Projected changes in climate extreme indices are assessed using an ensemble of 11 CMIP5-models for TXx and WSDI and 14 for RX5day and CDD and follows the methods outlined in Sect. . The model selection was done based on data availability. All available GCMs are assessed on a uniform grid with a 2.5∘ × 1.9∘ resolution. Multiple realizations of scenario runs for individual models are included when available, and in that case allow to estimate CDFs for natural variability that are derived based on pairwise realizations of model runs over the reference period (see SM Sect. 1.2 for further detail on the methodology applied).

We assess the changes in TXx and WSDI for a warming of 1.5 and 2 ∘C and derive changes of 20-year averages of extreme indices for the model-dependent warming-level time-slices at each land grid point relative to the 1986–2005 reference period. Changes in precipitation-related indices are described as relative changes while we consider absolute changes for the other indicators. For the CDF analysis for TXx, the absolute signal is normalized by the standard deviation over the reference period.

Uncertainty in model projections of precipitation extremes is considerably larger than that of temperature-related extremes. Figure  depicts the median projections for RX5day (Maximum accumulated 5-day precipitation, left panels) and CDD (Dry spell length, right panels), which exhibit contrasting patterns in terms of signal strength and robustness. The KS test illustrates the additional merit of a regional analysis of precipitation-related extremes (see Table S3). While all models in the ensemble indicate a robust difference between a 1.5 and 2 ∘C warming for both indices for the global land mass, the analysis for the separate world regions reveals different patterns.

A robust indication (more than 66 % of the models reject the null hypothesis of the KS test at the 95 % significance level, see Table S3) of a difference in RX5day is projected in particular for the high northern latitude regions, East Asia, as well as East and West Africa. While the high northern latitudes are also among those regions experiencing the largest increase in RX5day between the assessed warming levels (up to 7 and 11 %, median estimates for 1.5 ∘C and 2 ∘C, respectively), projections for other regions that experience a considerable increase under a 1.5 ∘C warming do not indicate a significant difference between the warming levels. This is in particular noteworthy for the Amazon region and North-East Brazil, where precipitation extremes are likely related to the South American monsoon systems and to a lesser extent for West Africa (see Fig.  and Table S3).

A different picture emerges for CDD as an indicator for dry spell length. For the majority of the global land area, little to no differences in CDD are projected relative to the reference period (see Fig. ). However, about 40 % of the global land area in the subtropical and tropical regions experience an increase in CDD length, including the Mediterranean, Central America, the Amazon as well as South Africa (compare Fig.  and Fig. ). In these regions, the KS test also reveals robust indications for differences in impacts between 1.5 and 2 ∘C. This difference is particularly pronounced for the Mediterranean region, where the median CDD length increases from 7 % (likely range 4 to 10 %) to 11 % (likely range 6 to 15 %) between 1.5 ∘C and 2 ∘C.

It is important to highlight that CDD is only an indicator for dry spell length and does not account for changes in evapotranspiration and soil-moisture related effects. It should hence not be interpreted as a direct indicator for agricultural or hydrological (streamflow) drought . Furthermore, CDD is a metric for short dry spells, which represent only a snapshot of the overall changes in dryness , while high-impact drought events like the Big Dry in Australia or the recent California drought stretch over months and potentially years . Nevertheless, CDD as well as RX5day can be seen as proxies for the precipitation-related component when assessing drought and flooding risks, respectively, and the results and impacted regions identified here are broadly consistent with projections based on more comprehensive indicators for droughts and flooding risk alike.

