Large variations in global irrigation withdrawals caused by uncertain irrigation efficiencies

An assessment of the human impact on the global water cycle requires estimating the volume of water withdrawn for irrigated agriculture. A key parameter in this calculation is the irrigation efficiency, which corrects for the fraction of water lost between irrigation withdrawals and the crop due to management, distribution or conveyance losses. Here we show that the irrigation efficiency used in global irrigation models is flawed for it overlooks key ambiguities in partial efficiencies, irrigation technologies, the definition of ‘large-scale’ irrigated areas or managerial factors. Once accounted for, these uncertainties can make irrigation withdrawal estimates fluctuate by more than one order of magnitude at the country level. Such variability is larger and leads to more extreme values than that caused by the uncertainties related with climate change. Our results highlight the need to embrace deep uncertainties in irrigation efficiency to prevent the design of shortsighted policies at the river basin-water-agricultural interface.


Introduction
Managing water withdrawals within water allocation balances desirable sustainable goals of attaining food and water security, boosting human health, fostering economic growth, protecting freshwater ecology and reducing conflict over water [1,2]. Central to this task of apportionment is knowledge of the large volumes of water withdrawn by irrigation, which informs discussions on whether global water availability can ensure future food production [3] and whether we can safely reallocate water from irrigation to other sectors [4]. Such knowledge is also key to related water management tasks such as determining water basin accounts [5], planning water storage and abstraction infrastructure [6], finding areas of untapped potential [7], managing licensed abstractions on rivers or apportioning limited water within specific drought events [8]. Climate change will further exacerbate the scale of these withdrawals and allocation challenges by increasing the variability of precipitation and boosting crop water needs due to higher temperatures and evapotranspiration [9, 10].
These ever-sharpening water tasks require increasingly accurate knowledge of withdrawn water at the irrigation system, basin, country and global levels. At the core of this knowledge there is the concept of irrigation efficiency [11,12], which helps to transform net crop-level consumption into water needs for the irrigation system, giving by extension water withdrawals at the basin and global levels. In its classical form [13,14], the concept of irrigation efficiency denotes the ratio of irrigation water beneficially consumed by the crop to that diverted from the water source and conveyed to the crop. The closer this ratio is to 1, the higher the irrigation efficiency of the irrigated area under study.
Although continuously alterable via design, operation and management, irrigation efficiency is often characterized with the static, sharp point-estimates proposed by irrigation engineers more than 50 years ago [15,16]. This is especially the case of global models (GMs) [17][18][19][20][21][22], spatially distributed algorithms that simulate hydrological processes at a global scale. For instance, WaterGap [23], H08 [18] or MAT-SIRO [17] characterize the irrigation efficiency of USA with a value of 0.6 [23], whereas PCR-GLOBWB [24] or LPJmL [25] use a value of 0.55 [26]. All these GMs have gained momentum over the last 20 years and their water estimates currently feed into the World Water Development Reports, the Global Environmental Outlooks or studies commissioned by the World Bank [27]. They are also regarded as paramount when discussing the sustainable development goals (SDGs) at the Water-Food nexus given their capacity to simulate connections between crops, water and humans over large spatial and temporal scales [28].
Here we provide a comprehensive analysis of the theoretical and empirical foundations of the irrigation efficiency values used by GMs to simulate irrigation water withdrawals. By means of a literature review, sensitivity auditing and uncertainty analysis methods [29,30], we show that they endorse a vision of irrigation that artificially downplays ambiguities and reduces real-world complexity to a set of easyto-manage numbers. Once this spurious accuracy is corrected for, irrigation efficiencies used by GMs turn from point-estimates to ranges that can span almost all the unit interval. Such variability engulfs the estimation of irrigation water withdrawals with an uncertainty much larger than that propagated by the uncertainties derived from climate change. Our results thus show how a relatively obscure step in irrigation planning (irrigation efficiency) governs estimates of, and discussions regarding, globally significant water balances, and concur with recent works suggesting that GMs promote tunnel vision in the irrigation policy field [31,32]. This can potentially misguide initiatives on the sectoral allocation of water out of agriculture [4], the planning for dams [33]; the viability of groundwater storage [34] or the pursuit of the SDGs [2]. We conclude by discussing the role that GMs should play in informing sustainable policies at the water-agricultural interface.

