The SM-based Delta approach estimates IWU by contrasting EO-derived and model-simulated soil water balance dynamics, with the latter excluding irrigation e.g.,. The underlying assumption is that, in irrigated areas, discrepancies between EO- and model-based estimates primarily reflect the influence of irrigation, which affects both SM and ET.

To ensure comparability between EO- and model-derived SM, satellite SM time series are first rescaled to the distribution of the model simulations using a mean–standard deviation adjustment. We further assume that EO-based and model-simulated ET agree under non-irrigated conditions, such that any departures in irrigated areas can be attributed to irrigation. This assumption is consistent with (their Fig. 5), who showed that EO-based and model-based ET products exhibit similar values over irrigated regions outside the irrigation season, while substantial differences emerge when irrigation is active. The EO SM and ET datasets used in this approach are described in Sect. .

The soil water balance equation for EO-based soil moisture (SMEO) can be written as: 1Z⋅dSMEOdt=P(t)+I(t)-ETEO(t)-R(t)-ΔSrest, and for model-simulated soil moisture (SMmodel) as: 2Z⋅dSMmodeldt=P(t)-ETmodel(t)-R(t)-ΔSrest, where P [mm] is precipitation, I [mm] is irrigation, ET [mm] is evapotranspiration, R [mm] is runoff, and ΔSrest [mm] represents other storage changes below the surface layer (e.g., drainage). Z [mm] is the soil depth used to convert volumetric soil moisture into water storage, fixed at 50 mm following .

Subtracting Eq. (2) from Eq. (1) expresses the EO–model discrepancies in terms of irrigation, under the assumption that differences in precipitation, runoff, and other storage terms are either negligible or do not systematically differ between the two formulations. The resulting IWU estimate is: 3I(t)=Z⋅dSMEOdt-Z⋅dSMmodeldt+max⁡0,ETEO(t)-ETmodel(t).

To reduce spurious irrigation signals due to noise in the satellite SM data, IWU is only considered between two consecutive time steps when the relative increase in soil moisture exceeds a predefined threshold of 0.12, as determined from the sensitivity analysis in .

The SM-based Inversion approach estimates IWU by inverting the soil water balance equation, following a formulation conceptually similar to the SM2RAIN method originally developed to retrieve precipitation from soil moisture. In this framework, temporal variations in soil moisture SM(t) are used to infer the total water input (precipitation plus irrigation), and the known precipitation component is subsequently removed.

The general form of the soil water balance is: 4nZdSM(t)dt=I(t)+P(t)-G(t)-SR(t)-ET(t), where n [–] is the soil porosity, Z [mm] the effective soil depth, SM [–] the volumetric soil moisture, I and P [mm] the irrigation and precipitation inputs (with precipitation taken from the ERA5 forecast fields; ), G [mm] the drainage, SR [mm] the surface runoff, and ET [mm] the actual evapotranspiration.

Defining the total water input as Win(t)=I(t)+P(t), Eq. () can be rearranged as: 5Win(t)=nZdSM(t)dt+G(t)+SR(t)+ET(t), from which irrigation is retrieved as 6I(t)=Win(t)-P(t).

Following , the drainage term is represented as G(t)=aSM(t)b, where a and b are parameters related to soil hydraulic properties. Actual evapotranspiration is expressed as ET(t)=FSM(t)PET(t), where PET [mm] is potential evapotranspiration and F [–] is a scaling parameter modulating the sensitivity of ET to SM. The parameters a, b, F, and nZ are calibrated jointly during rainfall-free periods over the non-irrigated season and rainfall days within the irrigation season. Surface runoff is assumed to be negligible, as the major irrigated areas analysed here are predominantly located in flat agricultural regions. Negative irrigation estimates are set to zero, and spurious low values are filtered out using a precipitation-based threshold, following and .

The Model-observation integration approach estimates IWU using simulations from the Noah-MP land surface model (v4.0.1; ) implemented within NASA's Land Information System LIS;. Irrigation is simulated following the sprinkler scheme of , in which irrigation is applied during the growing season whenever root-zone moisture availability (MA) falls below a prescribed threshold. Here, a threshold of 0.45 is used, following ; sensitivity tests confirmed that this value yields the most realistic irrigation behaviour (not shown). The start and end of the growing season are derived from a monthly climatological greenness dataset , with irrigation allowed only when greenness exceeds 40 % of its annual range .

