Last modified on Oct 26, 2026 11:14

Contributors: J. Haas (GFZ), E. Boergens (GFZ), J. Bannwart (UZH), W. Dorigo (TUW), M. Kosmale (FMI), J. Lems (TUW), K. Luojus (FMI), W. Preimesberger (TUW), E. Sharifi (GFZ), M. Zemp (UZH), A. Güntner (GFZ)

GFZ: GFZ Helmholtz Centre for Geosciences

TUW: Technical University of Vienna

FMI: Finnish Meteorological Institute

UZH: University of Zurich

Issued by: GFZ / J. Haas

Date: 17/04/2026

Ref: C3S2_313c_EODC_WP3-DDP-GWSC-v1_202512_ATBD

Official reference number service contract: ECMWF/COPERNICUS/2024/C3S2_313c_EODC

History of modifications

List of data sets covered by this document

Acronyms

General Definitions

Equivalent Water Height: Equivalent Water Height represents the mass change per unit area as if it were entirely due to a uniform layer of water. It is derived from changes in gravity and surface deformation and is typically expressed in millimetres or centimetres.

Glacier Mass Change: Glacier Mass Change refers to the gain or loss of ice mass in a glacier over a given time period expressed in terms of water equivalent. It reflects the balance between accumulation (e.g., snowfall) and ablation (e.g., melting, sublimation), indicating whether a glacier is growing or shrinking.

Glacial Isostatic Adjustment (GIA): Glacial isostatic adjustment describes the deformational behaviour of the solid earth in response to glacial loading processes, in particular resulting in surface displacements as in stress, gravity and sea level changes.

GRACE Follow-On (GRACE-FO): Identically constructed successor satellite mission of GRACE, launched in 2018. The mission is again a joint US-German project.

Gravity Recovery and Climate Experiment (GRACE): Twin satellite mission observing the time variable gravity field of the Earth from which water mass redistribution can be inferred. The mission was active between 2002 and 2017 and was a joint US-German project. 

Groundwater Storage Change (GWSC): the deviation or anomaly of groundwater storage in a certain epoch (e.g., a month) from the long-term mean groundwater stroage. Groundwater is here defined as water stored underground in the saturated zone of soil and rock.

Leakage: Leakage describes the inability to localise signals in the GRACE-derived data sets. This is due, among other factors, to the band-limited resolution of GRACE and the filtering. These two effects lead to apparent signal loss (leakage out) or gain (leakage in) inside a given integration region.

Level-0 data: Raw instrument data received from the satellites. 

Level-1 data: Level-0 data converted to engineering units (Level-1A). Time-tagging of the data of all different instruments, filtering, and downsampling results in Level-1B data. Level-1B data includes range rate data, global positioning system (GPS) positions, and accelerometer data.

Level-2 data: Time-variable, usually monthly, gravity fields given in spherical harmonic (SH) coefficients.

Level-2B data: Post-processed Level-2 data, still given in SH coefficients. The post-processing includes several corrections that are applied to obtain as accurate as possible TWSA data.

Level-3 data: Time-variable, usually monthly, gravity fields given in the spatial domain as gridded data, based on Level-2B data. TWSA data is a Level-3 data set. 

Level-4 data: Targeted component mass-change products derived from Level-2B spherical harmonic or Level-3 gridded gravity data using additional signal isolation methods, model integration, or removal of non-target water storage contributions. This GWSC product is a Level-4 data set.

Root Zone Soil Moisture (RZSM): RZSM refers to the amount of water stored in the soil within the plant root zone and represents the water actually available for plant uptake. In this product the root zone is fixed to a depth of 2 meters.

Snow Water Equivalent (SWE): SWE is the amount of liquid water that would result if a given volume of snow were completely melted. It quantifies the water content of a snowpack.

Spatial Correlation Analysis: Spatial Correlation Analysis is a statistical method used to quantify the degree to which a variable is correlated with itself or another variable across geographic space. It assesses patterns of similarity or dependence between observations as a function of their spatial proximity or arrangement.

Spherical Harmonics (SH): Mathematical functions defined on the surface of a sphere, commonly used to express potential fields such as the Earth's gravity field by solving Laplace's equation.

Spherical Harmonic Coefficients: Commonly used representation of a global gravity field model based on the Spherical Harmonics basis functions. They are jointly estimated by least-squares adjustment together with other (instrument and orbit) parameters using satellite observations as provided by GRACE and GRACE-FO.

Subtraction Approach: The Subtraction Approach (or Residual Approach) refers to the method in which a target water storage component is estimated by subtracting other independently quantified storage compartments (here: Snow Water Equivalent, Root Zone Soil Moisture, Glacier Mass, and Surface Water Storage) from TWSA. The remaining residual represents the unobserved component (here: Groundwater Storage Change) that cannot be directly measured.

Surface Water Storage (SWS): SWS refers to the quantity of water held on the Earth’s surface in rivers, lakes, reservoirs, and wetlands. It represents a rather dynamic component of the hydrological cycle, varying with precipitation, runoff, evaporation, and human management.

