Last modified on Apr 07, 2026 07:32

Contributors: E. Boergens, C. Dahle, J. Haas, H. Dobslaw, F. Flechtner, A. Güntner

GFZ Helmholtz Centre for Geosciences

Issued by: GFZ / E. Boergens

Date: 23/09/2025

Ref: C3S2_313c_EODC_WP3-DDP-TWSA-v1_202507_PQAR

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

History of modifications

List of datasets covered by this document

Acronyms

General definitions

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. 

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

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 (2003-01 - 2022-12) mean TWS in all hydrological water storage compartments: groundwater storage, soil moisture, surface water storage, snow storage, and glaciers. Globally, TWSA can only be observed with GRACE and GRACE-FO. 

Uncertainty: Uncertainty measures jointly the precision and accuracy of the TWSA data, expressed as a standard deviation. The uncertainties of the TWSA grids are influenced, among others, by the uncertainties of the sensors on the satellites, uncertainties in the background models applied in the processing chain, the orbit configuration of the missions (near-polar orbit), and environmental effects such as solar activity.

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 parameters (instrument and orbit), using satellite observations provided by GRACE and GRACE-FO.

Mass Concentration block (Mascon): Alternative definition of base functions to express the gravity potential field of the Earth. This approach does rely on external geophysical constraints about the expected location of mass changes, but does not require the filtering as the SH coefficients do. 

Level-1 data: Level-0 data converted to engineering units (Level-1A). Time-tagging of the data from all different instruments, filtering, and downsampling yield Level-1B data. Level-1B data includes range rate data, 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 TWSA data as possible.

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

SH-based TWSA data: A data set based on Level-2 data, utilising the SH synthesis to produce gridded TWSA data.

L1-based mascons TWSA data: TWSA data are directly estimated from Level-1B data based on the mascons approach, considering geophysical constraints.

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

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

Deterministic signals: The deterministic signals comprise linear trend, sinusoidal annual and semiannual signals, which are estimated with least-squares adjustment from a data time series. 

Residual signal: Signal remaining of a data time series after the subtraction of the deterministic signals. The residual signal contains both the high-frequency noise and the interannual signal variations.

Standard deviation: The standard deviation (abbreviation: std) is a measure of the amount of variation around the mean of the data. If the data is normally distributed, ~68% of the values are inside the interval [mean-std, mean+std], ~95% inside [mean-2*std, mean+2*std], and ~99% inside [mean-3*std, mean+3*std].

Signal-to-noise ratio (S2N): Signal-to-noise ratio is a measure of how much useful information (“signal”) is present in data compared to unwanted variability or errors (“noise”). A higher SNR means the true signal patterns stand out more clearly from random noise fluctuations.

GCOS Product Target Requirements: For each ECV, measurable requirements of the product performance are defined. These requirements encompass quantitative criteria along several dimensions, including spatial resolution, temporal resolution, measurement uncertainty, stability over time (bias drift), and timeliness (latency of data availability). For each target requirement, a threshold and a goal value are defined. Threshold is the minimum acceptable requirement. If a product fails this, it is presumably not useful for climate monitoring. The goal is the ideal level. Once this is met, further improvements in that criterion are not strictly necessary for most applications. 

Executive summary

The Copernicus Climate Change Service (C3S) Terrestrial Water Storage Anomaly (TWSA) data product provides global monthly TWSA fields derived from satellite gravimetry observations. This document presents the quality assessment of the TWSA Climate Data Record (CDR) v1.0, produced in June 2025. The data are provided on a 0.5° x 0.5° grid. The product covers the period from April 2002 to March 2025; however, some months are missing within this timespan. For further details on the product, please refer to the Algorithm Theoretical Basis Document (ATBD, Boergens et al., 2025a) and the Product User Guide and Specification (PUGS, Boergens et al., 2025b).