The model is forced with ERA5 forecast fields, which do not assimilate land-surface observations and therefore avoid introducing irrigation-related signals. Soil texture is taken from the Harmonized World Soil Database , and soil hydraulic properties follow with adaptations from .

Root-zone moisture availability MA is computed as: 7MA=θ-θWPθFC-θWP, where θ is the simulated volumetric soil moisture, and θWP and θFC are the water contents at wilting point and field capacity, respectively. When MA drops below the threshold of 0.45, irrigation is applied to restore the root zone to field capacity.

Noah-MP is run over all land pixels using a homogeneous cropland land-cover type to ensure that the irrigation scheme is active everywhere. A satellite-based irrigated-area map is then used to constrain the spatial distribution of irrigation, retaining simulated irrigation only over irrigated pixels and scaling it by the irrigated fraction within each 0.25° grid cell. For this study, we use the ensemble mean of 24 Noah-MP simulations driven by perturbed meteorological forcings radiation and precipitation, as in.

We use seven surface SM datasets, including both satellite-based and model-based products. The satellite products, which are expected to contain irrigation signals e.g.,, comprise three long-term records from the ESA Climate Change Initiative (CCI) Soil Moisture version 08.1 data collection . These datasets provide volumetric SM [m³ m⁻³] for the upper 0–5 cm soil layer at a daily time step and 0.25° spatial resolution. They include (i) the ACTIVE dataset, merging scatterometer observations from ERS-1, ERS-2, and ASCAT (MetOp-A/B/C); (ii) the PASSIVE dataset, combining microwave radiometer measurements from multiple missions and sensors (SMMR, SSM/I, TMI, AMSR-E, WindSat, AMSR2, SMOS, SMAP, FengYun, and GPM); and (iii) the COMBINED dataset, which integrates all active and passive retrievals into a single harmonised product. We also include three additional satellite datasets: Soil Moisture and Ocean Salinity (SMOS; ), Soil Moisture Active Passive (SMAP; ), and Advanced Scatterometer (ASCAT; ). Finally, ERA5-Land is used as a model-based reference dataset, providing volumetric SM for the upper 0–5 cm at hourly resolution and 0.1° spatial resolution. ERA5-Land does not assimilate land-surface observations (e.g., SM or land surface temperature) and does not include any explicit representation of irrigation. However, it is forced by ERA5 atmospheric fields, which may carry an indirect imprint of irrigation introduced through atmospheric data assimilation. In practice, our analyses (not shown) indicate that ERA5-Land exhibits no detectable irrigation signal in the study regions and can therefore be used as a non-irrigated reference.

We use four ET datasets. Two of them are observation-based products that integrate satellite information and therefore contain irrigation signals e.g.,: (i) SSEBop v5 , based on MODIS land surface temperature and vegetation data; and (ii) FLUXCOM (Remote Sensing version) , obtained by machine-learning upscaling of eddy-covariance fluxes using satellite-derived predictors. The remaining two datasets are model-based products that do not explicitly represent irrigation: Noah-MP ET (forced with ERA5 forecast meteorology) and ERA5-Land ET. Noah-MP ET is available for 2010–2022 for the CONUS and Murray-Darling Basin domains, while ERA5-Land ET is used for the remaining regions and periods. In addition, we use potential evapotranspiration from the GLEAM v3.7b dataset in the SM-based Inversion approach; GLEAM v3.7b potential evapotranspiration is computed using the Priestley–Taylor equation and meteorological forcing.

To constrain irrigation estimates in the Model-observation integration approach, we use the Landsat-derived Global Rainfed and Irrigated-Cropland product at 30 m resolution LGRIP30; for the nominal year 2015. LGRIP30 provides spatially detailed irrigated and rainfed cropland fractions based on Landsat surface reflectance time series and machine-learning classification. In addition, the Global Map of Irrigated Areas v5 (GMIA v5; ) is used in the SM-based Delta and SM-based Inversion approaches as a spatial mask to restrict the analysis to regions equipped for irrigation. GMIA v5, provided at 0.0833° resolution, compiles subnational agricultural statistics, census information, and international reports on irrigated areas for the period 2000–2008.

