Model scenarios

For this analysis, we used the results from nine integrated assessment models: AIM/CGE, COFFEE, GEM-E3, IMAGE, TIAM-ECN, POLES, REMIND-MAgPIE, MESSAGEix-GLOBIOM and WITCH. These models generated emission trajectories consistent with a large number of carbon budgets (that is, cumulative CO2 emissions) using two families of scenarios: EOC, which allowed for temperature overshoot, and NZ, which did not (see the modelling protocol in Supplementary Information). Models are not constrained to the level of temperature over the century and it can overshoot the temperature reached in 2100. We selected the scenarios entailing maximum warming of 2 °C in 2100. The protocol included a vetting exercise to ensure that model results were sufficiently close to historical data up to 2020. In particular, attention was devoted to harmonizing the energy system (that is, installed power plant capacities, investments and activities), greenhouse gases and aerosol emissions, the land-use sector and economic growth. Models also implemented policies in force, such as carbon taxes, constraints on fossil fuels, renewables standards, etc. The protocol did not require capturing the effect of the COVID-19 pandemic. A comprehensive description of the modelling process and the model scenarios is provided by17.

Uncertainty analysis

Various sources of uncertainty were considered in the analysis: the emission trajectories to reach a carbon budget, the global mean temperature through the climate sensitivity, and the CMIP5 model patterns in terms of geophysical impact response and country-level temperature. Supplementary Fig. 14 lists these sources of uncertainty and provides a representation of the uncertainty propagation.

Global mean temperature

The emissions pathways from all model scenarios were given as an input to the climate emulator MAGICC21,22 to compute global mean temperature projections until 2100 (median estimate, 5%, 10%, 25%, 75%, 90% and 95% quantiles). MAGICC was calibrated to represent the climate sensitivity uncertainty assessed in the IPCC special report on the impacts of global warming of 1.5 °C. The model scenarios were clustered on the basis of the median of the 2100 global mean temperature (Supplementary Table 1).

Temperature downscaling

Country-level annual population-weighted temperature projections were obtained from the median estimates of the global mean temperature using a linear response function calibrated for each CMIP5 model. We gathered monthly mean temperatures from historical data records and the RCP runs of 20 CMIP5 models with all available ensemble members (ACCESS1-0 (3 runs), BNU-ESM (4), CCSM4 (29), CMCC-CMS (3), GFDL-CM3 (8), GFDL-ESM2G (5), GFDL-ESM2M (5), GISS-E2-H (15), GISS-E2-H-CC (3), GISS-E2-R (15), GISS-E2-R-CC (3), HadGEM2-CC (7), HadGEM2-ES (19), IPSL-CM5A-LR (19), IPSL-CM5A-MR (7), IPSL-CM5B-LR (2), MPI-ESM-LR (12), MPI-ESM-MR (8), NorESM1-M (7) and inmcm4 (3)). We computed the gridded annual mean temperature and corrected the bias using a 1980–2016 observational baseline (Supplementary Fig. 21). Unbiased gridded annual mean temperatures were aggregated at the country level with population density weights based on the gridded population of the world in 2010 (GPW v4). Results are comparable with the original baselines from ref. 32 (see sensitivity analyses in Supplementary Figs. 26 and 27). Finally, to obtain an estimate of the annual local temperature, from the global mean temperature increase relative to 2005, we performed a linear regression over the period 1900–2100 for each CMIP5 model for each year and each country individually.

Physical impacts

For each model scenario, we computed 15 impact indicators (see the list and definition in Supplementary Table 5) every year for 6 regions (global and 5 macro regions: Africa, Europe, North America, South America, Asia). The physical impacts were computed from a look-up table of global and regional impacts of climate change at different levels of global temperature increase, differentiated for 23 CMIP5 climate models25. To apply those functions, the global mean temperature was shifted down by 0.014 °C so that the average temperature increase relative to the pre-industrial level is equal to 0.61 °C over the period 1981–2010 to replicate ref. 25. The impacts of intermediate temperatures were interpolated linearly. Linear interpolation provides better consistency across the impact functions (Supplementary Fig. 17). We also evaluated the spline interpolation, which resulted in some values being out of credible bounds (for example, negative values) for a few combinations of temperature and impact (Supplementary Fig. 18). The difference between the two methods of interpolation is much smaller than the impact values (Supplementary Figs. 19 and 20). The impact distribution results from the combination of the model scenarios, the global mean temperature distribution and the CMIP5-specific impact function. Using these distributions, yearly values and maximum over-the-century comparisons were performed for the impact analyses. Note that our study focuses on the transient response of climate and impacts, which cannot be fully captured by simple pattern scaling techniques36. However, this is the best available method that allows us to capture the uncertainties stemming from consistent impact estimates spanning 5 levels of warming and 23 climate patterns25.

Economic impacts using the growth-based damage function

The economic impacts were computed at the country level. We followed the procedure described in ref. 32 and implemented in ref. 37,38. GDP per capita is Gi,t = Gi,t−1(1 + ηi,t + δ(Ti,t)), where ηi is the growth rate coming from the Shared Socioeconomic Pathways (SSP) reference projection in which no climate change occurs39 and δ(Ti,t) is a response function of the temperature increase at year t. The projected warming effect was adjusted by the baseline temperature in 2000–2010. The analysis used the main damage function specification called BHM SR32.

Economic impacts from the level-based damage functions

These economic impacts were only computed at the global level. They were computed as the global output loss relative to the SSP reference projection without climate change (GDP_gross). The GDP loss is ({{Delta }}GDP,{{mbox{_}}}cc=GDP{{mbox{_}}},grosstimes (alpha gm{t}_{t}+beta gm{t}_{t}^{2}+gamma )), where gmt is the global mean temperature increase from pre-industrial levels and α and β are the two parameters of the quadratic damage function. For the Howard & Sterner function33, we used the preferred model specification of non-catastrophic damage, which was increased by 25% to account for the omitted damage in the empirical estimates (α = γ = 0, β = − 0.7438). For the Takakura et al. function34, we derived and used the SSP2 function parameters (α = 0.07625, β = 0.21465, γ = − 0.11746).

Tail heaviness analysis

We performed a statistical analysis to test whether the EOC distribution has a longer tail than the NZ distribution. The assumptions and the methodology for the tail heaviness analysis are provided in detail in Supplementary Methods.

Sea-level rise

We computed the global mean sea-level rise using the physical model provided by ref. 40, using their calibration. For this specific impact, we extended the time horizon of the computations until 2200, with a constant global mean temperature beyond 2100. Sea levels keep rising through the twenty-second century. We computed the sea-level rise for 3 quantiles (5%, 50% and 95%).

Avoided damages and mitigation costs

The additional damages associated with the overshooting of the temperature target were obtained by comparing GDP in the EOC and the NZ scenarios, when impacts from climate change were accounted for in both scenarios (Supplementary Fig. 11). Depending on the model characteristics, the proxy for mitigation costs used was either GDP losses or the additional energy system cost calculated with respect to a reference scenario where only policies in force are considered – the ‘NPi2100’ in the modelling protocol (Supplementary Methods). To ensure consistency across impact and mitigation costs, all economic values were expressed in USD2018 using the reference GDP projection.

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