At present, TWSA is observed exclusively by the GRACE and GRACE-FO satellite gravimetry missions. Consequently, TWSA cannot be independently validated, as no direct and comprehensive observational system exists that captures terrestrial water storage changes across all relevant components — surface water, soil moisture, groundwater, snow, and glaciers — at spatial and temporal scales comparable to GRACE and GRACE-FO. Ground-based observations, such as groundwater well measurements or in-situ soil moisture sensors, provide valuable but limited comparison data. These observations only reflect part of the water storage components represented in TWSA and are often sparse, localised, and inconsistent in terms of quality or availability across different regions. As such, the quality of a TWSA dataset can primarily be assessed through comparison with other independently processed TWSA datasets (also based on GRACE observations), or with modelled TWSA from global hydrological models. However, the latter have limitations, particularly the lack of representation of glacier mass changes. Accordingly, this quality assessment aims to demonstrate that the C3S TWSA dataset meets the quality standards expected of both external satellite-derived and modelled TWSA datasets.

Section 1 introduces the Product Validation Methodology used in this report, including the validated product itself (subsection 1.1) and the validation data sets, which consist of the independently processed TWSA datasets and the global hydrological models from which the modelled TWSA is derived (subsection 1.2). The validation regions are presented in subsection 1.3. Subsection 1.4 outlines the validation methods applied. Section 2 then presents the results of the defined validation metrics. The document concludes with section 3, which addresses compliance with the GCOS user requirements.

Product Validation Methodology

Validated products

The C3S TWSA data product provides monthly gridded TWSA fields from April 2002 onwards. TWSA is derived from observations of the GRACE (2002-2017) and GRACE-FO (since 2018) satellite missions. The inputs to the TWSA production system consist of spherical harmonic coefficients (Level-2 data) provided by the Combination Service for Time-variable Gravity Fields (COST-G, https://cost-g.org/). The COST-G Level-2 products can be regarded as the best monthly global gravity field models available, as they benefit from the strengths of various processing approaches of the different Level-2 processing centres contributing to an optimally weighted combination. Furthermore, the COST-G workflow includes a quality control of the input gravity field solutions as well as an internal and external validation to identify possible outlying or systematically biased input solutions (Jäggi et al., 2020). Figure 1 provides a flowchart detailing the processing steps taken to produce the TWSA CDR v1.0 (produced in June 2025), which is validated in this Product Quality Assessment Report (PQAR). A detailed description of the product generation is provided in the Algorithm Theoretical Basis Document (ATBD, Boergens et al., 2025a), and further information on the product's usage and limitations is given in the Product User Guide and Specifications (PUGS, Boergens et al., 2025b).

The validation and quality checks of this PQAR will focus on the primary variable 'twsa' of the provided netCDF file. Additionally, the uncertainties provided in the variable 'twsa_uncertainty' are also evaluated.

Figure 1: Overview of the processing steps from GRACE and GRACE-FO Level-2 data to the TWSA (Level-3) data product. The processing from Level-2 to Level-2B is conducted in the spherical harmonic (SH) domain (indicated in green), whereas the subsequent processing steps from Level-2B to the final TWSA product are performed in the spatial domain (marked in blue). Additional independent input data required for the processing of TWSA are referred to as auxiliary data.

Internal data quality check

During dataset production, several internal quality checks are performed. In the first step, the produced NetCDF files are checked for consistency of the variables, i.e., no repeating dates or coordinates in the longitude and latitude variables, or inconsistencies between the coordinate variables and the data fields.

In the second step, internal open-ocean noise is checked for outliers. Open-ocean noise is the area-weighted standard deviation σ(t) for each month t, defined in eq. (1), after removal of deterministic signals, i.e., trend, annual and semi-annual signals (twsa_red; see eq. (2), for details):

where a represents the number of open-ocean grid points, and wᵢ is the area weight of the i-th grid cell at longitude λᵢ and latitude θᵢ. σ(t) is not included in the published dataset, but becomes available during the dataset processing.