All input datasets were regridded to the 0.25° regular latitude–longitude grid used in the ESA CCI SM products. SMOS and SMAP were resampled using nearest–neighbour interpolation to preserve their native retrieval characteristics. All other datasets (ASCAT, ERA5-Land SM and ET, FLUXCOM, SSEBop, Noah-MP ET, and GMIA v5) were aggregated to the 0.25° grid using spatial averaging. The LGRIP30 irrigated area map, which provides a binary classification of irrigated versus rainfed cropland at 30 m resolution, was similarly aggregated by computing the fraction of irrigated pixels within each 0.25° grid cell.

A spatial mask was applied to the SM-based Delta and SM-based Inversion IWU outputs, retaining only pixels with at least 5 % of land equipped for irrigation according to the GMIA v5 dataset, in order to avoid spurious irrigation signals in non-irrigated areas. For the Model-observation integration approach, irrigation amounts are already restricted and scaled to the irrigated fraction within each grid cell using the LGRIP30 irrigated area map.

A temporal mask was applied to the SM-based Delta and SM-based Inversion estimates to restrict the analysis to active irrigation periods: April–September for CONUS, April–October for the Ebro Basin, September–March for the Murray-Darling Basin, and November–June for India. In India, irrigation also occurs during the monsoon months (July to October), but these months were excluded to ensure consistency across methods, as the SM-based Inversion approach uses this period for parameter calibration. For the Model-observation integration approach, a temporal mask was applied only in the Murray-Darling Basin, where the climatological greenness threshold from is outdated and cannot be used to define irrigation timing. Finally, all 0.25° IWU estimates were temporally aggregated to monthly values.

These spatial and temporal masks also serve as safeguards against potential confusion between snowmelt-driven soil moisture increases and irrigation signals, as snow accumulation and melt predominantly occur in mountainous areas and periods that fall outside the retained pixels and time windows.

Figure  presents a heatmap of the time-averaged spatial root mean square deviation (RMSD), bias, and Pearson correlation coefficient (R) computed between observed and estimated state-level irrigation volumes from FRIS and the corresponding IWU estimates. Each metric is derived from the comparison of state-level values (one point per state, as illustrated in Fig. b), and then averaged over the two FRIS reference years (2013 and 2018). Results for the two years evaluated separately are provided in the Supplementary Material (Table S1). To ensure consistency with the FRIS-reported units (km³ yr⁻¹ per state), IWU estimates originally expressed in millimetres were converted to cubic kilometres by multiplying by each state's area.

For SM-based Delta datasets, those relying on ET from SSEBop show the weakest agreement with the reference data, with mean RMSD of 9.6–10.1 km³ yr⁻¹ and biases of 5.6–6.3 km³ yr⁻¹. In contrast, SM-based Delta datasets using FLUXCOM ET perform better, with mean RMSD ranging from 5.4–6.1 km³ yr⁻¹, biases of 2.6–3.5 km³ yr⁻¹, and higher correlations.

For the SM-based Inversion approach, the CCI Passive dataset shows the closest agreement with the reference data, combining a low mean RMSD (4.2 km³ yr⁻¹) and bias (0.7 km³ yr⁻¹) with the highest correlation (R = 0.66) among all SM-based Inversion products. The CCI Combined dataset also performs reasonably well (RMSD = 5.8 km³ yr⁻¹, bias = 1.1 km³ yr⁻¹, R = 0.29), whereas datasets based on ASCAT, SMOS, and SMAP show weaker performance, with generally higher RMSD values (5.4–6.7 km³ yr⁻¹) and lower correlations (R = 0.22–0.39).

For the Model-observation integration approach, the Landsat-derived irrigation map dataset performs within the same range as the better SM-based datasets, with a mean RMSD of 3.9 km³ yr⁻¹, a mean bias of 1.1 km³ yr⁻¹, and a mean correlation of R=0.79.

