Economic consequences of spatial variation and temporal variability of climate change

Abstract

Damage functions in integrated assessment models (IAMs) map changes in climate to economic impacts and are central to estimating the social cost of carbon (SCC). However, these functions assume no spatial variation (Svar) and temporal variability (Tvar) in climate changes, potentially biasing estimates and policy advice. While the effects of Tvar have been studied, those of Svar and their interactions with Tvar have not. Here, we allow for Tvar, Svar, and seasonality of damages and show that ignoring these factors significantly biases loss and SCC estimates. Under a high emissions scenario, losses are underestimated by 17–45%, representing US$1.9–US$9.7 trillion by 2050 and US$19–US$70 trillion by 2100 (17–35%). The present value of losses over this century exceeds previous estimates by US$38–US$222 trillion, representing 37–218% of 2020 global gross domestic product (GDP). The present value of losses including climate variability represents about 1.2–11.7% of the present value of global GDP over 2020–2100. The SCC increases by US$20/tCO₂, reaching US$106/tCO₂. There is large sectoral and regional heterogeneity regarding losses and SCC, with India, Africa, and China accounting for 50% of global SCC, and health and other markets contributing 40%. A more complete climate description than global mean temperature is needed in IAMs to adequately estimate climate change costs.

Spatial variation and temporal variability are commonly missing in the economic assessments of climate change impacts. We show that omitting climate variability can lead to significant downward bias in the estimates of the costs of climate change, and we present an extension of commonly used damage functions that can be easily implemented in most current integrated assessment models.

INTRODUCTION

Climate is commonly defined as the long‐term weather conditions over a specific region. ¹ , ² In particular, the long‐term average or expected value of weather variables over a 30‐year period is referred to as climatology or climate normal, and, in practice, it is frequently used as a shorthand description of climate (see Supplementary Methods SM1 and SM3). However, this description is incomplete as it ignores variability and omits information that may be relevant for a variety of users/applications. The same is true for using only changes in the mean to describe climate change projections and to estimate its impacts, which are known to be a function of both changes in central tendency measures and variability. ³ , ⁴ , ⁵

Integrated assessment models (IAMs) of the climate and the economy usually translate changes in global or regional mean annual surface temperatures to economic damages through stylized mathematical representations called damage functions. ⁶ , ⁷ Temperature change projections in these models are produced by zero‐dimensional, stylized climate models, which approximate the response of global temperature to changes in radiative forcing (i.e., the climate change signal) but are not able to produce any type of temporal variability (Tvar) or spatial variation (Svar) (see SM1). Temperature change in IAMs excludes any pattern in the time and spatial domains. ⁸ , ⁹ These patterns are, at best, used in the calibration of the parameters of the impact functions, but not further considered after that.

This omission has two important implications. First, intra‐ and inter‐annual variability are assumed to have no effect on the warming rate. All months and seasons warm by the same amount, and variability modes such as the Atlantic multidecadal oscillation and the Pacific decadal oscillation cannot amplify or dampen the warming trend. Nor is there any interplay between variability and climate change that affects the projected damages. These are simplifications that keep IAMs as simple and transparent as possible, but do not compare well with what is known about climate change: warming rates do vary between months and seasons ¹⁰ , ¹¹ ; low‐frequency oscillations modulate the warming rate; there are important interactions and synergies between natural variability and the response of the climate system to changes in external forcing, and natural variability affects the magnitude of damages. ⁹ , ¹² Moreover, it is assumed that intra‐ and inter‐annual variability does not change in a warming world. ¹³ This is consistent with neither observations nor climate projections (SM2). Important changes in variability have been documented and are projected to occur, for example, in seasonality, which is fundamental to the climate and natural and human systems, ¹⁴ , ¹⁵ in the frequency, magnitude, and duration of extremes, ³ , ¹⁶ , ¹⁷ , ¹⁸ and in large‐scale circulation patterns. ¹⁹ , ²⁰ , ²¹ , ²² The importance of including changes in climate variability is even greater when considering tipping points and climate catastrophes, which entail large changes in climate patterns worldwide. ²³ , ²⁴ , ²⁵ , ²⁶

Second, IAMs incorrectly assume that warming is spatially homogeneous over continents or even the world. Observations, as well as climate models’ projections, show that warming rates and changes in other climate variables (e.g., precipitation) vary widely over space (SM2). ²⁰ , ²² In commonly used IAMs, global (or regional) mean annual temperature change acts as an index of changes in the relevant climate variables over space (and time) which drive the physical and economic losses that damage functions aim to represent (SM1). While there is considerable evidence in favor of spatial stationarity of changes in climate, this does not imply that the spatial variance of changes remains constant for different levels of warming. ³ , ²⁷ On the contrary, differential warming around the globe is clear from all global circulation climate models and implies that the variance of changes in temperature increases with global temperature rise (SM2). As an illustration, consider the case of the pattern scaling technique, which has been extensively evaluated and is considered to adequately approximate the output from complex physical climate models (SM4), particularly in the case of changes in mean surface temperatures. ²⁷ , ²⁸ , ²⁹ This technique assumes spatial stationarity of changes in variables such as temperatures and precipitation. Under such an assumption, a matrix of fixed weights $P^v=p_{i,j}^v$, which represents the spatial pattern of change for variable $v$ and for each pair of geographical coordinates $i,j$, can be obtained from climate models’ output to approximate what the magnitude of change at the grid cell would be for variable $v$ and for a given value of change in global mean annual temperature change $\mathrm{\Delta }{T}^g$. Even in this case of spatial stationarity, spatial variation would increase since $var(v)=var(\mathrm{\Delta }{T}^g{P}^v)={(\mathrm{\Delta }{T}^g)}^{2}var(P^v)$. As is shown in the next sections and in SM2, similar results are obtained using warming output from global physical models. Having spatial climate change projections that are consistent with physics is important for generating economic impacts of climate change in recently developed local IAMs, in which the economic exposure to climate impacts and vulnerability varies across space. ³⁰

