The green and blue crop water requirement WATNEEDS model and its global gridded outputs

This section provides a detailed description of the input data sources, the model components used for calculating crop water requirements, and the resultant time series of global gridded monthly crop water requirement maps.

The crop water requirement (mm yr-1) is the volume of water required to compensate for a crop’s evapotranspiration losses and to prevent crop water stress. This crop water requirement can be divided into two components: the green crop water requirement (met by available precipitation) and the blue crop water requirement (met by irrigation). The crop water requirement is fully satisfied only when there is enough water for the plant to take up during its growth (i.e. enough precipitation or irrigation) without undergoing water stress. In regions of the world where crop water demand cannot be met by rainwater, only part of the crop water requirement is satisfied by green water (i.e. actual evapotranspiration). Irrigation can be used to supplement the crop’s water needs, thereby allowing crops to evapotranspire at the potential rate. For the years around 2000 (i.e., looking at average results for 1998–2002) and the year 2016, we calculated yearly blue and green crop water requirements for 23 major crops – barley, cassava, citrus, cocoa, coffee, cotton, date palm, grapes/vine, groundnuts/peanuts, maize, millet, oil palm, potatoes, pulses, rape seed/canola, rice, rye, sorghum, soybeans, sugar beet, sugar cane, sunflower, and wheat – that currently account for 76% of global crop production and 95% of global harvested area16 and 3 crop groups (fodder grasses, others annual crops, and others perennial crops). Specifically, we estimated actual green water use in rainfed areas and green and blue water use in irrigated areas. We also assessed monthly green and blue water requirements for five major crops – wheat, maize, rice, sugarcane and soybean – that currently account for almost half of global crop production. Land use, soil characteristics, crop calendars and crop growing stages are kept constant in all years using values available for the year 2000.

Data sources

Monthly data on potential reference evapotranspiration (ETo) came from the University of East Anglia’s Climate Research Unit Time Series version 4.01 dataset (CRU TS v. 4.01; 0.5° × 0.5° resolution)17 and was calculated using the Penmann-Monteith equation, following Allen et al.13. Daily precipitation data between the latitudes 50° N and 50° S came from the Climate Hazards Group InfraRed Precipitation with Station version 2.0 dataset (CHIRPS; 0.05° × 0.05° resolution)18,19 while precipitation data for the remaining latitudes was taken from the National Oceanic and Atmospheric Administration’s Climate Prediction Center Global Unified Gauge-Based Analysis of Daily Precipitation dataset (CPC; 0.5° × 0.5° resolution)20. Soil information – maximum soil moisture storage capacity and maximum infiltration rate – were from Bajties et al.21 (0.08333° × 0.08333° resolution). Crop coefficients (kc) and growing stages came from Allen et al.13 Growing stages – originally reported as a percentage of the growing period of a crop – were then scaled to the planting and harvesting dates reported for the 402 regions and sub-regions included in the MIRCA2000 dataset15. Crop-specific rooting depths for irrigated and rainfed crops and critical depletion factors came from Allen et al.13. All gridded datasets were resampled to a 5 arcminute (0.08333°) spatial resolution.

Multiple growing seasons

For a number of regions included within the MIRCA2000 dataset15, more than one growing period is reported for certain crops. This is true for irrigated rice and wheat. For cases where more than two growing periods were reported, we averaged the growing periods with the harvested area reported by Portmann et al.15. In a limited number of cases, the harvested areas were reported as equal across all growing periods for a particular crop and region. In these instances, selection of the two dominant growing periods was complemented using the growing periods of Mekonnen and Hoekstra4, based on USDA22 and FAO23 information.

Atmospheric demand on crops

Evapotranspiration represents the rate of water flow to the atmosphere as water vapor. Potential evapotranspiration corresponds to the crop water requirement of plants (CWR) in the absence of water-stress; it can be reached when plants can take up from the soil the amount of water they need. This water comes from precipitation (green water – GW) and, in the case of deficiency, it is supplemented by irrigation (blue water – BW).

Potential evapotranspiration (E{T}_{i,t}left(frac{mm}{day}right)) can be assessed as

$$E{T}_{i,t}={k}_{c,i,t}times E{T}_{o,t}$$


where kc,i,t (−) is the crop coefficient of crop i, corresponding to the growing stage in which day t occurs; crop coefficients are taken from Allen et al.13. ETo is the reference evapotranspiration17.

