Introduction

Limiting global warming to 1.5 °C implies a remaining carbon budget of 580 Gt\({{{\rm{C}}}}{{{{\rm{O}}}}}_{2}\), and reaching carbon neutrality in approximately thirty years1. At the current levels of Gt\({{{\rm{C}}}}{{{{\rm{O}}}}}_{2}\) emissions, this remaining budget would be exhausted in about 6 years2. Nationally Determined Contributions (NDCs) are key components of the Paris Agreement3. The latest estimates suggest strict compliance of current NDCs will mitigate climate change risks, but an 80% increase in the average emission reduction is needed to avoid exceeding 1.5 °C globally1,4,5. However, the decarbonization of the economy has proven highly complex, and policy interventions are slowly implemented. Current per-capita average global emissions exceed by four tonnes of carbon dioxide equivalent the yearly budget for the 1.5 °C target6.

Climate and weather hazards intensified in the past years, affecting economies and societies through extreme events such as heatwaves7, floods, droughts, and storms8, as well as chronic impacts like decreasing crop yields9, health10, and rising sea levels11. Beside imposing huge costs on populations, these extreme events worsened inequalities and conflicts12,13,14, as exposure, hazard and vulnerability are heterogeneous among regions15,16,17. In response, the 27th Conference of the Parties advocated the establishment of a fund for loss and damage18. This initiative is grounded in the polluters-pay principle, and aims at establishing compensation schemes for vulnerable countries with small contributions to current global warming19.

Several metrics have been proposed to estimate the economic damages that climate change would cause under different GHGs emissions scenarios. The SCC is a key metric that estimates the economic costs an additional tonne of CO2 released into the atmosphere would produce in terms of impacts on natural and human systems. Despite several shortcomings of the SCC to realistically reflect the true cost of carbon20,21,22, and of the models that produce them13,23,24, it remains a convenient summary metric for advising policy making25. The SCC is a benchmark used in cost-benefit analysis to estimate the monetary benefit of emissions’ cuts by mitigation policy proposals26,27,28 and it guides governments in optimally pricing carbon emissions. Recently, the US administration re-established the Interagency Working Group (IWG) on Social Cost of GHGs emissions27, to inform the US climate policies. A recent study29 that uses a comprehensive modelling approach suggests that the SCC would be between USD$44/tCO2 USD$413/tCO2, with a central estimate of USD$185/tCO2. Estimates in the literature range more widely, depending on the assumptions and discount rate applied22,30,31.

The SCC is also used to evaluate the distribution of climate impacts and inequality concerns. These studies agree on large SCC heterogeneity among regions and countries such that those with large shares of global GDP and/or high sensitivity to climate change bear the largest shares28,30. These countries include India, China, the EU and the US. A recent study32 develops national-level damage functions that account for differences in income level and annual temperature. It finds that the national SCC is higher in lower-income countries with large populations than in the higher income ones. Consequently, middle- and lower-income countries33 would have the highest incentives to set the highest carbon prices if acting in their self-interest. In addition, estimates of the local cost of carbon are being proposed, defined as the social cost of carbon if everyone in the world were like the people in a particular locale34.

Urban agglomerations and cities are key in determining the global emissions pathway. Cities consume about 78% of the world’s energy and are responsible for almost 8 of every 10 tonnes of GHG emitted to the atmosphere. The top 100 emitting urban areas account for 18% of the global carbon footprint35,36,37. About 56%-85% of global population lives in cities and produce close to 80% of global GDP36,37,38,39. These trends are projected to accelerate in the coming decades37. The UHI effect occurs when natural landscapes are replaced by denser, higher thermal capacity materials which lead to a local energy imbalance and changes in local climate40,41,42. The UHI effect produces negative impacts such as intensified heat waves43, higher energy consumption44, lower labor productivity45, increases in human health risks and discomfort43,46, higher water demand47 and increased air and water pollution48,49. In large cities the UHI effect can add up to 4 °C of warming. When the UHI is included in the assessment of the economic impacts of climate change, global losses increase by at least twofold4,50,51. At the same time, cities have a disproportionate influence on national and global climate policy and can implement relatively low-cost local adaptation measures to reduce UHI warming50,52,53.

Here we investigate the contributions from urban and non-urban areas to global and regional SCC estimates. Moreover, urban SCC values are separated into their exposure and UHI effects. For this purpose, the CLIMRISK integrated assessment model4 is used (see Methods). This is a spatially explicit integrated assessment model that allows modelling the UHI effects and estimating the economic impacts of both global and local (UHI) warming for urban areas. CLIMRISK uses spatially explicit climate and socioeconomic data and damage function specifications, to include local scale hazard, exposure and vulnerability into risk and economic assessments. It also provides an encompassing set of commonly used global, regional and local damage functions to reflect the uncertainty surrounding loss estimates. CLIMRISK results are in a 0.5° × 0.5° global regular grid which can be aggregated in 13 world regions (see Table S14), as well as in 187 countries (see Table S15). Some of the damage functions (DF) in this model are path-, scenario-, and time-dependent, and vary both at the regional and grid-cell level. As discussed in detail in Methods, the main set of damage functions used in this paper are derived from a recent country-level assessment of economic losses from climate change based on a computable general equilibrium model54. These damage functions are downscaled to the grid cell level as a function of spatially explicit estimates of the Human Development Index. Estimates are divided into a set in which the UHI effects are not included (K) and another that includes such effects (KU). The main text focuses on the results based on the SSP585 scenario. The Supplementary Information offers results for the SSP370, SSP570, SSP245 and SSP126 scenarios, and a sensitivity analysis obtained with an updated and extended version of the DICE/RICE damage functions (R and RU) is also included in CLIMRISK (see “Methods”).