Overall, the best-performing SM-based datasets are CCI Passive & FLUXCOM for the SM-based Delta approach and CCI Passive for the SM-based Inversion approach. Together with the Landsat-based dataset from the Model-observation integration approach, these three products were retained for further analysis in this region.

Figure a shows mean annual IWU over CONUS (2010–2020) for the three selected datasets. The major irrigation regions identified in Fig.  (California Valley, Snake River Plain, Great Plains, and Mississippi Floodplain) emerge, particularly in the Model-observation integration dataset. Figure b presents state-level scatterplots comparing estimated and observed IWU volumes for 2013 (blue) and 2018 (orange), highlighting year-specific relationships and associated performance metrics.

The three IWU datasets exhibit distinct spatial patterns, which reflect the information content and assumptions of each approach. The SM-based Inversion (CCI Passive) dataset shows a relatively uniform distribution, with most pixels ranging between 50 and 150 mm yr⁻¹, consistent with the spatially averaged and potentially weak irrigation signal that may result from inferring irrigation primarily from soil moisture variations at 0.25° resolution. In contrast, the SM-based Delta (CCI Passive & FLUXCOM) dataset displays a west-east gradient, with many western areas exceeding 150 mm yr⁻¹ (locally >350 mm yr⁻¹), while the Mississippi Floodplain generally remains below 50 mm yr⁻¹, with the notable exception of Florida, where locally higher values are observed; the stronger spatial gradients in this approach likely reflect the additional use of ET differences, which are generally more sensitive to irrigation than near-surface soil moisture at this scale . The Model-observation integration dataset shows the strongest spatial heterogeneity, highlighting distinct irrigation hotspots: parts of the California Valley exceed 500 mm yr⁻¹, while the Mississippi Floodplain typically exhibits values between 150 and 200 mm yr⁻¹; this heterogeneity is largely inherited from the LGRIP30 irrigated-area fraction used to scale simulated irrigation within each 0.25° grid cell.

Figure  shows monthly IWU estimates from SM-based Inversion (CCI Passive, blue line), SM-based Delta (CCI Passive & FLUXCOM, green line), and Model-observation integration (Landsat-based map, red line) for the Great Plains, California Valley, Snake River Plain, and Mississippi Floodplain over 2010–2020. These four major irrigated regions, defined as in Fig.  (top-left panel), span a strong climatic gradient, from the arid western domains (California Valley, Snake River Plain) to the more humid Great Plains and Mississippi Floodplain. Values are spatially averaged by region, and mean seasonal cycles are also displayed.

Both the SM-based Delta and Model-observation integration datasets reproduce the July–August irrigation peak and show similar interannual variability, especially in the Great Plains. By contrast, the SM-based Inversion (CCI Passive) dataset yields lower summer IWU volumes and displays a different seasonal cycle. The SM-based estimates always start in April and end in September by design, whereas model-based irrigation sometimes starts earlier (in the Great Plains and California Valley) and continues slightly later in the year, which may reflect the absence of explicit harvest timing in the model .

Figure  presents a heatmap of RMSD, bias, and Pearson correlation (R) between observed monthly IWU and the generated IWU datasets at the aggregated district level in the eastern Ebro Basin over 2007–2020. Metrics were computed only for the irrigation season (April–October), and only pixels with at least 25 % of their surface area within the irrigation districts were retained.

Among the six SM-based Delta datasets, performance is relatively consistent, with all products underestimating irrigation volumes (mean bias of about -20 mm per month). The best agreement is obtained for the SM-based Delta (CCI Passive & FLUXCOM) and SM-based Delta (CCI Combined & SSEBop) configurations, with correlations of R=0.63 and R=0.60, RMSD of 29.0 and 27.3 mm per month, and biases of -17.1 and -17.2 mm per month, respectively.

For the SM-based Inversion datasets, the CCI Passive dataset performs best, with R of 0.63, RMSD of 30.0 mm per month, and bias of -23.0 mm per month, yielding results comparable to the best SM-based Delta products. Other SM-based Inversion datasets show weaker agreement, with lower correlations and larger negative biases.