Sensitivity auditing
Two main studies provide GMs with irrigation efficiency values: Döll and Siebert [23] (utilized by MAT-SIRO, H08, WaterGap and WBM plus [17-20]) and Rohwer et al [26] (used by LPJmL and PCR-GLOBWB [21,22,35,36]). Döll and Siebert's are regional estimates based on a literature survey, whereas Rohwer et al's are country-level estimates modeled as a function of partial efficiencies (field, conveyance and management efficiencies) and irrigation technologies (surface, sprinkler and micro-irrigation). GMs use the values proposed by either Döll and Siebert or Rohwer et al to transform country or region-based crop water needs into irrigation water withdrawals.
We cross-check the estimates by Döll and Siebert [23] and Rohwer et al [26] against the studies they cite to support their proposed irrigation efficiency values [15,16,[37][38][39][40][41][42]. Our goal is twofold: • To highlight the assumptions embedded in the calculation of irrigation efficiency. We rely on sensitivity auditing [29], an extension of sensitivity analysis to gauge the framing of mathematical models. Sensitivity auditing investigates the value-ladenness of key assumptions and normative frameworks of models. This is achieved by hunting for tacit or neglected assumptions, strategic minimizations of uncertainties and normative stances underlying the framing of the problem. Such scrutiny increases the transparency of model-based inferences and helps assessing their social robustness for policy-making.

Data collection from ISI-MIP
We retrieve irrigation water withdrawal estimates from WaterGap [19], H08 [44], PCR-GLOBWB [45] and LPJmL [25] in the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP) [46]. In ISI-MIP all these GMs assume an irrigation efficiency of 1 except LPJmL, whose irrigation efficiencies vary spatially. To make all estimates comparable, we correct the irrigation water withdrawal values produced by LPJmL following the indications given by ISI-MIP [47]. All these models have a spatial resolution of 0.5 • × 0.5 • and compute irrigation water withdrawals at the grid cell level. We retrieve data from 2010 at a monthly time step and allocate each cell to a country according to its coordinates. We produce annual irrigation water withdrawal estimates by adding all the values of all cells within the same country. We also retrieve from ISI-MIP the water withdrawal estimates projected by these models for 2050 under four different Representative Concentration Pathways (RCP2.6, RCP4.5, RCP6, RCP8.5). We aim to examine whether the preferential attention given in the literature to uncertainties related to climate change versus those related to irrigation efficiency appears justified [48,49].

The model
Irrigation efficiency (E p ) [-] is a key parameter to compute irrigation water withdrawals (I w ) [m 3 ], since where I c [m 3 ] is the water needed by the crop due to transpiration, evapotranspiration and evaporation from the soil surface. Hence lim Ep→1 I c = I w . To calculate E p we use the classical approach based on partial efficiencies [16, 37,50], also employed by Rohwer et al [26] and sanctioned by GMs, which reads as  [26] assume the existence of a management penalization due to scalar stress only in largescale surface irrigation systems (equation (3)), which they define as those larger than 10 000 ha based on the Global Map of Irrigated Areas (FAO-GMIA [51]).
The final E p is in the interval [0, 1], with higher irrigation efficiencies showing values closer to 1. Rohwer et al [26] calculated irrigation efficiency based on the 'predominant' technology in the country due to the sparcity of data on the specific proportion of flood, sprinkler and micro-irrigation at the national level. These data were recently produced by Jägermeyr et al [25]. To see whether the addition of spatial detail in the distribution of irrigation technologies improves the accuracy of the estimation, we also calculate the irrigation efficiency with the Jägermeyr et al [25] coefficients, as where E ps , E pp and E pm respectively denote the irrigation efficiency of surface, sprinkler and microirrigation (calculated as in equation (2)) and C s , C p and C m are constants denoting the fraction of irrigated area with surface, sprinkler and micro-irrigation as reported by Jägermeyr et al [25]. Note that equations (2) and (4) are different versions of the method known as the 'factorial' approach to irrigation efficiency. This method offers a single snap-shot of irrigation efficiency by multiplying different tiers of irrigation together (three in this case), which makes it very sensitive to errors or changes in the values of these tiers. The limitations of the factorial approach are thoroughly discussed in Lankford [52].