We assess future agricultural crop yields in a 1.5 and 2 ∘C warmer world for the four major staple crops – maize, wheat, rice and soy based on projections from the ISI-MIP Fast Track database . Projections for agricultural production depend on a complex interplay of a range of factors, including physical responses to soils, climate and chemical processes, or nutrient and water availability, but are also strongly determined by human development and management. The representation of these processes differs strongly between different agricultural models. While studies suggest an increase in productivity for some crops as a result of higher CO2 concentrations, large uncertainties remain with regard to temperature sensitivity, nutrient and water limitations, differences in regional responses and also the interactions between these different factors . According to their metabolic pathways of carbon fixation in photosynthesis, main crops can be categorized as C3 and C4 plants. C4 plants such as maize, sorghum and sugar cane have a high CO2 efficiency and as a consequence profit little from increased CO2 concentrations, whereas for C3 plants including wheat, rice and soy a positive CO2-fertilization effect is to be expected. At the same time, increased CO2 concentrations may lead to improved water use efficiency . However, the effect of elevated CO2 concentrations on plant growth is highly uncertain and the representation of this effect greatly differs between different agricultural models. As a consequence, the ISI-MIP protocol has been conducted with and without accounting for CO2-fertilization effects (further referred to as the CO2-ensemble and noCO2-ensemble, respectively). Recent findings also underline the importance of elevated temperatures and heat extremes , ozone concentrations as well as the potential of increasing susceptibility to disease as a consequence of elevated CO2 levels for agricultural yields, which may counteract potential yield gains by CO2-fertilization . Results for the CO2 and noCO2-ensembles are presented separately, showing the range of potential manifestations and the additional risks of regional yield reductions, if effects of CO2-fertilization turn out to be lower than estimated by the model ensemble.

The ISI-MIP ensemble contains simulations based on seven Global Gridded Crop Models (GGCM) for wheat, maize and soy and six GGCM for rice, run with input from five CMIP5 GCMs for further information see. For the CO2-ensemble, all model combinations are available (35, and 30 for rice), while for the noCO2-ensemble runs have been provided for 23 (18 for rice) GGCM-GCM combinations. We restrict future crop growing areas to present-day agricultural areas based on and assume no change in management type, meaning that “rainfed” and “irrigation” conditions are kept constant as well.

As in previous sections, the results presented here are based on 20-year time slices from the RCP8.5 simulations and changes are given relative to the 1986–2005 reference period. The choice of displaying relative changes comes with several advantages, but will also lead to a disproportional visual amplification of minor absolute changes for regions with small present-day yields, in particular in the high northern latitudes. An overview of the regionally resolved present-day share in global production is given in Fig. S5.

Since agricultural impacts depend both on climatological changes and changes in the atmospheric CO2 concentrations, the assumption of time-independent impacts underlying the time-slice approach as discussed above does not fully hold for agricultural projections accounting for the effects of CO2-fertilization (the CO2-ensemble) and will lead to increased inner-ensemble spread as a consequence. Please note that the regional aggregation for agricultural yields is not based on absolute yield change but on land area, as for the other indicators studied above. Since societal impacts of changes in agricultural production go beyond mere changes in yield, but also include for example local livelihood dependencies , our assessment of local yield changes (on a grid-cell level) supplements and extends previous yield-centered analysis . Maps for the projected differences of yield changes on a grid-cell basis are provided in the Supplement.

Our projections of local agricultural yields reveal substantial uncertainties in global median regional yield changes (Figs.  to ) with a likely range (66 % – likelihood) comprising zero. For wheat, rice and soy, our projections indicate differences between the CO2 and noCO2 assessments, which are generally much larger than those between a 1.5 ∘C and 2 ∘C warming. While substantial uncertainty renders a differentiation between impacts at 1.5 ∘C and 2 ∘C warming difficult in most world regions, a clear signal emerges for the noCO2-ensemble, that may serve as a high-risk illustration of potential climate impacts on agricultural production. In the noCO2-ensemble, local yields are projected to decrease between 1.5 ∘C and 2 ∘C for all crop types.

As discussed above, our crop-yield projections are subject to a range of uncertainties also related to extreme weather events. Uncertainties in both the bias-corrected climate model input as well as the impact model representation of such events limit the confidence in the projections of the effect of extreme weather events on crop yields. Observational evidence, however, indicates substantial impacts of specifically drought and extreme heat events on crop yields . Given the pronounced increase in extreme heat events under global warming in general and also specifically between 1.5 ∘C and 2 ∘C (compare Figs.  and , our estimates of the absolute change in local crop yields as well as the difference between 1.5 ∘C and 2 ∘C should be seen as a conservative estimate.