Terrestrial Water Storage Anomaly (TWSA): TWSA represents the deviation or anomaly of terrestrial water storage (TWS) in a certain epoch (e.g., a month) from the long-term mean TWS in all hydrological water storage compartments: groundwater storage, soil moisture, surface water storage, and snow storage and glaciers. Globally, TWSA can only be observed with GRACE and GRACE-FO. 

Uncertainty: Uncertainty measures jointly the precision and accuracy of a data set. The uncertainties of the individual data sets used in the Groundwater Storage Change (GWSC) prodcution system are propagated from various sources, such as uncertainties of the sensors on the satellites, uncertainties of models applied in the processing chain, or environmental effects. These uncertainties are, again, propagated to the final GWSC product.

Executive Summary

This document serves as the Algorithm Theoretical Basis Document (ATBD) for the Copernicus Climate Change Service (C3S) Groundwater Storage Change (GWSC) data product (version v1.0). The product is derived from observations made by the Gravity Recovery and Climate Experiment (GRACE) and GRACE-Follow-On (FO) satellite missions and data products on several Water Storage Compartments (WSCs) - Glacier Mass (GM), Snow Water Equivalent (SWE), Root Zone Soil Moisture (RZSM) and Surface Water Storage (SWS).

The ATBD outlines the processing steps required to generate gridded Level-4 GWSC data by subtracting WSC data from Terrestrial Water Storage Anomaly (TWSA) data. The GWSC production system picks up the following data sets which are described and linked to in section 2:

• Level-3 TWSA data from the C3S ECV product "Terrestrial Water Storage Anomalies",
• GM data from the C3S ECV product "Glacier mass change global gridded data from 1976 to present derived from the Fluctuations of Glaciers Database",
• SWE data from the Copernicus Land Monitoring Service (CLMS) product "Snow Water Equivalent 2006-2024 (raster 5 km), Northern Hemisphere, daily – version 1",
• RZSM data from the C3S ECV product "Soil moisture gridded data from 1978 to present", and
• SWS-related data from the Copernicus Emergency Management Service (EMS) Global Flood Awareness System (GloFAS) v4.0.

Accordingly, this document summarises the external data sets and describes the processing steps needed to further process these data sets to make them compatible to the subtraction approach. This includes spatial gap-filling, spatial and temporal harmonization, and spatial filtering of the WSC data sets. Additionally, this document gives details of the auxiliary data used, which includes land-ocean masks.

Section 1 summarises the satellite missions involved in all input data streams.

Section 2 presents all data sets used in the production system. Section 2.1 gives a summary on Level-2 GRACE and GRACE-FO data processing, which happens outside the C3S production system, and Level-2B and Level-3 TWSA processing done in the C3S TWSA production system. The following sections describe the input WSC data on Glacier Mass (section 2.2), Snow Water Equivalent (section 2.3), Root Zone Soil Moisture (section 2.4), and Surface Water Storage (section 2.5). Section 2.6 summarises the auxiliary data sets required in the production system, including several land-ocean masks.

Section 3 details the production system, dividing the processing into the steps necessary to prepare the input WSC data sets presented in section 2 for GWSC production (sections 3.1 through 3.5), and the GWSC production itself (section 3.6). Each section also includes details on uncertainty estimation or propagation for the produced variable.

Finally, Section 4 summarises the output fields of the final GWSC product.

Missions and Instruments

The GWSC product is a Level-4 product based on several other high-level products. No satellite mission or instrument is directly involved in the production system. However, a total of 37 missions were involved in the production of the input products listed below. The appropriate sections int the relevant ATBDs decribing each of the input data streams are indicated below.

Level-3 Terrestrial Water Storage Anomaly (TWSA) is derived exclusively from the GRACE (2002–2017) and GRACE Follow-On (GRACE-FO, since 2018) satellite missions. Both missions, each consisting of two satellites flying in tandem, measure changes in the Earth’s gravity field that result from mass variations on the Earth's surface, foremost water mass. Inter-satellite distance changes are tracked using microwave (and on GRACE-FO, laser) interferometry, while GPS, star cameras, and accelerometers provide precise orbit and attitude information. Monthly gravity field solutions constructed from these measurements enable the detection of monthly to long-term mass changes across the Earth system, supporting large-scale monitoring of water redistribution. For additional details on the missions, see the corresponding section 1 in the TWSA ATBD.

The data sets used for the Glacier Mass (GM) change product are not directly derived from any airborne or spaceborne instruments. The input and auxilliary data sets involved in the production of the GM product in the GWSC production system are brokered from various international sources and described in section 2.2. For more details on the airborne and spaceborne sensors used in these input and auxiliary data sets, we refer the reader to the C3S related product documentation (section 1.4 of the ATBD of the global mass-change product, section 2.5 of the PUGS and sections 1 and 2 of the ATBD of the glacier area data).

