The TWSA data set (a Level-3 product) is derived from temporal variations of the gravity field of the Earth, initially represented by a series of spherical harmonic (SH) functions and the corresponding sets of SH coefficients (called Stokes coefficients; a Level-2 product) (Tapley, 1989). The GRACE/-FO satellites provide gravity information by acting as test masses in a free fall experiment. The gravitational acceleration acting on the satellites is computed by the so-called “dynamic approach” (Tapley, 1989) from the satellites' trajectories, determined by GPS observations, and from the change in inter-satellite distance, observed with micrometre accuracy via a K-band microwave link (Tapley et al., 2004) or with nanometre accuracy using a Laser Ranging Interferometer technology demonstration on GRACE-FO (Abich et al., 2019). A near polar orbit with an inclination of 89.5° of the satellite pairs enables the computation of a global gravity field of the Earth. After one month, a spatial resolution of the gravity field of 200–300 km is achieved, depending on latitude and the actual orbit constellation during the particular month (Flechtner et al., 2016). To isolate the hydrological gravity variations of interest, mass change signals of oceanic, atmospheric, terrestrial and polar tides are removed. Non-tidal mass variations of the ocean and the atmosphere on sub-monthly time scales are reduced by the so-called atmosphere and ocean de-aliasing Level-1B (AOD1B), Dobslaw et al. (2017) products based on ECMWF atmospheric analysis data and an ocean circulation model (Shihora et al., 2022). The remaining temporal variations of the monthly gravity fields mainly encompass hydrological mass variations of water in liquid and solid form, and geodynamic variations of the Earth's crust, i.e., global isostatic adjustment and co-seismic deformation. GRACE/-FO processing towards the gridded TWSA product can be split into three parts as further described in the following: (i) processing of Stokes coefficients (Level-2); (ii) corrections to the Level-2 data in the SH domain (Level-2B); and (iii) SH synthesis to a gridded TWSA data set and corrections applied to the grids (Level-3).

Due to the diverse observation types of the GRACE/-FO satellites and poorly known instrument noise characteristics, the inversion from the instrument data to a global gravity field, including different types of empirical and pseudo-stochastic parameters, is a complex process. Therefore, in combination with several gravitational background models that all have specific error budgets, the formal uncertainties of the SH coefficients of the monthly gravity fields are somewhat different among GRACE/-FO analysis centres (ACs) and only realistic when calibrated by empirical covariance modelling techniques (Lasser, 2023). In order to profit from the strengths of the different processing approaches and to reduce the stochastic noise in the individual monthly gravity field models, a combination of the solutions from different ACs is performed by the Combination Service for Time-variable Gravity fields (COST-G) (Jäggi et al., 2023). For G3P, the combination scheme, initially designed by the European Gravity Field Service for Improved Emergency Management (EGSIEM) (Jäggi et al., 2019), has been further developed and adapted for the combination of GRACE-FO gravity fields. Meyer et al. (2023) provide details on the GRACE-FO quality control and combination process. The resulting COST-G Level-2 combination product by the University of Bern is the basis for the TWSA data set used in G3P.

During Level-2B processing, several corrections are applied to the Level-2 gravity field data, as detailed in Dahle et al. (2025) and summarized here. First, a mean field is reduced from all months to obtain gravity anomalies relative to the same epoch. Essentially, the choice of the long-term mean is arbitrary and has been defined for the current G3P version V1.12 and earlier versions to cover the period April 2002–December 2020. We then filter the Stokes coefficients with the anisotropic VDK2, VDK3, and VDK5 filters (Horvath et al., 2018). This filtering is necessary to optimally separate signal from noise in the GRACE/-FO data. The number of the filter name indicates the filter strength, with VDK2 the strongest filtering used in the processing and VDK5 the weakest. Different filter strengths are necessary to obtain the optimal results by combining differently filtered gravity fields, see also Level-3 processing below.

The Stokes coefficient with degree 2 and order 0 (C20) is related to the flattening of the Earth and poorly observed by GRACE/-FO. Thus, this coefficient is replaced by an estimate derived from a combination of GRACE/-FO with satellite laser ranging (SLR). Further, the Stokes coefficient with degree 3 and order 0 (C30) is poorly determined by GRACE/-FO in periods when accelerometer observations for one of the two spacecraft are not available (as for GRACE from November 2016 till the end of the science mission phase in June 2017) or are degraded (as for the whole GRACE-FO mission). In these periods, available accelerometer observations of one satellite are transplanted to the other. By incorporating an improved accelerometer transplant product for GRACE-FO (Behzadpour et al., 2021), the C30 coefficient is well determined and thus does not need to be replaced anymore for GRACE-FO. For the last seven months of the GRACE mission, C30 is replaced with estimates obtained from the same GRACE/-FO and SLR combination as mentioned above for C20. The GRACE/-FO observations system is insensitive to geocentre motion, which is related to the Stokes coefficients of degree 1 (C10, C11, and S11). Thus, these coefficients are set to zero by definition in the Level-2 data. In order to correctly estimate the terrestrial mass distribution, we approximate these coefficients using the approach described in Swenson et al. (2008) and insert them into the Level-2B products.