Each monthly value of σ(t) is compared to the mean of all σ(t) values. Months where σ(t) exceeds twice the mean σ(t) are flagged for further inspection. As there are known months with poorer data quality (see PUGS, Boergens et al., 2025b), such months may still be included in the final data product after manual review.

The final test is performed only for Interim Climate Data Records (ICDRs), i.e., when months are appended to an existing data product. For this test, the residual signal is again required, and the standard deviation of the residuals for a newly added month is compared to that of the residuals for all previously available months. If the former exceeds three times the latter, the month is flagged for further inspection. Again, an informed decision may still be made to include the month in the final product.

Validation data sets

Two different validation datasets are used for the quality assurance of the C3S TWSA product. First, the C3S TWSA dataset is compared to an ensemble of other operationally produced TWSA datasets (see subsection 1.2.1). Second, it is compared to an ensemble of global hydrological model outputs (see subsection 1.2.2), which represent the majority of water storage compartments.

TWSA data sets

The operational TWSA products can be categorised into two major processing approaches: those based on spherical harmonic (SH) synthesis and L1-based mass concentration blocks (mascons). The C3S TWSA data fall into the former category.

SH Synthesis: Datasets produced using SH synthesis employ monthly global gravity fields in the form of spherical harmonic coefficients (Level-2 data). Estimation of the Level-2 gravity fields from Level-1 data is unconstrained; however, for Level-3 data production, several processing steps are required—most notably, SH coefficient filtering. The choice of filtering method is an essential factor in the resulting TWSA dataset. Another critical factor governing the SH-synthesis-based TWSA data set is the maximum degree and order at which the synthesis is done. Refer to the ATBD (Boergens et al., 2025a) for details of the necessary steps. 

L1-based Mascons: These do not rely on Level-2 SH data but estimate monthly gridded TWSA fields directly from the range-rate measurements of inter-satellite distances (Level-1 data). Mascons are another form of gravity field basis functions, but defined in the spatial domain. During estimation, geophysical constraints—such as land-ocean boundaries—can be directly applied. Hence, the estimation is constrained, and no further filtering is necessary. Further details on mascons can be found in Watkins et al. (2015).

The different processing principles handle leakage differently. Furthermore, a lower maximum degree and order of the SH synthesis reduce the spatial resolution, thereby increasing the leakage effect. More details on leakage and its imposed limitations on TWSA datasets are described in PUGS (Boergens et al., 2025b), Section 1.2. 

Table 1 summarises the TWSA validation datasets, highlighting their key characteristics. For easier comparison, the C3S TWSA data have also been included.

Table 1: Overview of the TWSA datasets used for validation. For the processing principle SH synthesis, both the applied filtering and the maximum degree and order (max d/o) of the synthesis is stated. A lower maximum degree and order indicate a lower spatial resolution. For details on the filtering, especially VDK, please refer to the ATBD (Boergens et al., 2025a).

Preprocessing

The spatial grid resolution of the different TWSA datasets ranges from 0.25° × 0.25° to 1° × 1°. Owing to the unique characteristics of the spatial resolution of the three mascon datasets, it is not advisable to simply upsample or downsample the TWSA datasets to a common grid. Consequently, a grid-cell-wise comparison of the datasets is not feasible. To address this limitation, the datasets are validated against each other using regionally aggregated time series.

Validation is performed only for the time period common to all datasets, namely April 2002 to January 2025. Accordingly, all datasets are restricted to this time period during preprocessing.

Hydrological models

Several global hydrological models (GHMs) can produce estimates of TWSA as they simulate all or at least most of the water storage compartments that TWSA comprise. Outputs from five GHMs, along with the land surface model (LSM) Global Land Data Assimilation System (GLDAS)-Noah, are used to validate the C3S TWSA data. Model details are provided in Table 2. 