The input data to the Snow Water Equivalent (SWE) product come from satellite remote sensing products provided by the C3S cryosphere service. Detailed descriptions of the retrieval algorithm and product characteristics are available in the associated ATBD and the PUGS for SWE version 1.0.

The Root Zone Soil Moisture (RZSM) product builds on the C3S Soil Moisture COMBINED Surface Soil Moisture (SSM) product. 14 passive and 5 active microwave sensors on satellites are involved in the production of the SSM data set. A full list of these missions and instruments is provided in the ATBD of that product.

The Surface Water Storage (SWS) product is based on the model OS LISFLOOD. However, since this model does not consider the Caspian Sea, the data set is complemented with altimetry-based data for that lake. For details see section 2.5.2.

Input and Auxiliary Data

C3S Terrestrial Water Storage Anomaly v1.0 (TWSA)

TWSA represents monthly terrestrial water storage variations derived from GRACE and GRACE-FO satellite gravimetry. These satellites track temporal changes in Earth’s gravity field—mainly caused by variations in continental water stored in liquid or solid form. TWSA is provided as a gridded Level-3 product used as the primary input for the groundwater calculation. The following subsections provide a short overview of the necessary processing steps towards the C3S TWSA data product. More details on the processing can be found in the TWSA ATBD or in Dahle et al. (2025).

Level-2 Processing

This processing step is the first to transform the output from the measuring instruments on board GRACE and GRACE-FO into data actually describing gravity changes. For the C3S TWSA product, Level-2 data are merely an intermediate product on the way to the gridded Level-3 product. 

GRACE and GRACE-FO observations (GPS tracking, inter-satellite K-band ranging) are inverted into monthly spherical harmonic (SH) gravity field solutions. Because processing strategies differ among analysis centres, their individual solutions contain varying noise levels and error characteristics. To improve robustness, the Combination Service for Time-variable Gravity Fields (COST-G) merges gravity field solutions from several analysis centres into a single, higher-quality Level-2 product (Jäggi et al., 2020, Meyer et al. 2024). The C3S TWSA product is based on the latest GRACE and GRACE-FO data products provided by COST-G RL02. Note that the production of the COST-G data set is not part of C3S.

Level-2B Processing

Level-2B processing is the first step inside of the C3S TWSA production system. Here we convert the time series of changes in Earth's gravity field into a time series of changes relative to the mean of the time series over a fixed period. These are called anomalies. In this form it is easier for a user to assess changes in, for example, water storage over that period. Additionally, steps are taken to reduce the noise content of the measurements by a process called filtering. Furthermore, some corrections are carried out to replace less reliable measurements and to remove signals caused by the solid Earth still adjusting to the melting of large ice sheets since the last Ice Age.

Several post-processing steps are applied to the Level-2 SH gravity field coefficients. First, the mean-field from January 2003 to December 2022 is removed from the monthly gravity fields to obtain anomalies. To mitigate correlated noise and reduce striping artefacts, the solutions are spatially filtered using anisotropic VDK2, VDK3, and VDK5 filters (Horvath et al., 2018). Certain low-degree coefficients are replaced with more reliable Satellite Laser Ranging (SLR) estimates: the C₂₀ coefficient is substituted for the entire study period, and the C₃₀ coefficient is replaced for the interval from November 2016 to June 2017. Long-term solid Earth deformation is removed by applying a Glacial Isostatic Adjustment (GIA) correction based on the ICE-6G_D (VM5a) model (Peltier et al., 2018). Degree-1 coefficients representing geocentre motion are inserted using external estimates following Swenson et al. (2008). Finally, a 161-day alias correction is applied to suppress spurious periodic signals associated with the S2 tidal alias.

Level-3 Processing

In Level-3 processing the satellite data are converted into monthly global maps that show changes in water storage on a regular grid. Additionally solid Earth signals introduced by very strong earthquakes are removed. In this form it should be very clear and easy for users to read the data.

The Level-2B SH coefficients are synthesised into monthly mass anomaly fields on a 0.5° global grid. To preserve long-wavelength geophysical signals while suppressing high-frequency noise, we use a combination of VDK3 and VDK5 filtered solutions. Deterministic temporal components—namely, the linear trend, annual, and semi-annual variations—are then separated from the residual fields. When monthly ocean-based standard-deviation diagnostics indicate elevated noise levels, a stronger VDK2 filter is applied to the affected months. Large co-seismic gravity changes associated with major earthquakes, including the 2004 Sumatra, 2010 Chile, and 2011 Japan events, are removed. The resulting product represents monthly terrestrial water storage anomalies (TWSA), expressed as equivalent water height (in mm). Uncertainties are estimated at the grid level using a combination of oceanic residuals and a spatial covariance model (Boergens et al., 2022).

Glacier Mass (GM)

The Glacier Mass (GM) product used in the C3S GWSC production system is compiled from several resources, including measurements from planes, satellites or even by hand. While glaciers are only present on a rather small portion of the Earth's surface outside of Greenland and Antarctica, the signals introduced by them are very strong, change heavily over the course of the seasons and often dominate in the area around them.