Probability distributions
We describe the uncertainty in the parameters of equations (2) and (3) with probability distributions based on the literature review outlined in the section 2.1 (table 1). We model E a and E c for surface and sprinkler irrigation based on Bos and Nugteren [37], and E a and E c for micro-irrigation according to the ranges reported by Fairweather et al [41], Brouwer et al [16] and Rohwer et al [26]. With regards to Mf, we assume that m tends to 1 but that mismanagement and bad communication can eventually bring m down to 0.65, thus reducing the efficiency as proposed by Doorenbos and Pruitt [15]. For the parameter r L we set the upper bound at 0.5 following Rohwer et al [26] and assume that its lower bound may be zero given the existence of large irrigated areas successfully managed through time, such as the huerta of València or Murcia (Spain) [53].
Finally, we operationalize f L with two triggers (X 1 , X 2 ), e.g. random parameters that account for the uncertainty in two key aspects related with the characterization of 'large-scale' irrigated areas: the dataset used to document the extension of irrigation and the threshold size used to define 'large-scale' irrigated areas. Although Rohwer et al use the FAO-GMIA and 10 000 ha respectively, there are currently four different datasets informing on the extension of irrigation [51,54,55], and no clear agreement as to what 'largescale' irrigated areas are [56]. We thus employ X 1 to select one of these four irrigated area datasets and X 2 to define the threshold size beyond which irrigated areas are considered 'large-scale' (see section 2.5). This design results in ten uncertain parameters/ triggers (table 1).

'Large-scale' irrigated areas
We consider four irrigation maps to characterize X 1 : the FAO-GMIA [57], the IWMI-GIAM [55], the GRIPC [58] and the map by Meier et al [54]. The FAO-GMIA is based on spatially aggregated official statistics and reports irrigated areas relative to the total grid cell area. The IWMI-GIAM defines irrigated areas depending on the crop class, whereas the GRIPC and the Meier et al map provide a binary irrigation mask. To remain consistent with Rohwer et al [26], we adjust all datasets to the FAO-GMIA and determine the percentage of irrigated area in each grid cell. We identify 'large-scale' irrigated areas as contiguous grid cells with >50% irrigation coverage and a total irrigated area > p, where p is the uncertain threshold size operationalized by X 2 . We focus on p = 1000 ha, p = 3000 ha and p = 10 000 ha. We could not explore p < 1000 ha given the need for >50% irrigation coverage and the spatial resolution of the dataset. Table 1. Probability distributions used to describe the uncertainty in the parameters involved in the estimation of irrigation efficiency. TWei, TBeta and DU stand for truncated Weibull, truncated Beta and discrete univariate respectively. See figure S1 for a graphical representation of the selected probability distributions.

Uncertainty analysis
To appraise how these ambiguities affect the calculation of irrigation efficiency, we conduct a Monte Carlo-based uncertainty analysis with the R package sensobol [59]. We first create a sample matrix with N = 2 14 rows and k = 10 columns using Sobol' quasi-random numbers [60,61]. The Sobol' sequence is a base-2 sequence that explores the uncertainty space more effectively than random numbers, for it leaves smaller unexplored volumes. We allocate each column in the matrix to one of the ten uncertain parameters/triggers listed in table 1, and use a quantile transformation to bring the values populating each column to its appropriate probability distribution. Any point in this matrix can be designated as x υi , where υ indexes the row (from 1 to N) and i indexes the column (from 1 to k). We then run the model: for υ = 1, 2, . . . , N rows, we calculate the country-level irrigation efficiency E pυ based on the values defined by E aυ , E cυ , . . . following equations (2) and (3). This design allows the same set of simulations to be used also for sensitivity analysis, which helps pinpoint which parameters/triggers convey the most uncertainty to the model output [30,62]. Due to space constraints, we provide the results of the sensitivity analysis in the supplementary materials (available online at stacks.iop.org/ERL/17/044014/mmedia).

Large variability in irrigation efficiencies
At the regional level, the irrigation efficiency pointestimates used by GMs hide wide ranges. This is the case of the United States, whose assigned irrigation efficiency value (0.6) contrasts with the data compiled by Solley et al [40] at the state level ( figure 1(a) 1(b)). In some cases, the estimates do not seem to fall within the interval formed by the irrigation efficiency of countries within the region. This is the case of the Middle East (0.6), whose irrigation efficiency falls outside the range formed by the values of Egypt (0.3), Turkey (0.15) and Iran (0.29) reported by Bos and Nugteren [37]. We provide a detailed comparison between the point-estimates used by GMs at the regional level and the underlying irrigation efficiency data in table S1.