While several studies have focused on developing regional estimates of the costs of climate change and developing damage functions from them, ³⁰ , ³¹ , ³² , ³³ few studies ⁸ , ³⁴ , ³⁵ , ³⁶ have focused on incorporating the effects of climate variability or stochasticity into commonly used climate damage functions. These modified functions aim to represent the impacts of climate change in terms of mean and variability, which includes intra‐annual to decadal, centennial, and even longer frequency oscillations. However, these few studies only include variability in the time domain, ignore spatial variation, and do not account for the seasonality of climate impacts. Here, we show that these limitations have significant effects on estimates and conclusions. Moreover, we propose reduced‐form damage functions that can be easily implemented in most of the current IAMs. Estrada and Tol ⁸ proposed recalibrating existing damage functions in such a way that their parameters account for the stochasticity in climate time series projections. They focus on global average temperatures and show that the mean monetary impacts produced by the stochastic damage function are similar to those of the deterministic function, but that the welfare impacts are larger. ⁸ A recent study ³⁴ suggests that by accounting for interannual variability in global mean temperature time series, the risk of economic damages increases by trillions of dollars even if variability is assumed to be moderate. However, the expected losses are not biased and are the same as when temporal variability is not included. They use a zero‐dimensional stochastic climate model and the Weitzman damage function, one of the damage functions with higher response to temperature change, to project the distribution of losses. ³⁴ The authors calculate the risk premium of the effects of including internal variability in the time domain, combined with the uncertainty of the equilibrium climate sensitivity. They find that, while there is not a considerable effect on the estimated expected losses, the risk premium can be up to $46 trillion dollars (or about 58% of global output). About US$32 trillion of this risk premium is due to aleatory uncertainty and US$14 trillion to the interaction of aleatory and epistemic uncertainty. These studies provide relevant information about the effects of internal variability in the time domain on economic impacts and conclude that omitting this factor can have important effects on some aspects of the estimation of the consequences of climate change. Another study looking at past impacts showed that there are interaction effects between natural variability and external forcing that could bias the estimated costs of climate change. ⁹ That is, variability may affect not only the risk premium but also the estimated level of economic losses. Bilal and Känzig ³⁷ study the impact of small and unexpected variations in weather on economic growth. This cannot be extrapolated to the impact of climate change, which is large and anticipated. ³⁸

In the present study, we show analytically and numerically that the way internal variability has been handled in current studies of the economic costs of climate change leads to important downward biases. We expand previous studies by considering temporal inter‐ and intra‐annual variability and spatial variation, as well as by developing new annual, seasonal, and monthly damage functions designed to include climate variability and take advantage of sectoral estimates of damages available in the literature. Here, we focus on the Nordhaus‐type of damage function (i.e., any damage function with a quadratic functional form) which has remained prevalent in the literature, is easily implemented in most current IAMs, and has commonly been the basis for previous proposals to incorporate missing aspects (such as variability). Recent studies have proposed a variety of alternative approaches and extensions to the Nordhaus‐type framework. ³⁹ , ⁴⁰ , ⁴¹ , ⁴² , ⁴³ Of particular interest are the advances in sectoral and regional estimates to improve the empirical validity of damage functions. ³² , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ We have considered most of them to improve the damage functions calibration (SM6 and SM7). Our results show that considering internal climate variability in both the time and space domains significantly increases the projected economic damages—not just the risk premium a social planner would pay to avoid stochasticity. Therefore, the current estimates importantly underestimate the economic costs of climate change. Furthermore, we provide an analytic solution to include climate variability that does not require conducting simulation experiments and that is embedded in the most common, currently used type of damage functions. This extension can be easily adopted in most IAMs currently available, as we illustrate by extending the regional integrated model of climate and the economy (RICE) damage functions ³¹ , ⁴⁸ to calculate the regional social cost of carbon (SCC), which is recalibrated to match more recent global estimates (Methods).

MATERIALS AND METHODS

Climate and economic data

We use the global monthly gridded dataset of near‐surface temperature projection of the ensemble mean of the Coupled Model Intercomparison Project Phase 6 (CMIP6; one realization for each of the 37 climate models included). The sample period is 1850–2100. The SSP585 scenario was chosen to maximize the climate signal, not because of any consideration about its likelihood of occurrence. ⁴⁹ Extensive sensitivity analyses are presented for SSP119, SSP126, SSP245, and SSP370 in the Supplementary Information. We used realizations from different climate models with various ensemble sizes: ACCESS‐CM2 (ensemble mean of three realizations), CanESM (ensemble mean of 25 realizations), CESM2 (ensemble mean of 25 realizations), INM‐CM5‐0 (one realization), MPI‐ESM1‐2‐HR (one realization), and ACCESS‐ESM1‐5 (one realization). All simulations are expressed as anomalies with respect to the 1850–1880 period. For each model, we used three different procedures to separate the climate signal (systematic) from the weather (irregular) component. They produce smoothed versions of temperature time series in each grid cell such that the trend and seasonal components are preserved, and the noise is filtered out (SM1, SM3–SM5). The first procedure (SP) is particularly convenient for IAMs. It involves calculating the scaling patterns from general circulation climate models’ simulations, which allow the production of monthly, spatially explicit climate projections using a simple zero‐dimensional climate model. ²⁷ , ²⁹ , ⁵⁰ To generate these scaling patterns, we use ordinary least squares to estimate the slope parameters in regressions between local and global temperatures for each grid cell with geographical coordinates $i,j.$ ⁵¹ To construct spatially explicit future scenarios, these scaling patterns are then scaled with global temperature change projections. All global temperature projections used here were generated with MAGICC7. ⁵² , ⁵³ The use of different models to obtain the corresponding spatial patterns of change, scaled by a single realization of global temperature (per SSP investigated), allows us to evaluate the effects of variability in a separate manner from the uncertainty in climate sensitivity. In the second procedure (RM), we approximate the climate signal using a rolling mean smoothing procedure with a 31‐year window for each grid cell. ² This averaging minimizes the effects of high‐frequency oscillations and allows us to approximate the underlying climate of the chosen region. The third approach applies the Hodrick−Prescott (HP) filter, ⁵⁴ at the grid cell level, for producing two types of variability filtering: (1) the HP filter is applied to each of the 12 monthly time series at the grid cell level, producing time series that include seasonal variability, but not interannual nor high‐frequency variability. This preserves seasonality but smooths any other temporal variability; (2) to smooth seasonal and high‐frequency variability, the HP filter is applied to each grid cell using the 3012 months that cover the sample period. This produces time series that preserve low‐frequency variability, but filter out seasonal and high‐frequency variability. Figure S4 shows an example of a random geographical coordinate of the MPI‐ESM1‐2‐HR model under the SSP585 scenario.