Our results indicate that risks are region and crop specific and are in line with findings of previous model intercomparison studies . While high-latitude regions may benefit, median projections for local yields in large parts of the tropical land area are found to be negatively affected already at 1.5 ∘C. Risks increase substantially, if effects of CO2-fertilization are less substantial or counter-acted by other factors such as extreme temperature response, land degradation or nitrogen limitation . In a statistical analysis of climate impacts on wheat and barley yields in Europe, report an overall negative contribution of climatic factors in line with findings of a meta-analysis by , which questions the positive effects projected in our CO2-ensemble for this region and further support our approach of singling out noCO2-ensemble projections. Given that a 1.5 ∘C warming might be reached already around 2030, our findings underscore the risks of global crop yield reductions due to climate impacts outlined by , while giving further indications for the regional diversity of climate impacts with tropical regions being a hot-spot for climate impacts on local agricultural yields .

Projections for sea-level rise (SLR) cannot be based on a time-slice approach because of the importance of the time-lagged response of the ocean and cryosphere to the warming signal. Therefore, we selected two multi-gas scenarios illustrative of a 1.5 ∘C and 2 ∘C warming to assess SLR impacts over the entire 21st century from a large emission scenario ensemble created by . These scenarios were created with the integrated assessment modelling framework MESSAGE the Model for Energy Supply Strategy Alternatives and their General Environmental Impact,. For both scenarios, temperature projections are derived with the reduced complexity carbon cycle and climate model MAGICC in a probabilistic setup , which has been calibrated to be in line with the uncertainty assessment of equilibrium climate sensitivity of the IPCC AR5 . Each probabilistic setup ensemble consists of 600 individual scenario runs. The first scenario keeps GMT to below 2 ∘C relative to pre-industrial levels (1850–1875) during the 21st century with 50 % probability. The second scenario reduces emissions sooner and deeper, and keeps warming to below 1.5 ∘C relative to pre-industrial levels during the 21st century with about 50 % probability and returns end-of-century warming to below 1.5 ∘C with about 70 % probability. See Fig.  (upper panel) for median temperature projections for the 2 and 1.5 ∘C scenario and their associated uncertainty bands. Since the projections for coral reef degradation include a time-dependent adaptation scenario, the same approach is taken for the coral reef projections (see Sect. ).

SLR projections are based on , who developed a scaling approach for the various SLR contributions according to an appropriately chosen climate predictor – in this case GMT increase and ocean heat uptake. Coupled with output from the MAGICC model, this allows us to emulate the sea-level response of GCMs to any kind of emission scenario within the calibration range of the method that is spanned by the RCPs.

Consistent with the relationship found in CMIP3 and CMIP5 GCMs, ocean thermal expansion is assumed to be proportional to cumulative ocean heat uptake . Mountain glacier melt is computed following a widely used semi-empirical relationship between rate of glacier melt, remaining surface glacier area, and temperature anomaly with respect to pre-industrial levels. This approach assumes constant scaling between area and volume , with parameters chosen to account for current melt rate and known glacier volume Eq. 1 and Table 2 in. As already noticed by (their Fig. 5), the surface mass balance (SMB) anomaly from the Greenland ice sheet can be approximated with reasonable accuracy as a quadratic fit to global mean temperature anomaly. Here we adopted the same functional form, but calibrated it to more recent projections by . Following , we scaled up these projections by 20 % ± 20 % to account for missing dynamic processes (elevation feedback 10 % ± 5 %, changes in ice dynamics 10 % ± 5 %, and ±10 % arising from the skill of the SMB model to simulate the current SMB rate over Greenland). The climate-independent land-water contribution has been added for all scenarios following .

Beyond the scaling approach, the main advancement of our approach compared to the IPCC AR5 stems from the inclusion of scenario-dependent Antarctic ice-sheet projections following . Linear response functions were derived from idealized step-forcing experiments from the SeaRISE project as a functional link between the rate of ice shelf melting and dynamical contribution to SLR over four Antarctic sectors and various ice-sheet models. further assume linear scaling between global surface air warming, local ocean warming, and ice-shelf melting in each of the sectors. They adopted a Monte Carlo approach with 50 000 samples to combine the various parameter ranges, GCMs and ice-sheet models. To our knowledge, this is the most comprehensive attempt to date to link climate warming and Antarctic ice-sheet contributions to scenario-dependent sea-level rise over the 21st century.