Results

Global and regional SCC estimates for K and KU damage functions

The global SCC obtained using the K functions amounts to $187/tCO2 (Table 1) with a 90% confidence interval that includes the uncertainty in climate sensitivity of $167/tCO2 to $208/tCO2. Scenarios with emissions closer to what could be considered current policies (SSP245) imply values of SCC close to $100/tCO2, and $107/tCO2for a scenario consistent with the Paris Agreement goals (SSP126). The distribution of SCC among the different regions is highly heterogeneous. Africa, India, China and other low-income Asian countries (OASIA) account for about 83% of this value, while the EU, US and other high-income (OHI) only for 4–5%. As shown in Table S1, these proportions vary considerably if the regionalization patterns from the RICE model are used, with the US, EU and OHI accounting for about 20% of the global SCC (Tables S1–S5). Tables S6–S10 present a sensitivity analysis for a 3% discount rate and different SSP. Due to the spatially explicit resolution of CLIMRISK, damages can be separated into those that correspond to urban and non-urban grid cells (“Methods”). Even when ignoring the additional local warming generated by the UHI effect, at the global scale 78–86% of the total SCC corresponds to urban areas ($153/tCO2 K; $118/tCO2 R), while the remaining 22–17% originates from non-urban areas ($33/tCO2 K; $19/tCO2 R; Table 2). Focusing on the K set of damage functions, for India, OASIA and CHINA, urban areas account for 76%-84% of their regional SCC, while for Japan, Africa, Eurasia, Russia and MEAST this figure is in the range of 85%-89%, and it is around 90%-97% for LAM, EU, the US, Mexico and OHI.

Table 1 Social cost of carbon for different damage functions in CLIMRISK
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Table 2 Non-urban and urban SCC and the contributions of exposure and urban characteristics to urban SSC
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The omission of local warming in urban agglomerates has been shown to produce large downward biases in the assessment of the economic costs of climate change50,55. When the effects of the UHI in urban areas (KU) are accounted for, the global SCC value rises to $490/tCO2 (90% CI: $349/tCO2-$674/tCO2), which is about 2.6 times as large as the SCC estimate without UHI. Including the UHI effects produces close to a sixfold increase for Russia and Eurasia, about a threefold for the EU and the US, and about twofold increases for China, MEAST, Mexico and Africa, while for all the remaining regions their SCC nearly duplicates. The regions with the highest SCC values are Africa ($118/tCO2 (KU), $43/tCO2 (K)), India ($116/tCO2 (KU), $50/tCO2 (K)), OASIA ($79/tCO2 (KU), $39/tCO2 (K)) and China (USD$82/tCO2 (KU), $23/tCO2 (K)). In relative terms, for Russia and EURASIA, including the effects of UHI nearly triples their shares of the global SCC and it increases by 74% this share of the EU. For Japan, the share of global SCC decreases by about 34%, while for LAM and OASIA by 24%.

Figure 1 shows the SCC estimated for different SSP scenarios for the K, KU, R and RU damage functions and for 1.5% and 3.0% discount rates. This figure illustrates the large influence GDP, population and urbanization assumptions have on this metric (Tables S1–S5). It is notable that under high climate scenario, low urbanization rates and economic growth (SSP370), the global SCC values are lower than those obtained in a considerably lower warming/higher economic growth and urbanization scenarios (SSP245, SSP126). In contrast, if instead of the SSP3 socioeconomic scenario the SSP5 is used, the SSP570 gives very similar results to those of the SSP585.

Fig. 1: SCC estimates for different SSP scenarios, damage functions and discount rates.
Fig. 1: SCC estimates for different SSP scenarios, damage functions and discount rates.
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Light blue and green bars denote the use of the KU and K damage functions, while orange and dark blue bars show results obtained using the RU and R damage functions. The K damage functions are based on estimates in Kompas et al.54, while the R damage functions are an updated and extended version those in DICE/RICE28,50,67. KU and RU indicate that the UHI effects are included. The upper and lower sections of the figure present the estimated SCC values for 1.5% and 3% consumption discount rates, respectively.

Urban and rural contributions to the SCC and the effects of urban exposure and local climate change

Given the importance of the UHI effects for the global and regional SCC values, we further decompose urban damages into exposure and urban-specific effects (“Methods”). As shown in Table 2, the SCC values for urban areas are much higher than those for non-urban ones. At the global level, the estimated SCC value for urban areas is $457/tCO2, (CI: $320/tCO2$638/tCO2), about 11 times larger than that of non-urban ($33/tCO2; CI: $30/tCO2$37/tCO2) and represents about 93% of the global SCC that includes the UHI effects. Using a more conservative damage function (RU), the urban SCC is about $276/tCO2, which is 11 times as large as the non-urban SCC estimate ($23/tCO2; Table S11).