The effect of a pulse of 1 GtC on global temperatures is approximated using the stylized response function and parameter values proposed by Ricke and Caldeira. ⁵⁵ This approach is physically sound and easy to implement in IAMs for estimating the SCC values. It is composed of a three‐exponential function $\mathrm{\Delta }{T}_t=-(a_1+a_2+a_3)+a_1{e}^{-\frac{(t-t_0)}{{\tau }_1}}+a_2{e}^{-\frac{(t-t_0)}{{\tau }_2}}+a_3{e}^{-\frac{(t-t_0)}{{\tau }_3}}$, where the units of $\mathrm{\Delta }{T}_t$ are mK/GtC (see Table S20 for parameter values). The SCC estimates presented here are US dollars per tCO2, which is converted from tC by multiplying by 12/44.

To represent economic growth for the remainder of this century (2020–2100), we use the estimates of the global and the RICE regions gross domestic product (GDP) produced by the OECD Env‐Growth for the SSP5 narrative, included in the SSP Database. ⁵⁶ These projections were linearly interpolated from a 5‐year period to annual frequencies.

Derivation of the proposed damage functions

Stochasticity

The type of damage function originally proposed by William Nordhaus to transform global mean annual surface temperature increase from preindustrial times into economic damages ($I_t$) has been updated over the years, but its main features have remained the same. ⁵⁷ , ⁵⁸ , ⁵⁹ , ⁶⁰ This type of damage function is characterized by its functional form and the parameter values that are chosen. The Nordhaus‐type damage function consists of a quadratic functional form, commonly specified with a zero coefficient for the linear term (i.e., also called a power function) of annual mean global temperature change, scaled by some parameter values that represent the loss in global welfare for a given global mean temperature change and a calibration temperature value ($C$). The various versions of this type of damage function can be succinctly described by $I_t=a{(\frac{\mathrm{\Delta }{T}_t}{C})}^2=\alpha \mathrm{\Delta }{T}_t^2$, where $a$ represents the losses estimated for an increase of $C$ in global temperature and $\alpha =(\frac{a}{C^2})$. For the estimates presented here, parameter values $a=2.71\%$ and $C=2.5^{\circ }\mathrm{C}$ were obtained from a review of published estimates ⁶¹ (see Table S1).

Note that $\mathrm{\Delta }{T}_t$ represents the climate signal that results from the response of the climate system to changes in external forcing, or a climatological change (i.e., a change in climatology with respect to preindustrial times). The output from deterministic, reduced complexity climate models commonly included in IAMs directly represents the change in climatological conditions between the reference period and those in time t (SM1). A generalized expression based on a common definition of climatology is ² , ⁶²

$$I_t=\alpha \mathrm{\Delta }{T_t}^2=\alpha E{\left[\mathrm{\Delta }{T}_{t,i,j}\right]}^2,$$ (1)

where $E[\mathrm{\Delta }{T}_{t,i,j}]$ is the time‐dependent expected value of temperature change over the globe, which is a nonstationary variable under climate change, and i,j represent geographical coordinates. In practice, it is approximated by taking the sample mean using a sufficiently long period of time (e.g., 30 years; SM1 and SM3), by the use of filters or other smoothing techniques ² , ⁶² , and it is referred to as climate normal or climatology. ¹ Using the definition of the variance (i.e., $var(X)=E[X^2]-E{[X]}^2$), the original damage function $I_t$ can be seen as a restricted case of a more general damage function $I_t^{\ast }$:

$$I_t^{\ast }=\alpha \mathrm{\Delta }{T_t}^2=\alpha E{\left[\mathrm{\Delta }{T}_{t,i,j}\right]}^2=\alpha E\left[\mathrm{\Delta }{T}_{t,i,j}^2\right]-\alpha \left[var\left(\mathrm{\Delta }{T}_{t,i,j}\right)\right].$$ (2)

That is, the original Nordhaus formulation can be seen as a special case of a more general equation which can be interpreted as $\mathrm{\Delta }{T}_t$ is nonstochastic or its variance is restricted to be equal to zero ($var(X)=0$), so that condition $E[X^2]=E{[X]}^2$ holds and Equations (1) and (2) are the same: $I_t=\alpha E{[\mathrm{\Delta }{T}_{t,i,j}]}^2=\alpha E[\mathrm{\Delta }{T}_{t,i,j}^2]=\alpha \mathrm{\Delta }{T_t}^2$. Nordhaus’ formulation and description of this type of damage function ⁸ , ³¹ , ⁵⁷ , ⁶³ sets to zero the effects of variability over damages. However, this restriction can be relaxed, and the effects of variability incorporated.

Rearranging the terms in Equation (2):

$$I_t+\alpha \left[var\left(\mathrm{\Delta }{T}_{t,i,j}\right)\right]=\alpha E\left[\mathrm{\Delta }{T}_{t,i,j}^2\right],$$ (3)

from which a generalized damage function $I_t^{\ast }$ that includes variability is:

$$I_t^{\ast }=I_t+\alpha \left[var\left(\mathrm{\Delta }{T}_{t,i,j}\right)\right]=\alpha E{\left[\mathrm{\Delta }{T}_{t,i,j}\right]}^2+\alpha \left[var\left(\mathrm{\Delta }{T}_{t,i,j}\right)\right]=\alpha E\left[\mathrm{\Delta }{T}_{t,i,j}^2\right].$$ (4)

That is, the damages that include temperature variability can be efficiently calculated as $I_t^{\ast }=\alpha E[\mathrm{\Delta }{T}_{t,i,j}^2]$. As shown in SM8, Equation (4) allows for including spatial variation, temporal variability, seasonality, and potential interactions between them.

The difference between Equations (1) and (4) is that the first calculates the damages associated with the average temperature change over space and time domains, while the second represents the average damages of temperature change over both dimensions. As a simple illustration, consider the case of two numbers that are not the same, for example, 1 and 3. If the average of these two numbers is taken first and then raised to the power of 2, the result is ${[(1+3)/2]}^2=2^2=4$. In contrast, if the numbers are raised to the power of two and then the average of the two is taken, the result is $(1^2+3^2)/2=10/2=5$. This is an application of Jensen's Inequality. If there is variability in the data, the average of a sum of squares will be larger than the average of the same set of numbers raised to the power of 2. For the RM and HP approaches, the damages in the reference year (i.e., preindustrial times) $I_{t=0}^{\ast }$ may not be equal to zero as the variance will be positive. As such, to account for the effects of variability in preindustrial times, the calculations based on RM and HP presented in this paper subtract $I_{t=0}^{\ast }$ from Equation (4). Note that this is not the case for the main approach used in the paper (SP), since $\mathrm{\Delta }{T}^g=0$ and both spatial variation and temporal variability will be zero in the reference year (1850).