The five GHMs were selected as they are widely used in the community and commonly included in initiatives that generate TWSA, such as the Earth2Observe Water Resources Reanalysis (WRR) or the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP). The instance of Open-source LISFLOOD (OS LISFLOOD) used is specifically designed for comparison with TWSA and runs on-premises by members of the TWS team. From the ISIMIP ensemble, the Community Water Model (CWatM) and the Hanasaki 2008 model (H08) were selected as they provide the most comprehensive and suitable outputs for TWSA generation. Note that CWatM and H08 are driven by historical weather data up to 2014 and by modelled climate input thereafter. For details on modelled forcing, please refer to the links in Table 2.

The additional LSM GLDAS-Noah is included because National Aeronautics and Space Administration's (NASA's) Jet Propulsion Laboratory (JPL) offers a TWSA product based on it, gridded and averaged to match GRACE’s spatial resolution, and recommended for direct comparison.

It is important to note that all included models have inherent limitations. No model includes routines to fully represent glacier storage dynamics. Additionally, H08 does not account for canopy water and has a limited representation of surface water, and GLDAS does not account for groundwater or surface water (see Table 2 for details). As a result, discrepancies in TWSA variations may stem from these missing components. The impact of these limitations will be discussed again where relevant.

Table 2: Overview of the model datasets used for validation, including information about the modelled water storage compartments (Green - water storage is included; Yellow - water storage may be included; White - water storage is not included).

1) Only exorheic/open basins, i.e. basins draining into the ocean

2) Could be included in WGHM, but not in the present data

3) Only river and reservoir storage, no lakes.

Preprocessing

To facilitate further comparisons, the WGHM output fields are aggregated into monthly fields. Additionally, the OS LISFLOOD output is spatially downsampled to a 0.25° x 0.25° grid for computational efficiency. Similarly to the TWSA datasets for validation, no grid-cell-wise validation will be performed; instead, validation will be done only for regional aggregated time series.

The C3S TWSA dataset is typically provided as monthly data; therefore, the timestamp is given as the middle day of the month. However, in some cases, the timestamp deviates from this pattern (see PUGS, Boergens et al., 2025b, for details). Therefore, the timesteps of the model outputs are interpolated to match the TWSA data timesteps.

Validation is performed only for the time period common to all datasets, namely April 2002 to January 2023. Accordingly, all datasets are restricted to this time period during preprocessing.

GRACE-REC

Humphrey and Gudmundsson (2019) presented a publicly available reconstruction of climate-driven TWSA changes worldwide from 1901 to the end of 2019 (daily and monthly, 0.5° grid), named GRACE-REC. The dataset was produced with a trained statistical model using observations from the GRACE mission (2002–2017) together with long-term meteorological forcing data (precipitation and temperature) to infer TWSA over the last century — producing six ensemble reconstructions (using different GRACE products and forcing datasets). The dataset matches well with independent observations (e.g. sea-level budget, streamflow data), and can be used to bridge the gap between GRACE and GRACE-FO.

Validation regions

For the validation of the TWSA dataset, we employ two distinct validation regions:

River basins

We use the river basin outlines provided by the "GRDC Major River Basins of the World" (GRDC, 2020, https://www.kliwas.de/SharedDocs/ExterneLinks/GRDC/mrb_shp_zip.html, URL last accessed 08/10/2025), which incorporates data from the HydroSHEDS database (Lehner, 2013, http://www.hydrosheds.org, URL last accessed 08/10/2025). Due to the limited spatial resolution of the TWSA datasets — approximately 300 km — we restrict the analysis to basins with an area greater than 100,000 km², and then rasterise the polygons onto a grid. The resulting 121 basins are presented in Figure 2.  Appendix A provides more detailed information on these basins, including their MRBID (GRDC-issued basin ID), basin name, and the continuous ID used throughout this document.

Figure 2: Validation regions used for the assessment of the C3S TWSA dataset:  Outlines of 121 major river basins

Desert regions

We define four desert regions on the world’s continents, characterised by very low mean annual precipitation of less than approximately 100 mm/year, based on climatological data from the Global Precipitation Climatology Centre (GPCC; Schneider et al., 2014).

These regions include:

• the Sahara Desert, subdivided into East and West Sahara,

• the Arabian Peninsula, and

• the Gobi Desert in Central Asia.