Irrigation technologies do not have sharp, distinguishable efficiencies
The efficiency ladder in GMs is framed as surface < sprinkler < micro-irrigation, with each technological category unequivocally improving on the previous one in both field (E a ) and conveyance (E c ) efficiency. Micro-irrigation is positioned at the summit with almost perfect values (E a = 0.9, E c = 0.95) (table S2). This narrative sanctions an engineering perspective of irrigation in which technologies have essential features and perform independently from social-ecological particularities and farming practices. Yet data reported at the project level indicates largely overlapping, variable partial efficiencies for surface and sprinkler irrigation [37] ( figure 1(c)). The irrigation efficiency of surface, sprinkler and microirrigation are also reported as intervals laying considerably one over the other by Clemmens and Molden [63], Rogers et al [42] and Fairweather et al [41].

What are 'large-scale' irrigated areas?
By using Rohwer et al's data [26], many GMs assume that 'large-scale' irrigated areas have lower efficiencies due to mismanagement problems and scalar stress, penalizing the irrigation efficiency of irrigated areas larger than 10 000 ha [21,26,36]. In figure 1(d) we show that there may not be any difference in application (E a ) or conveyance (E c ) efficiency between irrigated areas below and beyond 10 000 ha, whereas in table S3 we report some alternative thresholds utilized in different countries to screen'large' from 'small' irrigation systems based on size (e.g. 100 ha, 1000 ha, 3000 ha). The case of Nepal is paradigmatic since the physical threshold varies one order of magnitude depending on the location of the irrigated area (flat areas: small < 500 ha, large > 5.000 ha; non-flat areas: small < 50 ha, large > 500 ha) [64].

Quantitative uncertainties
If we propagate all these uncertainties in the calculation of irrigation efficiency we obtain large irrigation efficiency ranges at the country level. We also observe that the accuracy of the estimation is not improved . For these countries, the selection of either a fine or a coarse-grained approach in mapping irrigation technologies already is a significant source of uncertainty in the production of irrigation efficiency estimates. The sharp and contrasting efficiency values assigned by GMs to surface, sprinkler and microirrigation do not stand once uncertainties are thoroughly accounted for (figures S3 and S4). We observe a 40%-50% overlap between the efficiency of surface and mixed irrigation, a 50% overlap between sprinkler and mixed irrigation and a 30% overlap between sprinkler and surface irrigation regardless of the continent under study. In Asia, the overlap between micro and mixed irrigation is of 8% (figures S5 and S6). Overall, the irrigation efficiency ranges produced with the uncertainty analysis for surface, sprinkler and micro irrigation are much larger than those previously reported, and include much lower values (figure 4). This is explained by the factorial approach to irrigation efficiency sanctioned by GMs, which is based on the multiplication of partial efficiencies [52] (Methods, equation (2)). Very low irrigation efficiency values may be produced when partial efficiencies are characterized with values at the lower end of their distribution. For instance, an irrigation efficiency of 0.1 for surface irrigation is feasible with the factorial approach given that the uncertainty ranges for E a , E c and M f include the values 0.4, 0.5 and 0.5 respectively, and thus 0.4 × 0.5 × 0.5 = 0.1.
All countries except Cyprus, the United Arab Emirates and Israel (∼0.48) display uncertainty ranges in irrigation efficiency larger than 0.5, with countries such as Somalia, Colombia, Serbia or Bolivia showing the largest ranges (∼0.78). Many of the top countries in irrigation water withdrawals (e.g. China, India, Iran, Spain) show uncertainty ranges larger than 0.6 (figure S7). If we let the irrigation efficiency values fluctuate within the uncertainty bounds just computed, the irrigation water withdrawals of these countries may vary by up to a factor of 50. Overall, the uncertainty in irrigation efficiency makes the irrigation water withdrawal estimates of 25%, 50%, Uncertainties in irrigation efficiency have a much larger effect on the estimation of irrigation water withdrawals than those derived from climate change (figure 5). In the case of India, potential water withdrawals range from 400 to 800 10 9 m 3 under climate change and from 400 to 7000 10 9 m 3 if irrigation efficiency uncertainties are accounted for (q 2.5 -q 97.5 ). A similar situation occurs for Mexico (40-70 10 9 m 3 under climate change; 90-500 10 9 m 3 under irrigation efficiency uncertainties), Egypt (50-180 10 9 m 3 ; 60-1300 10 9 m 3 ) or Spain (20-60 10 9 m 3 ; 30-170 10 9 m 3 ) (q 2.5 -q 97.5 ). Note how the integration of irrigation efficiency uncertainties makes Egypt and India produce irrigation water withdrawal values that extend out of scale, i.e. that are beyond the estimates projected by GMs at the global level for 2050 (3000-5000 10 9 m 3 ). This illustrates the extent to which current calculations of irrigation water withdrawals are constrained by arbitrarily precise irrigation efficiency values.
For 75% of the countries, the highest irrigation water withdrawal value produced after integrating irrigation efficiency uncertainties is at least two times higher than the highest value produced under climate change. For example, countries such as Bhutan, Guyana, Cameroon or Indonesia present values that are 100, 30, 20 and 17 times higher respectively. Only ten countries out of 143 (6%) (e.g. Benin,   Cyprus, Switzerland, United Arab Emirates) display higher irrigation water withdrawal values under climate change (figure S11).
Finally, we note that the integration of climate change uncertainties produces in some cases ranges that are narrower than the ranges produced by running the GMs alone (e.g. the blue error bar for Indonesia, Pakistan or China is narrower than the red error bar, figure 5). Given that the addition of uncertainties most often expands (and not contracts) the model output uncertainty [65,66], this feature suggests the presence of errors in the ISI-MIP simulations.

