Uncertainty constraints on economic impact assessments of climate change simulated by an impact emulator

Since many new generation Earth system models (ESMs) have been suggested to overestimate future global warming, the latest report of the Intergovernmental Panel on Climate Change used the constrained range of global warming instead of that in the raw ensemble. However, it is not clear how the constraints of climate change projections potentially reduce the uncertainty of impact assessments. Here, we show that the climate-related uncertainty of the economic impact of climate change in the world can be constrained. By applying an impact emulator, we estimate the economic impacts in nine sectors based on 67 ESMs’ future climate change projections and find that the impacts in eight sectors are closely related to the recent past trend of global mean temperature, which is the metric used for the constraint of global warming projections. Observational constraints lower the upper bound of the aggregate economic impact simulated by the single emulator from 2.9% to 2.5% of the world gross domestic product (the relative reduction of variance is 31%) under the medium greenhouse gas concentration scenarios. Our results demonstrate how advances in climate science can contribute to reducing climate-related uncertainties in impact assessments, while we do not examine uncertainties of emulators and impact models.


Introduction
Discrepancies (hereafter uncertainty) in climate change projections between Earth system models (ESMs) propagate to uncertainties in impact assessments (IPCC 2022). Therefore, constraints of uncertainty in future climate change projections are crucial to provide more reliable information for impact assessments (Shiogama et al 2011), even though ESMs are an ensemble of opportunities (Knutti 2010). A number of studies have proposed emergent constraints (ECs) to reduce uncertainties in future climate change projections (Hall et al 2019, Brient 2020. ECs consist of statistical relationships between aspects of observable current climate and projected future change across ESMs. We can potentially reduce the uncertainty of future climate change projections by combining emergent relationships with observations and physically understood mechanisms (Caldwell et al 2014, Schlund et al 2020. Many ESMs in the Coupled Model Intercomparison Project Phase 6 (CMIP6, Eyring et al 2016, O'Neill et al 2016 have higher global warming in the future (∆T gm ) than that in the previous ensemble (CMIP5, Taylor et al 2012) (Sherwood et al 2020). Tokarska et al (2020) and the others (Jiménez-de-la-Cuesta and Mauritsen 2019, Liang et al 2020, Nijsse et al 2020 found that ∆T gm of the CMIP5/6 ESMs is closely related to the trends of global mean surface temperature during the decades following 1980 (trT gm ). Many ESMs of the CMIP6 ensemble overestimate trT gm compared with the observations, suggesting that their upper ends of ∆T gm are less reliable and can be lowered. Based on multiple lines of evidence (Sherwood et al 2020), including the abovementioned EC studies of ∆T gm , the 6th assessment report of the Intergovernmental Panel on Climate Change (IPCC) used the lowered upper bound of ∆T gm ('assessed warming') instead of that in the raw CMIP6 ensemble (IPCC 2021). Shiogama et al (2022) also suggested that future increases in global mean precipitation (∆P gm ) are closely related to trT gm , and the upper bound of ∆P gm can be lowered.
Some recent studies have suggested that changes in crops yield (Jagermeyr et al 2021, Muller et al 2021 and changes in global ocean animal biomass (Tittensor et al 2021) in CMIP6 are larger than those in CMIP5. Although these differences in impact assessments between CMIP5 and CMIP6 can be partly attributable to 'hot ESMs' in CMIP6, little guidance has been made available to maintain consistency between impact assessments and the 'assessed warming' of the IPCC (Hausfather  To investigate uncertainty reductions in economic impact assessments in several sectors, we apply an impacts emulator recently developed by Takakura et al (2021). Since climate change will have various impacts on diverse sectors, it is not straightforward to handle these impacts. Monetization of the impacts is a useful way to treat them on a unified scale, and thus, we focused on the monetized impacts (or economic impact expressed in percentage of gross domestic product (GDP)) for multiple sectors in this study. However, please note that we do not claim the economic impact or GDP is the only and the best indicator to gauge the impact of climate change.