An equivalent approach for incorporating temporal variability and spatial variation into the damage function consists in making the variance a direct proportion of the change in temperature squared $var(\mathrm{\Delta }{T}_{t,i,j})=\beta E{[\mathrm{\Delta }{T}_{t,i,j}]}^2$. To incorporate the effects of stochasticity, the parameter in Equation (1) could be replaced by ${\alpha }^{\prime }=\alpha (1-\beta )$, where $\beta =\frac{var(\mathrm{\Delta }{T}_{t,i,j})}{E{[\mathrm{\Delta }{T}_{t,i,j}]}^2}$. However, $\beta$ is not necessarily constant and can be climate model and scenario dependent (see SM8).

Sectoral impacts

The damage functions expressed by Equation (1) assume that the impacts of climate change are uniform over the year. This is expected to be true for some of them, such as sea level rise, which is driven by thermal expansion and ice melt, that is, cumulative warming rather than warming in a specific month. However, such impacts as the demand for space heating or cooling, or cold‐ and heat‐related mortality and morbidity are tied to the projected warming in winter and summer, respectively. We can thus improve on the naive calibrations above. We first compiled results from past studies in which the economic impacts of climate change have been estimated (Supplementary Information S1), particularly those in which sectoral decomposition is included. We used nine studies that provide estimates for sectoral impacts, ³¹ , ⁴⁰ , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ⁶⁴ , ⁶⁵ and they are summarized in Table S1. The total damage from all sectors is estimated to be 2.71% of global GDP for a 2.5°C warming. ⁴⁰

Seasonality

As a first step to derive seasonal and monthly damage functions, for each sector, seasonal weights are assigned to each sector depending on how active the sector is at that time of year (Table S2 and SM7). The values given to these weights are to illustrate how accounting for temporal variability and spatial variation could affect the estimates of the economic damages of climate change. The nature and intent of this exercise is heuristic and provides a first exploration of the importance of these factors (SM7). The seasonal damage parameters become:

$${\alpha }_{k,j}^s={\omega }_{k,j}^s{\alpha }_j,$$ (5)

where ${\alpha }_{k,j}^s$ and ${\omega }_{k,j}^s$ are the parameter of the seasonal damage function for season and the weight for season $k$ and sector $j$, and ${\alpha }_j$ is the original damage parameter obtained from the literature for sector $j$. Using these weights, the total damages per season for 2.5°C warming are estimated to be 0.30%, 1.52%, 0.30%, and 0.58% for spring, summer, fall, and winter, respectively.

The seasonal weights and the differences in total GDP per hemisphere are used to derive monthly damage functions as described in the following equation:

$${\alpha }_{l,j}^m={\omega }_h^{GDP}\frac{1}{3}{\alpha }_{k,j}^s,$$ (6)

where ${\alpha }_{l,j}^m$ is the monthly damage coefficient for month $l$ and $l\in k$, ${\omega }_h^{GDP}$ is the ratio of GDP produced in hemisphere $h$ (US$77,800 and US$9,470 billion for the northern and southern hemispheres, respectively) and global GDP (US$87,270 billion). The monthly damage coefficients imply economic losses (%GDP) for a 2.5°C in warming of about 0.23% per month in winter (seasonal total: 0.68%), 0.10% per month in spring (seasonal total: 0.30%), 0.47% per month in summer (seasonal total: 1.42%), and 0.10% per month in autumn (seasonal total: 0.30%). Note that the sum of monthly (as well as seasonal) damages equals the annual total of 2.71%. Figure S1 shows the seasonal and monthly aggregated damages as a percentage of GDP for 1−6°C increase in annual mean global temperatures.

Regional damage functions

To illustrate how this method can be extended to regional scales, we adapt the regional damage functions included in the RICE model ³¹ , ⁴⁸ to include temporal and spatial variability. These 12 regional functions project economic damages based on changes in annual mean global temperature. The regions included in the RICE model are the US, Western Europe (WEU), Japan, Russia, Eurasia, China, India, Middle East (MEAST), Africa, Latin America (LAM), other Asian countries (OASIA), and other high‐income countries (OHI). ³¹ As the first step, we standardized the specification of these regional functions, as half of them (China, India, MEAST, Africa, LAM, and OASIA) include a linear term in addition to the quadratic term in Equation (1). We use an optimization method to find the values of parameter ${\alpha }_r$ for each region r that minimizes the squared differences between the original functions and the one that only includes a quadratic term for a range of global temperature change from 0°C to 6°C. This approximation provides a very good fit, with $R^2$ values larger than 0.99 in all cases. The original and fitted parameter values are provided in Table S16. For each region, the proposed damage functions that include temporal and spatial variability are obtained following Equation (4). Note that the proposed methodology can be applied to other sets of regional damage functions to take advantage of the growing literature on regional estimates of the economic costs of climate change. ³² , ³³ , ⁴⁵

Note that results from global damage functions such as the one in Equations (1) or (4) and the aggregated total obtained from regional damage functions (like those in RICE) do not exactly match. ³¹ To avoid discrepancies between results here, we scale regional results to exactly match those based on Equation (4). The scaling factor is the ratio of the results from the global damage function and the sum of those obtained for each region with RICE. This ensures that regional and global results are exactly consistent, while it maintains the regional differences generated by the region‐specific damage functions. Moreover, this procedure is also used to recalibrate the RICE damage functions to more recent global estimates of losses from climate change (e.g., 2.71% of global GDP in the aggregated results). While it retains the distribution of impacts across regions embedded in the RICE model, global and regional losses are updated to match those of the newly calibrated global damage function (see SM9 for a detailed description of the methodology).

