Overview of approach

The assessment uses global and regional damage functions (updated and enhanced from Arnell et al. 2016) which relate indicators of impact to increase in global mean surface temperature. Figure 1 shows global damage functions, and regional damage functions are presented in Supplementary Material.

Fig. 1 Global damage functions showing the relationship between change in global mean surface temperature (relative to 1850–1899 as a proxy for pre-industrial) and impact, for seven impact indicators. For population exposed to drought and flooding, and the energy indicators, the damage functions assume the 2100 SSP2 socio-economic scenario. The different lines represent 21 climate model patterns Full size image

The damage functions are constructed by calculating impacts using spatially explicit impact models with climate scenarios representing incremental increases in global mean temperature. Climate scenarios are derived from Coupled Model Intercomparison Project, Phase 5 (CMIP5) climate models (Taylor et al. 2012) using pattern scaling, and there is one damage function for each climate model. For socio-economic impact indicators, impacts are dependent on socio-economic scenario and time, so there is a different damage function for each socio-economic scenario and time horizon. The damage functions all show impact relative to a 1961–1990 baseline climatology, which (from HadCRUT4: Morice et al. (2012)) is 0.32 °C above 1850–1899, a proxy for pre-industrial levels.

The impacts that are avoided under one change in global mean temperature above pre-industrial relative to another are determined simply from the damage functions, assuming that all CMIP5 patterns are equally plausible. Impacts at temperature increases of 1 to 3 °C above pre-industrial levels in 2100 are compared with impacts at increases of 2 to 5 °C above pre-industrial. As a context, the median estimate of the increase in global mean temperature in 2100 under the high emission scenario RCP8.5 is 4.6 °C (IPCC 2013), and increases in 2100 with unmitigated emissions under the five Shared Socio-Economic Pathways (SSPs: Riahi et al. 2017) range from 3 to 5.1 °C: the ‘middle-of-the-road’ SSP2 scenario has an estimated increase of 3.8 °C (range 3.8–4.2 °C).

Climate scenarios

Spatial climate scenarios at a resolution of 0.5 × 0.5° were constructed for incremental changes in global mean surface temperature using the pattern scaling method (Tebaldi and Arblaster 2014). Patterns were diagnosed from 21 CMIP5 climate models (Taylor et al. 2012) using ClimGen (Osborn et al. 2016; Supplementary Material), in each case pooling across all available simulations for each model (across RCP forcing scenarios and, where available, ensemble members). Scenarios describe changes relative to the model 1961–1990 climate in mean monthly temperature, precipitation, vapour pressure and cloud cover, and—in an extension of traditional pattern scaling approaches—changes in the interannual variability of monthly precipitation (Osborn et al. 2016). The scenarios are applied to the 1961–1990 baseline climatology (CRU TS: Harris et al. 2014) using the delta method. The pattern-scaled scenarios represent just the effect of climate change forcing and do not incorporate the effects of unforced multi-decadal climatic variability which would increase the estimated range in future impacts for a given change in global mean temperature.

Pattern scaling involves several assumptions (Collins et al. 2013; James et al. 2017). The key assumption is that the relationship between global mean surface temperature and climate variable at a place is linear (after transformation in the case of precipitation). This is a reasonable assumption (Osborn et al. 2016) where the dimensionless patterns for a particular climate model are constructed by pooling all simulations made by that model (different forcings, different initial conditions), and deviations from this assumption are small relative to the spread between climate models. A more challenging assumption is that the change per degree change in global mean temperature does not vary with the rate of temperature increase. For example, the pattern of change in precipitation corresponding to an increase in global temperature of 1.5 °C is assumed to be the same regardless of whether that increase occurs by 2050 or 2100. A related assumption is that the patterns are the same for as long as global average temperature remains at the same level (for example, once temperatures have been stabilised), even though the slow response of parts of the climate system might lead to continued regional climate changes after global temperature stabilisation (as shown for example by Gillett et al. 2011). However, pattern scaling represents a ‘useful approximation’ (Collins et al. 2013), recognising that the scaling may be less reliable for scenarios where global average temperature stabilises. At low forcing levels, the regional effects on climate of land use change and aerosols may be large relative to the effect of increasing greenhouse gas concentrations, and these are not represented in the pattern-scaled scenarios. The implications of the potential limitations to pattern scaling are discussed in Sect. 5.

The only other potentially plausible method of constructing scenarios corresponding to specific changes in global mean temperature is to sample from climate model runs at the time when the defined changes occur (e.g. Schleussner et al. 2016; James et al. 2017). However, this approach is sensitive to multi-decadal variability, and differences between different time periods (and temperatures) will represent the combined effect of the different amount of forcing and multi-decadal variability. The approach also assumes—like pattern scaling—that the change per degree change in global mean temperature does not vary with the rate of temperature increase.

Impact indicators

Impacts are characterised by seven indicators, representing impacts on water resources, river flooding, agriculture, heat waves and the demand for energy for heating and cooling. In each case, the period 1961–1990 is used to characterise the reference ‘no climate change’ climate and is defined using the CRU TS3.22 global climatology (Harris et al. 2014).