Overall, the best-performing datasets are CCI Passive & FLUXCOM for the SM-based Delta approach and CCI Passive for the SM-based Inversion approach. These two datasets are therefore retained for further analysis in this region.

Figure a shows monthly in situ IWU observations (grey shading) together with estimates from SM-based Delta (CCI Passive & FLUXCOM, green line) and SM-based Inversion (CCI Passive, blue line), averaged over the merged irrigation districts for 2007–2020. Both datasets capture the timing of the irrigation season, with a marked peak in June–August, but they consistently underestimate irrigation volumes. They exhibit stronger interannual variability compared to in situ observations but show similar year-to-year fluctuations among themselves, suggesting that both methods respond similarly to interannual forcing in this region despite their different formulations.

Figure b shows maps of mean annual IWU over 2003–2020 for the two datasets. The SM-based Delta (CCI Passive & FLUXCOM) dataset indicates higher IWU in the eastern basin, broadly consistent with the distribution of irrigated areas in GMIA v5 (see Fig. ). The SM-based Inversion (CCI Passive) dataset also exhibits a heterogeneous pattern, with localised hotspots of high IWU, including the Ebro Delta in the south-east, a region of intensive irrigation. These differences are consistent with the methodological characteristics discussed for the CONUS (Sect. ). The consistent underestimation by both datasets may partly result from the dilution of irrigation signals within 0.25° grid cells, as the irrigated districts in this region are relatively small and fragmented. The location and extent of the irrigation districts with available in situ observations are shown in Fig. c.

Figure  presents a heatmap of RMSD, bias, and Pearson correlation (R) between monthly observed IWU and the corresponding estimates from each method-input combination. Metrics are computed over the irrigation season (September–March) and averaged across the four irrigation districts of the Murray–Darling Basin, with values reported as mean ± standard deviation across districts. Evaluation periods vary by dataset according to data availability, and only pixels whose centroids fall within district boundaries were included. District-level metrics are provided in the Supplement (Tables S2–S3).

For all datasets, performance varies considerably across the four irrigation districts, as indicated by the large standard deviations. Among the SM-based Delta products, those using SSEBop ET generally outperform those using FLUXCOM ET. The CCI Combined & SSEBop dataset, in particular, shows the most balanced performance across the three metrics, with the lowest RMSD (13.5 ± 1.9 mm per month), a moderate bias (3.8 ± 2.7 mm per month), and relatively higher correlations (R=0.29±0.20). For SM-based Inversion, CCI Combined, CCI Passive, and SMAP datasets perform best. SMAP shows the lowest mean RMSD (12.5 ± 2.6 mm per month) and lower bias (5.6 ± 2.6 mm per month), but is limited to the post-2015 period. CCI Passive reaches the highest mean correlation (R=0.38±0.16), while CCI Combined provides a more balanced trade-off between RMSD and bias. The Model-observation integration dataset achieves the highest mean correlation overall (R=0.47±0.11), but with large bias and substantial variability between districts.

No single method–input combination performs best across all districts, as reflected by the large standard deviations. However, some datasets show comparatively better and more consistent results across the three metrics and the four districts. For the following analysis, we therefore retain one representative dataset from each approach: SM-based Delta (CCI Combined & SSEBop), SM-based Inversion (CCI Combined), and Model-observation integration (Landsat-based map).

Figure a shows monthly IWU time series and mean seasonal cycles for the four Murray–Darling irrigation districts (districts shown in panel c), with in situ IWU in shaded grey and estimates from the three selected datasets SM-based Delta (CCI Combined & SSEBop), SM-based Inversion (CCI Combined), and Model-observation integration (Landsat-based map) in colour. All datasets exhibit substantial interannual variability, but their temporal fluctuations show limited agreement with the observed records.

The Model-observation integration dataset tends to overestimate IWU, except in the Murrumbidgee district, where values are closer to the observations than in other regions. The SM-based Delta (CCI Combined & SSEBop) and SM-based Inversion (CCI Combined) datasets exhibit IWU magnitudes generally closer to the observations than the Model-observation integration dataset, though both substantially overestimate in the Murray Wakool district. When averaged over all years, the mean seasonal cycle shows that only the Model-observation integration dataset reproduces the distinct January peak also seen in the in situ records.

