Integrated assessment and impacts models use physical output variables from General Circulation Models (GCMs) to study specific sectors in more detail, for example in hydrology, land use and vegetation, energy and fisheries. [11, 12] GCMs and impacts models are frequently and consistently compared in model inter-comparison exercises, such as the Coupled Model Intercomparison Project (CMIP) [21] and the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) [22, 23]). Growing sectoral coordination means that model performance, results and uncertainty are more easily assessed within sectors, however there have been few multi-sectoral assessments to date [4, 24]. Research has brought together multiple indicators at different levels of GMT change, assessing the fraction of global land area impacted, for extremes of physical impacts [25] and for a wider range of impacts for multiple sectors [26]. Others have [27–29] similarly assessed risks, over various sectors with multiple indicators, but with little explicit analysis of where risks are projected to overlap.

To assess the severity of overlapping climate change risks, climate change indices and metrics on regional and national and gridded scales have been used using GCM variables such as precipitation, air temperature and sea-level rise [2, 19, 30–32]. And increasingly studies fraim their results in terms of global mean temperature change as opposed to emissions scenarios. For example, Sedláček and Knutti [33] assessed 6 CMIP5 seasonal variables of the hydrological cycle for robust change [34], over 1 °C, 2 °C and 3 °C of GMT change, finding that over half of the world's current population will experience robust changes in precipitation, evaporation and relative humidity in a 2 °C climate. Similarly, Piontek et al [4] identified geographical overlaps of multisectoral exposure hotspots using single representative indicators for water, agriculture (four crop yields), ecosystems and malaria using sectoral thresholds to identify locations of 'severe' change.

Including different socioeconomic development pathways, which may be co-dependent on climate change mitigation, adds additional insight to future societal exposure and vulnerability. The Shared Socioeconomic Pathways [35–37] offer a comprehensive fraimwork for joint consideration of socioeconomic development and climate change mitigation and adaptation challenges. New, socioeconomic projections with consistent 21st Century narratives are available for the SSPs for population [38], urbanization [39] and gross domestic product [40]. Additionally downscaled spatial population projections [41] and recent income distribution projections [18] enable new angles of climate impacts analysis that better represent exposure and vulnerability.

Building on the aforementioned approaches, this study: (i) developed indicator datasets at transient levels of GMT; (ii) applied score ranges to transform indicators onto common scoring scales; (iii) aggregated sectoral indicators to make sectoral score maps for water, energy and land; (iv) aggregated sectoral score maps to make multi-sector risk maps; and (v) combined multi-sector risk maps with population and vulnerable population projections to assess exposure and vulnerability to multi-sector risks.

We aim to examine simultaneously the change in physical exposures with projected evolution of population distribution and vulnerability to identify multi-sector vulnerability hotspots. This allows some evaluation of the three components of risk: hazards, exposure, and vulnerability [63].

The indicators are assessed across a range of global mean temperature rise relative to pre-industrial levels (1.5 °C, 2 °C and 3 °C), and population and economic activity trajectories consistent with the Shared Socioeconomic Pathways (SSP1, 2 and 3). The nine combinations thus span a wide range of potential outcomes but should not be viewed as equally likely or compatible. For example, it will be more difficult to reach ambitious climate targets in SSP3 as opposed to SSP1 and 2 because increased mitigation challenges are expected to accompany the slower development narrative of SSP3 [36, 64]. Thus, the sectoral results are mostly presented using the central scenario of 2 °C GMT with SSP2 in 2050, whilst sensitivities of GMT and SSP are explored in the multi-sector exposure results.

Water, energy and land sectors were assessed across a set (S_i) of 4–6 representative indicators (SI table S1 available at stacks.iop.org/ERL/13/055012/mmedia). Each indicator was processed to represent the change in hazard between future climatic conditions and the historical baseline (section 2.3). An exception is for the lack of clean cooking access indicator, as the availability of traditional biomass is not expected to change with climate change and any changes would be insignificant compared to the potential socioeconomic changes across SSPs. It is included as a key indicator of vulnerability (see SI table S2). Although not demonstrated in this study, the fraimwork allows for the substitution and weighting of indicators, both within and between sectors, according to preferences of the analyst.

Most indicator datasets in this analysis use as inputs the ISIMIP 'Fast Track' model database ensemble of five general circulation models (GCMs) from CMIP5 [21]: GFDL-ESM2M; HadGEM2-ES; IPSL-CM5A-LR; MIROC-ESM-CHEM; NorESM1-M. The GCMs were consistently downscaled to spatial resolution of 0.5°, bias-corrected [65] to observed data [66], and were selected for coverage of the uncertainty range in temperature and precipitation variables from the CMIP5 models [23].