The GM change product builds on the combination of input data and auxiliary data brokered from international data repositories. The primary input is the global gridded glacier mass-change data distributed via the C3S within the Climate Data Store (CDS) (Dussaillant et al., 2023). This data set integrates both glaciological mass-balance time series and geodetic estimates of elevation change, building on observations compiled in the Fluctuation of Glaciers (FoG) database, brokered from the World Glacier Monitoring Service (WGMS, 2023). The auxiliary data source is the global glacier distribution (area and outlines) product, also accessed through the Climate Data Store (CDS, 2024). This product is derived from the Randolph Glacier Inventory (RGI) 6.0 (RGI, 2017), a community effort coordinated by the International Association of Cryospheric Sciences (IACS) under its glacier inventory working group. Further details on both data streams and their uncertainties are documented in the associated Algorithm Theoretical Basis Documents (ATBDs) for the global mass-change and glacier-area data products.

Snow Water Equivalent (SWE)

The Snow Water Equivalent (SWE) product used in the C3S GWSC production system is also compiled from several sources, but mainly from satellites and completed by data from computer models. However, for validation of the data direct measurements by humans are also relevant. Snow storage variations are very important as they affect a large portion of the Earth's surface and have a large amplitude across the year.

The water content of the snow cover can be derived using the essential climate variable (ECV) of SWE. In the groundwater processing scheme described here, the baseline SWE data originate from satellite remote sensing products provided by the C3S cryosphere service. Detailed descriptions of the retrieval algorithm and product characteristics are available in the associated ATBD and the PUGS for SWE version 1.0. The satellite-based SWE product covers the Northern Hemisphere only and excludes mountain regions due to constraints in the current algorithm methodology. To provide full global coverage, a combined product has been established that integrates both satellite observations and model-based estimates to enable global SWE assessments. SWE data for the Southern Hemisphere and for mountain areas are taken from the average SWE estimates of the reanalysis models ERA5-Land (Muñoz-Sabater et al., 2021) and MERRA2 (Gelaro et al., 2017). Model-based SWE is used to fill gaps in the satellite product and ensure spatial completeness. The combined SWE data set is produced at daily temporal resolution on a 0.25° regular latitude–longitude grid, and serves as an input for the groundwater processing steps described further in sections 3.3 and 3.6 of this report.

Root Zone Soil Moisture (RZSM)

The Root Zone Soil Moisture (RZSM) product used in the C3S GWSC production system relies on satellite measurements of soil moisture at the topmost few centimeters of the Earth's surface. Based on these measurements a model is used to estimate the soil moisture down to 200 cm depth, called the root zone. Among the water storage compartments relevant for TWSA, soil moisture is the one with the largest spatial coverage over land. It is only negligible in permanently glaciated regions and areas of exposed bedrock, and it is of minor importance in very dry regions, like hyper-arid deserts, and heavily sealed surfaces, like densely urbanized areas.

RZSM from satellite measurements describes gap-free soil moisture variations in the upper two meters of the soil column, split into four depth layers: 0–10 cm, 10–40 cm, 40–100 cm, and 100–200 cm. The product builds on the C3S Soil Moisture COMBINED Surface Soil Moisture (SSM) product. Note that the C3S Soil Moisture service already provides an RZSM data record, but this version is currently limited to a soil depth of 1 m and contains spatial and temporal data gaps. More details on the baseline algorithm are provided in the ATBD, information on the data quality is given in the PQAR. Adjustments applied to the RZSM algorithm for the GWSC production system are described in section 3.4 of this document. 

The underlying method used to propagate surface soil moisture into deeper layers is the Exponential Filter (EF) (Albergel et al., 2008; Wagner et al., 1999). The implementation of the filter to C3S Soil Moisture data, the layer-wise calibration to 2 m soil depth, and the uncertainty estimation approach are described in Pasik et al. (2023). RZSM and uncertainty estimates for GWSC are derived for all four depth layers mentioned above. The product is generated at monthly temporal resolution, available from 2002 onwards on a 0.25° regular latitude–longitude grid, and provided in volumetric units (m³/m³).

Surface Water Storage (SWS)

The Surface Water Storage (SWS) product used in the C3S GWSC production system is not observation-based, but comes from a model that simulates hydrological processes across the entire globe. The reason for this is that no observation-based SWS product with global coverage and full component representation is currently available, allthough several promising remote-sensing and data-assimilation initiatives exist and might be part of this production system in the future. In addition to modelled data, satellite measurements for the Caspian Sea are used. This lake is the largest lake in the world by area and is not modelled by the hydrological model used here. Surface water storage affects TWSA over relatively small areas. But where it exists, especially over large lakes and wetlands, it can dominate seasonal variability, much like snow does at high latitudes. The hydrological model used here does not produce a measure of uncertainty, unlike the other observation-based water storage compartments. However, uncertainty is important information for many users. As a consequence, the output of the hydrological model used here is compared to a set of other models and the differences are used as an estimate of uncertainty.

