Irrigated areas drive irrigation water withdrawals

The paper addresses how to reliably estimate global irrigation water withdrawals, a key component of food and water security. Two dominant approaches exist: FAO/Aquastat’s country survey-based statistics and Global Models (global hydrological, land surface, and earth system models) that simulate withdrawals using detailed sub-models (crop, climate, evapotranspiration, efficiencies, irrigated areas). Both face drawbacks including data reliability, heterogeneity, missing values (FAO), and high complexity, calibration challenges, opacity, and computational cost (Global Models). The research question is whether irrigation water withdrawals can be robustly predicted using only irrigated area, thereby reducing complexity while adequately capturing uncertainty. The study’s purpose is to evaluate the strength of the irrigated area–withdrawal relationship, quantify uncertainties and sensitivities, and test whether a parsimonious model can match FAO and Global Model outputs across regions and scenarios, thus improving transparency and utility for policy.

The paper situates its contribution within literature on global irrigation and water demand estimation. FAO/Aquastat compiles withdrawal statistics but suffers from data inconsistency, political and bureaucratic biases, and gaps. Global Models (e.g., PCR-GLOBWB, H08, LPJmL, WaterGAP, MPI-HM, DBHM, VIC, CLM) calculate irrigation withdrawals using complex formulations incorporating evapotranspiration, crop calendars, irrigation efficiency, and climate forcings. Prior works show considerable model spread and sensitivity to uncertain inputs (crop types, irrigation extent, climatic and soil conditions), with ensemble approaches not fully resolving uncertainty and adding complexity. Recent critiques suggest simple models can be more robust when facing irreducible uncertainties. Irrigated area mapping has evolved beyond FAO-GMIA to multiple datasets (e.g., MIRCA2000, HYDE, remote-sensing products), which can differ by orders of magnitude, underscoring structural uncertainty in area inputs that heavily condition model outcomes.

Data: The study uses country-level irrigation withdrawal estimates from eight Global Models (PCR-GLOBWB, H08, LPJmL, WaterGAP, MPI-HM, DBHM, VIC, CLM45), focusing on 2005 values (downscaled or from ISI-MIP, with climate forcings WFDEI, MIROC5, GFDL as applicable), and two FAO-based datasets (Aquastat 2012; Liu et al. 2016 imputed Aquastat). Irrigated areas are taken from FAO-GMIA (national level). For cell-level analysis, irrigated areas from HYDE 3.2 (which uses GMIA and MIRCA2000) are paired with model grid cells. Future projections (2050) are retrieved from ISI-MIP for PCR-GLOBWB, LPJmL, H08, MPI-HM under scenarios combining SSP2 with RCP2.6/6.0 and fixed-2005 socioeconomics with RCP2.6/6.0/8.5. Data are aggregated from monthly 0.5° cells to annual national totals. Model: The core model is a log–log linear regression: log(y_c) = α + β log(x_c), where y_c is irrigation water withdrawal and x_c irrigated area for country c. The goodness of fit is measured with r^2. Uncertainty analysis: Four uncertainty triggers are explored via Monte Carlo using Sobol’ quasi-random sequences: X1 (choice among 10 datasets: 8 GMs + 2 FAO-based), X2 (multiple imputation method for missing y: Bayesian regression, linear regression ignoring model error, linear regression with bootstrap), X3 (selection among d=40 imputations), and X4 (robust vs non-robust regression for r^2 to handle outliers). Missing values (69 across 28 countries) are multiply imputed to maintain consistent pairs of x and y. The computational design uses matrices A, B, and A*^i to estimate sensitivities, with N=2^13 rows, leading to 49,152 model runs per continent. Sensitivity analysis: Variance-based global sensitivity analysis with Sobol’ indices (first-order S_i and total-order T_i) computed via Jansen estimators quantifies contributions of X1–X4 and their interactions to variance in r^2. Predictive ranges: Using the ensemble of α, β from simulations (2,400 pairs), country-level prediction intervals for withdrawals are generated from irrigated areas and compared against point estimates from the 10 datasets. Additional scaling analyses are performed at subnational and system levels (Australian irrigation schemes, Colorado counties, U.S. states) and at grid-cell scale across GMs. Validation: Comparison includes current (circa 2005–2012) and future (2050) GM estimates under multiple RCP/SSP configurations, assessing the proportion of model outputs framed by the simple model’s prediction intervals.

