## Main

The 2015 Paris Agreement on Climate Change introduced ambitious global commitments to mitigate climate change and limit the global temperature increase to 1.5–2.0 °C above pre-industrial levels. The recent scientific literature suggests that achieving these targets will require immediate and rapid emissions reductions1, with promising emerging pathways that combine high carbon prices in the near term2 with the deployment of net negative emission technologies in the second half of the century3. Integrated assessment models are widely used to evaluate the efficacy and impact of these measures across a range of possible future scenarios4,5,6 that attempt to capture the complex interactions of energy, land-use, economic, water and climate systems. These studies generally develop global6 or regional analyses7 relying on economic abstractions of global welfare preferences, with less attention paid to the quantification of local-scale impacts of abatement options for diverse groups of stakeholders with potentially conflicting needs or preferences8.

This paper addresses this gap by investigating how multisector dynamics across interconnected water–energy–food (WEF) systems at the local scale are impacted by global climate change mitigation policies. Our analysis uses a river basin-scale model of the Zambezi Watercourse (ZW) in southern Africa that enables exploration of synergies, trade-offs and vulnerabilities for the WEF systems, including hydropower production, irrigation supply and ecosystem services in one of the largest transboundary river basins in Africa as well as in the world. The rapid economic development of the region is increasing both energy and water demands, triggering major investments in hydropower development and the expansion of irrigated agriculture. These trends make the ZW an emblematic example of most river basins in developing countries that now must find a balance among social, economic and environmental interests to promote development pathways that are inclusive as well as environmentally and economically sustainable9.

While previous studies10,11,12,13 have investigated primarily the local impacts of climate change and regional development plans, here we expand the scope of the analysis to explore the interactions of climate change with global socioeconomic teleconnections by considering a large ensemble of global scenarios simulated by the Global Change Analysis Model (GCAM14), a model widely used in major integrated climate–energy–economic assessments15,16,17. To explore the uncertainty space, we adopt an exploratory modelling approach to systematically sample the shared socioeconomic pathways (SSPs18) components along with multiple shared policy assumptions (SPAs19) that set a mitigation policy context, including regional participation in mitigation efforts and the pricing of carbon emissions20, resulting in 33,750 scenarios21 (Methods). Specifically, those scenarios include detailed, regionally specific and globally contextualized descriptions of population and economic growth, technological change and climate change mitigation policy fragmentation drawn from the SSP/SPA implementation in GCAM17. The resulting scenario database contains tens of thousands of self-consistent, multisector, multiscale, time-evolving scenarios of hundreds of climate, economic, demographic and land-use variables. We spatially and temporally downscale the GCAM outputs22 to generate projections of local irrigation demands at the basin scale23. We also bias adjust climate projections from different combinations of global and regional climate models for different representative concentration pathways (RCPs24) to force local hydrological models and produce projections of water availability. To ensure the consistency of the projected scenarios, we focus our analysis on an ensemble of scenarios that couple a projection of water availability driven by one RCP with a sub-set of projected irrigation demands based on the end-of-century radiative forcing as simulated by GCAM (Methods). We first explore the synergies and trade-offs across the WEF systems by analysing a set of alternative adaptive operating policies for managing major reservoirs and irrigation diversions in the basin under observed climate and irrigation demands, showing that hydropower generation and irrigation supply are not strongly in conflict today. However, our projections suggest the ZW will be exposed to severe risks of performance degradation across all the components of the WEF systems. Our results demonstrate these future vulnerabilities are generated mostly by global socioeconomic drivers, namely, the alternative land-use change (LUC) policies, rather than predicted changes in water availability due to climate change. Analogous vulnerabilities are found across most basins in southern and western Africa, raising concerns about the equity of these global climate change mitigation policies for African countries.

## The WEF nexus in river basins under development

Africa has more than 60 international river basins that are a primary factor in the location and production patterns of human settlements as well as in the structure and productivity of African economies25. At the same time, African rivers, lakes and wetlands are a major biodiversity reserve providing a large variety of ecosystem services, ranging from fishing and flood-recession agriculture to habitats for wildlife, migratory birds and endemic species of global conservation concern26. In many countries, however, the accelerated population growth and the fast economic development are motivating large-scale infrastructure investments to meet increasing water, energy and food demands27,28,29. These projects may constitute a major threat to natural ecosystems and local subsistence needs30. In these evolving contexts, a major challenge to policy makers is navigating the trade-offs of alternative development pathways between competing multisector dynamics, across different spatial scales and over different time horizons, including a broad array of potential climate, socio-techno-economic and policy futures31.