The following data sets are required and originate outside the GWSC production system.

OS LISFLOOD model outputs

The primary external input consists of the OS LISFLOOD model outputs produced within the Copernicus Emergency Management Service’s Global Flood Awareness System (GloFAS v4.0). OS LISFLOOD is a global hydrological model that delivers daily fields at 0.05° spatial resolution and supplies all key variables needed to represent surface water components. These include channel cross-sectional area and channel length used to compute river water volume, lake water level variations, and the time-variable filling state of reservoirs. Together, these variables form the baseline for calculating river, lake, and reservoir storage on a global scale.

Caspian Sea water levels

The GloFAS implementation of OS LISFLOOD does not include the Caspian Sea, so an additional data set is required to ensure complete global coverage. For this purpose, water level variations for the Caspian Sea are taken from the DAHITI project (Schwatke et al., 2015). DAHITI provides satellite-altimetry-based lake water level data.

Global Lake and Wetland Database (GLWD)

To correctly allocate storage volumes spatially, the GWSC production system uses lake and reservoir locations from the Global Lake and Wetland Database v1 (GLWD, Lehner & Döll, 2004). While OS LISFLOOD represents lakes and reservoirs only at their outlet cell, GLWD provides detailed polygons that describe the true geographic extent of each waterbody. These polygons are necessary to redistribute the modelled storage volumes across all grid cells belonging to each lake or reservoir and thus create spatially realistic storage fields.

Global Hydrological Model (GHM) outputs 

The following GHM model outputs from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) simulation round 3b serve as input for SWS uncertainty estimation. All ISIMIP data is freely available form the ISIMIP repository.

Water GAP Global Hydrological Model

CWatM

H08

MIROC-INTEG-LAND

Auxiliary Data

Land-Ocean Masks 

To distinguish continental areas from the oceans a set of global land-ocean masks is required. The masks used in the GWSC production system were produced during the Global Gravity-based Groundwater Product (G3P) project (https://www.g3p.eu/; URL last accessed 2025-12-12) based on the European Space Agency (ESA) Climate Change Initiative (CCI) global map of open water bodies v4.0 (CCI WB v4.0) and are freely available in different resolutions (Sharifi et al., 2025b). The final GWSC product is produced on a 0.5° x 0.5° grid where cells are considered land cells if they contain at least 50% land area. This is illustrated for Europe in Figure 1.

Figure 1: Land-ocean mask used in the GWSC product for Europe (land: green, ocean: blue), overlaid by the coastline of the Global Self-consistent, Hierarchical, High-resolution Geography Database (GSHHG, Wessel and Smith, 1996). 

Algorithms 

This section provides information about the algorithms of the GWSC production system. The reader is referred to Güntner et al. (2025) for more details on the algorithms. The processing of the input data sets after pickup from their sources are described in sections 3.1 to 3.5. The key differences between the GWSC product presented here and the product described in Güntner et al. (2025) are as follows:

• harmonization with C3S TWSA product in terms of spatial resolution and reference period (January 2003 to December 2022),
• reference period set to full years for user friendliness,
• use of publicly available, findable and citable land-ocean masks,
• general lower GWSC uncertainty due to lower TWSA input uncertainty,
• improved SWE input data, including patches of erroneous months,
• improved SWS uncertainty estimation with a larger model ensemble.

Figure 2 provides an overview of the processing chain of the GWSC production system.

Figure 2: Overview of the processing steps in the GWSC production system after pickup of the input data sets.

Terrestrial Water Storage (TWS)

The TWSA product is truncated to the common period of all input data sets, i.e. April 2002 to September 2023. No further processing of the TWSA data set is necessary.

Glacier Mass (GM) 

For the GM change product, spatially distributed glacier mass changes are derived at monthly temporal resolution by applying statistical modelling constrained by annual observations from the C3S global gridded glacier mass-change data set. The temporal downscaling approach, based on statistical fits to annual mass-change observations, has recently been described in Zemp and Welty (2023). The processing algorithm consists of five main steps, which are documented in figure 4 of Güntner et al. (2025) along with a description of the uncertainty estimation process in section 2.2.4. The GM change product has been compared to prior studies and to GRACE satellite gravimetry data, and additional cross-validation experiments have been conducted, which all showed generally good agreement. The comparisons for the annual product are published in Dussaillant et al. (2025). Seasonal comparisons have been carried out within the G3P project, but are not yet published.

Snow Water Equivalent (SWE) 

The water content of a snow mass can be derived using the essential climate variable (ECV) Snow Water Equivalent (SWE). The SWE product for the GWSC production system builds on a combination of input data from satellites and models. 

