Crop definitions

We consider 14 major food crops/groups: groundnut, maize, millet, oil palm, rapeseed, rice, roots (cassava; plantain; yam; other roots), sorghum, soybean, sugar beet, sugarcane, sunflower, tubers (potato; sweet potato) and wheat. These crops account for 72% of global crop production, 70% of global harvested area, 75% of all feed use, 83% of vegetal calories in the diet and 78% of dietary protein contributed by vegetal sources35. Owing to a combination of data limitations and substantial within-group variety for certain food groups, we do not consider vegetables, fruits or pulses and assume that their production remains constant and unaffected under crop replacement. Spatially distributed (5 arc minute; 1/12°; ~10-km resolution), crop-specific information on rainfed/irrigated yields (tonne ha−1), rainfed/irrigated harvested area (ha) and rainfed/irrigated agro-ecological suitability were taken from the Global Agro-ecological Zones (GAEZ) database of the Food and Agriculture Organization of the United Nations (FAO)36. Agro-ecological suitability (represented as a) describes the biophysical constraints (such as soil, terrain, temperature and precipitation regimes) that may limit a farmer from realizing the maximum attainable yield of a crop. Crop definitions for this data set closely matched those used in FAOSTAT35 with the exception of cassava and potatoes. In this study, we used the GAEZ ‘Roots’ data (cassava, cocoyam, plantains and yam) to represent cassava and the GAEZ tubers data (potato and sweet potato) to represent potatoes (Supplementary Table 14).

Per-capita demand for calories (2,724 kcal day−1; 16% from animal products) and protein (75 g day−1) were global averages for the year 200035. Following an earlier study37, calories for the portion of the diet coming from animal products were multiplied by a calorie input–output ratio of 2.4 that balances the feed calories consumed with the animal calories produced in the year 200035 (Supplementary Table 15). The resultant diet was then expressed in equivalent vegetal calories (3,343 kcal day−1). As noted before, while approximately half of the animal calories included in the human diet are supported by biomass sources not included in our analysis (such as grasses, roughage)6, we assume that this biomass will remain available and have shown that feed availability from the major crops considered here would increase under crop replacement (Supplementary Table 1). Per tonne crop values (US$ tonne−1) were calculated as the global production-weighted average of producer prices (year 2010)35. These values represent the price charged by a farmer at farm gate or at the first point-of-sale and therefore incorporate input costs as passed on to the consumer. Information on nutrient content was taken from the Global Extended Nutrient Supply (GENuS) database38 (Supplementary Table 2).

Crop consumptive water use (CWU) (that is, the amount of water required to compensate for a crop’s evapotranspiration losses) was calculated using several different input data sets. Long-term average monthly precipitation data (10 arcmin; 1961–1990) were taken from the University of East Anglia’s Climate Research Unit CRU CL2.0 data set39. Crop coefficients, planting dates, and growing stages were adapted from a previous study40 (Supplementary Table 16), and the same climate zones were used, adapted from an earlier work (Supplementary Figure 15). The total available water capacity for the dominant soil (5 arcmin) came from the Harmonized World Soil Database42.

All of the data used in this study are publically available or included in the Supplementary Information. In addition, the data that support the findings of this study are available upon request from the corresponding author.

Consumptive water use of rainfed and irrigated crops

Long-term average monthly reference evapotranspiration (ET o ; measured in mm month−1; 10 arcmin; 1961–1990) was taken from the FAO43. Each pixel was resampled into 4 new cells to obtain a 5 arcmin resolution and divided by the number of days in the corresponding month to convert from monthly to daily values. The actual evapotranspiration (ET a ) of crop i on day t was then calculated as:

$${ET}_{a,i,t}={k}_{c,i,t}{k}_{s,i,t}{ET}_{o,t}$$ (1)