The ZW is a typical example of river basins under development. From the headwaters in northwest Zambia, the river flows eastward for 2,750 km, also receiving water from the Kafue, Luangwa and Shire rivers, draining a catchment area of 1.39 million km2 shared by eight countries: Angola, Botswana, Malawi, Mozambique, Namibia, Tanzania, Zambia and Zimbabwe (Fig. 1). The basin provides services to a population of 40 million people, which is expected to grow rapidly up to 70 million by 205032. The high runoff in the upper part of the basin combined with a change in elevation of more than 1,000 m along the river’s course to the ocean provides large potential for hydropower energy production. The current installed capacity is about 5.5 GW, with an additional 8.4 GW planned by the end of 202333. Around 70% of this installed capacity is concentrated in two mega-dams: Kariba (1,830 MW) and Cahora Bassa (2,075 MW). Existing irrigated areas cover about 182,000 ha, with an annual water demand exceeding 6,300 Mm3 yr–1 (the average monthly demand is 525.6 Mm3 month–1, with a peak close to 1,051 Mm3 month–1), and the planned expansion will add other 336,000 ha (ref. 27). Major cultivated crops are sugar cane (23%), rice (17%), wheat (15%) and maize (14%)11. The ZW also provides numerous ecosystem services, which are being endangered by the development of hydropower and irrigated agriculture. These services include 82 key biodiversity areas34, numerous fisheries that represent the main source of proteins for the local rural communities and tourism primarily to Victoria Falls and other national parks that generate around US$10 million yr–1 (ref. 27). Moreover, the basin comprises several wetlands of international importance, including an extensive alluvial plain in the Zambezi delta covering approximately 1.2 million ha (ref. 26), where observed flows during the flooding season have been strongly reduced after the completion of Cahora Bassa relative to the pre-dam conditions35. This trend is expected to further worsen because of the planned dam construction and irrigated agriculture expansions. ## Future vulnerabilities across the WEF systems Given the ZW model and the local objectives for the WEF systems defined in collaboration with local stakeholders (Methods and Supplementary Sections 1 and 2), we first perform a multisectoral analysis on a set of 121 alternative operating policies for managing existing reservoirs and irrigation diversions that capture the optimal trade-offs (Pareto efficient36) across their competing multisectoral demands over historically observed conditions. Each Pareto-optimal control solution represents a different balance of compromises across the WEF objectives (Supplementary Fig. 1). The maximization of hydropower production negatively impacts environmental conditions in the delta (Supplementary Fig. 2). The trade-off between energy and irrigation supply is in turn weak and allows moving from a maximum deficit of 88.5 m3 s–1 to one of 21.7 m3 s–1 by accepting a 0.80 TWh yr–1 reduction in hydropower production, which means a 75% improvement at the cost of a 3% reduction in hydropower. Similar to previous results37, our analysis suggests that the system’s historical operations emphasize the maximization of hydropower production, under which existing irrigation demands are mostly satisfied. Yet a key question is whether multisector resource conflicts may become more severe in future scenarios that have climate-induced decreases in water availability, population-driven increases in irrigation demand, an intensification of agricultural activities in the region or a combination of the three. To investigate the future vulnerabilities of the modelled historical operations of the ZW system (Supplementary Fig. 1) to these potential conflicts, we sample six socioeconomic uncertainties as represented in the SSPs and simulated using GCAM (Methods). Those socioeconomic scenarios were paired with three climate projections corresponding to downscaled and bias-adjusted RCP 2.6, RCP 4.5 and RCP 8.5 scenarios. To ensure consistency between the socioeconomic and climate scenarios, the coupling was performed on the basis of the 2100 radiative forcing projected within GCAM (Supplementary Fig. 3). This coupling resulted in an ensemble of 7,317 interdependent scenarios (see Methods for details). For each RCP, the differences in the underlying irrigation demands introduce large variability in system performance. Reduction in hydropower production (Fig. 2a) appears driven mostly by the projected decreases in water availability. Similar to previous research11,13, the median estimated production decreases under RCP 2.6 and RCP 4.5 lie in the range of 15–25% relative to the historical production (20.16 TWh yr–1) while registering a 40% decrease under RCP 8.5. Similar patterns emerge with respect to the different climate models’ chains: the highest levels of hydropower production attained in each RCP are obtained using the projections characterized by the highest precipitation (Supplementary Fig. 5) that produce the highest streamflows (Supplementary Fig. 6). The temperature projections are instead consistent