Gap-filling SWE

The baseline SWE data set originates from satellite remote sensing products provided by the C3S cryosphere service, which is is derived from Passive Microwave satellite Radiometer (PMR) observations available since 1979. A detailed description of the retrieval algorithm is available in the Snow Water Equivalent (SWE) version 1.0: Algorithm Theoretical Basis Document (ATBD) and the product specifications are documented in the Snow Water Equivalent (SWE) version 1.0: Product User Guide and Specification (PUGS). The satellite SWE algorithm is based on works by Takala et al. (2011) and Luojus et al. (2021), including the latest improvements implemented within the C3S cryosphere service. The baseline satellite product is generated at daily temporal resolution on a regular 0.1° × 0.1° latitude–longitude grid. Because the retrieval utilises PMR measurements, the product is unaffected by clouds and polar night conditions, allowing for consistent observations at high latitudes. However, due to sensor saturation effects at snow depths > 1 m, which occur for example in alpine terrain, and due to the native satellite footprint of ~25 km, small-scale snow features in mountain areas cannot be sufficiently resolved. Mountain regions are therefore not available from this satellite-based product. Furthermore the retrieval methodology for this satellite-based SWE product combines PMR measurements with ground-based synoptic weather station observations using Bayesian non-linear iterative data assimilation. Because in-situ data are integrated through this assimilation approach, the current algorithm is limited to the Northern Hemisphere only and does not yet provide SWE estimates for Southern Hemisphere latitudes.

To achieve full global coverage, a combined SWE product integrating both model- and satellite-based estimates has been developed. This allows for global estimates of the total water mass stored in snow. SWE data for the Southern Hemisphere are provided by the estimates of the two reanalysis models ERA5-Land (Muñoz-Sabater et al., 2021) and MERRA-2 (Gelaro et al., 2017). Mountain regions, which are not represented in the satellite retrieval, are likewise covered by this model-derived SWE to fill spatial gaps in the baseline satellite product. Satellite- and model-based data sets are resampled by bilinear interpolation to a common spatial resolution on a regular 0.25° latitude–longitude grid to allow for merging.

A merged model dataset is derived by calculating the mean of ERA5-Land and MERRA-2 SWE estimates for each day. Regions with gaps in the satellite-based product, such as mountains and Southern Hemisphere land areas, are filled with then with the corresponding merged model data of the particular day and the grid-cell. The monthly mean estimates for the global gap-free Snow Water Equivalent product are then calculated by the gap-filled daily product and act as input on snow mass for the groundwater processor.

Skill assessment and uncertainty

The skill of the individual input datasets as well as the combined SWE product is assessed by validating each product against in-situ measurements. 

In-situ reference data consist of ground-based manual gravimetric snow course measurements conducted along predefined sampling transects. For the validation averaged SWE values along the measured transect path represent ground observations for the collocated satellite pixel or model grid cell. Transect-based snow course observations were available for Russia, Finland and Canada. Validation results show generally good agreement, with consistent Spearman correlation coefficients > 0.6 for all evaluated products over the relevant period (2002–2023). The combined SWE product also shows robust performance with respect to the available in-situ observations.

Pixel-level uncertainty of SWE are either directly the pixel-level uncertainty values coming from the baseline satellite product or respecively a merged model uncertainty. The satellite-based SWE data of C3S offers pixel-scale uncertainties which are derived by error propagation from raw satellite data through the algorithm. The reanalysis models used for gap filling do not provide uncertainty estimates on Snow Water Equivalent, though. In order to get pixel-level uncertainties for the models, a diagnostic uncertainty dependency of the error with respect to SWE measures is calculated, assuming that the observed RMSE gives a good representation of the overall product accuracy. A discussion on pixel-level uncertainties in remote sensing and estimating diagnostic uncertainties from validation results is described in A. Sayer, 2020. 

More details on the validation results of the combined SWE product for groundwater is given in Güntner et al. as well as the C3S Groundwater Product Quality Assessment Report (PQAR).

Root Zone Soil Moisture (RZSM)

RZSM required to derive GWSC differs from the product provided via the C3S soil moisture service in the following ways: 

Gap-filling SSM

The baseline C3S COMBINED Surface Soil Moisture (SSM) product contains data gaps, either because no satellite observation was available for a given day, or because available measurements were masked due to identified reliability issues. Since the GWSC subtraction model requires gap-free estimates for all storage compartments, the satellite-derived soil moisture observations are gap-filled. The gap-filling approach applied to SSM is a modified version of the Discrete Cosine Transform with Penalized Least Squares (DCT-PLS) algorithm originally introduced in Garcia (2010). Although initially developed as a 3-dimensional data smoother, the method has previously also been applied for gap-filling different (climatic) variables, including soil moisture. Building on this algorithm, Preimesberger et al. (2025) established an extended processing framework for the generation of gap-free daily SSM estimates.