RESULTS AND DISCUSSION

Effects on the estimates of economic losses of accounting for temporal variability and spatial variation in warming

From Equation (1) above (see Equations 1−4 and SM8), it follows that accounting for climate variability has a direct effect on the level of damages, and not only through the risk premium. ⁸ , ³⁴ Here, we quantify the losses attributable to changes in the mean of global temperature, to Svar and Tvar, and those that are produced by the interaction of both factors (see SM5 for definitions and construction of the different scenarios). The main estimates presented here correspond to the SP approach of the ensemble mean (one member per model) of the CMIP6, while the Supplementary Information contains a sensitivity analysis that considers the SP, RM, and HP approaches from six climate models with different ensemble sizes (See Methods and SM3). The differences in the number of realizations per model are used to illustrate the effects of different levels of noise around the climate signal.

Figure 1 compares the economic impacts with and without climate variability. Moreover, it decomposes these results into spatial and temporal effects. This figure underlines the important role of Svar in the change in temperature for projecting the economic damages of climate change. Allowing for both spatial variation and temporal variability (S&Tvar) in $\mathrm{\Delta }{T}_t$ leads at the end of this century to damages of about 12.99% of global GDP (red continuous line in Figure 1), which are about 2.66% of global GDP higher than when no variability is included in the calculations (10.33% of global GDP; dashed blue line in Figure 1). The largest change in the projected damages can be attributed to Svar, with damages rising to 12.26% of global GDP (green continuous line in Figure 1). The effect of incorporating Tvar by itself is quite small (0.01% of global GDP; dotted red line in Figure 1) and similar to what has been reported previously in the literature. ⁸ When variability in both spatial and temporal domains is allowed, the interaction effects of these two domains make losses noticeably larger, with an increase in damages of about 0.72% of global GDP (i.e., S&Tvar‐Svar‐Tvar). The differences in damages ($I_t^{\ast }-I_t$) increase with warming: according to the SP estimates, by 2050, if S&Tvar is ignored, damages would be underestimated by about US$2.2 trillion (US$1.9–US$3.0 trillion; Table S3) and about US$27 trillion by 2100 (US$24–US$38 trillion; Table S3). These results are like those obtained with the RM approach, except for those obtained with the CanESM5, which projects about 2°C larger than the CMIP6 ensemble mean by 2085. Also, since the RM estimates are based on 30‐year rolling statistics, the last year that can be calculated is 2085 and not 2100. In consequence, the magnitudes of these estimates are typically lower than those of the SP for 2100. In the case of the HP estimates, the underestimation of damages if S&Tvar is not considered would be US$3.2 trillion (US$1.8–US$9.0 trillion; Table S3) by 2050 and up to US$35 trillion (US$24–US$70.0 trillion; Table S3) by 2100. Using the HP filter to separate the intra‐ and inter‐annual temporal variability shows that the effects of changes in seasonality are the main contributors to the increase in damages from Tvar. The effects of inter‐annual variability alone are near zero, with damages increasing only by US$0.1 and US$3.0 billion in 2050 and 2100, respectively (Table S3). This result is consistent with what has been previously reported in the literature. ⁸ , ³⁴

FIGURE 1.

Projected economic damages (% GDP) as a function of changes in global temperature according to the aggregated annual damage functions and the SSP585 scenario. S&Tvar (red), Tvar (dotted pink), and Svar (green) denote the use of damage functions that include both spatial variation and temporal variability, temporal variability alone, and spatial variation alone, respectively. The dashed blue line (None) (overlapping the dotted pink line) shows results produced with the damage function that does not include any type of variability in temperature change.

Figure 2 shows the present value of the losses accumulated during the period 2020–2100 for each of the annual damage functions, using a 4% discount rate. Tables S3 and S4 present a sensitivity analysis using other climate models and the SP, RM, and HP approaches (SM3 and SM4). The present value of losses obtained with the damage function that excludes temperature change variability amounts to US$248,001 billion, while the present value including S&Tvar is US$312,107 billion (US$304,440–US$336,911 billion; Table S4), which represents a difference of about 63% of global GDP in 2020 (US$64 trillion with a range of US$56–US$89 trillion; about 26% higher than the original damage function). The present value of losses for the Svar damage function is US$294,740 billion (US$283,887–US$303,348 billion), and US$248,331 billion (US$248,053–US$248,390 billion) for Tvar, which is much closer to that of the original damage function. The results in Table S3 show that not only the differences in the level of warming by various models (RM, HP) strongly influence the projected losses, but that, even when the differences in warming are controlled for (i.e., using the pattern scaling method; SP), the variability in space and time of each model increases damages between 23% and 36%. Decomposing these additional losses (Table S4) reveals that, on average, 65% (60–73%) of them can be attributed to spatial variation and about 0.52% (–0.29% to 0.69%) to temporal variability. The interaction between spatial variation and temporal variability has a large effect, accounting for about 34% (27–39%) of the increases in losses. The effects of incorporating variability in the space and time domains are also important when comparing the costs associated with different reference and policy emissions trajectories. As shown in Table S5, when S&Tvar is included, the estimated damages are considerably larger for any emissions scenario. Moreover, using the SSP585 as an illustration, Table S5b,c shows that the benefits (in terms of avoided damages) are also larger for all levels of mitigation effort deemed possible under the SSP5 socioeconomic scenario. ⁶⁶

FIGURE 2.

Present value of losses accumulated over 2020–2100 for the SSP585 scenario. S&Tvar, Tvar, and Svar denote the use of damage functions that include both spatial variation and temporal variability, temporal variability alone, and spatial variation alone, respectively. The bar labeled “None” shows results produced with the damage function that does not include any type of variability in temperature change. Calculations are based on a 4% discount rate.

When using the monthly damage function with all sectors aggregated by month, the calculated damages are very similar to those obtained with the annual damage function (Tables S3−S5). For instance, using the S&Tvar damage function, the present value of losses is about 2% of global GDP smaller compared with that of the annual damage function. These differences are due to the heterogeneity in warming during the year. The differences become clearer when monthly damages are analyzed per sector (Tables S6−S11). While including spatial variation always leads to higher damages, temporal variability can lead to lower damages in some cases when compared with projections from the annual damage function. These are sectors that are strongly influenced by seasonal variation, such as agriculture, forestry, water, other markets, and air pollution (Figures S3 and S4). This occurs because the average annual warming is higher than the increase in temperatures in the months that are most relevant for the sector. In contrast, for some sectors, temporal variability increases impact significantly, as the warming that occurs in the relevant months is larger than the annual mean. These sectors are amenity, tourism, energy, health, and time use, a sector for which warming and seasonal variability produce benefits. This illustrates the importance of relaxing the assumption of zero variability that is implicitly made in most of the current damage functions (Equation 1). As suggested by Figure S4, damages to health, amenity, and time use would occur earlier in this century, reaching monthly losses exceeding 0.1% of global GDP during the 2050s and doubling in the 2070s for health. In the case of other markets, exceeding 0.1% would occur in the mid‐2030s and 0.2% in the 2050s. If mitigation efforts that lead to an emissions trajectory like that of the SSP245 are achieved, exceeding 0.1% of GDP in monthly damages in sectors such as health could be delayed to the mid‐2060s, while in other markets to the early 2040s and losses larger than 0.2% would not be attained during this century, with the exception of other markets, which would exceed this threshold by the mid‐2070s.

