time-dependent expectation operator over states, s, and models, m ∈ ω