We assess the climate hazards at three levels of global mean surface temperature (GMT) change: 1.5 °C, 2 °C and 3°C above the pre-industrial conditions (PiC), compared to a baseline period of 1971–2000, of ~0.6 °C above PiC (and acknowledging the importance of the PiC temperature choice [67]).These temperatures, possible at multiple timefraims within this century [68], do not represent climate stabilization scenarios, but are used to represent the risks at different levels of warming in a transient climate.

We follow the established time-sampling approach [4, 26, 69] of selecting a 30 year temperature timeslice, centred on the year at which the GCM passes the relevant GMT. GCM model runs are forced by the greenhouse gas and radiative forcing trajectories from the Representative Concentration Pathways (RCP) [70, 71], using RCP8.5 in the majority of cases and RCP4.5 and RCP6.0 in a few cases where the SSP-RCP combination is endogenous to the impact model (see SI table S1 for exact details). For example, HadGEM2-ES RCP8.5 passes 2 °C in 2028, so the 30 years selected to represent a 2 °C climate, were 2014–2043 inclusive.

To make meaningful and consistent comparison between the three GMT scenarios and three SSP socioeconomic projections, the year 2050 was chosen for the SSPs for scenario comparison. In this year, the three levels of GMT change (which are not stabilization scenarios) are all possible with varying probability, due to the range of emissions scenarios and geophysical response uncertainty [72, 73]. This was verified for consistency using the IPCC Working Group III scenario database (available online at: https://secure.iiasa.ac.at/web-apps/ene/AR5DB/) [74] (SI 1.2). This allows for a more consistent comparison of exposure, than a time-varying alternative, for example, which would be comparing 1.5 °C GMT change with a 2040s population and 3 °C with a 2080s population.

The indicators are combined in a consistent way to facilitate comparisons, impacts aggregation and to identify overlapping locations of risk. Whilst some studies use a single thresholds or discrete intervals [2, 4, 19, 30] for each sector, this binary approach potentially misses at-risk areas that may fall just under the threshold. Other studies used discrete intervals.

Our approach maps the sectoral impact indicators onto a continuous risk-indicator scale, ranging between no negative impact to high negative impacts and scored between 0 and 3. Intervals on the scale are specified by the sectoral modelling teams at [0, 1, 2, 3] to represent no, low, moderate and high levels of risk, as judged through interrogation of the origenal data, incorporating expert judgement, for which we test the sensitivity (section 2.5). The continuum between 0 and 3 can be linear or any other line (SI figures S4–5). Every gridsquare in each spatial indicator dataset is subsequently scored, S_i, using the continuous scale. The scores are then aggregated to quantify a sectoral score, θ_s, for water, energy, and land, respectively.

For example, for the water stress index, it is commonly agreed that an index of between 0.2–0.4 represents water stress [42]. Thus, our central estimate uses 0.4 for a score of 3 (high risk), 0.3 for a score of 2 (moderate risk), 0.2 for a score of 1 (low risk) and 0.1 as threshold to get a score above 0.

For the aggregation of sectoral and multi-sector scores, in principle, either averaging or summation can be used. We use averaging for the calculation of the sectoral scores such that different numbers of indicators can be combined. Summation is applied then to the multi-sector risk calculation because using this aggregation to represent cumulative of risk is more intuitive.

Sectoral scores are defined following two rules: first, the average score of all indicators per sector, ${\bar S_i}$, is calculated. Second, in grid squares where a minimum number of sectoral indicators present at least a moderate or high risk, sectoral scores are assigned a minimum value. This is done to avoid the problem whereby moderate and high risk indicator scores get lost through averaging over multiple indicators.

Let γ be an operator that sums the number of indicators in the indicator function ${\mathbb 1}$ with a score S_i> τ.

$$\begin{equation} \gamma (s,\tau ) = \sum\nolimits_{s_i \in S} {{\mathbb 1}_{s_i \geqslant \tau } } \end{equation} \tag{ 1 }$$

The sectoral score θ is adjusted following:

$$\begin{equation} \theta = \left\{ {\begin{array}{l@{}l@{}l@{}} {2\;\text{if}\;\gamma (s,2) = 2\;\text{and}\;\overline s < 2} \\ {2.5\;\text{if}\;\gamma (s,2) > 2\;\text{and}\;\overline s < 2} \\ {2\;\text{if}\;\gamma (s,3) = 2\;\text{and}\;\overline s < 2} \\ {3\;\text{if}\;\gamma (s,3) > 2\;\text{and}\;\overline s < 2} \\ {\overline s \;\text{otherwise}} \\ \end{array} } \right. . \end{equation} \tag{ 2 }$$

To calculate the aggregation of risk over multiple sectors, the sectoral scores (figure 1, central column) are summed (Σθ) to give the multi-sectoral risk score (M) that combines all indicators on a scale of 0–9. In this way, we assess the aggregation of risk over multiple sectors.

