Water savings potentials of irrigation systems : global simulation of processes and linkages

Global agricultural production is heavily sustained by irrigation, but irrigation system efficiencies are often surprisingly low. However, our knowledge of irrigation efficiencies is mostly confined to rough indicative estimates for countries or regions that do not account for spatiotemporal heterogeneity due to climate and other biophysical dependencies. To allow for refined estimates of global agricultural water use, and of water saving and water productivity potentials constrained by biophysical processes and also nontrivial downstream effects, we incorporated a process-based representation of the three major irrigation systems (surface, sprinkler, and drip) into a bioand agrosphere model, LPJmL. Based on this enhanced model we provide a gridded world map of irrigation efficiencies that are calculated in direct linkage to differences in system types, crop types, climatic and hydrologic conditions, and overall crop management. We find pronounced regional patterns in beneficial irrigation efficiency (a refined irrigation efficiency indicator accounting for crop-productive water consumption only), due to differences in these features, with the lowest values ( < 30 %) in south Asia and sub-Saharan Africa and the highest values (> 60 %) in Europe and North America. We arrive at an estimate of global irrigation water withdrawal of 2469 km (2004–2009 average); irrigation water consumption is calculated to be 1257 km, of which 608 km are non-beneficially consumed, i.e., lost through evaporation, interception, and conveyance. Replacing surface systems by sprinkler or drip systems could, on average across the world’s river basins, reduce the non-beneficial consumption at river basin level by 54 and 76 %, respectively, while maintaining the current level of crop yields. Accordingly, crop water productivity would increase by 9 and 15 %, respectively, and by much more in specific regions such as in the Indus basin. This study significantly advances the global quantification of irrigation systems while providing a framework for assessing potential future transitions in these systems. In this paper, presented opportunities associated with irrigation improvements are significant and suggest that they should be considered an important means on the way to sustainable food security.


Introduction
A major humanitarian challenge for the 21st century is to feed a growing world population in the face of climate change and sustainability boundaries (e.g., Foley et al., 2011).In addition to requiring institutional changes, global crop production will likely have to double to meet the demand by 2050 (Tilman et al., 2011;Alexandratos and Bruinsma, 2012;Valin et al., 2014).At present, irrigation is a key component of agriculture; global cereal production would decrease by 20 % without irrigation (Siebert and Döll, 2010), and climate change and population growth will further enhance its role in the future (Neumann et al., 2011;Plusquellec, 2002).In the past 50 years irrigated area roughly doubled Published by Copernicus Publications on behalf of the European Geosciences Union.(FAO, 2012;Siebert et al., 2015) and today about 24 % of the total harvested cropland is irrigated, producing > 40 % of the global cereal yield (Portmann et al., 2010).Irrigation is the single largest global freshwater user, accounting for ∼ 70 % of water withdrawals and 80-90 % of water consumption (Gleick et al., 2009).
However, as the planetary boundaries for freshwater use and land-system change are being approached rapidly or are already exceeded, there is little potential for increasing irrigation or expanding cropland (Steffen et al., 2015;Gerten et al., 2013).Thus, production gaps must be closed by increasing sustainable production and higher cropping intensities on currently harvested land through either increasing rainfed yields or optimizing the water productivity of irrigated cropping systems and ecologically sensitive transforming rainfed systems into irrigated systems (Alexandratos and Bruinsma, 2012).
Indeed, current irrigation efficiencies are often below 50 %, as much of the diverted water is lost in the conveyance system or through inefficient application to the plants.The magnitude of these losses is determined primarily not only by the irrigation system (e.g., sprinkler, surface, drip) but also by meteorological and other environmental conditions.At first glance, the often low efficiency suggests a high potential for water savings.However, only water that leaves the system without a benefit for crop growth, such as evaporation from bare soil and other non-beneficial components (e.g., weed transpiration; Fig. 1), should be considered a manageable loss (e.g., Keller and Keller, 1995).As the different water fluxes are difficult to separate empirically, non-beneficial consumption remains a poorly measured and studied element of the irrigation water balance (Gleick et al., 2011) and associated specific saving potentials are largely neglected in discussions on irrigation improvements (e.g., Perry et al., 2009;Frederiksen and Allen, 2011;Simons et al., 2015).Also, while reducing non-beneficially consumed water clearly enables local yield increases using the same amount of water (Luquet et al., 2005;Molden et al., 2010;Al-Said et al., 2012), it inevitably reduces return flows as well.This can have mid-term negative effects on crop production through faster soil water depletion or less available water for downstream users (Ward and Pulido-Velazquez, 2008).The net effect at the basin level, accounting for downstream effects, is difficult to track with current methods (Nelson et al., 2010;Jia, 2012;Perry and Hellegers, 2012;Simons et al., 2015).
These non-trivial dynamics currently revive an earlier debate on the water saving potential of irrigation improvements (Seckler, 1996;Cooley et al., 2008;Ward and Pulido-Velazquez, 2008;Perry et al., 2009;Pfeiffer andLin, 2009, 2014;Christian-Smith et al., 2012;Brauman et al., 2013;Simons et al., 2015).Previous studies of water saving potentials may have been too pessimistic, as they implicitly assume that total irrigation water consumption is beneficial (Burt et al., 1997;Perry et al., 2009;Simons et al., 2015).Furthermore, estimates of irrigation efficiencies are mostly based on rough assumptions for regions or countries, without dynamic quantitative water accounting.Advanced estimates of global agricultural water consumption, and of water saving and water productivity potentials at basin level require a spatially and temporally explicit and process-based simulation of the irrigation water balance.That is, the performance of irrigation systems shall be represented mechanistically, in direct coupling with vegetation dynamics, climate, soil, and land use properties.
In global agro-hydrological models, irrigation systems are insufficiently represented in this regard.For instance, many models only consider net irrigation requirements without accounting for water losses during conveyance or application (Haddeland et al., 2006;Siebert and Döll, 2010;Stacke and Hagemann, 2012;Elliott et al., 2015).Others employ globally constant indicative efficiency values from e.g., Brouwer et al. (1989), as a static input, (e.g., Wriedt et al., 2009;Wada et al., 2013).These estimates were regionalized for the dominant irrigation system in each country by Rohwer et al. (2007) and since have been often referenced (e.g., Rost et al., 2009;Wriedt et al., 2009;Wada et al., 2011a;Schmitz et al., 2013;Chaturvedi et al., 2015;Elliott et al., 2014), yet still until today they remain rough indicative estimates.Assessments of future irrigation water requirements under climate change also have been carried out using static and countrybased efficiencies, without accounting for local biophysical conditions (Fischer et al., 2007;Konzmann et al., 2013;Elliott et al., 2014).Sauer et al. (2010) endogenously determined the irrigation system based on biophysical and socioeconomic factors, but water fluxes are not simulated.
To our knowledge, besides LPJmL, PCRaster Global Water Balance (PCR-GLOBWB) (Wada et al., 2014)  With the aim of studying global irrigation systems based on an integrated process-based approach, we implement a representation of the three major irrigation systems (surface, sprinkler, and drip) for various crop functional types (CFT) into the global bio-agrosphere model LPJmL.The new irrigation module exceeds previous global modeling studies and replaces an existing scheme that is based on static efficiencies (Rost et al., 2008).It explicitly takes into account the daily surface and soil water balance (potentially limiting water withdrawal) and partitions irrigation water fluxes into transpiration (T ), soil evaporation (E), interception loss (I ), surface and subsurface runoff (R), and deep percolation (Dr), depending on daily weather conditions and solving the water and energy balance.Furthermore, we develop a new global data set on the distribution of irrigation systems for each CFT at the 0.5 • grid level by combining AQUASTAT data on irrigation system distribution, cropland extent, and irrigation suitability.
Based on this data and modeling framework, we first present a spatially explicit, process-based global distribution of irrigation efficiency estimates based on a new, more precisely defined indicator: beneficial irrigation efficiency (E b ).Second, we provide new estimates for irrigation water components on the basis of significantly more spatial, temporal and process details compared to previous studies.Third, we investigate at basin level how much non-beneficially consumed water could be saved, and by how much crop water productivity could be increased, if irrigation system efficiencies were improved.