Regional urban SCC values (KU) are on average 39 times as large as those for non-urban, with some regions such as OHI, Mexico and Russia reaching 86, 81 and 69 times, respectively. The four regions with largest urban SCC are Africa, India, China, and OASIA, and account for about 80%/74% of global urban/total SCC. The largest non-urban SCC occur in India ($11/tCO2), OASIA ($9/tCO2), Africa ($6/tCO2), and China ($4/tCO2). Different development paths defined by the SSP in terms of population, GDP and urbanization level lead to different contributions to regional SCC: regions like OASIA, India and Africa showing large variations in non-urban SCC, reaching up to 38%, 30% and 24%, respectively, under the SSP3. In that scenario, the global non-urban SCC reaches about 21% of the total global SCC (Table S12; and Fig. S4).

One of the main drivers of economic losses in both the literature of extreme events and climate change is exposure56,57,58. Typically, cities are subject to higher exposure than non-urban areas, due to the concentration of population and economic activities37,38, which are expected to contribute considerably to the SCC values (Figs. 2 and S1). The global SCC in urban areas without considering the UHI effects (Urban-noUHI) is USD$153/tCO2, about 4.6 times larger than the SCC for non-urban areas (Non-urban). That is, the differences in exposure between urban and non-urban (Inc-Exposure) alone amount to $120/tCO2 (Table 2). In all cases, increased exposure in urban grid cells leads to higher losses for every region, except for the SSP3 scenario in which India, Africa and OASIA show urban population and GDP shares below 50% during the century, leading to the highest non-urban contributions to SSC (Fig. S4). Regional heterogeneity is high: increased exposure represents 43% of the total SCC values for OHI, 42%-41% for Japan and LAM, 34% for Mexico, and 24% for the global SCC value (Fig. 2). The lowest values occur in Russia (10%), Eurasia (11%), the EU (18%) and China (19%). In addition to the effects of increased exposure on SCC, those of total urban exposure (Non-urban plus Inc-Exposure) are provided in Tables S12–S13.

Fig. 2: Contributions of non-urban areas, urban exposure, and UHI plus interactions in urban areas to regional and world SCC.
Fig. 2: Contributions of non-urban areas, urban exposure, and UHI plus interactions in urban areas to regional and world SCC.
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Dark blue fill denotes the contribution (percentages) of non-urban areas to regional/global SCC, orange fill shows the contribution of urban areas to regional/global SCC without considering increased exposure or UHI effects, green fill indicates the additional cost attributable to increased exposure in urban areas, and light blue fill represents the increase in regional/global SCC due to UHI warming and interaction effects with global climate change. The dashed purple rectangle indicates the components that constitute the SCC values that correspond to the K damage function, while the dashed black rectangle indicates those of the KU damage function. Numbers are in percentage of total SCC and sum 100% up to rounding errors. For reference, the contribution of UHI-int in dollars is shown in italics. Based on NCAR regional urban population projections.

Globally, the contribution of the UHI and interaction effects with global climate change (UHI-int) amounts to $304/tCO2 (Fig. 2). The UHI-int contribution to the SSC is almost twice that of the urban exposure. The largest contributions from UHI-int are in low- and middle-income regions such as Africa ($75/tCO2), India ($66/tCO2), China ($59/tCO2), and OASIA ($40/tCO2). While the UHI-int values for the US and the EU are comparatively smaller ($7/tCO2, and $10/tCO2), they represent about 71% and 78% of their total SSC values (including UHI; Tables S12 and S13), and these SCC values are threefold and fourfold those when the UHI is omitted.

At the global level, UHI-int accounts for 62% of the total SCC (Fig. 1). The UHI plus interactions effects dominate (>60%) in Russia (87%), Eurasia (85%), the EU (78%), the US (71%), MEAST (71%), Africa (64%), and Mexico (64%). Japan has the lowest contribution of UHI effects to its regional SCC.

In general, the contribution of non-urban areas to the total SCC is small, about 7% at the global level, and weighs less than 10% in most regions. The regions with the largest contributions from non-urban areas are OASIA (12%), India (9%), Japan (8%), China (5%), and Africa (5%). The Supplementary Information presents a sensitivity analysis using the R and RU damage functions (Fig. S1), an alternative definition of urban areas (Fig. S2) and for different SSP scenarios (Figs. S3 and S6).

Discussion

Current local warming in large cities can be as large as global warming projected under a medium-high emissions scenario by the end of this century50,59,60. Although global climate change alone implies large economic costs, these are considerably amplified by the additional warming large cities experience because of the UHI4,50.