across the climate model chains (Supplementary Fig. 4). The median simulated value of irrigation deficit (Fig. 2b) is also largely dependent on the climate scenarios, with substantially higher deficits under RCP 8.5 (more than seven times higher than the historical value) than under the other two climate scenarios. However, both the worst first percentile of hydropower production and the worst tenth percentile of irrigation deficit are registered under RCP 4.5. Last, the projected performance in terms of environmental deficit (Fig. 2c) shows an overall worsening of about 22% with respect to the performance under historical conditions across all scenarios, with the simulated values of flow deficits that correspond to about one-third of the flow target in the Zambezi delta. Interestingly, the median values of environmental deficit for the different RCPs are not ordered according to the predicted annual flow entering the river basin. The best performance is indeed obtained under RCP 2.6, but the worst performance is obtained under RCP 4.5 rather than under RCP 8.5, which is the climate scenario with the lowest projected natural water availability. ## Discovering the global drivers of local vulnerabilities The unexpected vulnerabilities under RCP 4.5 (Fig. 2) suggest that the socioeconomic scenarios and mitigation regimes associated with this climate projection play a major role in determining the future system dynamics. To infer the key controls of such dynamics, the scatterplot in Fig. 3a explores the growth of crop water consumption in southern Africa simulated by GCAM across a wide ensemble of socioeconomic scenarios, with colours distinguishing alternative policies of LUC emissions prices (see Supplementary Fig. 7 for disaggregated irrigation water growth). As implemented by refs. 17,21, the LUC emissions price is represented as a fraction of the underlying carbon price. We tested two LUC price regimes: a regionally differentiated and a globally uniform LUC price (roughly consistent with SPAs 4 and 2, respectively). In the regionally differentiated case, wealthy countries make strong attempts to curb LUC emissions, as represented by a high LUC emissions price, while developing countries have limited LUC policies, represented by a lower LUC emissions price (Supplementary Fig. 13). As a baseline, we also consider a case with no emissions price of any kind implemented. Our results show that emissions prices are effective at impacting the level of GHG emissions and the resulting end-of-century radiative forcing and that the nature of the LUC prices produces three clusters of regional crop water consumptions. Scenarios with no emissions price of any kind result in values of radiative forcing in the range 6–10 W m–2 that are associated with the RCP 8.5 scenario (red distributions in Fig. 2), with an average projected crop water consumption increase of about 300%. The application of a price on emissions successfully contains the radiative forcing below 7 W m–2 with many of these scenarios that are hence compatible with the RCP 4.5 climate projections (green distributions in Fig. 2). The scenarios with the lowest 2100 forcing are instead associated with the RCP 2.6 scenario (blue distributions in Fig. 2). While the scenarios emissions prices successfully limit the overall end-of-century radiative forcing, we found the nature of the LUC price regime can have a substantial impact on regional LUCs. In GCAM, land-use and cropping decisions are made on an economic basis (Supplementary Section 3). Regions that have some advantage for a particular use (due to climate, technology and so on) will attract more of that use. When an LUC emissions price is in place, the carbon intensity of any LUC factors into the economic decision of where different crops are grown. A fragmented LUC emissions price makes non-participating regions, such as southern Africa in our study, more favourable to agricultural expansion, and this dynamic explains the notable influence the type of LUC emissions price has on southern African agricultural water use. As described in Supplementary Section 3, the exact magnitude of this effect depends on dozens of other factors, but it is a robust phenomenon observed across the ensemble. All else held equal, fragmented LUC policies tend to concentrate new development where LUC is not priced as high, and this effect leads to between 50 and 300 Mt of additional crop production in southern Africa (Supplementary Fig. 20). The exact composition of this additional production depends heavily on scenario factors and varies widely across the ensemble, but in general, the large increases occur in corn, root tuber, sugar crop (for food) and miscellaneous crops (nuts and fruits). One interpretation is that the LUC price fragmentation produces favourable conditions for land grabbing practices38, with wealthy countries investing in the realization of extensive agricultural projects (for example, large-scale, intensive irrigation projects similar to the existing Mazabuka district). Under this fragmented scenario, crop water consumption in southern Africa (where the LUC emissions price is low) increases up to 700% due