There are mainly two distinct approaches to estimate economic impact of climate change. That is, statistical top-down approach and bottom-up approach using process-based economic impact models (Rose et al 2022). The bottom-up models tend to project smaller economic impacts compared to the top-down approaches. The behaviour of our emulator (Takakura et al 2021) is similar to the bottom-up economic impact models (Takakura et al 2019), whose projected impact is in line with many other bottom-up projections (Rose et al 2022). Thus, this study provides information on how ECs can reduce climate-related uncertainty range of economic impact projection based on bottom-up models. We do not investigate uncertainties of emulators and impact models.
By using temperature and precipitation simulation outputs of ESMs and an artificial-neuralnetwork-based technique, the emulator (Takakura et al 2021) can mimic the behaviours of bottom-up, process-based economic impact models (Takakura et al 2019). Unlike a simple damage function (Howard et al 2017), which typically considers only the global mean temperature, the developed emulator takes regional heterogeneity in temperature, precipitation, socioeconomic conditions, and their crossborder effects into account. The emulator covers economic impacts in nine individual sectors (agricultural productivity, undernourishment, heat-related excess mortality, cooling/heating demand, occupationalhealth cost, hydropower generation capacity, thermal power generation capacity, fluvial flooding, and coastal inundation) and the aggregate impact (see section 2 for details).
By combining the ECs of future temperature and precipitation changes and the emulations of economic impact costs in the nine sectors, we demonstrate the potential reduction of climate-related uncertainties in the economic impact of climate change. We investigate the averages of the initial-condition ensemble for each ESM of CMIP5/6. In the section 4, we also examine low (RCP2.6/SSP1-2.6) and high (RCP8.5/SSP5-8.5) GHG concentration scenarios. We investigate future changes of temperature and precipitation (2080-2099 minus 1851-1900) and the recent past  trend of global mean temperature (trT gm ). Precipitation changes are represented by the per cent of the 1991-2010 mean value. Future changes of global mean temperature and precipitation are denoted by ∆T gm and ∆P gm .

Economic impact emulations
We use the emulator of Takakura et al (2021) to calculate the economic impact of climate change. The original economic impact simulation, which the emulator mimics, is a global-scale, bottom-up economic impact assessment (Takakura et al 2019). From the viewpoint of sector and scenario coverage, it is one of the most comprehensive ones established recently. In the original situation, biophysical impacts were modelled by process-based models, and the impacts were directly monetized or monetized by a general-equilibrium-based economic model, Asia-Pacific Integrated Model (AIM) (Fujimori et al 2017). It includes both market values and nonmarket values of the climate change impacts. More details on the modelling process for the covered sectors can be found in previous papers: agricultural productivity ( The output of the emulator is the economic impact represented by the percentage of the regional GDP relative to the no-climate-change condition for each sector in 17 countries/regions used in the AIM economic model (Fujimori et al 2017). Climate conditions (mean temperature and precipitation in all the 26 regions of 'Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (SREX)' (IPCC 2012)) and socioeconomic conditions (population, GDP, and GDP per capita in all the AIM regions under the SSP2 scenario for this study) are the input variables to the emulator. The emulator is trained so that its output can be as close as possible to the original economic simulation results (Takakura et al 2019). Mathematically, constructing an emulator is identical to constructing a statistical regression model. Here the dependent variable (output) is the economic impact and the independent variables (input) are climatic and socioeconomic conditions. While there are various techniques that can be used for statistical regression, the emulator used in this study is constructed by a multilayer perceptron, which is a widely used artificial-neural-network-based technique. The parameters of the emulator were optimized using the gradient descent method. Then the emulator was validated by the cross-validation procedure, and we have confirmed that the developed emulator can reproduce the original economic simulation results in many situations. More details can be found in Takakura et al (2021). We aggregate the economic impacts in the 17 AIM regions to the world and the seven regions: Africa, Asia, Australasia, Europe, the former Soviet Union, North America and South and Central America.