SCC values are influenced by a complex interplay of factors, including population, urbanization, and GDP growth, local and global warming, sensitivity and vulnerability, at various spatial scales. Spatially explicit IAMs like CLIMRISK take advantage of high-resolution socioeconomic, climate and damage projections to assess the impacts of climate change from the grid cell to the global levels. Our decomposition of the SCC into urban and non-urban areas reveals that urban impacts dominate, both globally and regionally. This dominance persists even when UHI effects are omitted, as is common in most current estimates of climate change costs. Our analysis highlights the substantial underestimation of damage costs when urban warming is not accounted for. The consequences of unabated climate change at both global and regional scales are substantially higher than previously estimated. Approximately 93% of the global SCC is attributable to urban areas for high economic growth and urbanization scenarios (SSP5, SSP1). This proportion varies considerably with the urbanization and warming level assumptions embedded in SSP trajectories, with the lowest occurring for the SSP3 (79%) and SSP2 (86%). Outward migration from cities may be an adaptive response to local and global climate change impacts, although migration is a complex phenomenon61 and studies specific to cities are lacking.

Previous studies indicate that middle- and lower-income regions have the strongest reason to support high CO2 prices due to their vulnerability to climate change impacts. However, our findings reveal that global urban agglomerations are those with higher economic losses from climate change, both in middle- and lower-income and high-income regions. Consequently, urban dwellers have strong incentives to reduce CO2 emissions and advocate for higher CO2 prices. This closes the gap between the major contributors to global greenhouse gas emissions and those who are likely to face the largest SCC. These results also support UHI intensity reduction measures, such as the implementation cool and green roofs, cool pavements, increase in vegetated areas and water bodies52,62,63,64,65. Some of these measures have been shown to considerably reduce the costs of local and global climate change50,66.

Given their economic and political power, large cities play a crucial role in transitioning to lower emissions development paths. They also extensively influence national mitigation efforts and advocate for more ambitious international climate targets. Importantly, as shown here, stringent mitigation of greenhouse gases is in the best interest of urban regions worldwide, including those in high-income countries. These results can lead to enhanced urban mitigation efforts which are essential for achieving global climate goals and minimizing the substantial economic and environmental costs associated with climate change.

Methods

CLIMRISK description

CLIMRISK is a recent IAM of the climate and economy which allows projecting the economic impacts and risks of climate change at the global, regional and spatially explicit (0.5° × 0.5°) scales4. It is structured in four main modules: (1) Socioeconomic, which represents exposure in terms of total, urban and non-urban population and GDP; 2) Climate, it is divided in three sections which are a global climate model, a general circulation models emulator to produce spatially explicit temperature and precipitation projections, and a third section that projects UHI intensity in urban areas as a function of population counts; 3) Economic damages, which contains sets of global, regional and grid scale-defined damage functions (DF) to map increases in temperature to losses in GDP. Some of these DFs are time-, path- and scenario-dependent. The different set of damage functions include those based on enumerative and expert judgement28,67,68,69, computable general equilibrium54 and econometric23 approaches; 4) Risk evaluation, it combines the results from the climate and economic damages modules to produce uni- and multi-variate risk indices. Figure 3 shows a stylized description of the core modules of CLIMRISK. The model aggregates results in 13 regions which are described in Table S16, although results are also available at the grid-cell level and for 178 individual countries (Table S17). Note that while higher spatial resolution could be desirable for some analysis, and for potentially more precise estimates, the resolution in CLIMRISK reflects the current constraints in global datasets and computing power available to run the model. The following paragraphs present the improvements in CLIMRISK used in this paper. The reader is referred to the detailed description of the model contained in the Supplementary Information of Estrada and Botzen4.

Fig. 3: Schematic description of CLIMRISK’s model structure.
Fig. 3: Schematic description of CLIMRISK’s model structure.
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The model is composed of four main modules. The exposure module produces spatially explicit socioeconomic scenarios, including GDP and population from SSP, SRES datasets, as well as from user-defined trajectories. This module also includes RCP land use projections. The hazard module contains a stochastic version of a reduced complexity climate model (MAGICC6) and produces spatially explicit changes in temperature and precipitation by emulating 37 Atmosphere-Ocean General Circulation Models (AOGCMs) of the Coupled Model Intercomparison Project (CMIP6). It also produces estimates of the UHI intensity for urban cells. The vulnerability and impacts module generates projections of the economic impacts of climate change by means of a collection of global, regional and local damage functions, with specifications that range from conservative to highly nonlinear and catastrophic. The estimates produced can include the UHI effect and the persistence of climate change impacts. The risk evaluation module uses the output of the different modules to generate uni- and multivariate dynamic risk indices which can provide a more complete view of climate change risks.

Improvements in CLIMRISK’s climate module

The climate module in CLIMRISK has been updated to reflect some of the recent advances reported in the latest assessment report (AR6) of the IPCC70. CLIMRISK uses a triangular probability distribution to represent the uncertainty of the climate sensitivity parameter in MAGICC671,72, a reduced complexity climate model. The parameters of the triangular distribution have been updated to reflect the very likely range in the AR6. The triangular distribution in the current version of CLIMRISK is specified with 2 °C and 5 °C as the lower and upper limits, respectively, with a most likely value of 3 °C.

