In 2005, croplands covered an area of roughly 14 × 106 km2 (see Fig. S1 in the Supplement) . This corresponds to about 9 % of the global land surface and to 23 % of the potentially cultivable land (Fig. S1) . Our results show that for some arid regions, especially in Northern Africa, the Middle East and South and Central Asia, it may be impossible to maintain the current cropland area (see below). However, on the global scale, these potential losses can be more than compensated for by an expansion of croplands, especially in sub-Saharan Africa, South America and in higher northern latitudes. In the simulations, the cropland area can be tripled to roughly 38–42 × 106 km2, and almost three-quarters of all cultivable land can be farmed by the beginning of the next century (Fig. a, Table ). This expansion would require converting areas into croplands regardless of their present function in the Earth system, including those whose cultivation is highly debatable with respect to biodiversity and terrestrial carbon stores, e.g., the Amazon rainforest. There is no consensus on the extent of protected areas required to maintain the planet's ecological stability and consequently also no consensus on the area that, from an ecosystem perspective, could be transformed into croplands. Merely omitting areas presently placed under protection and those covered by tropical forests from the analysis already reduces the cultivated area in 2100 by roughly 15 % (Sect.  and Fig. S2). However, it is most likely that ensuring Earth's habitability will require the protection of a much larger fraction of the land surface (Sect. ).

The extent of present-day cropland is not in equilibrium with the constraints resulting from today's climate. Wide areas could be cultivated without requiring any changes in the conditions, i.e., temperatures and precipitation rates are already in a favorable range at the beginning of the century, and the largest potential for expansion is given in latitudinal zones in which crops are already being grown (Fig. a; right panel). At the same time, irrigation in dry regions relies partly on nonrenewable sources and the irrigable area is reduced substantially when the water withdrawals are limited to the fraction of renewable fresh water that exceeds environmental requirements (Fig. S4). The reduction in irrigation also affects the adjacent rainfed agriculture as the resulting decline in evapotranspiration leads to a reduced moisture recycling, thereby lowering precipitation rates. During roughly the first 25 years of the simulation, the net change in cropland area is less determined by changes in the climate and mostly an adjustment to the limits given by the simulations' initial conditions. Here, the area that can be cultivated without requiring any change in the conditions is far larger than the area that has to be abandoned as irrigation is limited to sustainable amounts. Consequently, there is a strong increase in cropland area to about 35 × 106 km2 (30 × 106 km2 when excluding protected areas). After 2025, the global cropland area increases at a much slower rate as their expansion and decline is now dependant upon changes in GHG concentrations and climatic conditions.

All simulations exhibit a temperature increase ranging between roughly 1 K for RCP2.6 (IR26) and 5.5 K for RCP8.5 (IR85; Fig. c). There are two opposing effects related to rising temperatures. On the one hand they can lead to increased productivity in energy-limited regions, prolonging growing seasons in the (higher) middle and high latitudes, which is especially important for the Northern Hemisphere where farming becomes possible even north of 60∘ N. On the other hand, increasing temperatures raise the crops' water requirements, leading to an increased water stress and reduced productivity in water-limited regions. Hence, the overall effect of increasing temperatures is also determined by the change in water availability (Fig. ) and thus by the change in precipitation.

The scenarios that exhibit a strong temperature rise also show a substantial increase in precipitation over land (Fig. d). For RCP4.5 (IR45) mean precipitation rates increase by up to 20 mmyr-1 and in IR85 they increase by about 60 mmyr-1, which amounts to more than 8 % of the terrestrial precipitation (as of 2005). Increased precipitation rates not only reduce the water stress for rainfed crops, but between 2025 and 2100 they also increase the water available for irrigation: globally by roughly 500 km3yr-1 for IR45 and by almost 2000 km3yr-1 for IR85 (Fig. e). As a consequence, the increased water demand of irrigated and rainfed crops resulting from higher temperatures can be met to the extent that, after 2025, there are only very few areas in the world in which farming becomes unsustainable. This, however, is only the case when fully accounting for the potential benefits due to the CO2 fertilization effect (CFE; see below). For the simulations with only a small increase in GHG concentrations (IR26) there is no permanent increase in precipitation; i.e., after a peak in the 2040s the rates decline to their initial levels, while the average temperature at the land surface increases by ≈ 1 K. Here, the plants' increasing water requirements cannot be met everywhere and in some dry regions in South and Central Asia, the Sahel zone and Australia, farming becomes unsustainable after 2025 and cropland areas have to be abandoned.