Figure b shows maps of mean annual IWU (2010–2020) for the three selected datasets. SM-based Delta (CCI Combined & SSEBop) yields values mostly between 100 and 250 mm yr⁻¹, with higher values in the northwest of the basin. SM-based Inversion (CCI Combined) also ranges between 100 and 250 mm yr⁻¹ but is more spatially uniform, with slightly higher values in the northern part. In contrast, the Model-observation integration dataset shows marked spatial heterogeneity, with the highest values (locally exceeding 500 mm yr⁻¹) concentrated in the southern basin.

As in the CONUS (Sect. ), the SM-based approaches produce more spatially uniform patterns, while the Model-observation integration dataset concentrates irrigation where the LGRIP30 map indicates the highest irrigated-area fractions. The overestimation by the latter in several districts likely reflects the parameterisation of the Noah-MP land surface model, including irrigation-triggering thresholds and soil hydraulic properties.

Table  summarises monthly mean IWU over the Gangetic Plain (aggregation domain shown in Fig. c) for three SM-based Delta and six SM-based Inversion datasets. Values are reported separately for two cropping seasons, Rabi (November–March) and Zaid (April–June), while the Kharif season (July–October) is excluded due to temporal masking. The “Annual” column corresponds to the mean over the combined November–June period. Reported values represent the mean over the full temporal coverage of each dataset, which varies depending on data availability (see the “Period” column in Table ).

SM-based Delta datasets yield annual mean IWU values between 20 and 32 mm per month, with relatively small differences between the Rabi and Zaid seasons. The associated standard deviations (8 to 14 mm per month) indicate marked month-to-month and interannual variability, generally higher during Rabi than during Zaid. SM-based Inversion datasets exhibit a much wider range of annual IWU, from about 39 mm per month (CCI Combined) to more than 80 mm per month (ASCAT), together with higher variability. Within this group, the CCI Combined product is the closest in magnitude and variability to the SM-based Delta datasets, whereas the other products (CCI Passive, ASCAT, SMOS, SMAP) systematically yield larger totals.

For the following analyses, we focus on SM-based Delta (CCI Combined & FLUXCOM) and SM-based Inversion (CCI Combined), as they provide the most consistent estimates across methods and align reasonably well with the magnitudes reported by . Since no direct validation data are available, this does not imply that these datasets are necessarily closer to real IWU, but they offer a pragmatic choice to ensure comparability between approaches.

Figure a shows monthly IWU time series (2003–2020) from the two selected datasets averaged over the Gangetic Plain, with the monsoon months (July–October) excluded. Both datasets generally reproduce a dominant Rabi season (November–March) and a smaller Zaid peak (April–June). The main difference lies in the timing and magnitude of the Rabi maximum: SM-based Inversion (CCI Combined) produces sharper and higher peaks in November–December, whereas SM-based Delta (CCI Combined & FLUXCOM) yields smoother dynamics, generally peaking in March.

Because the monsoon period (Kharif; July–October) is masked, both datasets likely miss an irrigation peak typically associated with this cropping phase. This is supported by FAO crop calendars , which indicate widespread irrigation for rice, maize, and other water-demanding crops during the monsoon months. For the Rabi season, the simulated magnitudes (10–50 mm per month, with a March maximum) are consistent with previous findings by , particularly matching the SM-based Delta (CCI Combined & FLUXCOM) dataset pattern.

Spatially, both datasets (Fig. b) identify the Gangetic Plain as an important irrigation hotspot. In this area, SM-based Delta (CCI Combined & FLUXCOM) shows values mostly between 20 and 50 mm per month, with higher levels (40–60 mm per month) in the northwestern part of the plain, near the Indus Basin. SM-based Inversion (CCI Combined) presents a more uniform distribution across the plain, with elevated values in the eastern part (around 40–60 mm per month).

The wider inter-method spread in India compared to other regions likely reflects the different climatic conditions and the complexity of the irrigation landscape, with widespread and multi-seasonal irrigation, which amplifies the sensitivity differences between methods discussed in Sect. .