Definition of irrigation efficiency
Irrigation efficiencies (E i ) are difficult to compare between studies, because there are various approaches to their definition and field measurements are difficult to assess (Burt et al., 1997;Perry et al., 2009).The generic definition is as follows (e.g., Bos and Nugteren, 1990;Seckler et al., 2003;Jensen, 2007): where W c is water consumption (evaporation from soil and water surfaces, transpiration, and interception) and W d is water withdrawal, i.e., the amount of water diverted from rivers, reservoirs, lakes, or groundwater.The remainder, the nonconsumed water, is the return flow (W r ), i.e., surface and lateral runoff and drainage or deep percolation.It thus equals the difference between diverted and depleted water (Lankford, 2006).
Water consumption includes both beneficial and nonbeneficial components.Plant transpiration belongs to the first category, as it occurs simultaneously with CO 2 uptake through the stomata and thus contributes to biomass buildup.The non-beneficial components, which are often of sizeable magnitude, include evaporation from soil and water surfaces, interception losses from vegetation canopies and puddles, and weed transpiration.Such non-beneficially consumed water is lost from the system and forms a real saving potential that is not reflected in E i (Fig. 1).This has already been proposed by Burt et al. (1997), but due to technical challenges to its measurement, evaporation could not be separated from beneficial consumption and thus E i was established as the common efficiency indicator.Here, we refine that definition and emphasize the use of a more precisely defined indicator, E b , given by the ratio of T and withdrawals: E b is further the product of conveyance efficiency (E c ) and field application efficiency (E f ).E c relates to water transport losses from the source to the field: where W f is the amount of water that reaches the field.E f relates to the water application on-field: Irrigation efficiency thus defined is scale dependent, both in time and space.E b is a valid indicator for assessing irrigation system performance at the field (and grid cell) scale, but it does not allow for assessing water saving potentials at the basin level, since it does not take into account that return flows remain partly available for downstream reuse.In this respect, the term effective efficiency was introduced, defined as beneficial consumption (W bc ) per unit of water consumed (W c ), which includes that return flows are assumed accessible (e.g., Keller and Keller, 1995;Seckler et al., 2003;Jensen, 2007).For our analysis of water savings, we focus on the reduction of non-beneficial consumption (W nbc ), and therefore we employ the inverse of effective efficiency, the ratio of non-beneficial consumption and total consumption: Throughout this study irrigation efficiencies are calculated from sums of daily water fluxes over the growing season on the irrigated fraction of each 0.5 • × 0.5 • grid cell in millimeters.As we use these annual values, water remaining in the soil storage is negligible for calculating irrigation efficiencies.
Moreover, we define crop water productivity as where Y irr is yield production in kcal from irrigated crops and W tc is total (blue and green) crop water consumption in liters.The model is able to trace the daily flows of both green water (directly originating from precipitation and infiltrating into the soil) and blue water (diverted from sources like rivers, lakes, reservoirs, and groundwater).Hereinafter, irrigation water fluxes always refer to the unfrozen blue water fraction unless specified otherwise (see Rost et al. (2008) for details).