The Earth's gravity field is affected by long-term secular trends due to Glacial Isostatic Adjustment (GIA), mainly in previously glaciated regions such as North America, Fennoscandia and Antarctica. The Level-2B products are corrected using the GIA model ICE-6G_D (VM5a) (Peltier et al., 2018). Finally, a harmonic signal at the frequency of 161 d, the alias frequency of the semi-diurnal solar tide S2, is fitted to the time series of Level-2 products and subtracted from the Level-2B products.

The Level-3 processing (see Dahle et al., 2025 for details) primarily uses Level-2B data filtered with VDK3 and VDK5. VDK2 is only used for months with low data quality (explained below). The first step converts the Level-2B Stokes coefficients to a global 0.5° grid of monthly mass anomalies, expressed as equivalent water height. We decompose these gridded data into the linear trend, the annual and the semi-annual sinusoidal signals (estimated with least squares adjustment) and the residual inter-annual signal. In order to reduce the influence of leakage, the deterministic signals (trend, annual, semi-annual) are taken from the fields that have been filtered with the weaker VDK5 filter and are combined with the stronger filtered VDK3 residual signal. For each month, we compare the global standard deviation of the residuals over the open ocean (distance to coast > 1000 km) to the mean of these standard deviations averaged over all months. If the standard deviation of a given month is twice as large as the mean standard deviation, we use the residuals from the even stronger filtered VDK2 field. For the available GRACE/-FO data set from 2002 to 2023, only February 2015 of the GRACE mission is affected by this stronger filtering.

Level-3 processing finally includes the removal of mass changes due to co-seismic deformations caused by the megathrust earthquakes of Sumatra-Andaman (2004), Chile (2010), and Japan (2011). This is done by estimating a step function in a spherical cap with a radius of 1000 km around the epicentre. The resulting data set represents the monthly TWSA data used in the subsequent G3P processing chain towards generating the groundwater product. Uncertainties of the TWSA data are provided as a grid-scale standard deviation, computed as the root mean square error (RMSE) of the residual signal over the open ocean (distance to coast > 1000 km) scaled by a spatial covariance model (Boergens et al., 2022, 2020).

Root-zone soil moisture is the water present in the soil column where plant roots directly access water and nutrients. Practically, and in most models, it is defined as the water stored in the upper 1 to 2 m of soil (Hirschi et al., 2014; Mishra et al., 2020), although the actual rooting depth may vary, e.g., as a result of plant species, geology, and climatic conditions (Fan et al., 2017). Especially in water-limited regions, RZSM controls plant growth and photosynthesis, plant water stress, and crop yield (Martens et al., 2017; Vreugdenhil et al., 2022).

The RZSM product used in G3P is a long-term (2002–2023), global, gap-free data record representing soil moisture in the uppermost 2 m of soil, based on the multi-satellite surface soil moisture (SSM) climate data record provided by the Copernicus Climate Change Service (Dorigo et al., 2018). Direct measurements of RZSM are only available at few, unevenly distributed in situ stations (Dorigo et al., 2021a). On the other hand, microwave satellite observations, such as the ones integrated in C3S SSM are globally available but only sensitive to water in the topsoil layer (∼ 5 cm) (Gruber et al., 2019). The RZSM product used by G3P seeks to make optimal use of both, without the intervention of any land surface of hydrological modelling (Pasik et al., 2023). To do so, it first fills gaps in the C3S SSM product related to, e.g., seasonal masking or instrument unavailability, to obtain global seamless coverage, and subsequently converts the gap-free SSM to RZSM using an infiltration model that has been calibrated with ground-based observations. Both methods are briefly summarised here.

Data gaps in the SSM product are filled using a standalone interpolation method (Preimesberger et al., 2025). This means that the gap-filling uses only available neighbourhood information (temporally and spatially) and that the resulting values are therefore independent of any other data records or ancillary data. The used method is based on the discrete cosine transform (DCT) penalized leased squares (PLS) method, which was initially designed as a smoothing algorithm (Garcia, 2010). The aim of the algorithm is to find a set of smoothed values y^ to represent the original input data y with (i) minimal Residual Sum of Square (RSS) and (ii) optimal reduced roughness P(y^) between (smoothed) elements as described in Eq. (2). Missing values are interpolated as part of the smoothing process and finally used to fill gaps in the observational data. 2Fy^=RSS+Py^=y-y^+sPy^

The parameter s in Eq. (2) is the only free model parameter that is optimised using a generalised cross validation (GCV) approach described in Eq. (3). 3GCVs=wRSS/n-nmiss1-TrH/n2

This iteratively optimises the interpolation function via weighted residuals (wRSS) with H being the hat matrix from the PLS controlling the trade-off between goodness of fit and smoothing between observations (n and nmiss refer to the number of available and interpolated data points).