Estimation of uncertainty ranges
We examine the 200 member realizations of observed temperature datasets of HadCRUT5 (Morice et al 2021). The spread of the 200 realizations represents uncertainties arising from systematic errors associated with observational methods, measurement and sampling errors and spatial analysis uncertainty. To consider the blending effect of surface-air temperature over land and ice and the sea-surface temperature over the ocean, 0.014 • C/10 years (Tokarska et al 2020) is added to the 1980-2021 temperature trends of HadCRUT5. To consider the uncertainty of the internal climate variability in the observed trends, we take 500 year data (ten 50-year-length segments) from a preindustrial control (piControl) run of each ESM (supplementary table 1). y is the vector of the trends of all 530 piControl segments added to all 200 realizations of observed trends. µ y and δ y indicate the mean and the standard deviation of y, respectively. The horizontal blue bars in figures 1(a), (b) and (c), mentioned below, are the 5%-95% range of y assuming a Gaussian distribution.
The raw 5%-95% uncertainty ranges of future climate changes and impacts are estimated by assuming Gaussian distributions of the ESM spreads. We compute their observationally constrained ranges by applying the hierarchical ECs framework (Bowman et al 2018), as in Shiogama et al (2022) and Thackeray et al (2022). Here, z and x are the future climate changes/impacts and trT gm of ESMs, respectively. µ z and δ z are the ensemble mean and standard deviation of z, respectively. µ x and δ x are the ensemble mean and standard deviation of x, respectively. The correlation between z and x is denoted by ρ.
We estimate the mean (E(z|y)) and standard deviation (δ(z|y)) of the constrained future projections/impacts by the following equations: The constrained range of future climate changes/impacts is estimated by assuming a Gaussian distribution with E(z|y)) and δ(z|y). Note that changes in long-term mean precipitation (e.g. 2080-2099 minus 1851-1900) can fit a Gaussian distribution due to the central limit theorem, although daily precipitation is not represented by a Gaussian process. The relative reduction of variance (RRV) is computed as follows:    figure 1). In all the SREX regions, the regional mean temperature changes in the future have significantly positive correlations with trT gm . In all the regions, the upper bounds are lowered. The relative reductions of variances, RRVs, are 17%-46%. In 13 out of the 26 regions, the regional mean precipitation changes in the future have significant correlations (positive for 12 regions and negative for Amazon) with trT gm . In the regions with significant positive correlations except for Sahara, the upper bounds are lowered. In the Sahara region, discussions of per cent changes in precipitation are difficult due to the very dry climatology. The lower bound is raised in the Amazon region. In those regions with significant correlations, the RRVs are 5%-22%. The aggregate economic impact in the world (% of GDP averaged over 2080-2099) simulated by the emulator also has a significant correlation with trT gm (r = 0.65) (figure 1(c)): ESMs with larger warming in the recent past tend to simulate a greater economic impact of future climate change in the world. The upper bound of the aggregate economic impact in the world can be lowered from 2.9% to 2.5%. RRVs are 41, 28 and 31% for ∆T gm , ∆P gm and the aggregate impact in the world, respectively ( figure 1(d)). These results are robust when we use only the CMIP5 or CMIP6 ESMs (supplementary figure 2).

Economic impact in each sector worldwide
Next, we examine the relationships between the economic impacts in each sector and trT gm (figure 2). It should be noted that the magnitudes of economic impacts in the heat-related excess mortality, cooling/heating demand and occupational-health cost sectors (figures 2(c)-(e)) are much higher than those in the other sectors (Takakura et al 2021). Therefore, the aggregate economic impacts in the world are mainly controlled by those three sectors. In those three major sectors, the ensemble mean impact costs are positive (i.e. damage from climate change). The correlations are significantly positive: ESMs with larger trT gm tend to have more positive economic impact costs in those three sectors due to greater ∆T gm and ∆P gm . The upper bounds are lowered from 1.4%, 0.23% and 1.2% to 1.2%, 0.20% and 1.0% in the heat-related excess mortality (RRV = 30%), cooling/heating demand (RRV = 32%) and occupational-health cost (RRV = 30%) sectors, respectively.