The results show that future climate is substantially impacted by the maximization of irrigation within sustainable limits. The precipitation rates in the RCP4.5 simulations with (IR45) and without (RF45) irrigation differ on average by roughly 15–30 mmyr-1, and in RF45 precipitation is persistently below present-day rates. This is a strong indication that a substantial part of the precipitation rise in the irrigation simulations is attributable to irrigation–precipitation feedbacks (Fig. d). Furthermore, for the RCP4.5 scenario, irrigation reduces the simulated 21st century temperature increase by almost 20 % (≈ 0.5 K averaged over the global land surface; Fig. c), and in irrigated regions the effect can amount to several K. Here, the irrigation-induced surface cooling can also have negative consequences, as it may affect regional circulations and reduce the poleward heat transport, shortening the growing season in high northern latitudes (Figs. S5–S7).

As an aggregate effect of changing conditions, the area in which farming becomes possible after 2025, i.e., mainly due to increasing temperatures in high latitudes, exceeds the cultivated area, which has to be abandoned due to increasing water stress in dry regions. Consequently, the global cropland area increases by an additional 4–7 × 106 km2, with the expansion for RCP8.5 being almost twice as large as for RCP2.6. Here, the simulated expansion of croplands not only depends on the changes in climate discussed above, but also on the CFE, i.e., the effect that plants increase their rate of photosynthesis with increasing CO2 levels. This effect is especially relevant for the cultivation of areas in the high northern latitudes where it allows for farming even in regions where growing seasons are still short. Additionally, the CFE effectively reduces the plants' water requirements, as it shortens the time that they are required to open their stomata for the uptake of carbon. As this may severely reduce the crops' water requirements, it also affects the sustainability of croplands in arid and semiarid regions. Studies have identified a greening in recent years that is in large part related to the CFE ; however, it is very uncertain which role it may play for future crop yields, and it is even possible that the benefits will be balanced completely by other factors such as nitrogen limitations .

In simulations with the MPI-ESM, the CFE is very pronounced, and to investigate the limits of food production without this highly uncertain effect, we performed an additional set of simulations (IR26∗, IR45∗, RF45∗ and IR85∗) that are identical to IR26, IR45, RF45 and IR85 but with the plant-available CO2 limited to the level of the year 2005, i.e., 380.00 ppmv. Prescribing the CO2 concentration in this manner affects croplands, especially for the RCP8.5 scenario. After 2050, the decrease in cultivated area in increasingly dry regions in middle and low latitudes almost completely balances the expansion in high latitudes and there is almost no increase in the global cropland area (Fig. S2). For the other scenarios, omitting the CFE has a similar effect, although much weaker. As a result, the total cropland area is very similar for the three scenarios, and they differ only in the spatial distribution of croplands. In simulations with higher CO2 concentrations the cultivated area in high northern latitudes is larger, while for the low GHG scenarios the area in arid middle and low latitudes is predominantly larger (Fig. S3).

Changes in climate and rising CO2 levels not only affect the potential extent of croplands, but also the productivity in existing cultivated areas. Thus, the global aggregate productivity of croplands is much more sensitive to increasing GHG concentrations and the changes in potential yield are not proportional to the increase in cultivated area. When fully accounting for the CFE and utilizing all land resources, production can be increased by a factor ranging between 3.5 and 5. When excluding protected areas, this factor still ranges between 2.8 and 4 (Fig. a and b). The largest yields are simulated for the high concentration scenario, and by 2100 yields are more than 40 % larger for RCP8.5 than for RCP2.6, while the cultivated area is only about 8 % larger. Furthermore, global crop production depends strongly on irrigation. Global yields are 16 % larger in the simulations with than without irrigation, while the cultivated area is only about 3 % larger.