Suitability of the dynamic process model LPJmL to simulate irrigation systems
The model LPJmL globally represents biogeochemical land surface processes of vegetation and soils (Bondeau et al., 2007;Rost et al., 2008;Fader et al., 2010), simulating daily water and carbon fluxes in direct coupling with the establishment, growth, and productivity of major natural and agricultural plant types.
The spatiotemporal distribution of natural vegetation, represented through nine plant functional types (PFTs), is dynamically simulated based on climatic and carbon dioxide forcing (Sitch et al., 2003).Agricultural land is represented by 12 specified CFTs, a class "others" including a suite of crops collectively parameterized as annual crops, and pastures (Bondeau et al., 2007), all either irrigated or rainfed.The spatial distribution of CFTs and their irrigated fraction is prescribed (see Sect. 2.5).
Photosynthesis modeling in LPJmL follows a modified Farquhar et al. (1980) approach and daily crop carbon assimilation is allocated to harvestable storage organs (e.g., cereal grain) and three other pools (roots, leafs, stems).Sowing dates are dynamically calculated based on climatic and crop conditions (Waha et al., 2012).Crops are harvested when they reach maturity, defined either through a CFTspecific maximum value of daily accumulated phenological heat units or expiration of the growing season.Storage organs are subsequently removed from the field.Root growth and distribution within soil layers is CFT-specific, while the soil profile is discretized into five hydrologically active layers and bedrock (Schaphoff et al., 2013).
Plant growth is currently not directly nutrient-limited in LPJmL, yet constrained by temperature, radiation, water, and atmospheric CO 2 concentration.We calibrate crop yields with national FAO statistics based on three model parameters (as in Fader et al., 2010) to account for CFT-specific management intensities.
LPJmL partitions precipitation (prec) and applied irrigation water into interception, transpiration, soil evaporation, soil moisture, and runoff.Infiltration rate of the surface soil layer is a function of the saturation level (Eq.A1).Surplus water that cannot infiltrate (iteratively in 4 mm slugs) generates surface runoff.Subsurface soil water above saturation runs off in lateral direction, while remaining soil water above field capacity (W fc ) percolates to the layer beneath, depending on its soil water content and hydraulic conductivity.Globally, 13 soil types are differentiated, according to their water holding capacity (WHC), hydraulic conductivity, and soil texture (Schaphoff et al., 2013).Surface and lateral runoff and seepage groundwater runoff, which is the percolation from the bottom soil layer, are added to cell runoff and are subsequently available for downstream reuse, routed along the river network.While in reality not all return flow is recoverable (due to degradation or inaccessibility; Fig. 1), LPJmL only considers the eventual outflow to oceans as nonrecoverable.
Beneficial water consumption, i.e., transpiration, is calculated as the minimum of atmospheric demand (D), equal to potential evapotranspiration (PET) in the absence of water constraints, and actual root-available soil water constrained by plant hydraulic traits (supply S).PET is computed after Priestley-Taylor but modified by above-plant boundary layer dynamics (Gerten et al., 2007).If D exceeds S, crops begin to experience water stress (Eqs.A1 and A2).Evaporation is a function of PET, soil water content in the upper 30 cm, vegetated soil cover, and radiation energy (Eq.A3).Interception loss is a function of leaf area index (LAI), the daily fractional vegetation coverage, leaf wetness, and PET (see Eqs. ( 9) and (10) below).
Moreover, we account for household, industry and livestock water use (HIL; assumed to be consumed prior to any irrigation; see Sect.2.5) and include a representation of dams and reservoirs to improve the simulation of available surface water (Biemans et al., 2011).
Thus, water fluxes are simulated in considerable detail, in direct coupling with vegetation dynamics, and responsive to climatic conditions.LPJmL is therefore well suited for studying water fluxes associated with differentiated irrigation systems in an internally consistent and process-based manner.