During periods of frozen soil conditions, a linear interpolation over time is applied to approximate the (constant) retention of liquid water in soil until thawing occurs and natural variability in soil moisture resumes. The framework further provides a method for estimating the uncertainties introduced during the interpolation process. Algorithm testing shows that gap-filling uncertainties increase with gap-size and are influenced by the quality of the underlying satellite observations, for example by factors such as vegetation density. Validation against independent reference data shows that agreement levels between the gap-filled and reference soil moisture estimates are comparable to those of the baseline satellite product. The output of the gap-filling process is a gap-free daily surface soil moisture record on a 0.25° latitude–longitude grid, covering the relevant GWSC period.

RZSM Modifications

The gap-free SSM product is subsequently used as primary input for the Exponential Filter (EF) method, following the methodology described in Pasik et al. (2023) and the ATBD of the satellite soil moisture service. Aside from the use of gap-free input, the only algorithmic modification is that RZSM is additionally extended to the 100–200 cm depth layer. The corresponding model calibration T-parameter T_opt and the value for the model structural error σ(EF) required for the uncertainty estimation of this additional layer are documented in Table 1. The EF model was calibrated by Pasik et al. (2023) on daily data (hence the unit of T in days). All SSM derived RZSM output layers are subsequently aggregated to monthly temporal resolution – via a temporal mean – for GWSC.

Pasik et al. (2023) found lower agreement with ERA5-Land for this layer compared to the three shallower layers, because the surface soil-moisture signal becomes weakly coupled to deeper layers, leaving the EF with less information to propagate downward. With increasing depth, both structural and parameter errors grow, leading to a decline in correlations and overall skill of the retrieval.

The 100–200 cm layer is nevertheless included in the GWSC production system, with the larger uncertainties explicitly represented in the product uncertainty field. After retrieval and uncertainty estimation, the four depth layers are merged by weighted averaging, following the formulation outlined in equation (1), to derive one combined RZSM layer covering 0–200 cm soil depth. RZSM_X-Y here refers to RZSM values derived at the respective depth layer, from X cm to Y cm depth. 

Finally, monthly mean values of the merged layer (0-200 cm) are computed as the final soil moisture storage compartment input for GWSC.

Surface Water Storage (SWS)

Temporal Aggregation and Resampling

Within the C3S GWSC processing system, OS LISFLOOD’s daily outputs are aggregated into monthly values and resampled from their original 0.05° grid to the common 0.5° grid using bilinear interpolation. This ensures temporal consistency with the monthly GRACE and GRACE-FO signal and spatial consistency with the target groundwater product.

River storage

River storage for each grid cell and time step is calculated by multiplying the modelled, time-varying wetted channel cross-sectional area by the river length given for that cell.

Construction of Lake and Reservoir Storage

Lakes and reservoirs in OS LISFLOOD are represented at their outlet cell only, requiring several additional steps to obtain spatially correct, gridded storage estimates. Lake water levels from OS LISFLOOD are converted into volume variations by multiplying them with the lake areas taken from the GLWD. Reservoir volumes are derived by multiplying the modelled filling state with the maximum storage capacity of a reservoir, given as an input data set in OS LISFLOOD.

Spatial Representation of Waterbodies

Because these waterbodies can extend beyond the single outlet grid cell used in OS LISFLOOD, their volumes must be redistributed spatially according to their real-world geographic extent. To translate OS LISFLOOD’s simplified representation into realistic distributed storage fields, the following procedure is used:

1. For each lake or reservoir outlet cell, the corresponding polygon in the GLWD is identified. All 0.5° grid cells whose centre lies inside this polygon are then assigned to the waterbody, ensuring that no grid cell belongs to more than one lake or reservoir.

2. The computed waterbody storage volume is distributed evenly across all assigned grid cells, thereby providing a spatially consistent representation of the waterbody.

3. River storage that falls within these assigned lake or reservoir cells is added to the total waterbody storage and subsequently removed from the river storage layer to avoid double counting.

Formation of SWS Anomalies

Once river, lake, and reservoir storage values are established, they are combined and converted into millimetres of equivalent water height. Subsequently, these storage values are transformed into monthly anomalies relative to the established reference period, i.e. January 2003 to December 2022.

Integration of Caspian Sea data

The time series of Caspian Sea water level changes are converted from meters to millimeters, assigned to all 0.5° grid cells within the polygon for the lake from the GLWD, and converted into anomalies relative to the reference period.

Uncertainty Estimation

Since OS LISFLOOD does not provide uncertainty estimates for its storage simulations, the GWSC production system derives a first-order uncertainty metric by comparing monthly SWS values from OS LISFLOOD with an ensemble mean of four global hydrological models presented above. This is done for each grid cell and time step by calculating the difference between OS LISFLOOD (including the merged Caspian Sea data) and the ensemble mean. The half of that difference is interpreted as a pragmatic proxy for spatially explicit and time-varying SWS uncertainty. Although this does not fully match the instrument- and algorithm-based uncertainty estimates available for observation-based WSCs, it still provides a useful indication of SWS uncertainty for the groundwater product.

Groundwater Storage Change (GWSC) 

At this point in the GWSC production system all datastreams are present as monthly values over the relevant period from April 2002 to September 2023. Before the final subtraction step, described in section 3.6.5, several further harmonization steps have to be taken.