where k c,i,t is the crop coefficient of crop i corresponding to the month in which day t occurs (Supplementary Table S16), and k s,i,t is the water stress coefficient calculated following the method described in a previous study44 as a function of the soil water content in the root zone (S), the maximum and actual water content in the root zone. For rainfed crop i on day t, k s,i,t was evaluated as:

$${k}_{s,i,t}=\left\{\begin{array}{cc}\frac{{S}_{i,t}}{(1-{p}_{i}){S}_{max,i}} & if\,{S}_{i,t} < (1-{p}_{i}){S}_{max,i}\\ 1 & if\,{S}_{i,t}\ge (1-{p}_{i}){S}_{max,i}\end{array}\right.$$ (2)

where S i,t is the depth-average soil moisture (expressed as a length), S max,i is the value of available soil moisture, and p i is the fraction of S max,i that a crop can uptake from the rooting zone as calculated in previous works44, 45. In the case of irrigated crops, k s,i,t was assumed to be 1 to represent conditions of no water stress, following an earlier study40. For a given crop and grid cell, S i,t was calculated by solving a daily soil water balance:

$${S}_{i,t}={S}_{i,t-1}+{\rm{\Delta }}t\left({P}_{e{\rm{ff}},t}+{I}_{i,t}-{ET}_{a,i,t}-{D}_{i,t}\right)$$ (3)

where S i,t–1 is the soil moisture of the previous time step, Δt is equal to one day, P eff,t is the effective precipitation (that is, the rainfall that is actually absorbed in the soil and not directly evaporated from the surface), I i,t is the additional irrigation water (used only in the case of irrigated crops) and D i,t is deep percolation below the root zone (which occurred when soil moisture exceeded field capacity (that is, the volume of water able to be retained in the soil)). Using a method from the literature46, daily precipitation was generated from monthly rainfall by using a mixed Bernoulli Gamma distribution function47, where the Bernoulli distribution was used to first randomly distribute the number of wet days over the month and the Gamma distribution was then used for the random distribution of precipitation over the wet days. Daily precipitation was then converted to P eff,t using the Soil Conservation Service method (for example, see refs 40 , 44 , 48).

Thus, for each day, each crop and each grid cell, we were able to calculate a rainfed ET a,i,t,rainfed — equal to the ‘green’ consumptive water use, and irrigated ET a,i,t,irrigated — equal to the potential evapotranspiration under no water stress. Blue consumptive water use was calculated as the difference between ET a,i,t,irrigated and ET a,i,t,rainfed and was only considered for irrigated crops. We then took a summation of the daily green and blue consumptive water use across a crop’s entire growing season to determine total green (for rainfed and irrigated crops) and blue (for irrigated crops only) consumptive crop water use (GWU and BWU, respectively) (Supplementary Table 3). These definitions of GWU and BWU are consistent with standard methodologies of water footprint calculation (see ref. 40) (Supplementary Table 17).

Current production and water demand

For each pixel where at least one of the rainfed crops considered here was grown, current (year 2000) rainfed production, p c , was calculated as:

$${p}_{c}=\sum \left({y}_{i}{a}_{i}\right)$$ (4)

where y i is the rainfed yield of crop i, and a i is the rainfed harvested area of crop i. These calculations were repeated separately for irrigated croplands. The combined totals of current rainfed and irrigated production for each crop agreed well with those reported in FAOSTAT35 (Supplementary Table 14). Crop yields, which were originally reported in tonne ha−1, were converted to kcal ha−1 and kg protein ha−1 using global values from FAOSTAT35 (Supplementary Table 18). While multi-cropping (that is, multiple crops harvest per year) occurs in a host of agriculturally important regions5, we did not attempt to disaggregate irrigated and rainfed production further between different growing seasons as planting dates vary widely across cultivated areas. This consideration may therefore limit the number of replacement options for a given crop and region.

