reflect the uncertainty surrounding SCC estimates. CLIMRISK aggregates results in 13 world regions defined in Table S15. Some of the damage functions (DF) in this model are path-, scenario-, and timedependent, and vary both at the regional and grid-cell level. In the results presented here four types of regional/local DF are used (see Methods): the R regional DF which are based on the RICE2010 model 48 , but that is driven by local temperature projections and that has been updated to match the calibration of the latest DICE DF 49 , as well as that of Weitzman 50 which aims to represent catastrophic damages from climate change; the RU regional and local DF that include the economic impacts from local climate change, particularly the urban heat island effect; RP regional DF that include the persistence of impacts from climate change in the economy, and; RPU regional and local DF that include both the economic impacts of urban warming and the effects of the persistence of impacts from climate change on the economy. Results in the main text are presented for the SSP585 scenario, and the Supplementary Information offers results for the SSP370, SSP245 and SSP126 scenarios. The global SCC obtained using the R functions amounts to $137/tCO2 (Table 1). Africa, India, China and OASIA account for about 63% of this value, while the EU, US and OHI only for 22%. However, the omission of local warming in urban agglomerates and the dynamics of impacts has been shown to produce large downward biases in the assessment of the economic costs of climate change 4,44,51,52 . The global SCC value rises to $262/tCO2 with the effects of the UHI in urban areas (RU). When including persistence of impacts (RP) and both persistence and UHI (RPU), the SCC values are $579/tCO2 and $1,074/tCO2, respectively. In all cases the distribution of SCC among the different regions is highly heterogeneous. The regions with the highest SCC values are Africa ($28/tCO2 (R), $293/tCO2 (RPU)), India ($25/tCO2 (R), $190/tCO2 (RPU)), and China ($17/tCO2 (R), USD$190/tCO2 (RPU)). Figure S1 shows the SCC estimated for different SSP scenarios and illustrates the large influence GDP and population assumptions have on this metric (Tables S1-S4). It is notable that under high climate scenario and low economic growth (SSP370), the global SCC values are lower than those obtained in a considerably lower warming/higher economic growth scenario (SSP245). In contrast, if instead of the SSP3 economic scenario the SSP5 is used, the SSP570 gives very similar results to those of the SSP585. Numbers in parenthesis indicate the fraction of global SCC for each region. Figures are expressed in US2005 dollars. 1.5% consumption discount rate. DICE2016 global DF. Global aggregates are not equity-weighted. The regional share of the global SCC is highly influenced by the assumptions made about urban effects and persistence of impacts. While for all regions the estimated SCC values increase as the UHI, persistence and both factors are included, the fraction of the global SCC that each region accounts for are correlated to their development level (see Tables S5-S8 for the Weitzman global DF and Tables S9-S12 for a 3% discount rate). For regions such as the EU, US, Japan, and OHI including persistence lowers in about 44%-55% their contribution to the global SCC, suggesting that, in comparison, other regions have more limited resilience and capacities to deal with climate shocks. On the contrary, for all regions, the fraction of global SCC increases when urbanization (RU) is included, except Africa (-4.03 percentage points(pp)), India (-1.40pp) and OASIA (-1.20pp). That is, the increases in costs due to urban effects and exposure in these developing regions tend to be smaller than in those that are highly developed. The increase in the fraction of global damages due to the inclusion of urban warming is largest in China (4.24pp), followed by the US (0.79pp), Russia (0.61pp), and EU (0.48pp). The fraction of SCC increases steeply for Africa (6.78pp) and China (5.78pp) when including persistence and urban effects. Given the importance of the UHI effects for the global and regional SCC values, we separate the urban (u) and non-urban (nu) contributions to these estimates (see Methods). Moreover, urban damages are further decomposed into exposure and urban-specific effects. 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 urban SCC value is between 7 and 14 times larger than that of non-urban areas depending on the comprehensiveness of the damage function. The contribution of urban areas to the total global SCC is about 93%, with a regional range varying from 85% (Eurasia) to 99.7% (India). On average, the regional urban SCC values are 41.4 times as large as those for non-urban, with some regions such as India and China reaching 357 and 47 times, respectively. In particular, the global urban SCC estimates are $245/tCO2 (RU) and $1,006/tCO2 (RPU). Table 2: Non-urban and urban SCC and the contributions of exposure and urban characteristics to urban SSC. 1.5% discount rate. Figures are expressed in US2005 dollars. Non-urban represents the SCC from non-urban areas; Urban shows the SCC value in urban areas when the UHI effect is accounted for; Urban-exposure provides the SCC value in urban areas but when the UHI effect is not considered; Inc-exposure separates the impact on SCC from increased exposure in cities; UHI-int shows the contribution to the SCC from including the UHI effect plus its interactions with global climate change (see Methods). The global non-urban SCC is $17/tCO2, and $71/tCO2 for R and RP, respectively. The regions with the largest non-urban SCC are Africa (R: $5/tCO2; RP: $34/tCO2), the US (R: $3/tCO2; RP: $7/tCO2), the EU (R: $2/tCO2; RP: $4/tCO2), LAM (R: $1/tCO2; RP: $4/tCO2), OASIA (R: $1/tCO2; RP: $5/tCO2), China (R: $1/tCO2; RP: $4/tCO2) and MEAST (R: $1/tCO2; RP: $4/tCO2). The global urban SCC estimates are much higher, and the heterogeneity in SCC values at the regional level is considerable.