Discussion
The irrigation efficiency values used by GMs are problematic. They rely on (and simplify) data produced 40-50 years ago despite all the work on the use, applicability and interpretation of the irrigation efficiency concept developed in the past decades [11,12,67]. GMs also sanction a technocratic vision of irrigation that includes sharp categories in the definition of irrigation efficiency values, e.g.
large-scale-small-scale, modern-traditional, microsprinkler-surface irrigation. These distinct categories are idealized because (1) labels classifying irrigation systems based on physical dimensions are highly contextual, (2) the same irrigated area may combine sprinkler with micro-irrigation or micro with surface irrigation [68,69], (3) irrigation efficiency values are highly contingent on maintenance and managerial activities besides technological features [70], and (4) remarkably different performances can arise within categories due to differences in design or lack of adjustment to specific features of the irrigated area, such as local topography, rising water scarcity and prevalence of drought.
The idealization of categories is especially apparent in the conceptualization of 'large-scale' irrigated areas and irrigation technologies: firstly, the term 'large-scale' does not necessarily refer to physical dimensions. An irrigation system may also be described as 'large-scale' if managed by an irrigation organization responsible for distributing water to the farmers or by a state, regardless of its dimensions [56]. With this qualitative criteria, very extensive irrigated areas such as the huerta of València or Murcia (Spain) (>11 000 ha) would not fit the 'large-scale' category given their bottom-up, decentralized management [53,71].
Secondly, the inclusion of surface, sprinkler and micro-irrigation in a sequence of increasingly irrigation-efficient technologies assumes that micro irrigation is always adopted to increase water efficiency because it leads to the largest efficiency gains [26, p 39]. But farmers may also embrace microirrigation to reduce workloads, to maintain a landlord status [70], to irrigate steep slopes [72], or simply as a bandwagon effect [73]. Governments can promote micro-irrigation to alleviate poverty or tame more informal, difficult-to-control irrigation [74]. And micro-irrigation may actually increase water consumption at the farm, system and basin levels if it goes alongside the extension of the irrigated area or a switch to more water-intensive crops, a phenomenon known as the rebound effect [75].
Our study reproduces the approach of GMs in computing irrigation efficiency but integrates the main uncertainties characterizing the data they rely upon. We show that these uncertainties impact the estimation of irrigation water withdrawals more than the uncertainties related with climate change: they generally lead to broader ranges and more extreme values at the upper end of the distribution (figures 5, S9 and S10). This relevance contrasts with the much larger attention given to climatic scenarios and their potential effect on irrigation water demands in the scientific literature [48,49,76,77]. Although the existence of irrigation efficiency uncertainties was noted when the concept of irrigation efficiency entered GMs [23,26], ambiguities received no formal recognition and ended up hidden behind artificially sharp point-estimates. This process fits with what Rayner calls 'displacement' [78,79], the process by which reality gets substituted by a more manageable surrogate, the model. With the vagueness of irrigation efficiency moved to the background and climate change increasingly permeating the public imagery [80], the study of climatic uncertainties and their effect on irrigation demands has taken center stage in the GMs field. Based on the weight of uncertainties, our results suggest that this order of priorities should be revised.
The use of spuriously precise irrigation efficiency values misguides high level policies relying on modelbased irrigation water withdrawal estimates. The extent of this deception may be appreciated with the example of Mexico, whose volume of water withdrawn for irrigation goes from 40-70 10 9 to 80-500 10 9 m 3 after integrating irrigation efficiency uncertainties. For the planning of water storage infrastructures, this means assuming a margin of error equal to the volume of water stored by either 2 or 13 Hoover dams (35 10 9 m 3 ). At the local level, it equals a measurement error of either 2 million or 16 million smallholder farmers whose access to water might be overlooked (assuming 1 l/s/hectare and 1 ha per smallholder). Note in this case how the uncertainty in irrigation efficiency alone boosts the uncertainty range in water withdrawals by one order of magnitude. In the