CLIMRISK uses the pattern scaling technique73,74,75,76 to generate spatially explicit annual temperature and precipitation scenarios (see ref. 4). Currently, the climate module in CLIMRISK contains a pattern scaling library of 37 Atmosphere-Ocean General Circulation Model (AOGCM) included in the Coupled Model Intercomparison Project (CMIP6). These patterns are produced using ordinary least squares regression as described in the original CLIMRISK paper4 and others75,76,77. Table S18 provides a list of names of the AOGCMs included in the current version of CLIMRISK.

Extension of damage functions in CLIMRISK

Country level and regional damage functions

CLIMRISK includes a variety of global DFs that can be used for the analysis of climate impacts at the regional and local scales, ranging from conservative, highly nonlinear and to catastrophic. For the results shown in the main text of this paper we use a new country and grid-cell level sets of damage functions derived from computable general equilibrium estimates of the economic impacts of climate change54. These damage functions were not available in the previous version of CLIMRISK and were developed for this study. Kompas et al.54 provide country and region estimates of economic damages for different levels of increase in global temperatures (1–4 °C). Using linear regression, a quadratic function of global temperature increase was fitted for each of the 140 countries/regions for which estimates were available, producing an average \({R}^{2}\) of 0.997. These damage functions are denoted in CLIMRISK with the letter K. The regional estimates presented in Kompas et al. (e.g., Rest of western Africa) were used to assign damage functions to countries not explicitly included in their analysis to complete 187 countries. CLIMRISK produces socioeconomic and climate projections at the grid-cell level (0.5° × 0.5°) and to take advantage of this spatially explicit exposure and hazard scenarios, subnational level spatial patterns of damages are produced. The approach used can be described as follows and it is applicable to a variety of damage functions (DF; see ref. 4 for a detailed description):

  1. (1)

    The economic impacts for country/region r are calculated using global temperature change, as done in the original non-spatially explicit source54,67:

    $${I}_{t,r}^{{DF}}={\Omega }_{t,r}{Y}_{t,r}=\left[{\beta }_{1,r}{\Delta T}_{t}+{\beta }_{2,r}{\Delta T}_{t}^{2}\right]{Y}_{t,r}$$
    (1)

    Where \({\Omega }_{t,r}\) is the percent of GDP lost due to climate change in country/region r at time t, \({Y}_{t,r}\) is the GDP for country/region r at time t, \({\beta }_{1,r}\) and \({\beta }_{2,r}\) are the linear and quadratic parameters of the damage function DF for country/region r and \({\Delta T}_{t}\) is global temperature change at time t.

  2. (2)

    The economic impacts for country/region r are calculated using grid-cell level temperature change and GDP, and country/region damage parameters:

    $${I}_{t,g}^{{DF}}={\Omega }_{t,g}{Y}_{t,g}=\left[{\beta }_{1,r}{\Delta T}_{t,g}+{\beta }_{2,r}{\Delta T}_{t,g}^{2}\right]{Y}_{t,g}$$
    (2)
    $${I}_{t,{r}^{*}}^{{DF}}=\sum\limits_{g}{I}_{t,g}^{{DF}}$$
    (3)

    Where g is the set of geographical coordinates (latitude, longitude) that correspond to each grid-cell in country/region r. \({I}_{t,{r}^{*}}^{{DF}}\) is the sum of economic losses in all grid cells in country/region r.

  3. (3)

    The subnational spatial patterns of impacts based on grid-cell exposure and hazard are constructed and damages are rescaled to match \({I}_{t,r}^{{DF}}\) at the country/regional level:

$${{SP}}_{t,g}^{{DF}}={I}_{t,g}^{{DF}}/{I}_{t,{r}^{*}}^{{DF}}$$
(4)
$${I}_{t,g}^{{{DF}}^{*}}={{SP}}_{t,g}^{{DF}}\cdot {I}_{t,r}^{{DF}}$$
(5)

Where \({I}_{t,g}^{{{DF}}^{*}}\) are the spatially explicit projected damages consistent with the original, country/region aggregated estimate \({I}_{t,r}^{{DF}}\). In the case of the Kompas damage functions, the corrected estimates are referred to as \({I}_{t,g}^{{K}^{*}}\).

Grid-cell level damage functions

Grid-cell level damage functions were derived from Kompas et al. taking advantage of the existing relationship between their country level damage estimates and the reported national Human Development Index56 (HDI; Fig. 4). Previously, downscaling of damages has been done based on per capita income78. Here we chose HDI because it is a comprehensive indicator that accounts for income, education and health and it has been shown to outperform several indices of social vulnerability to climate change79,80,81. As expected, high/low scores in the HDI are associated to lower/higher vulnerability to climate change (Fig. 4) This relationship was estimated using the following linear regression:

$${{{\mathrm{ln}}}}\, {D}_{r}^{K}={b}_{1}{{HDI}}_{r}+{b}_{2}{{HDI}}_{i}^{2}+\sum\limits_{i=1}^{4}{\gamma }_{i}{l}_{i}+{\varepsilon }_{i}$$
(6)

Where \({D}_{r}^{K}\) are the economic damages reported in Kompas et al.54 for the country r, \({{HDI}}_{r}\) are the corresponding HDI scores, and \({l}_{i}\) are dummy variables for the different levels of warming the estimates in Kompas et al. were reported (1–4 °C). This regression produces an \({R}^{2}\) of 0.62. The out-of-sample forecast performance was evaluated by retaining 119 observations, which led to a Theil inequality coefficient of 0.28, with a covariance proportion of 0.993, and bias and variance proportions of less than 0.01. Using spatially explicit HDI estimates, \({D}_{r}^{K}\) was projected onto a 0.5° × 0.5° grid and local scale damage functions (60,000+) were constructed following the linear regression approach described before.