Water resources

The impacts of climate change on water resources are characterised by the population exposed to drought. Drought is here represented by the standardised runoff index (SRI: Shukla and Wood 2008), calculated from monthly runoff simulated using the MacPDM.09 global hydrological model (Gosling and Arnell 2010). MacPDM.09 operates at a spatial resolution of 0.5 × 0.5° at a daily time step. It calculates daily runoff from daily precipitation and potential evaporation (calculated using the Penman-Monteith formula) and accounts for the storage of precipitation as snow and its subsequent melting. Daily precipitation is derived stochastically from the input monthly precipitation total and number of rain days (Gosling and Arnell 2010). MacPDM.09 has been included in global hydrological model intercomparisons (Haddeland et al. 2011) and shown to perform consistently with other global hydrological models.

The SRI is calculated here with the following steps. First, a time series of runoff accumulated over a given number of months (here 12) is constructed over the baseline 1961–1990 period. This time series is then standardised to calculate SRI by (i) estimating the exceedance probability of each value from its rank and (ii) converting these exceedance probabilities into standard normal deviates (with zero mean and unit variance). An empirical relationship is then constructed between accumulated runoff and SRI. This relationship is used to convert time series of simulated future runoff to SRI. A ‘drought’ is defined to occur when the SRI is less than − 1.5—which occurs 6.8% of the time in the baseline period—and drought frequency for a given time series of monthly runoff is determined by counting the number of months with SRI less than − 1.5. The average annual population exposed to drought is then calculated by multiplying grid cell population by the proportion of time the cell is in drought, and summing across all cells in a region. This indicator characterises exposure to drought rather than direct drought impact, because water management interventions are frequently implemented in order to reduce drought impacts.

At the global scale, the proportion of population exposed to drought increases under all 21 climate model patterns as global temperature increases (Fig. 1). However, there is considerable variability between regions (Supplementary Material). For example, drought frequency decreases in a large proportion of models in East Africa, South Asia and Central Asia, and in a substantial minority of models in West and Central Africa, and East Asia. In a number of cases, regional average drought frequency decreases for small increases in temperature and then increases as temperatures increase further. This regional-scale non-linearity occurs for a combination of two reasons. First, in some individual grid cells, drought frequency decreases as rainfall increases and potential evaporation increases, but increases once the increase in evaporation offsets the increase in precipitation. Second, different parts of a region may respond to increasing temperatures at different rates.

River flooding

Exposure to river flooding is characterised by the average annual number of people living in major floodplains affected by floods greater than the baseline 30-year flood. Flood frequency distributions for baseline and future climates are calculated by fitting a generalised extreme value (GEV) distribution to the daily flows simulated by MacPDM.09 for each 0.5 × 0.5° grid cell (Arnell and Gosling 2016), and the future frequency of the baseline 30-year flood determined from the future distributions. Floodplain boundaries are taken from the UNEP PREVIEW data set (preview.grid.unep.ch), and the proportion of grid cell population living in designated floodplains was calculated by overlaying a high-resolution gridded population data set with the floodplain boundaries. The proportion is assumed not to change over time. The indicator is similar in principle to that used by Hirabayashi et al. (2014), although they used the baseline 100-year flood as a threshold and counted exceedances rather than use fitted frequency curves. This indicator characterises exposure to flooding rather than direct flood impact, because it does not incorporate adaptations to the flood risk.

At the global scale, the population exposed to river flooding increases with increase in global mean temperature (Fig. 1). However, as with exposure to drought, there is considerable variability between regions (Supplementary Material). In some regions, one climate model produces responses very different to the others (but the anomalous model varies between regions), and in some regions—particularly central Europe, eastern Europe and Russia, and the USA—the relationship between impact and global temperature increase is complicated. This typically occurs in regions where flood peaks are currently usually generated by snowmelt, and as temperature increases, the relative contribution of snowmelt and rain-generated floods changes.

Cropland exposed to drought

The impacts of climate change on croplands is characterised by the average annual proportion of cropland that is exposed to drought. Here, drought is characterised by the standardised precipitation evaporation index (SPEI: Vicente-Serrano et al. 2010), calculated from monthly precipitation and potential evaporation (calculated using the Penman-Monteith formula). The SPEI is calculated from the monthly difference between precipitation and potential evaporation in exactly the same way as the SRI using a threshold of − 1.5, but using accumulations over 6 months. It is assumed that the area of cropland (Ramankutty et al. 2008) remains constant over time. Sensitivity analyses showed that varying the cropland area had little effect on the proportion exposed to drought.

At the global scale, the frequency of droughts affecting croplands increases with increasing global temperature (Fig. 1). Frequencies increase in all regions under virtually all climate model patterns (Supplementary Material). The damage functions for cropland drought exposure are different to those for water resources drought for three reasons. They are based on precipitation minus potential evaporation rather than on runoff (which is effectively precipitation minus actual evaporation), they are based on 6-month rather than 12-month accumulations, and they are spatially integrated across cropland rather than population.