The six regions with largest urban SCC are India, China, Africa, EU, OASIA, and US account for more than 80% of global SCC). One of the main drivers of economic losses in both the literature of extreme events and climate change is exposure. Typically, cities are subject to higher exposure than non-urban areas, due to the concentration of population and economic activities, which are expected to contribute considerably to the SCC values. We explore the composition of damages in urban areas by estimating the SCC values if no local climate change occurred, and if the sensitivity to global climate change in those areas would be the same as for the whole region (see Methods). The global SCC in urban areas without considering the UHI effects (Urban-exposure) is USD$119/tCO2 ($508/tCO2 including persistence), about 7 times as large as the SCC for non-urban areas (Non-urban). That is, the differences in exposure (Inc-exposure) alone amount to $102/tCO2 and $437/tCO2 for the damage functions that do and don't include persistence of impacts, respectively. In all cases, increased exposure in urban grid cells leads to higher losses for every region. However, the estimates of the contribution of increased exposure in urban areas are highly heterogeneous among regions. Increased exposure in urban areas (Inc-exposure) represents 56% and 50% of the total SCC values for India and OASIA, respectively, and 39% for the global SCC value. The lowest values occur in Russia, Eurasia and the US. Globally, the contribution of the UHI and interaction effects with global climate change (UHI-int) amounts to $126/tCO2 (RU) and $498/tCO2 (RPU). The UHI-int contribution to the SSC is similar in magnitude to that of the urban exposure. The largest contributions from UHI-int are in developing regions such as China ($27/tCO2 (RU); $121/tCO2 (RPU)), India ($19/tCO2 (RP); $83/tCO2 (RPU)), Africa ($15/tCO2 (RP), $102//tCO2 (RPU)), but also in the US and the EU with values close to $14/tCO2 (RP) and $30/tCO2 (RPU). 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 almost half of the regions. The regions with the largest contributions from nonurban areas are Eurasia (15.27%), the US, LAM, Africa, Russia (about 12%-13%), followed by OHI (10.72%). Regarding Mexico, EU and MEAST, the contribution of non-urban damages to their SCC is larger than the global estimate, while for India, China and Japan, these numbers are very small (0.28%-2.92%). At the global level, Urban-exposure and UHI-int account for about 48% and 46% of the total SCC, respectively. The regions in which urban exposure contributes more than 50% to their total SCC are India, Africa and OASIA. In contrast, the UHI plus interactions effects dominate (>50%) in Russia (64.81%), China (60.85%), Eurasia (55.28%), US (52.08), Mexico (51.33%). These effects are larger than the global estimate also for the EU, OHI, and MEAST. Africa, by far, has the lowest contribution of UHI effects to its regional SCC. These figures show that urban areas dominate the SCC, both at the global and regional levels. The reported SCC values and decomposition are the product of complex interplay between population and GDP growth and concentration, as well as warming, all at the grid-cell level. Different development paths defined by the SSP lead to different contributions to regional SCC, with regions like Africa, OHI, China and the US showing large variability (Table S13). A new metric defined as the Social Cost of the UHI (SCUHI) is applied for estimating the benefits the average urban dweller would experience from a marginal reduction in UHI. It is calculated as the variation in the present value of damages per average urban dweller from local and global climate change produced by decreasing the UHI by 1% in global urban areas over a prolonged period (e.g., 2100; see Methods). Note that keeping UHI reductions at 1% implies that the absolute mitigation of the UHI in terms of degree Celsius is likely to increase over time. This metric can be useful in climate urban policy design as it aims at providing a quantitative estimate of the expected benefits of local policies to reduce the UHI effect, such as expanding green nature, cool roofs and cool pavements. Globally and for the SSP585, the total benefits from reducing the UHI by 1% are estimated in the range of $2,344 billion (RU) and $9,132 billion (RPU). These benefits are large and comparable to 30%-40% of the present value of the accumulated climate change losses countries such as Mexico would face this century under a high-emissions scenario (Estrada and Botzen, 2021). The distribution of benefits is highly heterogeneous among regions and varies according to the SSP scenario and type of damage function (Figure 2). Globally, under the SSP585, the direct benefits of reducing the UHI for the average urban dweller range between $484 (RU) and $1,562 (RPU). Under the RU, the largest SCUHI values occur in the highest income regions, such as the US ($988), OHI ($805), the EU ($700) and Japan ($552). The lowest SCUHI values are in the least developed regions such as Eurasia ($196), OASIA ($247), India ($259), and Africa ($346). The distribution of SCUHI among regions is more mixed with the RPU damage functions: the largest SCUHI values occur in the US ($2,338), MEAST ($2,410), Africa ($2,398), Russia ($2,081), and OHI ($1,905), while the lowest SCUHI values are in EURASIA ($608), LAM ($1,051), OASIA ($1,072), and India ($1,124). For the other SSP scenarios considered, the SCUHI values are considerably lower but illustrate that higher SCUHI values can be obtained for lower warming scenarios depending on their socioeconomic assumptions and their effects on local warming and exposure (Figure 2). The consequences of unabated climate change at the global and regional scales are shown to be substantially higher than previously estimated. Omitting persistence of shocks, as is done in most current IAMs, implies that climate change damages only affect the period when they occur and have no influence on future periods.