To estimate how the changes in productivity relate to future food security, the simulated crop yields can be used to obtain a rough estimate of the supportable population sizes (Khum; Sect. ). When assuming the full benefit of the CFE, the largest Khum is given for RCP8.5. In the respective simulations, the global food supply can roughly be quadrupled during the 21st century, which places the respective Khum at about 27 bn people (22 bn when excluding protected areas). The lower GHG concentrations in the RCP2.6 simulation decrease Khum by almost 8 bn compared to RCP8.5, a number larger than the planet's current population. Here, the results seem to suggest that the high concentration trajectory is favorable with respect to food production; however, this is only the case if the CFE is as efficient as simulated by the MPI-ESM. When assuming no benefits due to increasing levels of CO2, the maximum crop yield is much smaller for all scenarios and the global food production can only be increased by a factor of about 2.5 (Fig. c and d). Furthermore, the maximum crop yield is reached when the extent of croplands has adjusted to present-day conditions and none of the simulations shows an increase after 2030. The effect from omitting the CFE is strongest for the high concentration scenario and the respective Khum is reduced by about 12 bn (compared to the RCP8.5 simulation including the CFE). Most importantly, after 2030, the RCP8.5 scenario exhibits a decline in yields and towards the end of the simulation it produces the smallest Khum of any of the simulations that account for irrigation. Here, the simulations provide strong evidence that, even with an optimized irrigation practice and the resulting irrigation–precipitation feedbacks, future increases in precipitation will not meet the additional water requirements due to increasing temperatures. Thus, the simulated changes in climate may not lead to a loss in the total cropland area but they are detrimental to global yields. Given the high level of uncertainty connected to the CFE, the range of climatic conditions that are favorable for food production is likely limited to the conditions resulting from the RCP4.5 scenario.

The RCPs are consistent with distinct socioeconomic pathways that differ strongly with respect to future energy demand and the mix of energy carriers. Included are assumptions about resource availability and climate policies, which determine the contribution of fossil fuels to the energy mix, as well as assumptions about the population development, which strongly affects future energy demands. Additionally, the scenarios take into account different land-cover and land-use change projections that reflect future food and energy demands as well as policies with respect to reforestation . RCP2.6 and RCP4.5 present intermediate scenarios with ambitious emission reductions, which in the case of RCP2.6 even include a decline in the use of oil. For RCP2.6 and RCP4.5 the population development corresponds to UN projections assuming low to medium fertility and life expectancy in the future . In contrast, RCP8.5 presents a highly energy-intensive scenario without the implementation of any climate policies. The high energy demand in this scenario partly results from strong population growth, which corresponds to a medium to high population trajectory in the UN development scenarios. In order to estimate the level of food security for a given combination of RCP and population development scenarios, the simulated Khum can be compared to the population levels proposed by the UN scenarios. Here, the simulations indicate that the ability to sustain future populations depends heavily on the strength of the CFE. When assuming the full benefits, only the population of the high-fertility (and life-expectancy) scenario may become unsustainable, i.e., the respective population trend surpasses Khum as simulated for RCP2.6 and RCP4.5, and only if protected areas are maintained (Fig. a and b). However, without the CFE the food requirements resulting from the high-fertility scenario cannot be met by any simulated supply, even if protected areas are converted into croplands (Fig. c an d). Also the population of the medium-fertility scenario is very close to Khum, indicating that we may need to cultivate almost all non-protected areas and to have a near-perfect system for irrigation in order to meet the future food requirements of this scenario. Here, our findings contradict the RCP's underlying scenarios. These assume that the population increase in RCP8.5 could be sustained without increasing the cropland area beyond 20 × 106 km2, while the population increase in RCP4.5 could even be met with a substantial decline in the cultivated area .