Implementation of the new irrigation scheme in LPJmL
We implement the three major irrigation systems -surface, sprinkler, and drip -according to their generic characteristics in direct coupling with the model's soil water balance, which overcomes the earlier scheme of fixed efficiencies as in Rost et al. (2008).Irrigation systems differ in the way they distribute water across the field.Surface systems (basin and furrow combined) flood the field, sprinkler uses pressurized sprinkler nozzles and micro/drip is the most costintensive system using localized water application directly to the plants' root zone.Indicative efficiency values (E i ) as-  Variables represented in grey-shaded boxes depend on system-specific parameters that are presented in Table 1.
In our model, irrigation water is supplied based on daily soil water deficit.Daily net irrigation requirement (NIR; mm) is requested for withdrawal, if S falls below D. We define NIR as the amount of water required in the upper 50 cm soil to avoid crop water limitation.It is calculated to meet field capacity: where w a is the actual available soil water in millimeters.Due to the above-described system inefficiencies, additional water needs to be requested to meet crop water demand.Therefore, we account for conveyance efficiency and calculate application requirements (AR) for each system, which add up to gross irrigation requirements (GIR; mm), the water amount requested for abstraction (Fig. 2): where "Store" is a storage buffer (see below).
For pressurized water transportation (sprinkler and drip), E c is set to 0.95, as we assume inevitable losses from leakage of 5 % (Brouwer et al., 1989).We associate surface irrigation with open-canal transportation and we further link E c to the hydraulic conductivity (K s ) of the soil type.E c estimates from Brouwer et al. (1989) are adopted; see Table 1.We assume half of conveyance losses are due to evaporation from water surfaces and the remainder is drainage and added to return flow.
AR is the additional amount of water necessary to distribute irrigation uniformly across the field, indicative of the farmer's estimate of application losses (that are simulated by the model).We calculate AR as a system-specific scalar of the free water capacity: where W sat is soil water content at saturation point, in millimeters; "DU" is the water distribution uniformity scalar, depending on the irrigation system (Table 1), and w fw is the available free water (actual soil water content between saturation and field capacity).Surface irrigation systems use large amounts of water to flood the field in order to uniformly distribute water, which results in considerable surface runoff and seepage (see our analysis below, and Rogers et al., 1997).This is represented through DU = 1.15, leading to temporary oversaturation of the field.For sprinkler systems, "DU" must not be smaller than 0.55 to securely deliver NIR into the upper 50 cm of the soil (Fig. S1 in the Supplement).Drip systems apply water localized to the plant and therefore distribution requirements are much lower; with DU = 0.05 average yield levels are slightly below the potential (modest form of deficit irrigation), yet allocating salt leaching requirements (Fig. S1).
Daily GIR and HIL add up to the total withdrawal request in each cell.This demand is met from local surface water, including reservoir water and if not sufficient, requested from neighboring upstream cells (Fig. 2 and Biemans et al., 2011).Actually withdrawn irrigation water is always reduced by conveyance losses.
Irrigation scheduling is simulated to be controlled by "prec" and the irrigation threshold (IT), which defines the allowed degree of soil water depletion prior to irrigation.In sensitivity analyses we found that "IT" is dependent on the CFT.C4 crops (maize, tropical cereals, sugarcane) are less sensitive to drought stress, because, in contrast to C3 crops, they use a more efficient enzyme on the pathway of CO 2 fixation (Amthor, 1995).The maximum yield for C4 crops is at IT = 0.7 (global median; Fig. S2).Values of "IT" for C3 crops (0.8-0.9) are found to be affected by annual "prec"; paddy rice is always parameterized with IT = 1 (Table 1).Available irrigation water is reduced by available precipita- tion and the amount that is not released (if S > IT; see Fig. 2) is added to "Store" (model-internal compensation for local water availability) and kept available until the next irrigation event.
Surface and drip systems are simulated to apply irrigation water below canopy, and sprinkler systems above canopy with associated interception losses: where "pt" is the Priestley-Taylor coefficient (1.32), f v is the fraction of vegetated soil cover, and "wet" is fraction of the day with wet leaf surface, calculated as where "intc" is a CFT-specific interception storage parameter (Gerten et al., 2004).Droplet evaporation with sprinkler systems, presumably < 1.5 % of the applied water (Meyers et al., 1970;Rogers et al., 1997), is implicitly accounted for.Furthermore, we restrict surface runoff for sprinkler systems, such that irrigation water that reaches the soil surface infiltrates and can only run off laterally or percolate into deeper layers.
We design drip systems, in contrast, with a loss-free infiltration into the first two soil layers, i.e., no surface or lateral runoff are subtracted from W i .Soil evaporation losses from drip systems (only blue water) are reduced by 60 %, to account for its localized subsurface application of water (Table 1).

Development of new input data set for grid-level irrigation system distribution
Currently, no sub-regional information on the global distribution of irrigation systems is available, which would provide the missing link to more accurate simulations of irrigation water requirements and performances.We therefore develop a new data set of the global distribution of irrigation systems, for each grid cell and CFT (Fig. 3).Country-level shares of irrigation systems can be associated with a series of socioeconomic and biophysical factors.A comprehensive explanation of these patterns is beyond the scope of this study, and here we simply adopt national statistics from AQUASTAT (FAO, 2014).Each country is assigned the respective share of the three irrigation systems (Table S1 in the Supplement), which we further disaggregate to the grid cell and the CFTs through a decision tree approach, using the extent of irrigated areas by CFT (Porkka et al., 2015;Siebert et al., 2015) and an irrigation system suitability table.The CFT suitabilities for each irrigation system (Table 2) are determined based on restrictions due to soil type, the CFT-specific tolerance toward moisture depletion, the characteristic planting and harvesting techniques, the specific physical habit of the crop, and its economic market value (e.g., low market value crops are excluded from drip irrigation), based on Sauer et al. (2010) and Fischer et al. (2012).The distribution of irrigation systems is adjusted annually (see Supplement for further details).

Simulation protocol
For this study, we ran LPJmL for the time period 1901-2009, forced with the Climate Research Unit's (CRU) TS 3.1 monthly climatology for temperature, cloudiness and wet days (Harris et al., 2014) and with the Global Precipitation Climatology Centre's (GPCC) precipitation data (Version 5) (Rudolf et al., 2010).Transient runs follow a 120-year spinup (recycling the first 30 years of input climatology) to bring sowing dates into equilibrium, which are fixed during the simulation period after 1960.Spatially explicit global information on cropland extent is obtained from the MIRCA2000 land use data set (Portmann et al., 2010).The extent of areas equipped for irrigation from 1900 to 2005 is imported from Siebert et al. (2015), who provide an improved estimate of historic irrigation expansion with a total global extent   2015).
Water use for non-agricultural sectors, HIL, account for 201 km 3 in the year 2000 based on recent estimates by Flörke et al. (2013).Our baseline simulation assumes that irrigation water withdrawal is constrained by local, renewable water storage, i.e., there is no implicit assumption about contributions from fossil groundwater or diverted rivers.If not indicated otherwise, results are presented as 1980-2009 averages.
In addition to the current distribution of irrigation systems, we ran three synthetic scenarios (hereinafter: all-surface, allsprinkler, all-drip), in which it is assumed that each system is respectively applied on the entire global irrigated area, irrespective of system suitability for crop types (Table 2).These scenarios were developed to investigate the global performance of each system and to provide an estimate of the effect of irrigation system transitions, they do not represent feasible transition targets.