to extensive agricultural LUC, from the conversion of grass and shrublands, pasture and other arable lands to new crop production. Conversely, the same scenarios under the globally uniform LUC price, representing a unified approach to LUC pricing, experience increases that do not exceed 300%, with virtually the same radiative forcing. The scatterplot in Fig. 3b confirms the key role of LUC emission policies by showing that the globally uniform LUC price produces a similar increase in crop water consumption between the southern Africa region and the rest of the world. The regionally differentiated LUC price, instead, introduces diverse responses with an increase in the southern Africa region that is much larger than the global one. These scenarios explain the divergent distributions of the irrigation deficit under RCP 2.6 and RCP 4.5 (Fig. 2b), which have similar conditions in terms of projected natural water availability. Moreover, high demands imply large water abstractions to serve the irrigation districts along the Zambezi River that reduce the water flowing into the delta. This practice negatively impacts the ecosystem services provided by the Zambezi River delta (Fig. 2c), showing how the impact of future socioeconomic conditions may offset the one of the projected climate conditions. ## Discussion and conclusions Our study indicates that global climate change mitigation policies can have side effects on local water demands. Containing GHG emissions and the resulting end-of-century radiative forcing may prevent substantial reduction of water availability in a river basin but does not necessarily result in better system performance. We find that the WEF systems in the ZW are exposed to severe risks of performance degradation that are generated mostly by global socioeconomic drivers, notably the alternative policies of LUC prices. Since the ZW is representative of many river basins where large dams are planned to support growing economies, we expect our findings to be generalizable to several other African regions. In our scenarios, the average continental increase of end-of-century crop water consumption relative to 2005 is equal to 140%, with diverse trends across the five African regions ranging from 395% and 152% increases in southern and northern Africa, respectively, to a 30% decrease in eastern Africa (Supplementary Fig. 8). Notably, the consumption increase under regionally differentiated LUC emission price is about two times larger than under globally uniform LUC price for both the southern and western Africa regions (Fig. 4). These two regions also include about 60% of all African dams currently planned or under construction39. These features suggest that both regions are expected to be exposed to increasing local demands and vulnerabilities comparable to the ones illustrated for the ZW case, which might be unintentionally underestimated by ignoring large-scale socioeconomic dynamics in the attempt to enhance the accuracy of local-scale models40. At the same time, decoupling water demands from the analysis of global climate policies could misrepresent local multisector dynamics, not only in terms of projected water demands but also for electricity capacity expansion41. We should therefore better understand the trade-off between targeting realism at the local scale and representing global socioeconomic teleconnections to be able to explore the full range of possible future scenarios42 when supporting policy makers in prioritizing mitigation and adaptation strategies across different spatial scales. Our finding highlights how well-intentioned climate change mitigation policies introduced in wealthier countries could have the unintended consequence of increasing vulnerabilities in river basins throughout the developing world. To avert these negative effects, policy makers may have to look beyond their borders to avoid water-use outsourcing and to ensure environmental and climate justice for all43,44. ## Methods We base our analysis on an integrated modelling approach that combines three main components (Supplementary Fig. 12): (1) a strategic model of the ZW; (2) the generation of climate scenarios that produced downscaled projections of precipitation and temperature, which are used as inputs for the hydrologic models of the ZW sub-basin; (3) the generation of irrigation demand scenarios that produce downscaled projections of demands for the irrigation districts in the ZW model. ### ZW model The model of the ZW (Supplementary Fig. 12c) relies on a combination of conceptual and data-driven models, including the hydrologic model of the sub-catchments, the dynamic model of the reservoirs and the irrigation diversions serving the agricultural districts located along the river (for details, see Supplementary Section 2). The Itezhi-tezhi, Victoria Falls and Luangwa sub-basins are represented through the conceptual hydrologic model Hydrologiska Byrans Vattenbalansavdelning (HBV)45, which simulate the soil–water balance and subsequent rainfall–runoff processes. This model has been used extensively for climate change impact assessments46,47,48, including previous research in the same basin49. The