Figure 3 shows the present values calculated per sector under the SSP585, using monthly damage functions and different assumptions about temperature change variability (see Tables S6−S11 for other SSP scenarios and climate models). Except for time use, climate change has negative effects in all sectors over this century and their magnitudes are highly dependent on the assumptions made about the temporal variability and spatial variation of warming. The largest losses correspond to the S&Tvar damage functions. Compared with the losses obtained under the no‐variability assumption, the aggregated present value is about US$58.5 trillion larger and the sectors with larger differences are health (US$15 trillion), amenity (US$10 trillion), other markets (US$8.5 trillion), and time use, for which climate change represents considerable benefits (US$9 trillion). In the case of the Svar damage function, the aggregated present value is about $46.5 trillion larger when compared with the damage function that assumes no variability. The magnitudes are smaller and the sectors with larger losses vary: other markets ($11 trillion), health ($8 trillion), amenity ($5.7 trillion), agriculture ($4 trillion), and time use (−$5.0 trillion). The differences in present values between Tvar and the original no‐variability damage functions are much smaller, about $272 billion. Tvar has a more complex effect on how damages compare with the no‐variability damage function. Due to the variability in warming, and for some sectors that have strong seasonal dependence, the present values are smaller than those obtained using the no‐variability damage function (other markets, agriculture, water, air pollution, forestry). This highlights the importance not only of incorporating temperature change variability, but also of developing intra‐annual, sectoral damage functions.

FIGURE 3.

Present value of the economic losses over 2020–2100 per sector. Panel (A) shows the present value of economic losses per sector for different assumptions about temperature change variability. Panel (B) depicts the present value of differences between the projections using the damage function in Equation (1) and from those that allow for different types of variability. S&Tvar, Tvar, and Svar denote the use of damage functions that include both spatial variation and temporal variability, temporal variability alone, and spatial variation alone, respectively. The bar labeled “None” shows results produced with the damage function that does not include any type of variability in temperature change. Calculations are based on a 4% discount rate.

SCC under different temperature change variability assumptions and SSP scenarios

The SCC is a commonly used metric to inform decision‐making about the impacts of adding an extra metric ton of CO₂ into the atmosphere, or put in a different way, the benefits society can have by mitigating a ton of CO₂. ⁵⁷ , ⁶³ , ⁶⁷ The SCC can be used in cost–benefit analysis of greenhouse gas mitigation projects, and its level can guide setting the optimal (Pigouvian) carbon tax. ⁴⁰ The SCC was estimated using a simple and physically robust response function of the marginal global mean near‐surface temperatures to a one‐time pulse of 1 GtC ⁵⁵ , ⁶⁸ released in 2020 (see Methods). This response was added to a set of baseline SSP global temperature scenarios. These scenarios represent a variety of narratives that encompass very high emissions and very high economic growth scenarios (SSP585), high emissions and low economic growth (SSP370), a middle‐of‐the‐road scenario consistent with current levels of international mitigation commitments (SSP245), and two high economic growth scenarios with the successful implementation of stringent mitigation policies (SSP126 and SSP119).

Figure 4A shows the estimated SCC values per ton of CO₂ for each of the damage functions discussed in this paper and for the SSP585, SSP370, SSP126, and SSP119 scenarios. These estimates are based on a 4% discount rate, but a sensitivity analysis based on 3% and 1.5% discount rates is also included in Table S12. In all cases, the results show that including spatial variation and temporal variability (S&Tvar) leads to considerably higher SCC values, followed by the Svar damage function, and that Tvar alone has a marginal effect on SCC. As expected, the largest values of SCC occur under the SSP585, reaching about US$83.96/tCO₂ in the case of the no‐variability damage function and up to US$105.69/tCO₂ with the S&Tvar damage function. The S&Tvar estimate for a 3% discount rate is US$162.02/tCO₂ (Table S12), which is about threefold that of the US government under the Biden administration for this discount rate, ⁶⁹ and about 25% larger than the price of the carbon tax in Sweden (US$130/tCO₂) which is one of the highest in the world. Note that even under the SSP126, which keeps global temperature change below 2°C during this century, the SCC is US$79.85/tCO₂ (3% discount rate), about 57% higher than the US government estimate. These figures provide further support for substantial climate taxes, which could be as high as those in countries with the most stringent climate policy, ⁴⁰ even using a conservative calibration for the damage function. These results are consistent with recent estimates that include a wider range of uncertainty from different sources than most previous studies. ⁷⁰

FIGURE 4.

Estimates of the social cost of carbon (SCC) per tCO₂ for five shared socio‐economic pathway (SSP) scenarios, 15 sectors, and 12 world regions. Panel (A) shows the SCC values for five SSPs and four damage functions with different assumptions about temperature change variability. Panel (B) shows the SCC values for 15 sectors and four damage functions with different assumptions about temperature change variability. Panel (C) shows the SCC values for 12 world regions and four damage functions with different assumptions about temperature change variability. S&Tvar, Tvar, and Svar denote the use of damage functions that include both spatial variation and temporal variability, temporal variability alone, and spatial variation alone, respectively. The bar labeled “None” shows results produced with the damage function that does not include any type of variability in temperature change. Calculations are based on a 4% discount rate.

Despite the large changes in climate, this trajectory implies the SCC values for the SSP370 are the lowest due to the much slower economic growth that is associated with such a socioeconomic scenario. Using the no‐variability damage functions, the SCC value reaches US$33.83/tCO₂ compared with US$42.58/tCO₂ using the S&Tvar damage functions (4% discount rate).