Current green and blue consumptive water demand of a cultivated pixel, w c,g and w c,b respectively (expressed in m3 yr−1), in irrigated cropland was calculated following a published method49 as:

$${w}_{c,g}=\sum (10{GWU}_{i}{a}_{i})\,and\,{w}_{c,b}=\sum (10{BWU}_{i}{a}_{i})$$ (5)

where GWU i and BWU i are the green and blue consumptive water use (expressed in mm yr−1) for crop i and the factor 10 converts the units for evapotranspiration to m3 ha−1 yr−1. Only w c,g was calculated for rainfed croplands in each pixel. Our estimates of green and blue water demand agreed well with published values40 (Supplementary Table 17).

Interpolating yields

To estimate yields for the replacement scenario, maps of current rainfed and irrigated crop yields (28 in total) were interpolated using the ArcGIS ‘Spline with Barriers’ tool. This tool “applies a minimum curvature method, as implemented through a one-directional multigrid technique that moves from an initial coarse grid, initialized in this case to the average of the input data, through a series of finer grids until an approximation of a minimum curvature surface is produced at the desired row and column spacing”50. This technique also ensured that splines were fit for each crop yield map and for each country independently, as stark discontinuities can occur at country borders (Supplementary Table 19). For each interpolated crop-specific rainfed yield map, we then applied two masks: (1) a cultivated area mask to consider only those rainfed areas where at least one of the 14 crops is currently grown; and (2) a buffering mask, which considers all pixels within a 25/12° (or ~250 km) Euclidean distance from where the crop is currently cultivated to ensure that our analysis considered only those interpolated areas with similar climate characteristics. This masking was repeated separately for irrigated crops and irrigated areas. Our examination of agro-ecological suitability supported this assumption, showing only modest variation in suitability (14%) within the 25/12° buffer. Of course, even if climate and soil conditions are suitable, certain crops may not currently be grown in a given area for a host of other reasons (such as a lack of indigenous knowledge, infrastructural constraints, dietary preferences and so on). However, at the distances we consider, there are probably minimal obstacles that would prevent the transfer of knowledge, technology, and agricultural inputs from locations where a crop is currently grown. Thus while these considerations were beyond the scope of this study, they should be kept in mind when considering the approach and findings presented here.

Minimizing water demand

Our replacement approach sought to minimize consumptive water use (m3 ha−1) for each pixel within currently cultivated lands without inducing decreases in caloric yield, protein yield, or farmer price. We performed this replacement approach separately for irrigated and rainfed croplands. The first approach we describe is for irrigated croplands. Because a single pixel could contain harvested areas for multiple irrigated crops, we assessed each irrigated harvested area within each pixel separately, starting with the crop with the largest harvested area and working towards the smallest. For the harvested area of interest, we applied a set of criteria aimed at minimizing the blue water footprint of irrigated crop production through the redistribution of cropping patterns. To do this, we replaced an existing crop with a crop that minimizes blue water use, provided that the following conditions were also met: (1) that green crop water requirement should not increase; (2) that calorie production should not decrease from current amounts; (3) that protein production should not decrease from current amounts; and (4) that the value of crop production should not decrease from current levels. Expressed together, the criteria form the multi-conditional statement:

$$\left({BWU}_{min} < {BWU}_{c}| {GWU}_{min}\le {GWU}_{c}| {p}_{min}\ge {p}_{c}| {l}_{min}\ge {l}_{c}| {v}_{min}\ge {v}_{c}\right)$$ (6)

where p is the crop protein yield (tonne ha−1), l is the crop calorie yield (kcal ha−1), v is the crop value (that is, the producer price in US$ ha−1), and the subscripts min and c represent the potential replacement crop and the current crop, respectively. The values p, k, and v were calculated as the product of the conventional yield (tonne ha−1) and the protein content (tonnes of protein per tonne), calorie content (kcal tonne−1), and value (US$ tonne−1) of the crop (Supplementary Table 18).