Global patterns of irrigation efficiency
A total of 51 % of total global diverted irrigation water is simulated to be consumed (mean global area-weighted E i = 58 %) and 26 % are beneficially consumed, i.e., transpired (mean global area-weighted E b = 33 %), following our process-based implementation.In Fig. 4 we show global spatial patterns of E b , which are to a large extent determined by the irrigation system in use (Fig. 3), but as importantly, by its performance under local biophysical conditions and the present crop type.Extensive regions in central, south, and Southeast Asia with high shares of surface irrigation (widespread rice cultivation) show low efficiency values of < 30 %. North China plains with high irrigation intensity and mainly maize and wheat varieties exceed 50 %, but particularly Europe and North America stand out with values well above the global average due to relatively high shares of sprinkler and drip systems.The latter also applies to Brazil, South Africa, and the Ivory Coast, where E b exceeds 60 %.To illustrate system performances unaffected by their current geographical distributions, Fig. 5 displays E b for the three irrigation systems separately, each assumed to be applied on all irrigated areas.Under this condition, global average values of E b for surface, sprinkler, and drip systems are 29, 51, and 70 %, respectively.Across all three scenarios, we find a remarkable low efficiency in Pakistan, northeast India, and Bangladesh, opposed to above-average levels in the Mediterranean region, North China plains and the US Great Plains.Moreover, E b varies considerably between crop types due to different plant physiology and different cultivation regions/climate zones (Fig. 6; see next section).The values for maize, sugarcane, and temperate roots are above the average across CFTs in our simulation, while rice, pulses, and rapeseed form the lower end.E b is also sensitive to precipitation, soil properties, and other biophysical factors, as characterized in Sect.3.4.We provide an online versions of global patterns of beneficial irrigation efficiencies (second SI, illustrated in Fig. S4) as gridded input for other studies.

Global irrigation water fluxes
Global irrigation water withdrawals simulated with our newly developed, process-based irrigation scheme are 2469 km 3 per year, averaged for the time period 2004-2009; 1212 km 3 return to the river system, while 1257 km 3 are consumed (1458 km 3 including consumption from nonagricultural sectors HIL), of which 649 km 3 are beneficially consumed, i.e., transpired by crops (Table 3).The remainder, 608 km 3 , is non-beneficially consumed and is indicative of the substantial water saving potentials associated with irrigation improvements (see Sect. 3.3 for details).
Figure 6 illustrates the decomposition of irrigation water fluxes for each CFT and all three irrigation systems.Transpiration is relatively constant across irrigation systems (irrigation target).However, on a global average, drip systems achieve 9 % less transpiration compared to sprinkler systems (beneficial consumption; Table 3).This result reflects that drip irrigation systems generally do not aim to saturate the soil and thus conduct a modest form of deficit irrigation not designed to maximize yields but to save water.
Return flow with surface irrigation forms the major part of non-beneficial fluxes, exceeding by a factor of 2 the nonbeneficial consumption (evaporation from soil and water surfaces).Sprinkler systems have a considerably lower return flow fraction (34 % of withdrawal), which further declines with drip systems (13 % of withdrawal), and is here smaller than the fraction of non-beneficial consumption (Table 3 and Fig. 6).Conveyance losses are significantly lower with sprinkler or drip systems due to pressurized conveyance.Evaporation losses are relatively similar between surface and sprinkler systems, while drip systems show lower losses due to their system design.Interception losses with sprinkler systems (surface and drip apply water below canopy) form only a minor contribution to non-beneficial fluxes (Fig. 6).(excl. "others" and pastures).This figure is based on theoretical scenarios, in which each system is respectively assumed to be applied on the entire irrigated area.