models were calibrated over the period 1981–1998 and validated over the period 1998–2006 (in the case of Luangwa, the periods 1981–1990 and 1996–2001 were used due to the presence of several gaps in the available time series). The average coefficient of determination in validation for the three HBV models is equal to 0.75 (for more details, see Supplementary Table 1). The Shire sub-basin, which includes also Lake Malawi, is modelled by using a data-driven artificial neural network reproducing the net inflows to the lake (inflows minus evaporation losses) coupled with a mass-balance equation reproducing the lake dynamics. The coefficient of determination of the combined model is equal to 0.63. Precipitation data are taken from the Climate Hazards Group Infrared Precipitation with Station gridded dataset50, which provides daily time series starting in 1981 with a spatial resolution of 0.05°. Temperature data are taken from Observational Reanalysis Hybrid gridded dataset, which provides daily time series of minimum and maximum temperature from 1981 to 2005 with a spatial resolution of 0.1° (ref. 51). Last, streamflow data are from the Zambezi River Authority using the following gauging stations: Kafue Hook Bridge, Victoria Falls, Great East Road Bridge and Mangochi. The monthly dynamics of the main reservoirs—Itezhi-tezhi, Kafue Gorge, Kariba and Cahora Bassa—are described by the mass balance of the water volume stored in each reservoir. The release volume is determined by a nonlinear, stochastic function that depends on the release decision52. This function allows representing the effect of the uncertain inflows between the time at which the decision is taken (beginning of each month) and the time at which the release is completed (end of the month). The actual release might indeed not be equal to the decision due to existing legal and physical constraints on the reservoir level and release, including spills when the reservoir level exceeds the maximum capacity. According to the monthly time step of the model, the river reaches are modelled as plug-flow canals with negligible travel time and without any lamination effect. An exception is made for the Kafue flats, an extensive floodplain where the river flows slowly for 250 km, taking about two months from Itezhi-tezhi to reach Kafue Gorge. Minimum environmental flow constraints protect the ecosystems at Victoria Falls and in the Kafue flats: the diversion to the Victoria Falls power plant should ensure 250 m3 s–1 in the mainstream; the releases from Itezhi-tezhi should guarantee a streamflow equal to 40 m3 s–1 (315 m3 s–1 in March) in the Kafue flats35. The four reservoirs are connected to an associated hydropower plant. In addition, a run-of-the-river hydropower plant is in operation at Victoria Falls. The total installed capacity is 5.12 GW. The seven agricultural districts are characterized by time-varying irrigation demands associated with a corresponding diversion channel that is regulated by a nonlinear hedging rule53. The historical water demands are taken from ref. 27, which specifies also the cultivated crops (mostly wheat and maize, except for the districts along the Kafue River that cultivate sugar cane), and the irrigation districts area is retrieved from the Global Map of Irrigation Areas by the Food and Agriculture Organization’s AQUASTAT54, which reports the areas equipped with irrigation in 2005 over a grid with spatial resolution of 0.083°. Different objective functions representing the three components of the WEF nexus were formulated though a participatory process involving key stakeholders active in the system, who participated in dedicated meetings called negotiation simulation labs held during the DAFNE research project (Supplementary Section 1). The water component of the nexus is associated with the protection of the ecosystems in the Zambezi River delta and is formulated as the environmental deficit with respect to a target pulse during the peak flow season26,37. The energy component of the nexus is related to the total hydropower production obtained as the sum of the production in all the modelled hydropower plants. According to the Zambezi River basin master plan32 and considering that all these power plants are connected to the Southern African Power Pool, where they export hydroelectric energy (based on International Energy Agency data: https://www.iea.org/), the hydropower production is measured at the basin-wide scale, thus neglecting potential competition across countries. The food component of the nexus is captured by two distinct objectives. The first is the irrigation deficit, considered as a proxy for the food production, which is formulated as the total average water supply deficit over all the irrigation districts; the second is the variance of the average squared water supply deficits across the districts to avoid unbalanced water allocations. The coordinated operation of the four reservoirs and seven diversion channels is determined by a closed-loop operating policy55 that depends on the month of the year, the four reservoirs’ storage volumes and the total previous month inflow. This allows simulating