For an illustrative 2 ∘C scenario, we project a median SLR of about 50 cm (36–65 cm, likely range) by 2100 and a rate of rise of 5.6 (4–7) mm yr-1 over the 2081–2100 period. Under our illustrative 1.5 ∘C scenario, projected SLR in 2100 is about 20 % (or 10 cm) lower, compared to the 2 ∘C scenario (see Table ). The corresponding reduction in the expected rate of SLR over the 2081–2100 period is about 30 %. More importantly, and in contrast to the projections for the 2 ∘C scenario, the rate for the 1.5 ∘C scenario is projected to decline between mid-century and the 2081–2100 period by about 0.5 mm yr-1, which substantially reduces the multi-centennial SLR commitment .

The projected difference in SLR between the 1.5 ∘C and 2 ∘C scenarios studied here is comparable to the difference between the RCP2.6 and RCP4.5 scenarios , while the projected median GMT difference between the two RCP scenarios is about 0.8 ∘C for the 2081–2100 period. The relatively higher sensitivity of SLR in the 21st century to temperature increase at low climate warming is probably related to the earlier peaking of GMT under such scenarios and thus an already longer adjustment period for the time-lagged ocean and cryosphere. This leads to a larger share of committed multi-centennial SLR to occur in the 21st century. On multi-centennial timescales these scenario-dependent differences are expected to vanish. A long-term difference, however, may arise from contributions by mountain glacier melt, which are particularly vulnerable to GMT increase and thus differences in melted mountain glacier volume are higher for lower emission scenarios.

While SLR projections for the two illustrative 1.5 and 2 ∘C differ substantially, this effect is strongly scenario dependent. In particular, most emission pathways labelled as 1.5 ∘C scenarios allow for a temporal overshoot in GMT and a decline below 1.5 ∘C with a 50 % probability by 2100 , whereas the illustrative 1.5 ∘C scenario used here does not allow for a GMT overshoot, but stays below 1.5 ∘C over the course of the 21st century. For time-lagged climate impacts such as SLR that depend on the cumulative heat entry in the system, the difference between a scenario allowing for a GMT overshoot and one that does not will be significant.

Sea-level adjustment to climate warming has a timescale much larger than a century as a result of slow ice-sheet processes and ocean heat uptake. This means that in all emission scenarios considered, sea level will continue to rise beyond 2100. have shown that on a 2000-year timescale, sea-level sensitivity to global mean temperature increase is about 2.3 m per ∘C. In addition to that, report a steep increase in long-term SLR between 1.5 ∘C and 2 ∘C as a result of an increasing risk of crossing a destabilizing threshold for the Greenland ice-sheet . The disintegration process that would lead to 5–7 m global SLR, however, is projected to happen on the timescale of several millennia.

Recent observational and modelling evidence indicates that a marine ice sheet instability in the West Antarctic may have already been triggered, which could lead to an additional SLR commitment of about 1 m on a multi-centennial timescale. Spill-over effects of this destabilization on other drainage basins and their relation to GMT increase are as yet little understood , and there are indications that a destabilization of the full West Antarctic ice-sheet could eventually be triggered . Similarly, report a potential marine ice-sheet instability for the Wilkens Basin in West Antarctica containing 3–4 m of global SLR. The dynamics of these coupled cryosphere-oceanic systems remain a topic of intense research. Current fine-scale ocean models, suggest increased intrusion of warm deep water on the continental shelf as a result of anthropogenic climate change and thus indicate an increasing risk with increasing warming . Given the risk of potentially triggering multi-metre SLR on centennial to millennial timescales, this clearly calls for a precautionary approach that is further underscored by evidence from paleo-records, which reveals that past sea-levels might have about 6–9 m above present day for levels for a GMT increase not exceeding 2 ∘C above pre-industrial levels .