This algorithm was already widely used to interpolate SSM, generally with good performance that is on par with other, more complex, and often covariate-dependent methods (e.g., Shangguan et al., 2023; Guo et al., 2022). DCT-PLS is applied on a moving window basis, meaning the smoothing parameter s is locally tuned from data within a 15° bounding box, to take into account globally changing levels of soil moisture variability within different climate regimes. Soil moisture during seasonally frozen periods (identified from modelled ERA5 soil temperature data (Hersbach et al., 2020) is linearly interpolated over time to represent a constant or slowly changing level of stored (frozen) water in the soil.

SSM is then converted to RZSM assuming a globally uniform soil depth of 2 m using an exponential filter (EF) based model (Pasik et al., 2023; Albergel et al., 2008) which simulates the drainage of water from the surface into deeper layers, by smoothing and delaying the measured SSM signal. Various studies have shown that this yields a good approximation of actual root-zone conditions, especially for layers until about 1 m depth (Paulik et al., 2014; Wang et al., 2017). Equation (4) summarises the method: 4RZSMtn=RZSMtn-1+Kn⋅SSMtn-RZSMtn-1

RZSM at time t_n is approximated by a weighted combination of the SSM observation made at t_n and preceding RZSM at t_(n-1). The gain factor K ranges from 0 to 1 and is calculated as follows (Eq. 5): 5Kn=Kn-1Kn-1+e-tn-tn-1T

At initialization, when no preceding estimates are available, the EF calculation is started with K0=1 and RZSM(t0) = SSM(t0). However, the EF model is purely time-based, integrating weighted surface observations over a pre-defined preceding period (T). There is no parameter controlling the actual infiltration depth. Hence, to allocate T to depth layers, Pasik et al. (2023) optimised EF based RZSM with measured in situ RZSM to find T-values (6, 15, 48, 70) that best represent RZSM at the four corresponding depth layers (0–10, 10–40, 40–100, 100–200 cm) globally. The optimised T-value for each depth layer is the one that maximises the Pearson correlation between satellite soil moisture, after applying the EF to the SSM estimates, and field measurements taken within that depth interval, sourced from the International Soil Moisture Network (ISMN).

Uncertainties in the satellite SSM observations are estimated using Triple Collocation Analysis (TCA) (Gruber et al., 2016). They represent spatially varying levels of (random) error variance (“noise”) for each of the merged sensors relative to the strength of the retrieved soil moisture signal. This depends on the sensor characteristics such as the observation frequency band, in conjunction with confounders such as vegetation density. Uncertainties from the SSM product are propagated through the EF to subsequently describe RZSM uncertainties (De Santis and Biondi, 2018). To account for the considerable uncertainty the EF introduces when approximating RZSM from surface observations, Pasik et al. (2023) introduced an additional term to the error propagation, i.e. the model structural error σ2EF. This uncertainty component was quantified using in situ observations from stations measuring SSM as well as RZSM. For these stations, the EF is applied to in situ SSM to simulate in situ RZSM. The discrepancy between the predicted and observed RZSM represents σ2EF for the respective integration depth. σ2EF was found to increase with depth ranging from 0.03 m³ m⁻³ at layer 1 to 0.04 m³ m⁻³ at layer 4.

The RZSM data is influenced by uncertainties in input SSM measurements, as well as the assumptions made during gap-filling and the conversion from SSM to RZSM, as described above. The quality of the generated RZSM data varies temporally and spatially due to the coverage of available satellite observations and the uneven global distribution of in situ stations.

The water content of a snow cover is described by the ECV quantity SWE. Satellite remote sensing with passive microwave sensors (PMR) allows for spatially and temporally continuous SWE monitoring. However, current satellite remote sensing-based SWE products are available for the Northern hemisphere only (Pulliainen et al., 2020). To cover the full globe and the GRACE/-FO period from 2002–2023 as required for G3P processing, a combined SWE product derived from PMR satellite observations and model-based SWE from MERRA2 an ERA5-Land was developed here. Satellite-based SWE for the period of 2002–2005 is derived from GlobSnow v3.0 (https://www.globsnow.info/, last access: 1 September 2025), while the Copernicus Land Monitoring Service (CLMS) SWE product (https://land.copernicus.eu/global/products/swe, last access: 1 September 2025) serves as baseline input for the years 2005–2023. GlobSnow v3.0 SWE is available on a 25 km EASE grid, CLMS SWE produced in Near-Real-Time (NRT) is available on a 0.05 × 0.05° geographical latitude/longitude grid. Both satellite SWE datasets apply the retrieval methodology by Luojus et al. (2021). The SWE retrieval combines PMR measurements with ground-based synoptic weather station observations via Bayesian non-linear iterative assimilation. The GlobSnow v3.0 SWE includes monthly bias-correction (Pulliainen et al., 2020) which significantly enhances the retrieval results. A detailed description of the PMR-based SWE methodology is given in Luojus et al. (2021).