Figure 3 shows the outlines of these regions.

Figure 3: Validation regions used for the assessment of the C3S TWSA dataset: Defined desert regions: the West and East Sahara, the Arabian Peninsula, and the Gobi Desert.

Description of Product Validation Methodology

This section provides details about the validation methods used in this document. We begin by introducing the mathematical background of signal decomposition in subsection 1.4.1, as this is necessary for the subsequent validation methods. These validation methods of the  TWSA dataset are then split into three major parts:

1. Validation methods to compare the TWSA dataset against other operational TWSA datasets, subsection 1.4.2
2. Validation methods for the TWSA uncertainties, subsection 1.4.3
3. Validation methods to compare the TWSA dataset against the TWSA output of global hydrological models, subsection 1.4.4

Signal decomposition

In the validation methods, the TWSA time series must be decomposed into deterministic signals (trend, annual, and semiannual), as well as the residual time series. This is mathematically expressed in eq. (2) as

t is the time epoch given in decimal years. twsa_red(t) is the residual signal, a is the offset, b the trend value, c and d describe the sine and cosine components of the annual signal, and e and f describe the sine and cosine components of the semiannual signal. The model coefficients a, b, c, d, e, and f are estimated in a least-squares approach.

The amplitude, amp, of the seasonal (annual) signal can be computed from c and d  as given in eq. 3 with

and the phase φ of the seasonal signal as given in eq. 4 with

Similarly, the phase and amplitude of the semiannual signal could be computed. However, compared to the annual signal, semiannual variations are globally negligible and will not be further considered in this document.

Comparison to TWSA data sets

Noise level over desert regions

The open-ocean noise level is commonly used in the GRACE data processing community to assess the relative quality of different data sets (e.g., Meyer et al., 2019). It is defined as the standard deviation, σ(t), of the residual TWSA signal twsa_red across all ocean grid points. After removing the trend and seasonal components, it is assumed that no interannual signal remains in the ocean data. The residuals can therefore be interpreted as the noise level of the solution.

Since the open-ocean noise level is not available for all TWSA data sets, we use the noise level over desert regions as a substitute. As with the ocean, it is assumed that after removing the trend and seasonality, no significant signal remains. Eq. (1) is applied in the same way, except that the averaging is performed over the desert grid cells, without distinguishing between different desert regions.

Although hydrological signals over deserts are generally weak, some interannual variability does occur. As a result, the desert noise level reflects both residual hydrological signals and general data noise, making it systematically larger than the open-ocean noise. Nevertheless, because this effect is consistent across all TWSA data sets, it does not affect their relative comparison.

Comparison of time series in the river basins

For each of the river basins and each of the TWSA datasets, a mean time series is computed. Here, the agreement between the C3S TWSA dataset and the other datasets is assessed by comparing, in each time step, the differences between the C3S TWSA value at time step i (twsa(t_i)^c3s) and the mean TWSA value computed from the seven validation datasets. For easier comparison across the basins, this difference is also normalised by the scatter, expressed as standard deviation, of the validation data. These normalised differences twsa_norm(t)^c2s are then expressed as in eq. (5):

Here data is in {JPL masons, CSR mascons, GSFC mascons, GFZ GravIS, GFZ Tellus, CSR Tellus, JPL Tellus}.

A value of twsa_norm^c3s below 1 indicates that, in the considered month, the value falls within the one-sigma envelope of the validation data sets' values. To further assess these normalised differences across all basins, the distribution of twsa_norm^c3s can be plotted with a box-and-whisker plot. 

The coloured box of a box-and-whiskers plot (see Figure 4) spans the range between the 25th (Q25, first quartile) and 75th (Q75, third quartile) percentiles of the values, with the median value indicated by a horizontal bar. The interquartile range (IQR) is the difference between Q75 and Q25. The ends of the whiskers are defined in eq.s (6) and (7) with 

and

 All values of twsa_norm(t)^c3s outside the whiskers are plotted as outliers.