Potential of irrigation system transitions
We simulated three theoretical "all-one-type" scenarios to investigate the global potential of irrigation system transitions.Replacing a surface system by sprinkler or drip systems could, on average, reduce the target value -non-beneficial consumption -by 54 and 76 %, respectively, while maintaining yield production at the global level (indicated by W bc in Table 3).Withdrawal amounts would decrease by 44 and 68 %, and return flows by 63 and 92 %, respectively.While upgrades of irrigation systems thus appear to be beneficial locally and mostly easing water diversion, major reductions of return flows can also have negative local impacts on downstream users.To evaluate the net effect along rivers and identify river basins that are most sensitive to irrigation improvements, we assessed water saving potentials and changes in water productivity at river basin level for each transition scenario.
Currently, the ratio of non-beneficial consumption to total consumption is particularly high in some south Asian basins (Indus, Ganges, Mahanadi), Korea, the Sahel, and Madagascar (Fig. 7a).A transition from surface to sprinkler or drip systems is simulated to cause a distinct reduction in nonbeneficial consumption mainly in these regions, but also in temperate regions in Europe, North America, the Yangtze basin, Brazil, Argentina, and South Africa (Fig. 7c and e).Mean basin-level reductions in non-beneficial consumption would amount to 54 % when moving from surface to sprinkler systems and 76 % when moving to drip systems (Table 4).
Current global mean water productivity is simulated to be 2.83 kcal per liter, but with very distinct regional patterns (Fig. 7b) due to a combination of many factors, mainly heterogeneous crop management intensities and current distribution of irrigation systems.We find a strong gradient from very low values (< 2 kcal per liter) in Central America, sub-Saharan Africa (SSA), and south Asia, to medium levels in east Asia and high values of ∼ 4-5 kcal per liter across North America and Europe.Replacing a surface system by a sprinkler or drip system would increase crop water productivity   averaged over the respective growing seasons and cultivated areas.For better comparability, each system is individually applied on all irrigated areas assuming the same, optimal management.The number at the top of each stack represent the CFT-specific beneficial irrigation efficiency (E b , in %).Tropical roots are not irrigated.by (globally averaged) 9 and 15 %, respectively (Table 4).
In individual basins, e.g., in extensive regions in central and south Asia, Mediterranean region, and the Nile, in the Sahel, in South Africa, and in the Colorado basin, effects would be even more pronounced: at basin level production increases of ∼ 20 % (sprinkler) and ∼ 30 % (drip) would be attained (Fig. 7d and f).Moreover, we show explicitly that transpiration and total water consumption do not form a one-to-one relation, as is often argued when discussing the potential of irrigation transitions (e.g., Perry et al., 2009).Surface, sprinkler, or drip systems follow individual slopes, disclosing saving potential (Fig. 8).Overall, this pilot analysis of irrigation system transitions shows that water saving potentials and water productivity improvements could be significant in many regions, on local farms, and across basins.

Evaluation of simulation results
Our estimates of global irrigation water withdrawal and consumption (W d : 2469 km 3 ; W c : 1257 km 3 ) agree well with previously published, but not always state-of-the-art estimates.Country statistics for W d reported for the period 1998-2012 are 2722 km 3 (FAO, 2014), while model estimates range between 2217 and 3185 km 3 (Wada and Bierkens, 2014;Döll et al., 2014;Siebert and Döll, 2010;Wada et al., 2011b;Alexandratos and Bruinsma, 2012;Döll et al., 2012).Estimates for W c range from 927 to 1530 km 3 (Hoff et al., 2010;Chaturvedi et al., 2015;Döll et al., 2014).Döll et al. (2012) concludes that 1179 km 3 (Wada and Bierkens, 2014, 1098 km 3 ) stem from surface water and an additional 257 km 3 from groundwater resources.This is supported by Wada et al. (2012), who also point out that non-renewable groundwater abstractions are expected to contribute ∼ 20 % to the global GIR.In this study we did not account for fossil groundwater and desalination.However, 80 % of groundwater abstractions are assumed to be recharged by return flows (Döll et al., 2012); thus, it is plausible that W d as simulated here is somewhat lower than in studies that simulate (fossil) groundwater contributions.It is also important to point out that irrigation water estimates are sensitive to the precipitation database employed (Wada et al., 2014).
Irrigation efficiencies are difficult to validate due to nonhomogeneous definitions and problems in its measurement in the field.Nevertheless, in Table 5 we put our results into the context of comparable literature results.At the global level, we meet established indicative estimates of field application efficiency by Brouwer et al. (1989).These have been downscaled to the country level by Rohwer et al. (2007) and the area-weighted global mean is 49, 69, and 90 % for the three systems.Another independent estimate of field efficiency at the sub-continent level is provided by Sauer et al. (2010) with global mean values of 42, 78, and 89 %.Our estimates  (c, d) and surface to drip systems (e, f), respectively (all-surface, all-sprinkler, and all-drip scenarios).Pastures and "others" are excluded.are well in line with these numbers, although some regional patterns from Sauer et al. (2010) are not represented in our results (Table 5).They find very low surface irrigation efficiencies in Middle East and North Africa (MENA) and SSA, while we arrive at slightly above-average values in MENA and particularly low values in south Asia, which is supported by Döll and Siebert (2002) and Rosegrant et al. (2002).For Malaysia, e.g., Ali et al. (2000) confirms below-average values.Furthermore, our estimates of global water productivity agree very well with previous estimates (e.g., Brauman et al., 2013;Zwart and Bastiaanssen, 2004;Rosegrant et al., 2002).Overall, the performance of our new irrigation model is well in line with the patterns reported in previous studies (while being much more detailed in terms of process representation, spatial, and temporal patterns), rendering this implementation operational.
With Fig. S3 we can show that mechanistically simulated irrigation water fluxes (and thus efficiency patterns) follow expected biophysical dependencies.We are able to fit significant empirical relations between components of the irrigation water balance and biophysical explanatory variables, although each component is affected by interlinked processes and input variables, which themselves exhibit spatiotemporal patterns (e.g., local climatic conditions, crop type, crop phenology, LAI, length of the growing season, soil parameters).For instance, return flow mainly depends on "prec" and WHC; WHC is more relevant for surface systems, while "prec" appears to be most decisive for drip systems.Above-