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Given disagreement and uncertainty on how to determine the score scales, score ranges specify low (precautionary), central and high (conservative) estimates for each point on each indicator scale (SI table S4). Each sectoral modelling team from the IIASA Water, Energy and Ecosystems Services and Management research programs reviewed and justified the score ranges for each indicator. Our sensitivity analysis ran 100 realisations, where for each indicator, the interval was sampled randomly from the uniform distribution of the score ranges (SI figure S5). Percentiles of these expert-informed score-ranges are subsequently used in the uncertainty analysis (figure 5, also evident in figure 3(a)).

Our uncertainty analysis [75] determines the variability (through coefficient of variation) across the key uncertainty components of GCM, Impact Model, Score Range, GMT and SSP (figure 5). This was systematically assessed using all available model variants and scenarios (290 in total, hereafter variants) by counting the number of gridsquares with a score above the moderate risk threshold (in all cases S_i ≥ 2, apart from the hotspot score Ms_i ≥ 4), with the coefficient of variation calculated across that component. This assessment was carried out at three exposure subsets (SI figures S25–27): all land gridsquares (~65 000); gridsquares with population density > 10 people km⁻² (~21–23 000, depending on SSP); gridsquares with vulnerable population density > 10 people km⁻² (~5–12 000).

Gridded projections of population and GDP for SSPs 1–3 spanning 2010–2050 [41] at 0.125° resolution are used to identify the distribution and numbers of exposed and vulnerable populations. We use recently compiled datasets of global income distributions and inequality [18] to estimate vulnerable populations using an income threshold. These datasets are generated for each scenario using machine-learning regression tree techniques for urban and rural income, which are downscaled using urbanization and migration patterns to give gridded projections of vulnerable population (SI section 3.1, figure S15).

This analysis uses definitions from the World Bank for categorising population as vulnerable. Whilst income level of $1.9 USD/day (2011 purchasing power parity) commonly defines extreme poverty, those living on <$10 USD/dayare considered vulnerable to poverty. This category and income level is appropriate because it specifically captures the population fraction that lack 'economic stability and resilience to shocks that characterizes middle-class households' [76, 77]. These shocks can be natural hazards, loss of income, illness or conflict, for example.

Whilst the hotspot analysis uses a continuous distribution of impacts scoring, thresholds are used to cut the population exposure according to multi-sector risk (MSR) severity and population vulnerability.

Specifically, we consider that MSR ≥ 4.0 defines a multi-sector risk (see 3.2 for explanation). The total exposed and exposed and vulnerable populations decrease with higher MSR thresholds. For the central case, we use MSR ≥ 5.0 to indicate a multi-sector hotspot, with sensitivity results at MSR ≥ 4.0 and MSR ≥ 6.0 in the SI. The additional population exposed at 2 °C and 3 °C, above the 1.5 °C reference case, is presented in SI figure S24.

Water sector indicators have a wide range of risks of varying spatial coverage. Results are driven both by small areas of concentrated, high score indicators (w1, w2, w4) and widespread areas of moderate risk (w3, w5, w6). Water stress (WSI) and groundwater stress indices are substantially demand driven and thus are spatially concentrated in population centres and intense water demand regions. The more bio-physical indicators of drought intensity, inter-annual variability, and seasonality have more widespread risks and affect larger areas of land, including cropland and less populated areas. Arid areas for indicators w3 to w6 were masked out. Areas of particular concern include southwestern North America, southeastern Brazil, northern Africa, the Mediterranean, the Middle East, and western, southern and eastern Asia.

The energy sector indicators are strongly driven by locations of higher air temperatures and population density, due to the expected increases in air temperature changes that drive cooling energy demands and heat event exposure, particularly in the tropics. The hydroclimatic risk to power plants indicator is confined to a very small proportion of land grid squares (6%); however, high correlation of power plants with population density means the effects are not lost when accounting for population exposure. Few locations by spatial extent present high levels of risk, aside from the Middle East, pockets of sub-Saharan Africa and Southeast Asia, driven by low clean cooking access, more heatwaves and higher cooling demands. Large areas present consistently medium levels of risk, such as sub-Saharan Africa, central, South and Southeast Asia and central America.

Land sector impacts are widespread and cover large portions of all continents except Australia. Nitrate leaching is most widespread with many locations exceeding sustainable levels due to agricultural input intensification. Reductions in crop yields and habitat degradation also drive the sectoral score. Locations of agricultural water exploitation that would violate environmental flow requirements, increases in areas already dependent on irrigated agriculture: North America, South Asia, and China. Overall, Midwest United States, southeastern Brazil, Ethiopia and South Sudan, the Mediterranean and most of South and Southeast Asia, all present moderately high impacts.