Unit harmonization and coastal correction

GM is stored as Gt glacier mass change and converted to mm equivalent water height per grid cell by normalizing mass by cell area. RZSM is stored as m³/m³ volumetric content and is converted to mm by multiplying with relevant soil depth of 2000 mm. SWE and SWS are already present in mm. Once all WSCs are converted to mm, the values in coastal cells are scaled to their land fraction by multiplying their value with the corresponding land fraction given in the land-ocean mask of their native resolution (SWE and RZSM: 0.25°, GM and SWS: 0.5°). By this, values represent land-only storage within cells that are partially covered with water.

Transformation to anomalies

Absolute monthly storage time series of GM, RZSM and SWE are converted to anomalies by subtracting each cell’s mean over the reference period (January 2003 to December 2022). TWSA and SWS are already produced as anomalies.

Spatial resampling to common 0.5 degree grid

As mentioned in section 2.6.1 the final GWSC product is produced on a 0.5° x 0.5° grid where cells are considered land cells if they contain at least 50% land area. Accordingly all input data streams, i.e. TWSA and the WSCs are resampled to this common mask using bilinear interpolation before further processing.

Spatial correlation analysis and filtering with Gaussian filter

To make WSC data spatially compatible to TWSA data they need to be filtered to emulate the spatially smoothed patterns of TWSA. As mentioned above, GRACE and GRACE-FO observations are filtered with VDK filters. However, these filters can not be applied to data without the GRACE-like error correlations, like the WSC data used here. Doing so would introduce false stripes and signal distortion. Instead, Gaussian filters must be used.

Unfiltered WSC anomalies show very different spatial correlation lengths, depending on their spatial characteristics. For example, long and smooth for soil moisture, or sharp and localized for glaciers and river-network storage.

In the procedure presented in Sharifi et al. (2025a), spatial auto-correlation functions are computed for WSC anomaly fields at multiple smoothing levels. These smoothed outputs are generated using a range of Gaussian filter strengths, expressed as different filter widths (50 to 600 km in 50 km intervals). Correlation-decay models based on a Weibull stretched-exponential form are empirically fitted to the spatial auto-correlation functions of a) the individual water-storage anomaly components and b) the aggregated combination of all WSC, quantifying how spatial correlation decays with distance for every tested filtering strength. For option b) the filter width of 250 km resulted in a spatial correlation decay almost identical to VDK-filtered TWSA and yielded the lowest structural mismatch between aggregated WSC data and TWSA.

Accordingly, in the GWSC production system WSCs are aggregated before filtering and a Gaussian kernel of 250 km width is used.

It has to be noted that validity of the Gaussian filter width needs to be checked for every future iteration of the GWSC product. Sharifi et al. (2025a) report that the optimal filter width has already been adjusted in the course of the G3P project, increasing from 200 km to 250 km between G3P versions v1.11 and v1.12.

Subtraction approach

The aggregated and filtered WSC anomalies (here indicated by an A after the corresponding abbreviation) are then subtracted from TWSA following this simple water budget equation (2):

This is done in all grid cells defined as land. Greenland and Antarctica are excluded from the GWSC product. This is because in those regions the TWSA signal, on which the GWSC product is based, is highly dominated by the signals from glaciers and ice sheets. Due to the high uncertainties attached to glacier and ice mass changes, a reliable estimate of GWSC is not feasible. This may change with future improvements in observation technology or regional changes in ice cover.

Uncertainty propagation

Each of the WSCs and TWSA comes with an uncertainty characterisation detailed in the corresponding sections above. The uncertainty field of each WSC is variance propagated through the same Gaussian filter as applied to the WSC. Here, it is assumed that the gridded WSC uncertainties do not have spatial correlations. These filtered uncertainties are then propagated to the GWSC product by standard variance propagation with the following equation (3):

Output Data 

Table 2 lists the output fields generated by the GWSC production system and made available to users. Detailed information on each field and the file format are provided in the Product User Guide and Specification (PUGS).

Table 2: Overview of output data fields.

Figure 3 shows the final data product for the example of the month March 2008 with (a) the GWSC and (b) the GWSC uncertainty.

Figure 3: Fields of the final data product. (a) shows GWSC from the final data product for the example month of March 2008 stored in the gwsc variable in the netcdf file; (b) shows the uncertainty of GWSC for the same month, stored in the gwsc_uncertainty variable of the netcdf file.

Acknowledgements

We would like to thank and acknowledge the modelling groups, the ISIMIP sector coordinators and the ISIMIP cross-sectoral science team for their roles in producing, coordinating, and making available the ISIMIP input data and impact model output.

We thank Peter Salamon and Stefania Grimaldi from JRC, and Ervin Zsoter from ECMWF for their support and provision of the OS LISFLOOD data.

We thank Adrian Jaeggi and Ulrich Meyer from the Astronomical Institute of the University of Bern for their provision of the COST-G Level-2 GRACE data.

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