In the agricultural productivity and undernourishment sectors, the ensemble averages of impact costs are negative (i.e. benefit from climate change) because a modest temperature rise can increase  (b)). The correlations are significantly positive, suggesting that a higher ∆T gm ( figure 1(a)) leads to a greater reduction in agricultural productivity (Müller et al 2021). The upper bounds are lowered from 0.0020% and −0.068% to −0.0002% and −0.077% in the agricultural productivity (RRV = 35%) and undernourishment (RRV = 16%) sectors, respectively.
The correlation value is significantly negative for hydropower generation (figure 2(f)): ESMs with larger trT gm tend to have greater ∆P gm ( figure 1(b)), leading to higher hydropower generation capability in some regions (Zhou et al 2018b). The lower bound of the economic impact is raised from −0.0046% to −0.0044% (RRV = 14%).
ESMs with larger trT gm tend to have more positive impact costs of thermal power generation (figure 2(g)) because greater future warming ( figure 1(a)) causes more heating and a shortage of the ambient air and river water used to cool power plants (Zhou et al 2018a, 2018c). The upper bound is lowered from 0.090% to 0.086% (RRV = 15%).
The correlation is not significant in the fluvial flood sector (figure 2(f)). In the coastal inundation sector, the ensemble average is positive, and the correlation is significantly positive (figure 2(i)). The upper bound is slightly lowered from 0.0404% to 0.0397% (RRV = 11%).

Regional economic impacts
Next, we investigate economic impact costs in the seven regions: Africa, Asia, Australasia, Europe, the former Soviet Union, North America and South and Central America. In all the seven regions, the aggregate economic impacts have significantly positive correlations with trT gm (r = 0.54-0.69) (figure 3). In all the regions, the upper bounds of the aggregate impacts are lowered (for example, from 4.6% to 4.0% in Asia). RRVs are 21%-35%. Figure 4 shows the regional impact costs in the three major sectors: heat-related excess mortality, cooling/heating demand and occupational-health cost. The impact costs of heat-related excess mortality are larger in Africa, Asia and the former Soviet Union than in the other regions. This is because of larger population in Africa and Asia, and the higher vulnerability to heat in colder region (i.e. the former Soviet Union). The impact costs of cooling/heating demand are large in the former Soviet Union and Europe due to additional demand for cooling devices where cooling devices are not needed under the current climate. The upper bounds of these two sectors are lowered in all regions. Occupational-health costs in Asia and Africa are large because the economic costs of heat-related illness prevention for outdoor workers through breaks are vast in those regions (Takakura et al 2017(Takakura et al , 2019(Takakura et al , 2021, and their upper bounds are apparently lowered. Economic impacts (% of GDP) of (a) heat-related excess mortality, (b) cooling/heating demand and (c) occupational heat cost in each region. Pearson's correlations between trTgm and impacts are significant at the 5% level in those sectors and regions. Box plots indicate the 50th percentile (black line) and 5%-95% ranges (vertical bar) of impacts (% of GDP) in each region for the raw CMIP5/6 ESMs (orange) and the constrained ranges (blue).

Summary and discussion
By combining the recent advances in research of ECs on future temperature and precipitation changes (Tokarska et al 2020, Shiogama et al 2022 and the emulator of economic impact assessments (Takakura et al 2021), we lower the upper bound of the aggregate economic impact cost in the world averaged over 2080-2099 from 2.9% to 2.5% of GDP under the medium GHG concentration scenarios (RCP4.5/SSP2-4.5). Supplementary figures 3 and 4 are the same as figure 1 but under the high (RCP8.5/SSP5-8.5) and low (RCP2.6/SSP1-2.6) GHG concentration scenarios, respectively. The upper bounds of the aggregate economic impact costs in the world are lowered regardless of GHG concentration scenarios. The RRVs of aggregate impact costs are larger in higher GHG concentration scenarios.