Fig. 4: Scatterplot of \({D}_{r}^{K}\) and. \(HD{I}_{r}\) with a quadratic regression fit.
Fig. 4: Scatterplot of $${D}_{r}^{K}$$ D r K and. $$HD{I}_{r}$$ H D I r with a quadratic regression fit.
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Blue circles represent the relationship between projected climate change economic impacts (\({{{{\boldsymbol{D}}}}}_{{{{\boldsymbol{r}}}}}^{{{{\boldsymbol{K}}}}}\)) and the Human Development Index (\({{{{\boldsymbol{HDI}}}}}_{{{{\boldsymbol{r}}}}}\)) across 140 countries. The red line shows the fitted quadratic regression curve.

With these grid cell estimates the Eq. (2) in step 2) was replaced by:

$${I}_{t,g}^{{DF}}={\Omega }_{t,g}{Y}_{t,g}=\left[{\beta }_{1,g}{\Delta T}_{t,g}+{\beta }_{2,g}{\Delta T}_{t,g}^{2}\right]{Y}_{t,g}$$
(7)

The regularization described in step 3) was applied to ensure consistency with the original estimates in Kompas et al.54, producing the \({I}_{t,g}^{K}\) estimates. As discussed in the following sections, CLIMRISK identifies grid cells that contain urban areas and the local UHI warming can be incorporated into the urban area temperature projection. For these areas the corresponding K grid cell damage function adjusted using its HDI value is used to project urban damages. The KU estimates combine the \({I}_{t,g}^{K}\) estimates with local damage functions in urban areas that include UHI warming (see below for a description).

The Supplementary Information includes a sensitivity analysis based on updated versions of CLIMRISK’s R and RU damage functions. The global damage function that was selected for the update is the DICE2016R28, which is still widely used. Note that other global/regional damage functions can be chosen, such as those that focus on catastrophic climate change68,82. The R and K sets of damage functions provide contrasting views about the seriousness of climate change impacts to the global economy, with the DICE2016R commonly considered as conservative.

To produce these updated versions of the R damage functions, the following steps are conducted:

  1. a.

    To produce the grid-cell level estimates consistent with the regional RICE2010 damages, steps 1) to 3) described in the previous section are applied to produce \({I}_{t,g}^{{R}^{*}}\).

  2. b.

    The total global damage for time t is calculated summing over all g coordinates in all regions, \({I}_{t}^{{R}^{*}}={\sum}_{g}{I}_{t,g}^{{R}^{*}}\).

    The grid-corrected, regional consistent \({I}_{t,g}^{{R}^{*}}\) are used to construct the spatial patterns (downscaling patterns) for the RICE2010.

    $${{SP}}_{t,g}^{{R}^{*}}={I}_{t,g}^{{R}^{*}}/{I}_{t}^{{R}^{*}}$$
    (8)
  3. c.

    The global damages are calculated using the target global damage function driven by global temperature change \({I}_{t}^{{target}}=\Phi \left({\Delta T}_{t}\right){Y}_{t}\), where \({Y}_{t}\) is global GDP at time t.

  4. d.

    The estimates of the target damage function \({I}_{t}^{{target}}\) downscaled using the RICE2010 grid-cell/regional spatial patterns are obtained as:

$${I}_{t,g}^{{target}}={{SP}}_{t,g}^{{R}^{*}}\cdot {I}_{t}^{{target}}$$
(9)

In addition, features in CLIMRISK such as the inclusion of the UHI effect can be incorporated, given rise to modified versions of the RU DFs, as described in ref. 4 and ref. 50. For simplicity of notation, we will still refer to the updated versions these damage functions as R and RU.

Definition of urban areas

In the previous version of CLIMRISK4, urban areas were declared in grid cells with population counts larger than 1 million inhabitants. This calibration was found to be very conservative as it led to underestimating the global urban population (about 40%) and GDP (about 50%). In the current version of the model, two approaches are used. The first approach consists of replicating the urban population projections available for each of the SSP trajectories83 by optimizing for each region the population threshold parameter that is used in CLIMRISK to determine urban grid cells. The optimization procedure consists in minimizing the sum of squared residuals between the original and fitted regional urbanization projections by varying the urban threshold parameter over a wide range of values (1000 and 3.5 million inhabitants in steps of 10,000 inhabitants) per grid cell in each region. This was done for the period 2010–2100 in 10-year time steps. Fig. 5 compares the SSP5 urbanization shares projections in ref. 83. with those of CLIMRISK for each of the 13 regions used in this paper. At the global level under the SSP5 scenario, the urban population share starts at 50% in 2010 and reaches about 90% in 2100. The urban GDP that corresponds to the identified urban cells corresponds to 70% in 2010 and about 90% in 2100. As mentioned below, these figures are broadly consistent with estimates of global urban population and GDP shares. The proportion of urban population varies substantially among the different SSP trajectories, with the lowest levels of urbanization occurring under the SSP3, reaching about 60% at the end of the century (Fig. S3). The projections of urban population and GDP shares for different SSP scenarios are shown in Fig. S4.