The Southern Hemisphere remains a challenging area in remote sensing of SWE with PMR. Additionally, mountain areas are not covered in the standard GlobSnow and CLMS operational SWE products. To fill these gaps, a merged product using SWE from satellites and models has been established (Fig. 2). Simulated SWE from three land surface models and reanalysis systems was examined: GLDAS2.2 LIS (Li et al., 2019), ERA5-Land (Muñoz-Sabater et al., 2021) and MERRA2 (Gelaro et al., 2017). The skilfulness of the all datasets was evaluated by comparing to in situ SWE observations from snow course transect measurements conducted across Russia (Bulygina et al., 2011), Finland (Haberkorn, 2019) and Canada (Brown et al., 2019). The in situ data consist of manual gravimetric snow measurements carried out at multiple locations along a pre-defined transect, of which an averaged value was used as representative for the corresponding pixel or grid cell of the model or remote sensing dataset to be validated. ERA5-Land and MERRA-2 resulted in the best validation results (Fig. 3, middle panel) while GLDAS2.2 showed a clear underestimation of SWE, especially in Canada, and was discarded for further processing. With a relatively high Spearman correlation of over 0.6 against the in situ observations throughout all years, both satellite baseline SWE products GlobSnow v3.0 as well as CLMS SWE perform well in the Northern hemisphere and are consistent among each other (Fig. 3, left panel). All satellite- and model-based datasets were resampled with bilinear interpolation to a common resolution on a regular 0.25° grid to allow for merging. The gaps of the satellite-based data were then filled with the grid-cell mean SWE value of ERA5-Land and MERRA-2 to achieve full global coverage, excluding the area covered by glaciers (RGI, 2017; Sect. 2.2.4). The validation results of the final merged G3P SWE product version v2.0 with respect to in situ observations is shown in Fig. 3 (right panel). Overall, the validation results such as the site-specific and averaged correlation coefficients showed reasonable performance of the estimated SWE values, especially for winter months with high absolute snow mass.

The satellite-based SWE data of GlobSnow and CLMS offer pixel-scale uncertainties which were derived by error propagation from raw satellite data through the algorithm, see Takala et al. (2011) and Pulliainen (2006) for details. The reanalysis models used for gap filling do not provide SWE uncertainties, though. In this case, grid-scale uncertainties were obtained by diagnostic uncertainty estimates as the absolute difference between the model-based and the in situ-based SWE. A summary of existing prognostic and diagnostic approaches for quantifying uncertainty and evaluating uncertainties is given in Sayer et al. (2020).

The glacier mass change product for the G3P processing chain builds on the combination of input data and auxiliary data brokered from international data repositories. As input data, we use the glacier mass change global gridded data available from the C3S Climate Data Store (CDS) (Dussaillant et al., 2023). This dataset is based on glaciological and geodetic time series of glacier mass and elevation changes, respectively, as available from the Fluctuation of glaciers database (FoG) brokered by the World Glacier Monitoring Service WGMS (WGMS, 2023). As auxiliary dataset, we use the glacier distribution data also available from the C3S CDS (C3S CDR, 2024). In turn, this dataset is based on the Randolph Glacier Inventory RGI 6.0 (RGI, 2017), which is a community product generated within the RGI working group of the International Association of Cryospheric Sciences (IACS). For more details on these input and auxiliary datasets, we refer the reader to the C3S related product documentation.

For G3P, inspired by previous methodological frameworks (Zemp et al., 2020, 2019), we developed a new approach to combine the temporal variability of the glaciological in situ observations with the long-term change rates of geodetic observations – mainly from satellites – for all glaciers existing in the RGI inventory (Dussaillant et al., 2025). For the G3P processing chain, all individual WSCs need to deliver their data sets with monthly temporal resolution. This was a major challenge for the glacier compartment, since glacier observations are available only in multi-annual, annual, or at most, seasonal temporal resolutions. Still, accurate globally integrated glacier changes can only be achieved at a minimum annual temporal resolution. For G3P we further developed our methodology to obtain distributed glacier changes at monthly temporal resolution by applying a seasonal sine wave function, informed by the available winter and summer mass change observations (Zemp and Welty, 2023) over the annual glacier changes from Dussaillant et al. (2025). The down-sampling of annual glacier observations to monthly resolution comprise large assumptions which are reflected in the large uncertainties of the glacier change product used in G3P.