sequences of control actions that optimally respond to the evolving system conditions, thus representing an upper-bound solution that removes the myriad of institutional and geophysical factors that can cause actual operations to deviate from optimal rules 56. The optimal policies are designed via evolutionary multiobjective direct policy search method57, a reinforcement learning approach that combines direct policy search, nonlinear approximating networks and multiobjective evolutionary algorithms. The policies are defined as Gaussian radial basis functions58, and the policy parameters are optimized using the self-adaptive Borg multiobjective evolutionary algorithm59, a combination that has been demonstrated to be effective in solving these types of multiobjective policy design problems for large-scale water systems60. These adaptive operating policies are applied through the simulation period. Accounting for potential changes to institutions or values that introduce new objectives, values, constraints or allowable actions to compensate objectives suffering persistent deficits and to adapt the system operations to the projected changes in climate and society is beyond the scope of this work and remains a grand challenge in water resources and socioenvironmental systems modelling61,62. ### Generation of climate scenarios Climate projections (Supplementary Fig. 12a) are obtained from the CORDEX project 63. Specifically, we use a total of nine scenarios that include three RCPs, namely, RCP 2.6, RCP 4.5 and RCP 8.5, as simulated by three different combinations of global climate models (GCMs) dynamically downscaled by a regional climate model (RCM), which provides simulated trajectories of precipitation and temperature with a spatial resolution of 0.44°: the MPI-ESM-LR GCM downscaled using the RCA4 RCM, and the ICHEC-EC-EARTH GCM downscaled by either the RCA4 or the RACMO RCMs. Despite the incompleteness of CORDEX Africa RCM–GCM matrix, these combinations allow exploring the uncertainties associated with both global and regional climate models. As CORDEX Africa does not provide multiple downscaled realizations for the same GCM–RCM model combination, in this work we did not explore the uncertainties related to internal model variability. However, previous studies64 showed that results based on the ‘one simulation, one vote’ approach are often robust regardless of the choice of the specific RCMs or GCMs. In the future, it would be worthwhile to investigate the sensitivity of our results to the climate projections considered and more broadly explore the climate models’ dynamics by using a larger ensemble of scenarios, possibly including downscaled Coupled Model Intercomparison Project phase 6 projections when they become available. We further bias-adjusted these scenarios using a time-varying quantile mapping technique to match the cumulative density function of the RCM simulations over the control period (1981–2005) with the cumulative density function of the observations, generating a correction function depending on the day of the year and the quantile of the distribution. The correction function is then used to unbias day by day and quantile by quantile the considered variable over the projection period (2006–2100). The pattern of change of the resulting trajectories (Supplementary Figs. 4 and 5) seems to be driven primarily by the considered RCP scenario, while the differences introduced by the three GCM–RCM combinations are less outstanding (see also the indices from the Expert Team on Climate Change Detection and Indices65 reported in Supplementary Fig. 9). Last, the downscaled projections of trajectories of precipitation and temperature are used as inputs to the local hydrologic models for generating streamflow projections (Supplementary Fig. 6). ### Generation of irrigation demand scenarios The socioeconomic scenarios used in this study (Supplementary Fig. 12b) were developed by ref. 21 through a factorial sampling of the SSPs and SPAs. That work aggregated the SSP assumptions into six categories: socioeconomics (population, gross domestic product), changes in energy demand (transportation, building, industrial), agricultural productivity and dietary trends, fossil fuel extraction costs, renewable energy costs, and carbon capture and sequestration costs. Within each category, discrete sampling levels tied to the SSP quantification by ref. 17 were defined. Scenarios were generated through a full factorial combination of all sampling levels across all uncertainty categories. Three long-term CO2 price trajectories were used to simulate different levels of global emissions reductions: a no-tax business-as-usual case, a low-tax case (US$10 tCO2–1 in 2020, increasing at 5% per year) and a high-tax case (US\$25 tCO2–1 in 2020, increasing at 5% per year). Policy implementation uncertainty, as described in the SPAs19, was also sampled (Supplementary Table 2). Specifically, whether a delay in the universal adoption of the CO2 price would occur and the extent (geographic and level) to which LUC emissions would be priced. In total, 33,750 global change scenarios were generated and simulated using the GCAM.