SPEI is used as a proxy for climate impacts on agricultural production, which will of course also be affected by changes in crop growth (dependent on changes hot and cold spells, carbon fertilisation and nutrient availability) and agricultural practices.

Heat waves

The effect of climate change on hot extremes is characterised by the average annual number of ‘heat wave days’. A hot day is defined to occur if the daily maximum temperature is more than two standard deviations above the reference climate (1961–1990) warm season average maximum temperature, where the warm season is defined by the 3-month period in the reference climate with the highest average temperature. The standard deviation is calculated from the days in the reference climate warm season. A heat wave is defined to be a period of at least five consecutive hot days, and the number of heat wave days is the number of days in a heat wave. This definition means that neither periods with fewer than five consecutive hot days nor the first 4 days of a heat wave are counted. The regional average number of heat wave days is constructed by weighting each 0.5 × 0.5° grid square by its 2010 population.

Hot days and heat waves are calculated from daily maximum temperatures, which are constructed from the monthly climate scenarios by interpolating to produce a smooth annual cycle and adding historical daily temperature anomalies calculated from the WATCH climate data set (Weedon et al. 2011). These daily anomalies preserve the historical variability in temperature anomalies from day to day, and it is assumed that this variability continues into the future. This may change as climate changes. However, preliminary analyses using the ISIMIP projections (Warszawski et al. 2014) suggest little consistency between models in changes in variability, and a sensitivity analysis assuming that the anomaly standard deviation increases with temperature found that this had no effect on the difference in impacts between different changes in global temperature.

The frequency of heat wave days increases dramatically as global mean temperature increases (Fig. 1), and although it increases in each region (Supplementary Material), the amount of increase varies. It is greatest in tropical and sub-tropical regions where the standard deviation of warm season daily maximum temperature is least, and therefore, a smaller increase in temperature leads to a larger increase in heat wave frequency.

Energy demands for heating and cooling

The impacts of climate change on demands for energy are characterised by the estimated residential demands for energy for cooling and heating. These are simulated using a variation on Isaac and van Vuuren’s (2009) residential energy demand model, which essentially estimates heating and cooling requirements from accumulated degree days below (for heating) or above (for cooling) specific thresholds, along with projected future population, wealth, household size and assumptions about the changing efficiency of cooling and heating technologies. Whilst heating energy demands are a simple function of heating degree days, cooling energy demands are a more complicated function of temperature because the penetration of air conditioning is assumed to increase with temperature as well as GDP. A threshold of 18 °C is used to define both heating and cooling degree days.

As expected, global residential heating demands decrease and cooling demands increase (Fig. 1). However, the total heating and cooling demand shows a much more complicated pattern, globally and regionally (Supplementary Material). This is because the relative contribution of heating and cooling demands to total demands, and the sensitivity of demands to temperature change, varies between regions. At the global scale, total demand changes little with increases up to 2 °C above 1961–1990, for example, and in Australia, total demand falls at first and then increases as the rise in cooling demands offsets the fall in heating demands. The implications for the energy supply system of changes in cooling and heating demands are different, because these demands occur in different seasons.

Socio-economic scenarios

The water resources and river flooding indicators require projections of future population, and the energy indicators require both population and GDP projections. The analysis here focuses on the SSP2 middle-of-the-road scenario (Fricko et al. 2017) which has a population of nine billion in 2100. Sensitivity analyses (Supplementary Material) use other socio-economic scenarios.

An overview of the indicators and the characterisation of differences in impacts at different warming levels

The analysis here uses a small set of indicators of impact, which do not incorporate the effects of adaptation to changing risks: they characterise exposure to impact rather than projected actual impacts. For most of the sectors, there are a number of alternative indicators, and these could give different indications of the effect of achieving climate policy targets on the impacts that are avoided.

The damage functions exhibit a range of shapes, and—particularly at the regional level—can describe relationships between temperature and impact that change direction beyond a particular increase in temperature. As outlined above, this occurs for three reasons. In some cases, the relationship between temperature and impact changes direction in a specific location, for example where increasing temperatures alter the balance between snow and rain-generated floods. In other cases, changes occur at different rates in different parts of a region, so (e.g.) the regional aggregate change peaks before declining at higher temperatures. This occurs with the drought indicators. In a third set of cases, the sum of two competing impacts can show a complex response to increasing temperature: this occurs with the total residential heating plus cooling demand indicator.

For each of the indicators, climate change can in principle have either adverse or beneficial impacts. At the global scale, impacts on exposure of both people and cropland to drought and exposure to river flooding are adverse for any increase in temperature, but this is not necessarily the case at the regional scale (see regional damage functions in Supplementary Material). Exposure to heat waves and increases in demand for cooling energy increase everywhere, and demand for heating energy decreases everywhere (a benefit). The sum of heating and cooling demands increases in some regions and decreases in others, depending on the relative importance of the two. The effects of achieving a policy target on the impacts of climate change are therefore complicated, and there are a number of potential outcomes. These are classified in Fig. 2. In essence, a climate policy may not only result in lower adverse impacts but also lower beneficial impacts, and can also result in adverse impacts becoming worse and adverse impacts becoming beneficial or beneficial impacts increasing.