Irrigation-based agriculture constitutes about 70 % of humanity's fresh water demand, while municipal, industrial and other agricultural demands constitute about 30 % . Here, irrigation and nonirrigation water withdrawals differ in one important aspect. While irrigation is mostly a consumptive water use, i.e., water is transpired by plants or evaporated from bare soil areas, the largest fraction of the water used by other sectors is returned to the river after its use . Thus, when assuming that all wastewater is treated to the extent that it can be reused, nonirrigation requirements only have a minor effect on the overall volume of utilizable water and the water management scheme represents them only indirectly (see below).

In the present version of the MPI-ESM, lakes do not exist on the subgrid scale, and for the standard resolution of T63 only a few very large lakes are accounted for in the model. Additionally, aquifers are not explicitly represented, and subsurface flows, together with the surface runoff, constitute the lateral inflow into the river network. Hence, all precipitation that reaches the terrestrial surface and is neither stored in the soil's pore space nor given back to the atmosphere is eventually routed towards the oceans via the streamflow. This makes modeling the water withdrawals in JSBACH straightforward, as all accessible fresh water is combined within the discharge of rivers.

In all simulations, the MPI-ESM was run using a temporal resolution of 450 s, a vertical resolution of 47 tmospheric model levels, 40 vertical levels in the ocean and 5 vertical soil layers in all terrestrial grid boxes. The horizontal resolution was T63 (1.9∘ × 1.9∘), which corresponds to a grid spacing of about 200 km in tropical latitudes. On the land surface, spatial subgrid-scale heterogeneity was represented by 15 tiles, which were aggregated using a simple flux-aggregation scheme . Besides the 11 tiles that represent natural vegetation, pasture and bare soil areas, rainfed C3 crops, rainfed C4 crops, irrigated C3 crops and irrigated C4 crops are each represented by an individual tile. The model's dynamical vegetation scheme was active in all the simulations, and in the noncultivated part of the grid box, the cover fractions representing natural vegetation were calculated based on the plants' productivity and their natural and disturbance-driven mortality .

In total 14 simulations were performed covering the period 1995–2114. These correspond to five sets of two simulations in which the two simulations that constitute a set differ only due to slight alterations in the initial conditions. The two simulations were compared to evaluate the simulated impacts against the model's internal variability. In the analysis we always show the mean of the two simulations and for simplicity refer to this mean as one simulation. We simulated three sets, i.e., IR26, IR45 and IR85, in which the crop and water management schemes are both active and that differ only due to the prescribed GHG concentrations, i.e., RCP2.6, RCP4.5 and RCP8.5. To be able to quantify the impact of irrigation, we performed one set of simulations that were forced according to RCP4.5 in which only the crop management scheme was active but with the irrigation scheme disabled, i.e., RF45. To quantify impacts due to climate change without CO2 fertilization, we conducted four additional simulations (IR26∗, IR45∗, IR85∗ and RF45∗) that were identical to IR26, IR45, IR85 and RF45, but with the plant-available CO2 limited to 380.0 ppmv. Comparing the above simulations to the present-day conditions of a reference set (REF) allows us to estimate the potential change in cultivated area, food supply and climate for the respective scenarios.

In these reference simulations, the distribution of irrigated and nonirrigated crops was prescribed based on their present-day extent (Fig. S1) . Note that the respective data correspond to the year 2005 and all comparisons to “present-day” or “current” conditions are made with respect to this year and not 2017. Furthermore, it was assumed that the water supply is not limited to the fraction of the streamflow that exceeds environmental flow requirements. Whenever the irrigation demands surpass the available water in these simulations, the deficit is provided by adding water to the system. This approach does not conserve the water balance, but it is consistent with the assumption that at present irrigation requirements are partly satisfied from non-sustainable sources that are not represented in the model.