calculation of irrigation water withdrawals by GMs there are other sources of uncertainty besides irrigation efficiency [32], such as the area under irrigation (hard to precisely define due to unreliable country-based statistical data or sources of error in the remote sensing of irrigated areas [55,81]), the crop evapotranspiration (there are several equations to compute it and no agreement as to which one works best [82]), or the precipitation dataset (prone to ambiguities due to sparcity in the gauge network, inaccuracy in measurements or errors in data collation and synthesis) [83]. These are likely to expand the uncertainty in the estimation of irrigation water withdrawals even further due to the 'uncertainty cascade' effect [65].
While we value the benefits of more research on irrigation efficiency, we argue that uncertainties in the estimates used by GMs are unlikely to disappear. Firstly, because the collection of field data at the scale required by the simulations is unfeasible. Secondly, because sharp single values may be elusive regardless: a fine-grained study conducted on micro-irrigation plots in Morocco documented a coefficient of variation of 34% for irrigation efficiencies due to different irrigation and maintenance activities [70]. Other ranges may apply elsewhere given the local character of agrarian practices. Thirdly, because by the time the collected data has been introduced in the models, field realities might have changed significantly due to the dynamical nature of agricultural systems [84]. In general, the increase of our knowledge on a specific topic tends to open up unexpected uncertainties not considered in the original problem framing [85]. This is well-known by the climate change community after more than 30 years collecting data on climate sensitivity (the average global warming that would be produced by doubling CO 2 atmospheric concentration from 280 to 560 ppm), leading to ever-larger uncertainties [86].
The ranges proposed in this paper are produced with the irrigation efficiency data underpinning the irrigation efficiency values used by GMs. They are also conditioned by the GMs' factorial approach to irrigation efficiency, known to magnify errors and misrepresent efficiencies [52]. Hence they should not be taken at face value but as evidence of important unattended ambiguities, with critical implications for the production of irrigation water withdrawal estimates and the design of robust policies at the water-agricultural interface. The 'inexact' nature of Hydrology as a science [87] matches poorly with the use of sharp point-estimates: once audited, the rhetorical nature of these numbers (e.g. their use as tools to constrain complexities and confirm pre-existent narratives) is often revealed. In the case of existing ecological or agricultural estimates this frequently leads to a redefinition, reversal or even a rebuttal of the associated policy implications [88], with the subsequent delay in the design of appropriate responses to social-environmental challenges.
Rather than attempting to drive uncertainties out, GMs might increase their social and policy relevance by thoroughly-and more realistically-exploring their uncertain space, including both quantitative uncertainties and the impact that disciplinary or normative assumptions have in the production of the model output [32,89]. Opening up the box of the modeling process should be backed up by a disclosure of the conditionalities underpinning the model inferences. This approach minimizes the knowledge asymmetry between modelers and model users (e.g. regulators) and prevents a reductionist framing of the problem, thus circumventing the formation of tunnel visions that would align policies along a single, possibly non-optimal direction.

Data availability statement
The irrigation efficiency data generated in this study is available in Puy [90]. The datasets needed to reproduce our results are available in Puy [90] and in https://github.com/arnaldpuy/irrigation_efficiency. The irrigation water withdrawal estimates produced by GMs can be retrieved in www.isimip.org.

Acknowledgment
A P has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant No. 792178.

Code availability
The R code to replicate our results is available in Puy [90] and in https://github.com/arnaldpuy/irrigation_ efficiency.

Author contributions
A P designed the research, retrieved the data and conducted the simulations. A P and A S designed the uncertainty and sensitivity analysis. J M curated the data from the irrigated area maps. A P, B L, J M, S V K and A S interpreted and discussed the results. A P lead the writing of the paper, with major contributions of B L, S V K and A S in the introduction and discussion sections. All authors edited, revised and approved the final version.