GCAM is a global integrated assessment model that pairs a representation of various natural systems (primarily the climate) with representations of various human systems, including the agricultural, energy, transportation and building sectors. GCAM was one of four models used to develop the RCPs15, was one of five models used to quantify the SSPs17 and was used in the IPCC’s Fifth Assessment Report16. GCAM divides the world into 32 energy–economic zones, which are further sub-divided into 233 river basins and 283 agro-ecological zones14. The model is modular, allowing sectors in different regions and basins to be represented with varying levels of detail. Sectors and regions are linked by markets for energy and agricultural goods. This linkage allows for the incorporation of economic teleconnections in regional resource analyses. For example, the impact of population growth or technological innovation in one region on agricultural water consumption in another can be quantified. GCAM is a partial equilibrium model, in which prices are adjusted in each simulation period such that supply equals demand for all goods in all markets in all regions.

Factors such as population growth, changing preferences and per capita income growth will impact the global demand for various crops. Regional differences in agricultural productivity, land availability and LUC emissions policies determine regional crop production levels in each of the 33,750 scenarios developed by ref. 21. This regional crop production is divided into irrigated and rainfed production, and the corresponding water consumption based on fixed ratios (Supplementary Section 3) is then spatio-temporally downscaled to monthly crop irrigation demands (Supplementary Fig. 10) on a 0.5° grid using the Tethys model22. The resulting gridded irrigation demands enter directly to the ZW model. In the future, it would be worthwhile to investigate the impacts on the ZW dynamics of projected non-agricultural demands that are not considered in this study. As most SSP scenarios include an increase in the global population by 2100, most scenarios in Fig. 3b see an increase in global crop water consumption: there are more people to feed. The magnitude of the global increase is tied to many factors (population, technology and so on), but the distribution of the increase is heavily tied to the nature of the mitigation policy. Worlds with a regionally differentiated LUC emissions regime will concentrate new agricultural production in regions where LUC emissions are not priced and sufficient land is available. Under the SPA assumptions employed in this study, that includes much of Africa (see also ref. 66).

A promising direction of future work would be assessing the impacts on the WEF systems in the ZW of other climate change mitigation options, including afforestation67, power plant expansions11 and alternative carbon price regimes66. Notably, a carbon price regime not considered here is a fossil fuel and industrial carbon tax that applies no price to LUC emissions. The impact of such a regime on trade-offs in the Zambezi are difficult to anticipate. Recent work suggests that such a tax would encourage agricultural global extensification, in part for biofuels and in part irrigated, while policies including LUC emissions encourage greater water use through intensive irrigation66.

### Generation of interdependent scenarios

We generated an ensemble of interdependent scenarios through an a posteriori coupling of the irrigation demand scenarios with the climate projections based on the 2100 radiative forcing simulated by GCAM and used as a starting point for the generation of the climate scenarios. Specifically, we associated with the three RCP projections the scenarios of irrigation demands generated by a simulation of GCAM, returning a value of radiative forcing in 2100 within a window of 0.2 W m–2 centred in 2.6, 4.5 and 8.5 W m–2, respectively (Supplementary Fig. 3). Notably, none of the GCAM simulations produces a forcing value compatible with the projections of RCP 2.6. This is because ref. 21 considered relatively moderate carbon price trajectories while high carbon prices are needed to achieve RCP 2.6 forcing in most sampled worlds. We therefore associate this climate projection with the irrigation demand scenarios characterized by the smallest forcing values simulated by GCAM. The coupling of climate and socioeconomic projections substantially reduced the number of the irrigation demand scenarios: starting from the 33,750-member ensemble, the resulting ensemble of interdependent scenarios includes 2,439 demand scenarios for each GCM–RCM combination, yielding a total of 7,317 ensemble members.

The nature of the coupling in this analysis will introduce some small inconsistencies as the exact forcing trajectories produced by the socioeconomic scenarios will deviate somewhat from the RCP trajectories (Supplementary Fig. 3). In this study, this means that the water availability is computed using slightly different global forcing levels than the irrigation demand. However, for such small forcing deviations, GCM uncertainty is more impactful on river discharge than is forcing uncertainty68. Relaxing the strict coupling allows a richer exploration of the drivers of irrigation demand than is typically afforded.