This is equivalent to assuming perfect resilience and autonomous adaptation which, in addition, is costless 51 . The warming in local temperatures in large cities is comparable to that estimated for global temperatures under a high-emissions scenario at the end of this century. By itself, the UHI effect has large economic costs, and global climate change can considerably amplify them 44 . By decomposing the SCC into urban and non-urban areas, results show that impacts in urban areas dominate the SCC, both at the global and regional levels. Depending on the region, UHI effects or persistence can dominate the increase in damages. Cities are one of the main contributors to global greenhouse gas emissions and results show that they are also likely to experience the largest SCC. The decomposition of SCC into urban and non-urban components shows that about 93% of the global SCC comes from urban areas. Previous studies suggest that poorer regions would have the largest incentives to support the highest CO2 prices, as they would be the ones that suffer most climate change impacts. The detailed treatment of urban areas in CLIMRISK allows for the decomposition of urban and non-urban SCC and shows that global and regional urban population is the most affected. Urban dwellers have the largest incentives for reducing CO2 emissions and promote higher CO2 prices. This is of particular importance since large cities have economic power and political capacity to transition to lower emissions development paths. Moreover, they wield considerable influence for enhancing mitigation efforts at national level and advocating for more ambitious international targets in global climate negotiations. A more stringent mitigation of greenhouse gases is in the best interest of urban regions in the world, particularly those in the most developed regions. In addition, local adaptation strategies to reduce the damages from global and local climate change have low political and economic implementation costs. The SCUHI metric indicates that the benefits for urban dwellers from these measures are substantial. CLIMRISK is a new generation IAM of the climate and economy which allows projecting the economic impacts and risks of climate change at the global, regional and spatially explicit (0.5ºx0.5º) scales 4 . It is structured in four main modules: 1) Socioeconomic, which represents exposure in terms of population an 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 (RU, RP, RPU); 4) Risk evaluation, it combines the results from the climate and economic damages modules to produce uni-and multi-variate risk indices. 3 shows a stylized description of the core modules of CLIMRISK. The model aggregates results in 13 regions which are described in Table S15. The following paragraphs present the improvements introduced in CLIMRISK in this paper. the reader is referred to the complete and detailed description of the model contained in the Supplementary Information of Estrada and Botzen 4 . Th climate module in CLIMRISK has been updated to reflect some of the recent advances reported in the latest assessment report (AR6) of the IPCC 53 . CLIMRISK uses a triangular probability distribution to represent the uncertainty of the climate sensitivity parameter in MAGICC6 54,55 , 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 2ºC and 5ºC as the lower and upper limits, respectively, with a most likely value of 3ºC. CLIMRISK uses the pattern scaling technique [56][57][58][59] 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 paper 4 and others 58,60,61 . Table S16 provides a list of names of the AOGCMs included in the new version of CLIMRISK. In this version of the model, a variety of global DFs can be integrated into the analysis of climate impacts at the regional and local scales. In particular, in this paper CLIMRISK includes the DICE2016 global DF 23 , and the global DF proposed by Weitzman (2009) which is a highly nonlinear function of global temperatures (results in Supplementary Information). These two global DF were chosen because they represent contrasting views about the seriousness of climate change impacts to the global economy. The first DF is commonly considered as conservative, and the latter focusses much more on the possibility of extreme outcomes and climate catastrophes from global warming. Here we use CLIMRISK to downscale the global aggregated economic impacts proposed by these global DF using the regional DF from RICE, which are adjusted in CLIMRISK to produce grid-cell level estimates (R DF) which are consistent with the chosen global DF. In addition, features in CLIMRISK such as the inclusion of the UHI effect and persistence can be incorporated, given rise to modified versions of the RU and RPU DFs. The downscaling procedure consists in calculating a scaling factor from the global damages 𝐼 𝑡 𝐷𝐹 * calculated with the target global DF (e.g., DICE2016) and the globally aggregated 𝐼 𝑡 𝑅 obtained using the R DF in CLIMRISK:

This scaling factor is applied to the grid-cell projections obtained with the different DFs included in CLIMRISK, namely R, RU, RPU. In the previous version of CLIMRISK 4 , 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, the population count threshold is calibrated to be better aligned 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 population 33,62 . 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, which is aligned to estimates in the literature 30,32,63 . 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 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 losses 4,44 . CLIMRISK's DF include the temporal dynamics of climate change impacts. The DF in most IAMs assume that climate impacts only affect the period when they occur have no persistence. The omission of impact dynamics can be interpreted as assuming an autonomous, unlimited, costless and effective reactive adaptation capacity 51 . Persistence of socks is a stylized fact of macroeconomic time-series that has been long documented in the literature 64 . Similarly, impacts in human and natural systems tend to dissipate only after a certain period of time. Most of IAMs and assessments of the economic impacts of climate change ignore this feature which can lead to large biases in estimates with 𝐼 𝑟,𝑡 𝑝 representing the aggregated economic losses when the effects of persistence for region r are accounted for, and the persistence parameter is restricted to 0 ≤ 𝜑 ≤ 1. The regional values of 𝜑 are reported in Table S21 of ref 51 . 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 Caldeira, 2014) 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:

Where 𝑎 1 = -2.308, 𝑎 2 = 0.743, 𝑎 3 = -0.191, 𝜏 1 = 2.241, 𝜏 2 = 35.750, 𝜏 3 = 97.180 (see 68 ). The units of ∆𝑇 𝑡 are mK/GtC. The year of the pulse (𝑡 0 ) is chosen to be 2010. 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 R and RU DFs. Note that the same decomposition applies to the RP and RPU DFs. First, the total SCC value (𝑆𝐶𝐶 𝑅𝑈 ) is the sum of the non-urban 𝑆𝐶𝐶 𝑛𝑢,𝑅 and urban 𝑆𝐶𝐶 𝑢,𝑅𝑈 values. In the 𝑆𝐶𝐶 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 R (without urban effects) and RU (with urban effects). As such, 𝑆𝐶𝐶 𝑛𝑢,𝑅 represents the SCC from nonurban grid cells using the R DF (i.e., no urban effects are included), and 𝑆𝐶𝐶 𝑢,𝑅𝑈 is the SCC from urban cells when the UHI effect is considered (RU DF). This can be expressed by the following equation:

the urban SCC estimates (𝑆𝐶𝐶 𝑢,𝑅𝑈 ) 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 with 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 R DF) and is denoted by 𝑆𝐶𝐶 𝑢,𝑅 . The contribution of the urban effects (including the UHI) plus interactions is 𝑆𝐶𝐶 𝑢,𝑅𝑈 -= [𝑆𝐶𝐶 𝑢,𝑅𝑈 -𝑆𝐶𝐶 𝑢,𝑅 ], the difference between the SCC value from urban grids considering the damages from urban effects 𝑆𝐶𝐶 𝑢,𝑅𝑈 and 𝑆𝐶𝐶 𝑢,𝑅 . 𝑆𝐶𝐶 𝑢,𝑅𝑈 -is referred to as UHI+int in Table 2. The complete decomposition is given by: 𝑆𝐶𝐶 𝑡,𝑅𝑈 = 𝑆𝐶𝐶 𝑛𝑢,𝑅 + 𝑆𝐶𝐶 𝑢,𝑅𝑈 = 𝑆𝐶𝐶 𝑛𝑢,𝑅 + 𝑆𝐶𝐶 𝑢,𝑅 + 𝑆𝐶𝐶 𝑢,𝑅𝑈 -

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 those with exposure concentration). Note that both 𝑆𝐶𝐶 𝑛𝑢,𝑅 and 𝑆𝐶𝐶 𝑢,𝑅 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 𝑆𝐶𝐶 𝑑,𝑅 = 𝑆𝐶𝐶 𝑢,𝑅 -𝑆𝐶𝐶 𝑛𝑢,𝑅 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. 𝑆𝐶𝐶 𝑑,𝑅 is referred to as Exposure in Table 2.
In contrast, 𝑆𝐶𝐶 𝑢,𝑅𝑈 -in equation ( 2) represents the increase in SCC due to urban characteristics including local climate change (UHI), vulnerability/sensitivity, 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 RPU functions. Acknowledging the relevance of the UHI effect on the economic costs of climate change, we propose a new metric called the Social Cost of the Urban Heat Island (SCUHI). This metric evaluates the variation in the present value over this century of damages from local and global climate change produced by decreasing the UHI by 1%, in all urban areas for the remaining of this century. Analytically, the SCUHI is obtained as follows. Taking the partial derivative of the DF for urban areas described above 𝐷 𝑡 = 𝛼 𝑅 𝑇 𝐺𝐻𝐺,𝑡 + 2𝛼 𝑈 𝑇 𝐺𝐻𝐺,𝑡 𝑇 𝑈𝐻𝐼,𝑡 + 𝛼 𝑈 𝑇 𝑈𝐻𝐼,𝑡 2 results in:

The present value of the damages associated with a marginal change in 𝑇 𝑈𝐻𝐼 is:

𝜕𝐷 𝑡 𝜕𝑇 𝑈𝐻𝐼 Moreover, since 𝑇 𝑈𝐻𝐼 is modelled as 𝑇 𝑈𝐻𝐼 = 𝑎𝑃 𝑏 , where 𝑎 and 𝑏 are fixed parameters and 𝑃 is the urban population count 44,69 , SCUHI can be defined both in terms of changes in mitigation of the UHI and urban population. We first consider the impact, at the margin, of measures to reduce the urban heat island effect. Let's assume such measures affect a. Then,

And the SCUHI is:

This is how the SCUHI is calculated for the estimates presented in this paper, as what we propose relates to the benefits of mitigating the UHI. The SCUHI values are reported per urban dweller. Alternatively, the SCUHI can be defined in terms of marginal changes in urban population:

Note that we assumed that the effects of urban population growth have a permanent effect on the urban built-up and, thus, in the local energy imbalance and in the local warming. SCUHI is then the present value of the damages associated with a marginal change in 𝑃:

Note that the SCUHI is different for each urban conurbation. The P in the above equations is the population of particular cities, rather than the global population. Similarly, greenhouse warming is different in different locations. Numbers in parenthesis indicate the fraction of global SCC for each region. Figures are expressed in US2005 dollars. 1.5% discount rate. DICE2016 global DF. Numbers in parenthesis indicate the fraction of global SCC for each region. Figures are expressed in US2005 dollars. 1.5% discount rate. Weitzman global DF. Numbers in parenthesis indicate the fraction of global SCC for each region. Figures are expressed in US2005 dollars. 3% discount rate. DICE2016 global DF.