Significance of results
This study presents for the first time spatially and temporally explicit estimates of irrigation system performances (separately for the world's major crop types) at the global level, based on process-based simulation of underlying local biophysical conditions.Hence, this study advances the global quantification of irrigation systems while providing a framework for assessing potential future transitions in these systems as likely required in view of projected increases in world food demand.Our global irrigation water estimates and regional efficiency values are well in line with existing literature, but we find distinct spatial patterns that were not available before with such a level of spatial, temporal, and process detail.Generally, it has been assumed that economic and agronomic drivers control spatial patterns of irrigation efficiencies (e.g., Sauer et al., 2010;Schmitz et al., 2013).
Here we show that biophysical factors additionally have nontrivial effects on spatial patterns of system efficiencies.Moreover, we show that enhanced irrigation techniques offer substantial opportunities to reduce irrigation water consumption while maintaining beneficial transpiration rates and, thus, crop production levels at the river basin level.We also identify river basins in south Asia, in the Mediterranean region, and the Sahel to be most sensitive to irrigation improvements resulting from the combination of local crop types, climate, and soil conditions and the current irrigation system.These findings contribute to the current debate on global opportunities associated with irrigation systems and results suggest that irrigation improvements are an important contribution to sustainably increase food production (among various other means, e.g., Kummu et al., 2012;Jalava et al., 2014).The new implementation is a prerequisite for followup studies of global crop production and yields under changing climate, production potentials of irrigation system transi-tions and expansions, and climate change impacts on irrigation efficiencies and demands.

Modeling issues
Previous LPJmL estimates of W d and W c (Rost et al., 2008;Konzmann et al., 2013) are now improved with this study.Those earlier estimates tended to be lower than comparative studies, because first, the extent of irrigated land was scaled down for reasons of multi-cropping (see Fader et al., 2010, for details).Second, we believe that the new implementation accounts for a more realistic simulation of irrigation fluxes and the soil water balance, which on the one hand increases water demands, and on the other hand improves discharge dynamics, in that applied irrigation water percolates through soil layers and runoff rates are more realistically delayed.
Generally, not all of the area equipped for irrigation is being irrigated every year, especially where supplementary irrigation is practiced.Such deficits can be considerable, mostly in temperate and humid regions (Siebert and Döll, 2010;Siebert and Ewert, 2014).We claim that they are mostly considered in our simulations as it is a key component of our irrigation module to dynamically trigger or pause the application of irrigation water based on soil water deficit and blue water availability.However, variations in irrigated area due to other reasons (not reflected in the land use input data set) cannot be accounted for.
Validation of the new map of subnational distribution of irrigation systems remains a challenge until independent data of such becomes available at a large scale.Nonetheless, regional patterns are in accordance with national statistics and the recent literature, as our map is based on FAO country shares and explicit locations of irrigated cropland (Sect.2.4).The reliability of our subnational distributions is strengthened across smaller countries (one national value controls a smaller area).But since irrigation efficiencies are generally better documented than the distribution of irrigation systems, we oppose efficiency values simulated in this study with published local and regional studies (Sect.3.4).Irrigation efficiencies depend to a large degree on the geographical distribution of irrigation systems.
The CFT group "others" pools a variety of crops including perennial and annual types (e.g., cotton, citrus, coffee) but is generically parameterized as perennial grassland.Therefore, the growing season length for these crops is systematically overestimated, which may lead to somewhat too high estimates of total water use and demand.This potential overestimation might be counterbalanced by an overestimation of accessible return flow, as LPJmL cannot account for the fact that return flows are only partly recoverable (physically or economically), and that they are often degraded through nutrient leaching and salinity.
Irrigation can have other purposes than satisfying crop water requirements, like salt leaching, crop cooling, pesticide or fertilizer applications, or frost protection.These irrigation applications are however beyond the scope of this study and are not explicitly considered in the withdrawal demand.Salt leaching below the root zone, as for the most significant of those, is critical in regions with marginal precipitation and can be controlled through applying an additional 5-10 % irrigation water (Jensen, 2007).Figure 6 shows that in our implementation the runoff share with drip irrigation is, on average, large enough to meet this requirement.
Irrigation improvements can also be achieved by means other than completely replacing the system, e.g., through better scheduling (incorporating climate and soil data to precisely meet crop water demand), advanced management (deficit irrigation), and technical improvements.For instance, much water might be saved from evaporation and seepage if open-canal conveyance systems were replaced by lined or pressurized installations.For the purpose of simplicity, in this study we bundle these various opportunities into the three different simulated generic systems and represent improvements through system transitions.

On irrigation system transitions
From a sustainability perspective, the primary objective in regions with irrigation overdraft is the reduction of irrigation water consumption.In the face of a growing human population and various rapidly approaching planetary boundaries (Steffen et al., 2015), an immediate question thus is, by how much global crop water productivity and crop production can be improved with sustainably available water resources.Water saved through improved irrigation systems could allow either for an expansion of irrigated areas or for a production increase on irrigated yet water-limited farms.Throughout this paper we argue that the water saving potential is mostly constrained to the non-beneficially consumed fraction, as return flows are often accessible downstream.Egypt's Nile valley is an example of a multiple use-cycle system with a high basinlevel efficiency but low local efficiencies (Keller and Keller, 1995).
Many authors thus argue that irrigation efficiencies add up close to 100 % at the basin level and therefore assume that water saving potentials through efficiency improvements are very limited (Seckler, 1996;Perry et al., 2009;Frederiksen and Allen, 2011).These findings are based on an assumption that crop transpiration follows a one-to-one relation with water consumption (Perry et al., 2009); saving potentials within the consumed fraction are largely neglected.Herein, we show that transpiration and consumption are not as closely linked as previously assumed, and that adapting modern irrigation techniques can indeed bring this dependency closer to the one-to-one line (Fig. 8).Accordingly, we show that transpiration rates (hence crop production) can be maintained while cutting the consumed volume in many regions at the basin level.
However, the implementation of such technical water saving potential does not necessarily imply that less water would be diverted.Farmers' decisions are often driven by maximizing their return and rarely by environmental concerns; if they pursue efforts to save water, they often use it to expand their irrigated areas or shift to higher value crops, rather than losing water allocations (Ward and Pulido-Velazquez, 2008;Perry and Hellegers, 2012;Pfeiffer and Lin, 2014;Shah, 2014).From a food security perspective, however, irrigation improvements drive water productivity and thus increase gross crop yield, consuming the same amount of water.
Nevertheless, increasing irrigation systems at the global scale while respecting sustainability boundaries, requires a complex combination of substantial investments, institutional water policy regulations, and cultural changes.Intelligent water pricing (currently rarely reasonable) is for instance a measure to achieve trade-offs at basin level through economic incentives (e.g., Molden, 2007;Molle and Berkoff, 2007;Ward and Pulido-Velazquez, 2008).
Overall, this study suggests that the potential of irrigation improvements might be more substantial than often anticipated in recent discussions.Nonetheless, such investments should be combined with other measures available to sustainable intensification (e.g., mulching, reduced tillage, and rain-water harvesting).