Fig. 5: SSP5 projections of urban population shares for 13 regions in CLIMRISK.
Fig. 5: SSP5 projections of urban population shares for 13 regions in CLIMRISK.
Full size image

The reference SSP5 urban population shares projections are shown in slashed red lines and the fitted CLIMRISK projections are shown in blue continuous lines.

The Supplementary Information presents a sensitivity analysis of the main results in the main text using a second approach for determining urban populations shares (Fig. S2, Tables S14 and S15). This second approach is based on selecting a global population count threshold which is calibrated to align with observed estimates of the percentages of global urban population and GDP. These estimates are uncertain, but urban population is estimated to represent between 56% and 85% of the total global population39,84. The population count threshold per grid cell to declare a urban area was chosen to be 250,000 inhabitants, which leads to population counts that represent about 62% of global population and about 78% of global GDP in 2010, which is aligned to estimates in the literature36,38,85. In the grid cells that are identified as containing urban areas 75% of the population and 95% of GDP are assumed to be urban. These quantities are used to calculate the UHI and the urban GDP that is subject for the urban damage function that is explained next.

Projecting the UHI intensity in CLIMRISK

The intensity of the canopy UHI has been estimated in the literature by observation-based methods, physical climate models and by empirical-statistical relationships. The first two are mostly available for a restricted number of cities due to the data quality and availability requirements, as well as to large computational costs in the case of physical models. Moreover, damage functions are calibrated for climatological (i.e., long-term) values of changes in global and/or local temperature change. Such estimates are rarely found in the literature using physical climate models or observational estimates. Empirical-statistical methods take advantage of correlations between UHI intensity and variables representing changes in local conditions, such as population41,86,87, land cover, and elevation88. CLIMRISK projects the intensity of the UHI based population counts per grid cell using the following functional form87,89,90,91

$${UHI}=a\times {{Pop}}^{b}$$
(10)

where \(a=0.00174\) and \(b=0.45\) and \({Pop}\) is the population count as in ref. 4,92. The projected values of UHI intensity in CLIMRISK are broadly similar to those one of the few global studies of UHI using a global physical climate model4,93. For the SSP5, the average city has a UHI intensity of 0.83 °C, while for grid cells with more than 1 million inhabitants the average UHI intensity is 1.17 °C, which agrees with estimates in the literature94.

The UHI effect and the urban damage functions in CLIMRISK

Consider a Nordhaus-type damage function \(D\left(T\right)=\alpha {T}^{2}\), where \(D\) are the projected losses in GDP (%) which are a function of temperature change \(T\). Including local temperature change caused by the UHI effect in urban areas results in:

$$D\left(T\right)= {D}_{R}\left({T}_{R}\right)+{D}_{U}\left({T}_{U}\right)={D}_{R}\left({T}_{{GHG}}\right)+{D}_{U}\left({T}_{{GHG}}+{T}_{{UHI}}\right)\\= {\alpha }_{R}{T}_{{GHG}}^{2}+{\alpha }_{U}{\left({T}_{{GHG}}+{T}_{{UHI}}\right)}^{2}=\alpha {T}_{{GHG}}^{2}+2{\alpha }_{U}{T}_{{GHG}}{T}_{{UHI}}+{\alpha }_{U}{T}_{{UHI}}^{2}\\= D\left({T}_{{GHG}}\right)+2{\alpha }_{U}{T}_{{GHG}}{T}_{{UHI}}+{\alpha }_{U}{T}_{{UHI}}^{2}$$
(11)

Where \({D}_{R}\) and \({D}_{U}\) represent losses in rural and urban areas, \({T}_{{GHG}}\) is the change in temperature due to global warming (i.e., anthropogenic forcing), and \({T}_{{UHI}}\) is local warming in urban areas due to the UHI. In words, total damage equals rural damage plus urban damage. Urban temperature change equals rural warming plus urban warming. If the damage is a power (=2) function in temperature, total damage equals total damage of greenhouse warming plus urban damage of urban warming plus the interaction of urban and greenhouse warming. Ignoring the urban heat island effect, \({T}_{{UHI}}=0\), as is done in other integrated assessment models downward biases economic losses4,50.