Our algorithm produces a global gridded product of monthly glacier changes in five processing steps summarized in Fig. 4. First, for each glacier of the RGI 6.0, we estimate the detrended temporal variability of annual mass change of the glacier (calculated as the glacier mean annual mass change anomaly with respect to the reference period 2011–2020) using the interannual variability of nearby glaciological time series. Second, we calibrate the mean annual mass balance anomaly to all available long-term trends from the geodetic samples, i.e., glacier elevation-change observations from airborne and spaceborne sensors, available for the respective glacier. Third, we integrate all of these calibrated time series into a single weighted average, considering the uncertainty as well as the temporal coverage of the geodetic surveys. This results in a data-fused mean calibrated annual mass change time series that is unique for every individual glacier. Fourth, for every region, we build a regional seasonal sine curve from all available seasonal (winter and summer) mass balance observations of this region. Years without seasonal observation are fitted on a climatic mean winter and summer value calculated per region. We then interpolate the regional sine wave over each individual glacier, by fitting the individual annual values from the mean calibrated annual mass change time series from step 3. The mean calibrated monthly mass change time series are interpolated for each region following the hydrological year monthly distribution (1st October to 30 September in the Northern Hemisphere; 1 April to 31 March in the Southern Hemisphere), except for glaciers in low latitude regions where we linearly interpolate through the year due to the lack of winter and summer seasons. Finally, we aggregate the mean calibrated monthly mass change time series as an area-weighted mean in a global regular grid of 0.5° to fit the G3P resolution.

The glacier product uncertainty estimation for annual values is described in detail on the C3S glacier mass change global gridded product documentation (see above). When applying the regional seasonal sine curve to downscale to monthly data (Step 4), the mean annual mass change time series uncertainty is multiplied by 1.5 to get the relative monthly uncertainty. This multiplication factor is somewhat arbitrary, but it ensures that the monthly downscaled product has a larger uncertainty than the annual product. A thorough accuracy assessment and validation is also available for the C3S annual glacier mass change global gridded input dataset by (i) comparing the annual estimates with previous global studies from annual direct observations (Zemp et al., 2019; Hugonnet et al., 2021) and by (ii) performing a detailed leave-one-block-out cross-validation experiment of mean calibrated annual mass change estimates over selected reference and benchmark glaciers. The accuracy of the downscaled monthly glacier changes was analysed by comparing with monthly glacier changes derived from GRACE (e.g., Wouters et al., 2019). There is a good agreement at the global level but the amplitude of the seasonal cycle of our glacier mass change is smaller than the one derived from GRACE. We note that our uncertainty assessment is still rather on the first order, further developments are still needed to propagate annual uncertainties to monthly estimates and to validate the accuracy of the seasonal cycle of our glacier mass change product at monthly time resolution (an effort currently accounted by the international community through the GlaMBIE project; The GlaMBIE Team, 2025).

Our final product provides monthly glacier mass changes (in Gigatonnes per year) and related uncertainty at global scale with a spatial resolution of 0.5° for the entire GRACE/-FO study period. Yearly updates based on the integration of latest glaciological balances from the FoG database are possible with a lag of one year. The basic concept of the approach, latest improvements of the methodology, and a detailed leave-one/block-out cross-validation is given in Dussaillant et al. (2025) and is ready for implementation in future versions of the G3P product.

SWS includes water stored in rivers, lakes, man-made reservoirs and wetlands. Several promising approaches have been explored in the past years to quantify these components, some of which have also been tested in the context of G3P development: For estimating river storage, the semi-operational hydrological forecasting platform HYFAA which couples the MGB model (Collischonn et al., 2007) with data assimilation of water level data from satellite altimetry was set up for the Niger and Congo basin, with positive validation results when compared to in situ discharge data and global hydrological models. For a set of 250 lakes operationally monitored in the Copernicus Global Land Service and an additional 150 lakes from different sources, lake storage time series were calculated using satellite altimetry and hypsometric curves linking lake water level and extent (Crétaux et al., 2018). However, neither approach results in the required global coverage for G3P. Further promising efforts include the DAHITI project (Schwatke et al., 2015), offering satellite-altimetry-based lake level time series for over 10 000 lakes or the Satellite-based Wetland Observation Service (SWOS) (Weise et al., 2020). At the time of developing G3P, however, there was no observation-based surface water storage product with global coverage available, less so for a holistic assessment of all the surface water components, i.e., rivers, lakes and man-made reservoirs.