The daily actual evapotranspiration (ETa,i,t) (left(frac{mm}{day}right)) of crop i on day t is then calculated as:

$$E{T}_{a,i,t}={k}_{s,i,t}times E{T}_{i,t}$$


where ks,i,t (−) is the water stress coefficient calculated as a function of the soil water content in the root zone (Si,t) and the maximum and actual water content in the root zone, as in Allen et al.13. For crop i on day t under water stressed conditions (i.e., when only precipitation is provided), ks,i,t was evaluated as:

$${k}_{s,i,t}={begin{array}{cc}{frac{{S}_{i,t}}{RAW}}_{i} & ,if,{S}_{i,t} < RA{W}_{i} 1 & ,if,{S}_{i,t}ge RA{W}_{i}end{array}$$


where Si,t (mm) is the depth-average soil moisture and RAWi (mm) is the readily available water. RAW is calculated as:

$$RA{W}_{i}={p}_{i}times TA{W}_{i}={p}_{i}times ({theta }_{fc}-{theta }_{wp})times {z}_{r,i}$$


where TAWi (mm) is the total available water (i.e., the amount of water that a crop can uptake from the rooting zone), pi (−) is the critical depletion factor (i.e., the fraction of TAWi that a crop can uptake from the rooting zone without experiencing crop water stress), ({theta }_{fc}-{theta }_{wp})(left(frac{mm}{m}right)) is the maximum soil moisture storage capacity dependent on soil texture (i.e., the difference between the water content at field capacity and the water content at the wilting point)14, and zr (m) is the crop rooting depth7. For conditions of no water stress (where supplementary irrigation is available), ks,i,t was assumed to be equal to 1 (see ref. 13).

Vertical soil water balance

For a given crop and grid cell, soil moisture (Si,t) was calculated by solving a daily soil water balance:

$${S}_{i,t}={S}_{i,t-1}+{Delta }ttimes ({P}_{eff}-E{T}_{a,i,t}-{D}_{i,t}-{R}_{i,t})$$


where Si,t-1 (mm) is the soil moisture of the previous time step, Δt is equal to one day, Peff(left(frac{mm}{day}right)) is the effective precipitation – where we assume that 5% of precipitation is partitioned to surface runoff following Hoogeveen et al.14, Ii,t(left(frac{mm}{day}right)) is the additional irrigation water (used only in the case of irrigated crops), and Ri,t(left(frac{mm}{day}right)) is the sub-surface runoff. Di,t(left(frac{mm}{day}right)) is deep percolation below the root zone (which occurs when soil moisture exceeds field capacity (i.e., the volume of water able to be retained in the soil)) and was calculated as:

$${D}_{i,t}={begin{array}{cc}{F}_{max}times frac{{S}_{i,t}-RA{W}_{i}}{TA{W}_{i}-RA{W}_{i}} & ,if,RA{W}_{i}le {S}_{i,t-1}le TA{W}_{i} 0 & ,if,{S}_{i,t-1} < RA{W}_{i}end{array}$$


where Fmax(left(frac{mm}{day}right)) is the maximum infiltration rate depending on soil type24. In time steps where the sum of balance (i.e., Si,t-1 + Peff - Eta,i,t - Di,t) is negative, the ETa,i,t and Di,t were scaled proportionally in order to close the balance. In time steps where the sum of the balance (i.e., Si,t-1 + Peff - Eta,i,t - Di,t) is positive and exceeds TAWi, Ri,t – the sub-surface runoff – is calculated as the difference between the sum of the balance and TAWi.

For each day, each crop, and each grid cell within a MIRCA2000 region for which data on growing period was available, we calculated a stress ETa,i,t,s – equal to the ‘green’ crop water requirement – and unstressed ETa,i,t,u – equal to the actual evapotranspiration under no water stress ETi,t,s. ‘Blue’ crop water requirement was calculated as the difference between ETa,i,t,s and ETa,i,t,u and was only considered for irrigated areas. We then took a summation of the daily ‘green’ and ‘blue’ crop water requirements across each month of a crop’s growing season to determine monthly ‘green’ (for rainfed and irrigated crops) and ‘blue’ (for irrigated crops only) consumptive crop water requirements (Table S1). These definitions of ‘green’ and ‘blue’ crop water requirements are consistent with standard methodologies of water footprint calculation1,4.

Model initial and non-growing season conditions

The model was initialized assuming an initial soil moisture condition of 50% of TAW. Following Hoogeveen et al.14, the model was then run for three years prior to the study start date using three randomly selected years of climate data. Because we ran multiple simulations (one for each crop), these three randomly selected years were held constant across simulations. For the months that fell outside of the growing season, we assumed a kc value of 0.5. We also examined the sensitivity of our results to this off-season kc value and found only limited variation.

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