Modelling of a CO2 pulse in global temperature

The estimation of the SCC requires introducing the effects on temperatures from a pulse in CO2. In this version of CLIMRISK we adopt the approximation proposed by Ricke and Caldeira95 (which is physically sound and easy to implement in IAMs. Following the authors, the effect of a pulse of 1GtC on global temperatures can be approximated using three-exponential functions:

$$\Delta {T}_{t}=-\left({a}_{1}+{a}_{2}+{a}_{3}\right)+{a}_{1}{e}^{-\frac{\left(t-{t}_{0}\right)}{{\tau }_{1}}}+{a}_{2}{e}^{-\frac{\left(t-{t}_{0}\right)}{{\tau }_{2}}}+{a}_{3}{e}^{-\frac{\left(t-{t}_{0}\right)}{{\tau }_{3}}}$$
(12)

Where \({a}_{1}=-\!2.308\), \({a}_{2}=0.743\), \({a}_{3}=-\!0.191\), \({\tau }_{1}=2.241\), \({\tau }_{2}=35.750\), \({\tau }_{3}=97.180\) (see ref. 95). The units of \(\Delta {T}_{t}\) are mK/GtC. The year of the pulse \(({t}_{0})\) is chosen to be 2010.

SCC calculation

The SCC values presented in the main text were calculated using a 1.5% discount rate and a sensitivity analysis based on a 3% discount rate are included in the main text (Fig. 1) and in the Supplementary Information (Tables S6–S10). The selection of discount rates is based on recent survey96 which places the social discount rate between 1% and 3% and the 1.7% discount rate suggested in the Circular A-4 of the Office of Management and Budget97 which provides guidance for federal agencies on the development of regulatory analysis. The terminal year for calculating the SCC is 2100 as is common practice in integrated assessment modelling due to the availability of socioeconomic and climate projections under the SSP scenarios.

Decomposing the SCC into urban and non-urban contributions

We use CLIMRISK’s explicit spatial resolution and special modelling of urban areas to calculate SCC values and to decompose these figures into dominantly urban and non-urban (mixed and rural) contributions. Moreover, exploiting the set of damage functions included in CLIMRISK, it is possible to disaggregate the influences of urban exposure and effects from UHI and urban sensitivity, including their interaction with exposure.

In what follows we explain the procedure to compute urban and non-urban SCC for the K and KU DFs. Note that the same decomposition applies to the R and RU type of DFs. First, the total SCC value \(({SC}{C}^{{KU}})\) is the sum of the non-urban \({SC}{C}^{{nu},K}\) and urban \({SC}{C}^{u,{KU}}\) values. In the \({SC}{C}^{{xx},{YY}}\) terms, xx refers to the type of grid cell with nu and u denoting non-urban and urban, respectively, and YY refers to the type of DF used K (without urban effects) and KU (with urban effects). As such, \({SC}{C}^{{nu},K}\) represents the SCC from non-urban grid cells using the K DF (i.e., no urban effects are included), and \({SC}{C}^{u,{KU}}\) is the SCC from urban cells when the UHI effect is considered (KU DF). This can be expressed by the following equation:

$${SC}{C}^{{KU}}={SC}{C}^{{nu},K}+{SC}{C}^{u,{KU}}$$
(13)

the urban SCC estimates (\({SC}{C}^{u,{KU}}\)) can be further decomposed in: 1) the contribution of exposure and; 2) the combined effects of hazard (including UHI), the differences in sensitivity of the urban area to changes in climate and the interaction of these factors and exposure. The contribution of increased exposure in urban areas is obtained by calculating the SCC in urban areas without considering damages from urban effects (i.e., using the K DF) and is denoted by \({SC}{C}^{u,K}\). The contribution of the urban effects (including the UHI) plus interactions is \({SC}{C}^{u,K{U}^{-}}=[{SC}{C}^{u,{KU}}-{SC}{C}^{u,K}]\), the difference between the SCC value from urban grids considering the damages from urban effects \({SC}{C}^{u,{KU}}\) and \({SC}{C}^{u,K}\). \({SC}{C}^{u,K{U}^{-}}\) is referred to as UHI+int in Table 2. The complete decomposition is given by:

$${SC}{C}^{t,{KU}}={SC}{C}^{{nu},K}+{SC}{C}^{u,{KU}}={SC}{C}^{{nu},K}+{SC}{C}^{u,K}+{SC}{C}^{u,K{U}^{-}}$$
(14)

This decomposition allows us to compare the role of exposure concentration in cities under global climate change with the contribution of local climate change and urban sensitivity, within the context of global climate change (i.e., allowing for their interactions and the effect of exposure concentration). Note that both \({SC}{C}^{{nu},K}\) and \({SC}{C}^{u,K}\) share the same damage function (sensitivity) and that, in both cases, damages are driven by global climate change alone. Differences in damages are solely due to dissimilarities in exposure and hazard levels from global warming due to location.

Finally, we define \({SC}{C}^{d,K}={SC}{C}^{u,K}-{SC}{C}^{{nu},K}\) as the change in SCC produced by an additional tonne of CO2 between urban and non-urban context derived only from differences in exposure and global climate change. \({SC}{C}^{d,K}\) is referred to as Inc-Exposure in Table 2. In contrast, \({SC}{C}^{u,K{U}^{-}}\) in Eq. (14) represents the increase in SCC due to urban characteristics including local climate change (UHI), vulnerability, and the interactions between local and global climate change, as well as exposure. This information can be of use for decision-makers at the city level to better understand and address local and global climate change impacts, vulnerability, and adaptation. The proposed separation can be readily applied to the RU functions.