Figure 1 shows global-scale impacts at different increases in global mean temperature above pre-industrial levels. Table 2 shows the median estimate of impacts at 1.5, 2 and 4 °C from the 23 models together with the lowest and highest values, and Fig. 2 summarises global impacts across the indicators. Figure 3 shows the chance that impacts exceed specific thresholds, assuming that all 23 model patterns are equally plausible and are representative of the range in possible patterns. Figure 4 shows impacts at 1.5, 2 and 4 °C above pre-industrial levels for each indicator by continent (similar plots showing impacts by region are shown in Supplementary Material 4, along with plots summarising all the indicators for each region).

Fig. 1 Impacts at different levels of increase in global mean temperature above pre-industrial levels: the global scale. The horizontal dotted line shows the impacts with the 1981–2010 climate, and the vertical dotted lines show 1.5, 2 and 4 °C above pre-industrial levels. The individual lines show the 23 climate model patterns Full size image

Table 2 Global-scale impacts at 1.5, 2 and 4oC above pre-industrial levels, and impacts with the 1981-2010 reference climate. The table shows the median (bold), minimum and maximum (italics) across the 23 climate model patterns Full size table

Fig. 2 Summary of the global-scale impacts across the indicators, at 1.5, 2 and 4 °C above pre-industrial levels. The horizontal coloured lines show the median impact, the dark shading shows the inter-quartile range and the light shading shows the 10th to 90th percentile range. The vertical lines show the range between lowest and highest impact Full size image

Fig. 3 The chance that impacts exceed specified thresholds at different levels of increase in global mean temperature above pre-industrial levels: the global scale. The thresholds are shown in each panel. The vertical dotted lines show 1.5, 2 and 4 °C above pre-industrial levels Full size image

Fig. 4 Impacts at 1.5, 2 and 4 °C above pre-industrial levels: the continental scale. The horizontal black lines show impacts with the 1981–2010 climate. The horizontal coloured lines show the median impact, the dark shading shows the inter-quartile range and the light shading shows the 10th to 90th percentile range. The vertical lines show the range between lowest and highest impact Full size image

At the global scale, almost all the impacts that could be either adverse or beneficial become worse as global mean temperature increases. Floods, droughts, heatwaves and hot spells all become more frequent, and crop growth duration reduces. The risk of lower growing season rainfall increases for maize, winter wheat and rice under all climate model patterns, but the picture is more mixed for soybean and spring wheat. The frequency of cold spells and accumulated heating degree days reduces. Increasing global mean temperature has a greater relative effect on the frequency of major heatwaves than smaller heatwaves, and the different crops are differently sensitive to hot spells as temperature rises.

The shape of the relationship between change in global mean temperature and impact varies between indicators, as was found in previous studies (Arnell et al. 2016b). For some of the indicators, the relationship is effectively linear (e.g. cooling and heating degree days and some of the agricultural drought indicators and crop hot spell indicators). Some relationships increase to a specific change in global mean temperature, and then the rate of increase declines. For the heatwave frequency indicator, this is because once the increase in global mean temperature reaches a certain value (approximately 3 °C) then at least one heatwave is likely each year. For the runoff change indicator, this is because the area which can be exposed to a reduction (or increase) in runoff is constrained by the spatial variability of change in precipitation. Once all the areas with an increase in precipitation sees a ‘significant’ increase in runoff, for example, the area can increase no more.

Most of the indicators show increases in impacts at small increases in temperature, in particular those characterising the frequency of heatwaves and hot spells (for most of the crops considered), and crop growth duration. The hot-humid day indicator shows little impact at the global scale until the temperature increase exceeds 3 °C.

For the indicators which are influenced by changes in precipitation, there is both a very large spread in the estimated impacts at a specific increase in temperature and a variety in the shape of the relationship between temperature increase and impact. The distribution of impacts at a given increase in temperature across the 23 model patterns is not necessarily unimodal. This may reflect sampling biases in the 23 models (which are of course not completely independent), or fundamental differences in the projected spatial patterns of climate change between climate models. The difference in projected impacts on agricultural drought between the SPI and SPEI indicators demonstrates the importance of changes in evaporative demands for future agricultural drought risk. In some regions (including much of Africa and Asia, Eastern Europe and Canada), SPI drought duration and likelihood are projected to reduce under some of the 23 patterns, but SPEI drought duration and likelihood increase everywhere under all patterns. The uncertainty range is also considerably smaller with the SPI drought indicator than with SPEI. This is because SPEI is effectively the difference between two uncertain values (precipitation and evaporation).

The global plots of the chance of impacts exceeding different thresholds (Fig. 3) illustrate the obvious point that the chance depends strongly on threshold. The gradients of the risk curves reflect the range between the 23 climate model patterns. The steepest curves occur where the range between the models is small, for example, with the heatwave frequency, heating/cooling and crop duration indicators. In a few cases for some thresholds, the chance of an impact decreases at first and then increases as global temperature increases further (e.g. the flood and SPI frequency indicators). This arises because some of the damage functions for these indicators show a reduction then an increase in impact, which typically occurs because increases in the magnitude of impacts in one place begin to exceed reductions in others (at the point scale, this shape may arise because of local non-linear relationships between force and response).

The regional plots (Fig. 4) show the regional variation in the magnitude of impact and the relationship between impacts at different levels of temperature increase. For most of the indicators, variability between regions is considerably greater at 4 °C than at 1.5 or 2 °C, suggesting increased regional variability in impact at higher levels of warming. Some of the indicators show very strong regional concentrations of impact. For example, the increase in hot-humid days is concentrated in Asia (and particularly South Asia) and parts of Africa, and hot spells damaging to spring wheat remain very rare in Europe and North America even with 4 °C of warming.

The global and regional plots show the ranges in impacts across the 23 model patterns, without distinguishing between the individual models. The relationships between impacts in different places and across sectors are therefore not apparent. In practice, this means that it cannot be assumed that the maximum impact at, say, 4 °C will occur simultaneously for all regions and indicators: the aggregate ‘worst case’ is not equal to the sum of the individual regional and sector worst cases.