For this reason, the SWS data for the G3P version presented here are not observation-based but derived from the global hydrological model OS LISFLOOD (Van Der Knijff et al., 2010) in its implementation in the Copernicus Emergency Management Systems' Global Flood Awareness System (GloFAS) version 4.0 (Choulga et al., 2024), complemented with observations for the Caspian Sea from the DAHITI project (Schwatke et al., 2015) as this lake is not considered in OS LISFLOOD. OS LISFLOOD output has a daily resolution on a 0.05° grid (3 arcmin). From the model output, we derived global-scale river storage and storage in 463 lakes and 687 reservoirs worldwide, with varying degrees of further processing as described below. Depression storage and interception storage were not considered in the G3P surface water product due to their negligible storage variations. While OS LISFLOOD in the version used here does not explicitly represent wetland dynamics, inundated areas are considered by widenings of the channel profile.

As a first processing step, all relevant OS LISFLOOD output files were aggregated from daily to monthly values and resampled from the native 0.05° to the common 0.5° G3P grid. OS LISFLOOD river storage was calculated by multiplying the river length per grid cell given as model input with the state variable of channel cross-sectional area of water flow, which is available for each grid cell as mean value per model time step.

For calculating lake and reservoir storage variations, three major issues need to be resolved: (i) OS LISFLOOD depicts a lake or reservoir as part of the river network, represented in the model by a single grid cell at the location of the outlet of the waterbody, even if its area exceeds the size of this cell. For the purposes of G3P, where a spatially accurate water mass distribution is required, the water stored in this one cell has to be re-distributed to the real-world spatial extent of the lake. (ii) The river water storage of the cells that fall into the area of a lake or reservoir has to be added to the storage of that waterbody. (iii) Reservoir storage can simply be calculated by multiplying the model input layer of reservoir storage capacity, given as a volume in m³, with the simulated time-variable state of reservoir filling, given as a percentage value in the model output. The OS LISFLOOD lake routine, however, only calculates lake water level variations but not the volume changes.

Thus, the routine for calculating lake and reservoir storage for G3P includes the following steps: (i) for each outlet cell of a waterbody, the corresponding lake or reservoir polygon was selected from the Global Lake and Wetland Database (GLWD) (Lehner and Döll, 2004). In case of an ambiguity, we checked if one of the conflicting waterbodies already had another outlet cell, otherwise we chose the larger one; (ii) all 0.5° grid cells of which the centre point is inside the polygon were assigned to the waterbody. This ensures that every grid cell can only be part of one lake or reservoir; (iii) lake or reservoir volume variations were computed from OS LISFLOOD output by multiplying the simulated water level at each time step with the lake area from GLWD; (iv) the resulting water volume was distributed over all grid cells assigned to the lake or reservoir, (v) river storage of each grid cell that was assigned to the lake or reservoir was summed up and evenly distributed over the area of the waterbody and added to its storage; (vi) cells assigned to lakes or reservoirs were masked out of the river storage layer to prevent double accounting.

Finally, all surface water storage compartments (rivers, reservoirs and lakes) were converted to mm equivalent water height and combined to a single global data set of SWS anomalies. As OS LISFLOOD does not provide uncertainty estimates for its simulation results, a first-order SWS uncertainty assessment was used by calculating the SWS difference at each monthly time step and for each grid cell to the SWS simulation results of other global hydrological models, here the WaterGAP Global Hydrological Model (WGHM) (Müller Schmied et al., 2021). The uncertainty value was then taken as half of this difference. This step was done after GRACE-like spatial filtering of both model-based SWS data sets (see Sect. 2.3.3) to mitigate errors that are only due to a subtle misalignment of surface water bodies in both models, e.g., if the location of a river stretch varies by one cell from one model to the other.

For a consistent combination of the individual WSCs and TWSA in the G3P subtraction process, it is important to assure that the water storage (water mass) information of all data sets is assigned to identical spatial units across the global, i.e., cells of a global grid, both with respect to their geographic position and size, and also with respect to consistently assigning land and ocean areas across all data sets. As the basis for defining the land-ocean masks in G3P, we used the ESA CCI Water Bodies Map v4.0 (Lamarche et al., 2017) at 150 m resolution. This high-resolution map was aggregated to generate global land-ocean masks for each resolution at which the individual WSC datasets are produced. For the aggregation, the fraction of land fland was calculated for each grid cell at the coarser resolution by considering the number of land pixels (nL) and ocean pixels (nO) of the high-resolution 150 m map according to Eq. (6): 6fland=nLnL+nO

For the target masks, all grid cells with fland> 0 are classified as land cells, all other cells are classified as ocean cells. The target land-ocean mask with the binary land-ocean assignment at the required spatial resolution was then forwarded to each processing group of individual WSCs and of TWS, with the requirement of generating storage data for each land cell. The target masks deliver a large number of land cells globally, even though their actual land fraction can be very low. Nevertheless, this procedure guarantees that each individual storage data set is provided with uttermost spatial coverage at the global scale, preventing gaps in single data sets that would be adverse for the consistent data combination step later on.