• Strong linear relationship: At the country level, irrigated area explains most of the variance in irrigation withdrawals across continents. Linear regressions with irrigated area as predictor fit well, while other GM parameters (irrigation efficiency, total/potential evapotranspiration) show little additional explanatory power.
• Goodness of fit (r^2): Africa P2.5–P97.5 ≈ 0.75–0.90; Asia 0.68–0.92; Americas 0.68–0.95; Europe 0.50–0.89. Lower r^2 modes are associated with specific GMs (e.g., CLM45, MPI-HM, VIC, PCR-GLOBWB depending on continent).
• Dominant uncertainty driver: The dataset choice (X1) explains 72% (Africa) to 95% (Asia) of variance in r^2. Robust vs non-robust regression (X4) adds ~12% in the Americas; remaining variance arises from higher-order interactions (e.g., X1–X2–X3 contributing ~5–10%).
• Predictive validity: The simple model’s prediction intervals captured 7 or more of the 10 point estimates for 99/139 countries (71%), and all 10 estimates for 26 countries (18%), including major consumers (Egypt, South Africa, USA, Mexico, Brazil, Afghanistan, India, Pakistan, Italy, Spain, France). For China, 9/10 were framed (VIC was outside).
• Outliers: Countries with poor framing include Malta (none), Seychelles (1), Cuba and Kuwait (2), Ethiopia, Puerto Rico, Indonesia, Philippines (3). VIC frequently falls outside intervals in Africa (~51%), Asia (~58%), Europe (~43%); CLM45 does so in the Americas (~33%).
• Future projections: For 2050, across SSP2×RCP scenarios, the simple model frames GM estimates for most countries as well as for current conditions; ~80% of countries have high coverage for both present and future estimates.
• Multi-scale consistency: The irrigated area–withdrawal relationship holds at irrigation system (Australia), county (Colorado), state (USA) scales with r^2 ~0.7–0.9, and at grid-cell level in several GMs (notably CLM45, MPI-HM) and countries across continents.
• Scaling exponent β: At continental scales, β varies by dataset (can be <1, ≈1, or >1), preventing a universal scaling law; for Australian systems and Colorado counties β≈1; for U.S. states β>1, indicating disproportionate water use with larger irrigated areas.
• Model dependence on irrigated area datasets: GMs are highly sensitive to the FAO-GMIA irrigated area inputs; alternative global irrigated area datasets can differ by up to four orders of magnitude at country level, implying much larger uncertainty if accounted for. Uncertainty in future irrigated areas (300–800 Mha by 2050, extremes to 1800 Mha) will expand uncertainty in projected withdrawals.

Findings demonstrate that irrigated area largely determines irrigation water withdrawals across scales, and a simple log–log linear model predicts withdrawals with accuracy comparable to complex Global Models and FAO statistics. The dominance of dataset choice (X1) highlights structural uncertainty, especially the heavy dependence on FAO-GMIA for irrigated area parametrization. This suggests that improving and fully propagating uncertainty in irrigated area datasets would yield greater gains in predictive reliability than adding complexity to model structures. The weak additional contributions of parameters like irrigation efficiency or evapotranspiration (conditional on area) indicate potential for surrogate statistical emulators to replace computationally expensive sub-models without losing predictive skill, enhancing transparency and enabling comprehensive global sensitivity analyses. Regional differences (e.g., Europe’s broader r^2 spread) point to contextual factors or data issues affecting fit, warranting further investigation. The variability in β across datasets precludes a definitive scaling rule at continental scale; however, local-scale analyses show β≈1 in some contexts and >1 in others (e.g., U.S. states), which has implications for the efficiency and sustainability of expanding irrigated areas.

The study provides a parsimonious, transparent approach to estimate irrigation water withdrawals using irrigated area alone, closely matching outputs from eight Global Models and two FAO-based datasets while enabling full uncertainty and sensitivity appraisal. By revealing the primacy of irrigated area in driving model outputs, it calls for prioritizing improved measurement and uncertainty characterization of irrigated areas over increasing model complexity. The approach scales across geographic levels and reproduces both current and future GM estimates. Future research should investigate the weaker fits observed in Europe, test the scaling relationship in additional systems and sub-regions, and evaluate when β departs from unity to inform design and management of irrigation schemes. Developing emulators for complex sub-models and conducting rigorous global sensitivity analyses can further align model realism with computational efficiency and policy relevance.

• Dependence on irrigated area datasets: Results hinge on FAO-GMIA inputs; alternative datasets show large divergences, implying that unaccounted uncertainty in area estimates could widen withdrawal uncertainties.
• Variability in scaling exponent β: Dataset-driven volatility prevents establishing a consistent scaling law at continental scales; β can be <1, ≈1, or >1 depending on dataset and region.
• Regional disparities: Europe shows lower and more variable r^2, suggesting regional data or process complexities not captured by the simple model.
• Missing data and imputation: Although multiple imputation was employed, some datasets (e.g., Aquastat in the Americas) had higher missingness, introducing additional uncertainty.
• Unresolved interactions: While many parameters seem minor after controlling for area, potential interactions in complex model formulations could still matter; comprehensive GSA across full model structures is rare and computationally challenging.
• Scope: The simple model is not proposed for plot- or scheme-level process monitoring; physical-process models remain necessary at fine scales and for temporal dynamics.