Compared with the SSP245, the SSP126 and SSP119 imply considerably different levels of warming: while the SSP245 leads to about 2.72°C increase in 2100 with respect to preindustrial values, the warming under the SSP126 and SSP119 is about 1.77°C and 1.43°C, respectively. At the end of this century, the GDP levels under the socioeconomic trajectories SSP2 and SSP1 are very similar, but economic growth is faster during midcentury in the SSP1. Due to the combinations of warming and growth rates, the SCC value is slightly higher under the SSP126 scenario, reaching about US$52.28/tCO₂ (US$41.54/tCO₂) using the S&Tvar (None) damage functions; for the SSP245, the SCC values are US$51.65/tCO₂ (US$41.03/tCO₂) with the S&Tvar (None) damage functions (4% discount rate). Slightly lower SCC values are obtained with the SSP119 of about US$47.63/tCO₂ (US$37.84/tCO₂) dollars using the S&Tvar (None) damage functions.

The SCC was decomposed into 15 sectors, which added up only approximately to the SCC totals described in the previous paragraph due to differences in warming between the various months and annual warming (Table S13). A sensitivity analysis of the discount rate is presented in Tables S14 and S15. Figure 4B shows the results for the SSP585 scenario obtained using the four sets of monthly sectoral damage functions (results for all SSPs considered are shown in Figure S5). The sectors with the highest SCC values are other markets (S&Tvar: US$22.71/tCO₂; None: US$19.83/tCO₂) and health (S&Tvar: US$19.96/tCO₂; None: US$14.87/tCO₂) which represent about 20% each of the total SCC, followed by amenity (S&Tvar: US$13.73/tCO₂; None: US$10.22/tCO₂; about 13% of total SCC), agriculture (S&Tvar: US$8.27/tCO₂; None: US$7.13/tCO₂; about 8% of total SCC), and catastrophe (S&Tvar: US$8.19/tCO₂; None: US$6.51/tCO₂; about 8% of total SCC), while the only sector with negative SCC value is time use (S&Tvar: −US$12.06/tCO₂; None: −US$8.98/tCO₂). These estimates allow us to identify that about 63% of the total SCC comes from impacts on four sectors (other markets, health, amenity, and agriculture). Most of the damages occur in the winter and summer, and damages in two of these sectors would exceed 0.1% of global GDP per month around 2050 (Figure S4). This suggests prioritizing adaptation in these sectors and seasons is key to reducing climate change impacts. These figures are illustrative, as assessments of the impacts of climate change for a wide variety of sectors are scarce at the monthly level and the empirical basis needs to be improved. Recent studies have focused on developing estimates of mortality SCC and expanding the empirical foundation of sectoral damage functions. ⁷¹ , ⁷² Given the differences in levels of aggregation, those results are difficult to compare with the health estimates presented here. However, such studies show how improvements in the representation of sectors (and particular aspects of them) can significantly increase the estimates of the SCC. For some sectors, the SCC values obtained from the Svar damage functions are greater than those from the S&Tvar functions (other markets, agriculture, forestry, water, and air pollution; Tables S13−S15). In these sectors, the SCC values from the Tvar damage functions are smaller than those obtained from the damage functions that consider no variability (None). Similar to what is discussed in the previous section, these results are produced in sectors that have strong seasonal dependence and in which at least some of the relevant months show lower warming than the annual mean warming. It is important to note that sectoral contributions to global GDP and sectoral damages are expected to vary across different SSP narratives, ⁷³ which remains a modeling challenge in current IAMs.

Using modified and updated versions of the damage functions from the RICE model (Table S16), the global SCC estimates were decomposed into 12 world regions. Figure 4C shows the SCC values for the SSP585, while Tables S17−S19 show the results for the SSP370, SSP245, SSP126, and SSP119, and three discount rates (4%, 3%, and 1.5%). The damages produced by an extra ton of CO₂ are distributed in a highly heterogeneous way, concentrating in the most vulnerable regions. The highest SCC values occur for India (S&Tvar: US$19.27/tCO₂; None: US$15.31/tCO₂), Africa (S&Tvar: US$19.22/tCO₂; None: US$15.27/tCO₂), and China (S&Tvar: US$15.58/tCO₂; None: US$12.37/tCO₂). These three regions account for about 45−51% of the global SCC value, depending on the SSP scenario. In contrast, the SCC values are about one order of magnitude lower for Eurasia (S&Tvar: US$1.34/tCO₂; None: US$1.06/tCO₂), Russia (S&Tvar: US$1.45/tCO₂; None: US$1.15/tCO₂) and Japan (S&Tvar: US$2.09/tCO₂; None: US$1.66/tCO₂). The SCC for the most developed regions (US, WEU, and OHI) represents 22−25% of the global SCC value.

CONCLUSIONS

Most IAMs and economic assessments of the impacts of climate change rely on the assumption that changes in the mean of a chosen index (e.g., global mean annual temperature) provide an adequate representation of the effects of this phenomenon on natural and human systems. Although this assumption helps keep IAMs as simple and tractable as possible, it has two important limitations. First, it fails to take advantage of the advancement that climate modeling has had over the last 30 years in producing spatially explicit projections with better representation of low‐ and high‐frequency variability, ⁷⁴ and of the development of methods to emulate the output of complex climate models with much simpler and low computing costs. ³⁰ , ⁷⁵ Second, as is shown here, this simplification produces nontrivial biases in the estimated costs. Contrary to past studies which have focused on evaluating the effects of temporal variability, here we show that omitting spatial variation produces large downward biases on the estimates of the costs of climate change, and that the interaction between temporal variability and spatial variation increases these biases. We show that current IAMs can be easily extended to account for these limitations and provide a more accurate representation of the effects of changes in climate both in the mean and its variability. We developed a set of damage functions that can account for temporal and spatial variability in temperature change. Moreover, annual, seasonal, and monthly sectoral damage functions are proposed to fully take advantage of seasonal and spatially explicit temperature change projections.

Results show that accounting for variability in warming affects the expected level of losses, and not only the risk premium, as proposed in previous publications. Spatial variation and temporal variability together always lead to higher present value of losses and SCC estimates when aggregated across sectors. However, for sectors in which there is a strong seasonal dependence and in which the warming in months that are relevant for the sector is lower than the annual average, economic losses can be smaller than under the assumption of no seasonal variability in warming.