Conclusions
This study presents for the first time spatially and temporally explicit estimates of global irrigation system performances for the world's major crop types, based on processbased simulation of underlying local biophysical conditions.Hence, this study significantly advances the global quantification of irrigation systems while providing a framework for assessing potential future transitions in these systems.We arrive at an estimate of global annual irrigation water withdrawal of 2469 km 3 (2004-2009); irrigation water consumption is calculated to be 1257 km 3 , of which 608 km 3 are non-beneficially consumed.We find distinct spatial patterns in irrigation efficiency governed by biophysical conditions, which have been largely neglected in most previous studies.This new map of irrigation efficiencies is provided for incorporation into other global hydrological and agricultural studies, serving as a prerequisite e.g., for refined simulation of crop yields under conditions of future climate change and growing food demand.At the river basin level, i.e., accounting for downstream effects, we reveal, for many basins, the potential for sizeable reductions in non-beneficially consumed water (54-76 %) and related significant increases in crop water productivity (9-15 %) through transitions from surface to sprinkler or drip systems.These findings clearly suggest that irrigation system improvements should be considered an important means on the way to sustainable food security.

Figure 1 .
Figure1.Pathways of irrigation water fluxes.All diverted water is either consumed (non-)beneficially, or re-enters rivers, reservoirs and aquifers, which makes it recoverable through return flow.Nonbeneficial consumption and non-recoverable return flow can be considered losses (at the basin scale).

Figure 2 .
Figure2.Irrigation water flows in LPJmL from plant-specific net irrigation requirement to actual field application.Variables represented in grey-shaded boxes depend on system-specific parameters that are presented in Table1.

Figure 3 .
Figure 3. Global distribution of irrigation systems at country level, based on AQUASTAT statistics.Cells that include irrigated areas are hatched, based on Siebert et al. (2015).

Figure 4 .
Figure 4. Global patterns of beneficial irrigation efficiency (E b , ratio of transpired and diverted water) as area-weighted mean over CFTs (exclusive "others" and pastures) and based on the system distribution in Fig. 3.

Figure 5 .
Figure 5. Global patterns of beneficial irrigation efficiency (E b , ratio of transpired and diverted water) for each irrigation system -(a) surface, (b) sprinkler, and (c) drip, calculated as area-weighted mean overCFTs (excl."others" and pastures).This figure is based on theoretical scenarios, in which each system is respectively assumed to be applied on the entire irrigated area.

Figure 6 .
Figure6.Decomposition of beneficial and non-beneficial irrigation water fluxes for each simulated CFT and irrigation system, in mm day −1 averaged over the respective growing seasons and cultivated areas.For better comparability, each system is individually applied on all irrigated areas assuming the same, optimal management.The number at the top of each stack represent the CFT-specific beneficial irrigation efficiency (E b , in %).Tropical roots are not irrigated.

Figure 7 .
Figure 7. Basin-level aggregation of ratio of non-beneficial consumption and total consumption (RNC; a), and water productivity (kcal from irrigated crops per consumed liter of blue and green water; b) given the current distribution of irrigation systems.(c)-(f) show the relative change in E b and water productivity given a transition from surface to sprinkler(c, d) and surface to drip systems (e, f), respectively (all-surface, all-sprinkler, and all-drip scenarios).Pastures and "others" are excluded.

Figure 8 .
Figure 8. Relation of blue water consumption and blue water transpiration for the three scenarios all-surface, all-sprinkler, all-drip, and each grid cell, compared to the 1/1 line.
per unit crop area based on surface and soil water balance, yet only for two crop classes without partitioning beneficial and non-beneficial water consumption.LPJmL as described herein now solves the complex irrigation water balance with considerable spatial and temporal detail (see Sect. 2.2).

Table 3 .
Global annual sums (km 3 ) of irrigation water withdrawal (W d ), return flow (W r ), irrigation water consumption (W c ) further split into beneficial (W bc ) and non-beneficial consumption (W nbc ), and global mean E b (average across irrigated cropland, in %), given as 2004-2009 averages.Values are for actual conditions and the all-surface, all-sprinkler, and all-drip scenarios.

Table 4 .
Mean basin-level changes in non-beneficial consumption (W nbc ) and crop water productivity (CWP) through system transitions from surface to sprinkler and drip; area-weighted means over all simulated basins in %.

Table 5 .
Comparison of field application efficiencies (for reasons of comparison, we employ here the traditional definition: consumed per applied irrigation water) for major world regions compared with literature values in %.This study's results are area-weighted averages, based on current distribution of irrigation systems (Fig.3).