It should be noted that at the 0.5° resolution, a second land-ocean mask was produced in which only the grid cells with fland>0.5 were classified as land cells. This land-ocean mask (output mask) was used to subset the 0.5° grid cells at the global scale for which valid storage data are provided after spatial filtering (Sect. 2.3.3) and in the G3P output files, excluding predominantly ocean-covered cells. The land-ocean masks are open-access available (see Sect. 5).

First, the individual WSC data sets with daily resolution were aggregated to a monthly resolution by taking the temporal mean for each month.

Second, the individual WSC and the TWSA data sets were, if needed, converted from their original units (such as mass in Gigatons) to the common unit of millimetre water equivalent (mm). This is done for each grid cell by dividing mass by the latitude-dependent grid cell area. For coastal cells (i.e., cells where fland< 1, see Eq. 5), the storage value in mm w.e. is additionally multiplied by fland in order to take into consideration that the storage value represents the land part of the cell only, being smaller than the total cell area.

Third, the cell-based time series of absolute monthly storage values of each WSC were transformed into anomaly time series (WSCA), representing the storage deviation at month t from an arbitrary time series mean value WSC‾ (Eq. 7). This step is required as TWS data from GRACE/-FO cannot be given as absolute values of water storage, but only by monthly anomalies relative to a mean value, i.e., TWSA (or as TWS change from one month to another, not used here). For the data sets presented here, the period April 2002–December 2020 was defined for calculating the time series means. 7WSCAt=WSCt-WSC‾

Fourth, the WSC data sets that were produced at a higher resolution than 0.5° (see Table 1) were resampled to this common target resolution using bilinear interpolation, as used in previous GRACE–hydrology studies (e.g., Ali et al., 2022).

Due to the nature of data acquisition and processing of GRACE/-FO and the need to reduce noise components, such as North-South-oriented stripes, gravity-based TWSA exhibit spatially smoothed patterns. Real-world water storage anomalies that are concentrated in comparatively small regions, such as surface water storage variations along a large river, for instance, will be represented in the TWSA data set smeared out over a few hundred kilometres. These spatial characteristics of gravity-based TWSA are reflected by high spatial autocorrelation values over large distances (Fig. 5).

For a consistent data combination approach, such as in G3P where WSC data sets are subtracted from TWSA, it is imperative to have a similar spatial structure of the involved storage data. Otherwise, for example, subtracting spatially confined (non-smoothed) SWS anomalies from the smoothed TWSA may result in spurious groundwater storage anomalies at the locations of the SWS anomalies. One option to tackle this issue is by applying cell-based or river basin-based scaling factors to the TWSA data to restore signals that may have been smoothed out by the data processing steps before (e.g., Landerer and Swenson, 2012; Long et al., 2015). This approach comes with a considerable uncertainty in determining the scaling factors. They are usually derived from the comparison of simulated TWSA from hydrological models before and after spatial smoothing that is deemed to mimic the smoothing imposed by GRACE data processing. For G3P, we follow a different approach in which the WSC anomalies are smoothed in a GRACE-equivalent way before they are subtracted from TWSA. Sharifi et al. (2025a) show that smoothing the WSC anomaly data with the anisotropic DDK or VDK filter that is used for GRACE Level-3 processing (see Chap. 2.2.1) leads to spurious striping features in the filtered WSC data. GRACE-equivalent filtering is thus achieved by optimizing the strength of an isotropic Gaussian spatial filter (Jekeli, 1981) in a way that the empirical spatial autocorrelation function of the filtered WSC data matches the observed spatial autocorrelation function of gravity-based TWSA to the best possible form. The approach is described in detail in Sharifi et al. (2025a), resulting in an optimal filter width of the Gaussian filter of 250 km (Fig. 5). Herein, the filter width represents the radius at which the spatial filter weighting function declines to 50 % of its maximum value. Sharifi et al. (2025a) furthermore show that filtering of the four WSC anomaly data sets (RZSM, SWE, GM, SWS) individually and then building the sum of the four is equivalent to first computing the sum of the four WSCs and then applying the Gaussian filter. Given its lower computational effort, the second approach, i.e., filtering of the combined WSCs anomaly data, was taken in the G3P processing chain described here.

Following the basic approach of Eq. (1), the combined and filtered WSC anomalies (see Sect. 2.3.3) were subtracted from TWSA in a simple algebraic cell-based operation for each month with available GRACE/-FO data within the data set period April 2002 to September 2023. This step was performed for all 0.5° land cells as defined by the output land-ocean mask (see Sect. 2.3.1), and excluding Greenland and Antarctica.