We examine the ensemble mean from each ESM instead of all the ensemble members. Even if an ensemble mean of trT gm of a single ESM is out of the range of the observed trend, some members of that ESM may be within the range of the observed trends. However, it is not good practice to use all the ensemble members in our analyses because ESMs with larger ensembles (e.g. 50 members) could have greater weights than ESMs with only one member. Here, as a sensitivity test, we inflate the variance of the internal climate variability added to the observed trends (section 2) by a factor of 2 ( √ 2 for the standard deviation) to consider the possible contributions of the internal natural variability in the difference between the observations and ESMs (supplementary figure 5). Although the RRVs of supplementary figure 5(d) are smaller than those of figure 1(d), it is confirmed that the upper bounds of ∆T gm , ∆P gm and the aggregate impact costs are lowered. Although the emulator can well reproduce the aggregate and major sectors' impact simulations, the emulator is not perfect (Takakura et al 2021). The emulator of Takakura et al (2021) used outputs of single impact model for each sector. Note that the original simulation (Takakura et al 2019) did not fully incorporate, for example, catastrophic impacts, feedback effects, and nuanced socioeconomic assumptions in the scenarios whereas some autonomic adaptations were modelled in the framework. Although the original impact simulation took into account impacts of climate extremes in the original ESMs' simulations, but uncertainties of climate extremes (Quilcaille et al 2022, Tebaldi et al 2022 were not sufficiently considered. Therefore, even if the emulator can reproduce the original economic simulation results, it does not necessarily mean the emulated economic impact is accurate. In addition, there are intrinsic discrepancies (or uncertainty) in projected economic impacts between impact models (Drouet et al 2021, Jägermeyr et al 2021, Müller et al 2021, van der Wijst et al 2021, Rose et al 2022. In general, statistical top-down approaches tend to project larger economic impact with greater uncertainty (Rose et al 2022) because of the assumption that temperature variations affect the economic growth, while this assumption is still debatable (Kalkuhl andWenz 2020, Newell et al 2021). To reduce the overall uncertainty in the projection of economic impact of climate change, these economic impact model uncertainties also need to be addressed, but it is beyond the scope of this study.
Although there are abovementioned limitations, it is an important finding that we can significantly reduce climate-related variance of economic impact assessments simulated by the single emulator (31% in the case of RCP4.5/SSP2-4.5 under the SSP2 socioeconomic scenario). This benefit of EC will be held even if different impact models are adopted, and if EC is applied to more climate-sensitive impact models, the benefit can be larger. If economic impacts of ESMs with greater warming are larger than that of ESMs with lower warming in each impact model, each emulator and each socioeconomic scenario, our EC approach has a possibility to reduce climate-related variances of economic impacts derived from multi-emulators based on multi-impact models under multi-socioeconomic scenarios. This assumption is not proven but reasonable. If outputs of multi-emulators based on multi-impact models of multi-sectors, multi-socioeconomic scenarios, and multi-ESMs (e.g. ISIMIP3b) are available, we can examine how our EC approach can reduce the variance of more comprehensive impact assessments. Therefore comparison studies of multiemulators using the outputs of ISPMIP3b would be worthwhile.
Little guidance has been made available to maintain consistency between impact assessments and the 'assessed warming' of the IPCC working group 1 (Hausfather et al 2022). Our work provides a guidance to maintain the consistency by combining impact emulations and ECs. Impact assessments using the CMIP6 ensemble including 'hot ESMs' will be an important basis for the potential next assessment report of IPCC. Analyses of 'hot ESMs' can be useful when we examine low-probability-but-highimpact cases. However, for example, simply taking an average and standard deviation of the full CMIP6 ESMs or a small subset of ESMs including 'hot ESMs' could lead to risk of reporting impact assessments that are inconsistent with the 'assessed warming' in the IPCC working group 1 (Hausfather et al 2022). Our approach can be a key for keeping the consistency between the working groups 1 and 2 in the potential next assessment report of IPCC.

Data availability statement
The data that support the findings of this study are available upon request from the authors. Zhou Q, Hanasaki N and Fujimori S