Figure 4: Example of a box-and-whisker plot with the relevant values marked.

Agreement in trend and amplitude in the river basins

For all basins and TWSA datasets, the trends and amplitudes of the annual signals are examined to determine if the C3S-dataset-derived values agree within the envelope of all other TWSA datasets. The linear trend value is the parameter b in eq. (2), and the amplitude is given with amp in eq. (3). To test the agreement, a two-sided one-sample t-test (also known as Student's hypothesis test) is applied.

The hypothesis is that the trend or amplitude of the C3S dataset is equal to the trends and amplitudes of all other TWSA datasets, given the data uncertainty. The test statistic t is calculated in eq. (8) as

where x is either the trend or the amplitude value, and data in {JPL masons, CSR mascons, GSFC mascons, GFZ GravIS, GFZ Tellus, CSR Tellus, JPL Tellus}.

The test is declined (x^c3s unequal to x^data) following the rule of eq. (9).

where: F_df^-1(x) is the percent point function (inverse function of the cumulative distribution function) of the t-distribution with df the degree of freedom (i.e. the number of time steps); α is the significance level, here α = 0.05. 

This mathematical formulation can be turned around for the definition of the confidence interval given in eq. (10), in which the value would be accepted as equal:

Signal-to-noise ratio over the river basins

This validation measure of the TWSA dataset is based on the assumption that the ratio between signal content and noise level should be maximised. To this end, the signal-to-noise ratio (S2N) is computed for each of the major river basins. The signal content is defined as the standard deviation of the full signal twsa(t). Due to the unavailability of a noise component in all TWSA comparison data sets, the noise is defined as the standard deviation of the residual signal twsa_red(t) as defined in eq. (2), i.e., annual, semiannual, and trend signals have been removed. The S2N is then defined in eq. (11) as

Uncertainty validation

In the absence of external validation data, the provided TWSA standard deviations are difficult to assess and validate. Thus, we follow the idea of Boergens et al. (2022) to validate the standard deviation over the desert regions of the Sahara Desert (East and West), the Arabian Peninsula, and the Gobi Desert. In all four regions, the given C3S TWSA standard deviation, twsa_uncertainty,  is compared to empirical uncertainty estimations. The empirical uncertainty estimates are based on the residual TWSA time series (trend, annual, and semiannual signals removed), i.e., its empirical standard deviation σ(t). This assumption is based on the premise that no further hydrological signal is detectable in these regions; therefore, the empirical uncertainty serves as a sufficiently accurate approximation of the true uncertainty. For statistical stability, the empirical uncertainty is not estimated on a monthly basis but is temporally combined across the different mission phases. Namely, early GRACE (before December 2004), quiet solar activity (January 2005 — April 2011), the onset of battery degradation (May 2011 — September 2016), failure of the accelerometer (after October 2016), and GRACE-FO (since June 2018).

Thus, the empirical uncertainty is estimated with the formula provided in eq. (12): 

Here, N is the number of timesteps between t_start and t_end of the phases, twsa_red(t) as defined in eq. (2), a represents the number of grid points in the region, and wᵢ is the area weight of the i-th grid cell at longitude λᵢ and latitude θᵢ.

Comparison to hydrological models

For the comparison between the C3S TWSA data set and the global outputs of hydrological models, i.e. modelled TWSA, a subset of the validation methods for the TWSA data sets is used.

Noise level over desert regions

The noise levels in the modelled TWSA over the desert regions are compared with those of the C3S TWSA dataset. See details in subsection 1.4.2.1.

There, the noise level of the modelled TWSA can be understood as a combination of the residual hydrological signals, the uncertainties of the hydrological models stemming from uncertainties in the input data, and mismodelling of some hydrological processes in the models.

Comparison of time series in the river basins

The differences in the time series of the modelled TWSA and the C3S TWSA dataset are analysed across the major river basins. For details, please refer to subsection 1.4.2.2.