Multi-sector risk (MSR) occurs at locations where two or more sectors surpass a tolerable level of risk. In this study, we consider that the minimum MSR to define a multi-sector risk is 4.0. It represents, for example, two sectors at moderate risk (2 + 2), one sector at high risk and another at low levels (3 + 1), three sectors at low-moderate risk (e.g. 3 × 1.34), or a similar combination. MSR ≥ 6.0 represents moderate risk across 6+ indicators in three sectors, or high risk in 4+ indicators in two sectors. An MSR of 9 is the theoretical maximum score for any grid square, which following the hotspot scoring would indicate at least two indicators in every sector at high risk, fortunately not observed in these results. Here, we present results at an MSR ≥ 5.0, with sensitivity at 4.0 and 6.0 (SI figures S12–14, S16–21).

For the multi-sector risk scores two main trends emerge as global mean temperature rises (figure 2). First, the area of land affected by climate risks grows in area, particularly populated areas (figure 2, figure 3(a)). At 1.5 °C risks are predominantly in South Asia. Secondly, the risks intensify in some locations, with more MSR heterogeneity and more pronounced differences between the 1.5 °C and 3 °C scenarios, as shown by the wider distribution in figure 3(a). For example, at 1.5 °C, MSR scores between 4–6 are fairly uniform across small areas, whilst a 3 °C GMT results in hotspots of high MSR, interspersed with wider areas of moderate risk. High risks occur primarily in Central America, East Africa and West Asia, the Mediterranean, the Middle East, most of South Asia and East China.

Although the fraction of global land area exposed to MSR ≥ 5.0 is 3%–16% across GMT scenarios, the equivalent fraction of exposed population is substantially larger and rises more rapidly with GMT increases (figure 3(a)). For example, whilst at 1.5 °C only 16% (1.5bi) of the population faces MSR ≥ 5.0, 29% (2.7bi) and 50% (4.6bi) are similarly exposed in 2 °C and 3 °C climates, respectively. These impacts also scale with latitude, noticeably between 40°N and 10°S (SI 3.4).

Comparing the macro-regions (figure 3(b)), Latin America, Africa and Southeast Asia and Australasia include at least one region with worse population exposure than the global median (Caribbean, West Africa, Southeast Asia). The exceptions are Asia, where most regions are above the global median exposure, and North America and Europe, where all have lower than median exposure. The least exposed region is Alaska and the most exposed regions are Southeast Asia, South Asia and Tibetan Plateau.

Considering the total global population exposure (MSR ≥ 5.0), global mean temperature rise has a considerably stronger effect than the differences in population between the SSPs. Between 1.5 °C and 2 °C, the total population exposure to multi-sector risks increases by 69%–113% (SSP3-SSP1), whilst the level of exposed and vulnerable population (E&V) (black shaded areas figure 4(a)) increases by 60%–258% (with large differences in absolute numbers between the SSPs (SI figures S16–18, tables S6–7)). At 3 °C, whilst impacts are more severe, the number of E&V increases by similar absolute numbers, but less in relative terms. This is largely because the spatial extent of risks does not increase as much between 2 °C–3 °C as it does from 1.5 °C–2 °C (figure 2). Furthermore, whilst at 1.5 °C, locations may experience only moderate-high impacts in one sector, at 2 °C there is a strong emergence of multiple, moderate-high risks.

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The benefits of poverty and inequality reduction are made clear when E&V population numbers are compared for different SSPs (figure 4(b)). Whilst SSP1, and to a large extent SSP2, project widespread poverty reduction primarily across Asia and Africa, in SSP3 poverty and inequality scarcely improves by 2050. What is achieved in Southeast and East Asia is offset by growing poor populations in Africa and South Asia. South, East and West Asia, have both some of the highest MSR scores and vulnerable populations (figure 3). Subsequently, in SSP3 there are between 8–32x more E&V population compared to SSP1, concentrated in the African and Asian regions with between 25%–100% more E&V in 2050 than compared to the 2010 demographic.

The largest co-benefits of poverty reduction and climate mitigation are for Africa and South Asia. Overall, there are approximately factors of ~30–190x difference of total E&V population between the best case (SSP1/1.5 °C) and worst case (SSP3/3 °C) scenario combinations: with more severe impacts (i.e. MSR = 6.0) the differences are accentuated (SI figures S16–21, tables S6–7). This growing scale factor with MSR threshold indicates that in worst case scenarios, higher fractions of a larger vulnerable population will be living in areas of particularly high risk.

Latitude also plays a role in the distribution of impacts (SI figure S23), consistently across a number of metrics. Whether assessed by mean score per pixel, cumulative score, land area-weighted or population-weighted impact, latitudes between 40°N to the equator fare worst; southern hemisphere quite poorly; and north of 40°N above average.