The projections of the degradation of coral reef sites uses the coral bleaching model developed in based on the two illustrative 1.5 ∘C and 2 ∘C global emission pathways introduced in Sect. . The framework applies a threshold-based bleaching algorithm by , which is based on degree heating months (DHMs), to sea surface temperature (SST) pathways of 2160 individual geospatial locations of coral reef sites (see http://www.reefbase.org) and generates as output the fraction of coral reef locations subject to long-term degradation. DHMs are a measure for the accumulated heat stress exerted on coral reefs due to elevated SST (see Fig. S6 for a graphical illustration of the methodology). Within a 4-month moving window the monthly SST above a reference value (here the mean of monthly maximal temperatures, MMM) are accumulated and compared to a threshold value (critical DHM threshold) that is associated with mass coral bleaching. The value of the critical DHM threshold depends on the scenario assumptions (see below). In order to translate coral bleaching events into long-term coral degradation, we refer to the assumption that reef recovery from mass coral bleaching is usually very limited within the first 5 years . Therefore, we assume a maximum tolerable probabilistic frequency of 0.2 yr-1 for bleaching events causing long-term degradation. The MMM is calculated from a 20-year climatological reference period (1980–2000) individually for every coral location and SST pathway. Thus, the MMM serves as an indicator of temperatures to which the corals of a certain reef location are generally adapted. In order to generate a scenario-independent description of coral reef response to different levels of global warming (e.g. any given global mean air temperature pathway) we apply the algorithm to a large number of SST pathways and reassign the fraction of 2160 mapped coral reef locations subject to long-term degradation back to global air temperature pathways. In total, we use the SST pathways of 19 Atmosphere-Ocean General Circulation Models (AOGCMs) from the multi-model CMIP3 project and seven different emission scenarios leading to 30 728 model years. We also used a wide range of critical DHMs (from 0 to 8∘), which allows for the testing of risk scenarios with constant and variable critical DHM thresholds (e.g. thermal adaptation).

The condensed output of the global coral bleaching assessment allows for the implementation of different coral adaptation scenarios. In the standard scenario (Constant) a constant DHM threshold of 2 ∘C is assumed. This means that corals can resist a cumulative heat stress of 2 ∘C (accumulated over a 4-month period) above the long-term maximum monthly mean (MMM) sea surface temperature for a given location. It has been demonstrated that this value serves as a good proxy for severe mass coral bleaching .

In addition to the constant scenario, an extremely optimistic scenario of strong thermal adaptation of the corals is assessed (Adaptation). Under this scenario, the critical DHM threshold constantly increases from 2 ∘C in the year 2000 up to 6 ∘C in 2100. The assumption of a thermal adaptation of 0.4∘ per decade appears very ambitious given the long creation times of reef-building corals and the consequently slow rate at which evolutionary adaptation occurs. Furthermore, additional environmental stressors such as ocean acidification and disease spreading have to be expected to slow-down coral growth and to reduce the adaptive capacity of tropical coral reefs. As a consequence, this scenario should be seen as an absolute lower boundary for degradation of coral reefs globally.

Finally, a third scenario takes the negative effect of the acidification of the oceans into account which reduces the calcification rates of the corals and thus promotes further degradation of coral reefs (Saturation). We derived a transfer function based on atmospheric CO2 concentrations due to the fact that tropical surface aragonite saturation levels are in equilibrium with atmospheric CO2 concentrations on a timescale of years to decades . With an assumption of the effect of the aragonite saturation on the critical DHM threshold (see supporting material of ) this translates into a measurable increased stress to corals.

Coral reef systems are slow-growing, complex ecosystems that are particularly susceptible to the impacts of increased CO2 concentrations, both through warming (and resulting coral bleaching) and ocean acidification . Our analysis reiterates earlier findings that the risk of coral reefs to suffer from long-term degradation eventually leading to an ecosystem regime shift will be substantial as early as 2030 . We find that this risk increases dramatically until the 2050s, where even under a 1.5 ∘C scenario, 90 % and more of all global reef grid cells will be at risk of long-term degradation under all but the most optimistic scenario assessed (the Adaptation case, see Sect. ). However, long-term risks towards the end of the century are reduced to about 70 % of global coral reef cells under a 1.5 ∘C scenario but not under a 2 ∘C scenario (compare Fig.  and Table ).

Our approach only includes the effects of increased CO2-concentrations, but does not account for other stressors for coral reef systems such as rising sea-levels, increased intensity of ENSO-events , tropical cyclones , invasive species and disease spreading , and other local anthropogenic stressors, which ranks our projections of long-term coral reef degradation rather conservative. These projected losses will greatly affect societies, which depend on coral reefs as a primary source of ecosystem services, e.g. in the fishery and tourism sector . estimate that about 25 % of the world's small-scale fishers fish on coral reefs. report that a loss of less than 60 % of global coral reef coverage, that could very well be reached already in the 2030s, would inflict damages of more than USD 20 billion annually.