The individual WSC data sets are provided with gridded monthly time-varying uncertainties denoted as σ. After converting these uncertainties into the unit mm w.e. (see Sect. 2.3.2), they underwent a Gaussian filtering process in a similar way as the storage anomalies data (Sect. 2.3.3). The uncertainty of the resulting groundwater storage anomaly data set was calculated by standard uncertainty propagation following Eq. (8) at the 0.5° grid cell scale. 8σGWSA=σTWSA2+σRZSM2+σSWE2+σGM2+σSWS2

The Paris Basin, located in Northern France, is a multi-layered aquifer system with several main aquifer layers separated by low permeability formations (Contoux et al., 2013). The aquifer system includes unconfined and confined portions, with shallow unconfined aquifers laterally adjacent to or underlain by confined aquifers (Maréchal and Rouillard, 2020). The climate of the basin is temperate oceanic, with an average annual precipitation of around 650–900 mm (Habets et al., 2013; Joly et al., 2010). The main aquifers within the basin are highly productive, which have been intensively used for irrigation and water supply of the region (Maréchal and Rouillard, 2020).

The correlation between G3P GWSA and in situ GWLA of the Paris Basin is moderate to strong (r=0.63), indicating overall moderate agreement in temporal patterns (Table 2; Fig. 16). Both datasets reflect similar interannual and seasonal variations. The in situ data show slightly larger normalized amplitudes at the seasonal scale, while G3P shows more short-term variability. The latter can be related to the uncertainties of the G3P components, in particular of TWSA at this comparatively small spatial scale. Prior to the year of 2013, G3P values tend to be higher than in situ estimates and lower afterwards, possibly related to a stronger negative long-term trend over the study period seen by G3P for the Paris basin.

The High Plains Aquifer, which covers an area of about 450 000 km² across eight US states, is one of the largest aquifers in the world. It is generally unconfined and consists of unconsolidated sediments of late Tertiary and Quaternary periods (Dennehy, 2000; Strassberg et al., 2009). The climate of the region is mostly semiarid with high evaporation (Strassberg et al., 2007). The aquifer is intensively used for irrigation, accounting for about 30 % of groundwater used for irrigation in the US.

The correlation coefficient of the two standardized datasets is high (0.82) (Table 2; Fig. 16), suggesting strong agreement between G3P and in situ estimations, with both long-term and seasonal variation patterns being consistent. The correlation is higher before 2016, while after 2016 in situ data show lower values, especially during periods of overall low groundwater storage. For in situ monitored data, groundwater depression cones can occur locally around the pumping wells during pumping periods. The measured groundwater levels with low spatial coverage (Fig. 6) do not necessarily represent the overall condition of the whole aquifer, which may cause discrepancies to the G3P data.

The Guarani Aquifer System is a transboundary aquifer of approximately 1.2 million km². It is one of the largest groundwater reservoirs in the world, covering parts of Argentina, Brazil, Uruguay and Paraguay. It consists mainly of sandstone formations overlain by thick Cretaceous basalt flows (Gonçalves et al., 2020; Hirata and Foster, 2021). The aquifer is mostly confined by the underlying and overlying deposits and almost totally storage-dominated with old to very old water (from 4000 to > 100 000 years) (Hirata and Foster, 2021; Sindico et al., 2018). The climate varies from subtropical in the south to tropical savanna in the north, with precipitation ranging from 1000 to 1800 mm yr⁻¹ (Wendland et al., 2006). The aquifer is a strategic source and heavily exploited for the four countries that it covers.

The correlation coefficient of standardized datasets indicates a good positive correlation (0.81) (Table 2; Fig. 16). While the available time period for comparison is comparatively short, the interannual temporal patterns of groundwater storage changes are highly consistent. Regular sub-annual or seasonal variations are not pronounced in either data set. These smooth storage variations in particular for the in situ observations are consistent with the characteristics of a confined aquifer system. The G3P time series additionally exhibits random noise at monthly scales.

In summary, the evaluation case studies presented here demonstrate the applicability of G3P to capture temporal variations in groundwater storage change and its potential value for groundwater assessment across different hydrogeological and climatic settings. All three aquifers exhibit moderate to high correlation between G3P GWSA and in situ GWLA (r= 0.63–0.82), with the High Plains Aquifer and the Guarani Aquifer System showing particularly strong agreement, validating the performance of G3P in both unconfined and confined systems. Observed discrepancies between G3P and in situ time series are not surprising in view of the differences in spatial extent, spacing and resolution of both data sources but also highlight the importance of considering anthropogenic activities (localized pumping effects), aquifer type (recharge or storage dominated) and local heterogeneities when interpreting G3P and in situ monitoring data. Further considerations of G3P evaluation are given in Sect. 5.