If all five criteria were met, the current irrigated crop in the harvested area of interest was replaced by the crop that minimizes blue consumptive water use. If at least one of the conditions was not met, we then repeated the assessment of the five criteria (equation (6)) using the irrigated crop with the next lowest BWU value for the pixel, and so on through all 14 crops. If no potential replacement crop met all five criteria for the harvested area, then the current crop was maintained. If a replacement occurred for the harvested area of interest, the replacement crop could not be further considered within the pixel, thereby largely preventing a transition to monoculture. However, preventing a loss of crop diversity in every case would have been computationally impractical because every permutation of yield, harvested area and water footprint would need to be considered for each pixel. Thus, there were some instances wherethe replacement crop in one harvested area was the same as the current crop in another harvested area for the same pixel. In 92% of the cultivated area, crop redistribution resulted in either no loss of crop diversity or only a reduction by one crop. Thus a crop may be replaced in a given harvested area, but each harvested area within a pixel is treated as fixed. Our approach therefore represents a combinatorial optimization in that we draw from a finite (that is, discrete) number of feasible solutions, all of which reduce consumptive blue water use. Our method does not necessarily attain the absolute minimum because it operates under the assumption that the areas cultivated with different crops remain the same whereas the crop types change. This assumption, however, ensures that crop diversity is overall conserved (except for certain small reductions noted above). This entire methodology was repeated for rainfed croplands with the only difference being that BWU was not considered among the replacement criteria as there is no irrigation component for rainfed production.

The replacement analysis for rainfed and irrigated crop production was also repeated for three other scenarios. In the first alternative scenario, the replacement criteria for rainfed crops remained the same; for irrigated crops, we removed the criterion for GWU, as it is possible for replacing crops to have a lower BWU and higher GWU relative to the current crop. In a second alternative scenario, we kept the original replacement criteria in place, with soybean areas held constant (we did not allow replacement) in case this might prevent any potential degradation of the soil nutrient pool. For the third, we held soybean, sugar beet and sugar cane areas constant for the same reason as the second alternative scenario as well as to avoid any impacts on biofuel production. For all four scenarios — no constant, no constant (based only on BWU for irrigated crops), constant soybeans, and constant soybeans/sugar beet/sugar cane — we found consistent benefits in terms of consumptive water demand and calorie and protein supply as a result of crop replacement (Supplementary Table 13). A summary of all data sets and sources is provided in Supplementary Table 20.

Water scarcity assessment

Water scarcity was calculated as the ratio of total consumptive water demand (w c,g + w c,b ) to the long-term average renewable water availability (1970–2000) for each of 10,105 watersheds within currently cultivated areas. Data on renewable water availability (surface + groundwater) came from a study17 that used the WaterGAP3 integrated global water resources model. These data include precipitation within the watershed and/or upstream inflows that are stored in or pass through the watershed and do not account for interbasin transfers or desalination17. Using long-term average renewable availability allows for an examination of whether freshwater withdrawals and consumption can be sustained by a watershed through time. If total consumptive water demand exceeds the average renewable water available (that is able to recharge annually) then the difference must be met through non-renewable sources (such as groundwater pumping) and can lead to the depletion of surface and groundwater sources.

Data availability

Spatially distributed crop-specific information on rainfed/irrigated yields, rainfed/irrigated harvested area, and rainfed/irrigated agro-ecological suitability were taken from the FAO’s Global Agro-ecological Zones (GAEZ) database36. Information on nutrient content was taken from the Global Extended Nutrient Supply (GENuS) database38 (Supplementary Table 2). Long-term average monthly precipitation data (10 arcmin; 1961–1990) were taken from the University of East Anglia’s Climate Research Unit CRU CL2.0 data set39. Crop coefficients, planting dates, and growing stages were adapted from a previous study40 (Supplementary Table 16), and the same climate zones were used, adapted from an earlier work41 (Supplementary Fig. 15). The total available water capacity for the dominant soil (5 arcmin) came from the Harmonized World Soil Database42.

All of the data used in this study are publically available or included in the Supplementary Information. In addition, the data that support the findings of this study are available upon request from the corresponding author.