We show that traditional damage functions that rely on annual mean global temperature change may severely underestimate the expected losses from climate change. Under the SSP585 scenario, by 2100, global annual losses are projected to be about US$19–US$70 trillion dollars higher when spatial variation and temporal variability are accounted for, in comparison to commonly used damage functions that ignore warming variability. Similarly, the corresponding present value of losses during this century (2020–2100) is about US$38–US$222 trillion dollars higher using the S&Tvar damage functions. It is important to underline that the reported estimates are based on conservative calibrations of global damage functions and a relatively high discount rate is used (4%) for the main estimates. Compared with previous estimates from Calel et al., ³⁴ there are differences to point out. Calel et al. ³⁴ report that the expected damages do not change when accounting for this factor, but that the risk premium does by US$32 trillion. Here, we show that spatial variation and temporal variability do affect the expected value of damages, increasing losses in the range of about 37–218% of annual global GDP in 2020. These estimates are much larger than those in Calel et al. ³⁴ although they use one of the damage functions that produce the highest damages in the literature. ⁷⁶ Another important difference is that Calel et al. ³⁴ conclude that accounting for temporal variability has no effect on the SCC. Our results show that ignoring spatial variation and temporal variability produces an important negative bias on SCC estimates.

The SCC estimates are also highly sensitive to the assumptions about warming variability embedded in damage functions. If spatial and temporal variability are included, the SCC values are about 17–45% higher than under the assumptions in traditional damage functions. Moreover, developing monthly sectoral damage functions allows us to understand better how sectors with strong seasonal components can be affected by climate change and, in some cases, to avoid overestimating losses. As commonly acknowledged in the IAM literature, current damage functions have significant limitations, which add to the epistemic uncertainty and limitations in climate, impacts, and adaptation modeling (SM6 and SM7). ⁷⁷ , ⁷⁸ Assessing the economic costs and risks of climate change is a daunting task that requires iterative improvements to models and methodologies across various disciplines. Here, we contribute to this process by showing that ignoring temporal variability and spatial variation produces important downward biases in damage estimates, and providing reduced‐form damage functions that account for them and that are easily implemented in current IAMs. In addition to these types of extensions, it is of prime importance to continue improving the empirical basis of damage functions through sectoral and regional damage assessments. ³² , ⁴⁴ , ⁴⁵ , ⁴⁶ , ⁴⁷ , ⁷¹ , ⁷²

The damage functions developed in this paper are expected to be particularly useful when applied to climate scenarios in which warming spatial and temporal patterns are highly modified. This type of scenario includes climate catastrophes such as the shutdown of the thermohaline circulation, the Amazon dieback, and the disintegration of the West Antarctica ice sheet. Overly optimistic estimates of the costs and consequences of such events may be largely due to current IAMs ignoring large‐scale and profound changes in climatic patterns and concentrating only on the changes these events produce over global mean warming.

AUTHOR CONTRIBUTIONS

F.E., R.S.J.T., and W.B. contributed equally to this work.

COMPETING INTERESTS

The authors declare no competing interests.

CODE AVAILABILITY STATEMENT

The authors will make the code available upon request.

PEER REVIEW

The peer review history for this article is available at https://publons.com/publon/10.1111/nyas.15335.

Supporting information

Table S1. Summary of estimates of economic impacts (% of global GDP) per sector for a 2.5°C increase in global temperature.

Table S2. Seasonal weights per sector used to calibrate the proposed damage functions.

Table S3. Differences between damage estimates from $I_t$ and $I_t^{\ast }$ incorporating spatial variation and temporal variability.

Table S4. Present value of the aggregated economic losses from climate change using different climate models, approaches to create climatological values, and ensemble sizes.

Table S5. Present value of the aggregated economic losses from climate change for different SSP trajectories and the benefits of mitigation.

Table S6. Present value of the economic losses from climate change for 15 sectors and different SSP trajectories.

Table S7. Present value of the economic losses from climate change for 15 sectors under the SSP585 and different climate models.

Table S8. Present value of the economic losses from climate change for 15 sectors under the SSP370 and different climate models.

Table S9. Present value of the economic losses from climate change for 15 sectors under the SSP245 and different climate models.

Table S10. Present value of the economic losses from climate change for 15 sectors under the SSP126 and different climate models.

Table S11. Present value of the economic losses from climate change for 15 sectors under the SSP119 and different climate models.

Table S12. Global social cost of carbon for five SSP scenarios and three discount rates.

Table S13. Social cost of carbon for 15 sectors and different SSP trajectories (4% discount rate).

Table S14. Social cost of carbon for 15 sectors and different SSP trajectories (3% discount rate).

Table S15. Social cost of carbon for 15 sectors and different SSP trajectories (1.5% discount rate).

Table S16. Original parameter values of the RICE model and optimized parameter values for a quadratic term specification.

Table S17. Social cost of carbon for 12 regions and different SSP trajectories (4% discount rate).

Table S18. Social cost of carbon for 12 regions and different SSP trajectories (3% discount rate).

Table S19. Social cost of carbon for 12 regions and different SSP trajectories (1.5% discount rate).

Table S20. Parameter values for the response function of global mean temperatures to a pulse of 1GtC.

Figure S1. Seasonal and monthly damage function projections for different levels of warming.

Figure S2. Projected economic damages (% GDP) as a function of changes in global temperature according to the aggregated monthly damage function and the SSP585 scenario.

Figure S3. Projected economic damages (% GDP) as a function of changes in global temperature according to the sector‐level monthly damage functions and the SSP585 scenario.

Figure S4. Projected economic losses. Projected economic damages (% GDP) per sector and month for different SSP trajectories.

Figure S5. Sector‐level SCC values for different SSP trajectories using four damage functions.

Figure S6. Illustration of the HP filtering used for separating intra‐ and inter‐annual variability in temperature series.

Supplementary Information

Estrada, F. , Tol, R. S. J. , & Botzen, W. (2025). Economic consequences of spatial variation and temporal variability of climate change. Ann NY Acad Sci., 1547, 170–182. 10.1111/nyas.15335

DATA AVAILABILITY STATEMENT

Data used are publicly available from the Coupled Model Intercomparison Project Phase 6 (CMIP6) website https://pcmdi.llnl.gov/CMIP6/ and the KNMI Climate Explorer https://climexp.knmi.nl/.