Agreement in amplitude in the river basins

The amplitudes of the annual signals of the C3S TWSA data set and the modelled TWSA are compared. For details, please refer to subsection 1.4.2.3.

One of the major sources of TWSA trends originates from trends in glacier mass loss. Thus, due to the absence of glaciers in all the hydrological models (see Table 2), a comparison of trends is not meaningful. 

Assessment of the Product Stability

To assess the stability of the TWSA product across the two satellite missions, GRACE and GRACE-FO, both the stability of the hydrological signals and the stability of the noise level are evaluated using the methods described below.

Assessment of signal stability

The signal stability is assessed by comparing the estimation of the annual amplitude for the GRACE period with that for the GRACE-FO period for each of the 121 river basins. To this end, the deterministic signals are estimated as described in eq. (2) from which the amplitude of the annual signal is estimated (eq. (3)). Here, the uncertainty of the results is included in the parameter estimation. This results in amp_GRACE with σ_grace and amp_GFO with σ_GFO. The equality of amp_GRACE and amp_GFO can be tested using Welch's t-test (Welch, 1947), which is applied to test the null hypothesis that two sets have equal means. For details on the test, we refer to the literature.

To assess the stability of the interannual signal between GRACE and GRACE-FO, simulated TWSA data from GRACE-Rec are used. Here, the bias between GRACE and GRACE-Rec is tested against the bias between GRACE-FO and GRACE-Rec. Again, the Welch test, as described above, is applied.

Assessment of noise stability 

The stability of the noise is assessed by comparing the noise level over desert regions for the GRACE period with that of the GRACE-FO period (see section 1.4.2.1). The equality of these two noise levels can be assessed using the Mann-Whitney U test, a nonparametric test for comparing two sets with the same statistical distribution (Mann and Whitney, 1947).

Validation results

Results of the comparison to operational TWSA data sets

Noise level over desert regions

For each of the TWSA datasets, the noise over the desert regions is estimated and shown over time in Figure 5. The noise level of the C3S dataset lies well within the range of the other datasets. Temporal variations correspond with known mission characteristics. For instance, towards the end of the GRACE mission (post-2016), data quality declined due to instrumental issues. In addition, months with short repeat orbits—such as September 2002 or February 2015—exhibit notable peaks in noise levels. For further details on months with compromised data quality, please refer to Section 2.2.3 of the PUGS (Boergens et al., 2025b) documentation.

Figure 5: Noise levels over desert regions, with the C3S TWSA dataset highlighted in blue.

Comparison of time series in the river basins

For each of the 121 major river basins (with areas exceeding 100,000 km²), the normalised differences between the C3S TWSA dataset and the mean of the ensemble of all other TWSA datasets are calculated. Figure 6 presents the distribution of these differences across all basins. In only three basins—Colorado (South America), Paranaíba (South America), and Lake Eyre (Australia)—does the median of these differences exceed the 1-sigma threshold. In 67 basins, even the third quartile (the upper bound of the box) remains below the 1-sigma value. This indicates that, for the vast majority of basins, the C3S TWSA time series is in good agreement with the ensemble of the other TWSA datasets.

Figure 6: Box-and-whisker plot showing the normalised differences between the C3S TWSA basin time series and all other TWSA datasets. The top and bottom edges of the coloured boxes represent the first and third quartiles, respectively. Colours correspond to those used in the basin map in Figure 2.

Agreement in trend and amplitude in the river basins

The linear trend and annual signal amplitude are compared across the various TWSA datasets, with an assessment of whether the value derived from the C3S dataset falls within the range defined by all other TWSA datasets (see Figure 7 for detailed results). For the trend, only three out of 121 basins fall outside the confidence interval, and just two for the annual amplitude (see Table 3 for detailed values). The most notable deviation in annual amplitude occurs in the Flinders River Basin in Australia, which is among the smallest basins in both area and seasonal amplitude.

These findings once again highlight the strong consistency between the C3S TWSA dataset and the other TWSA datasets.

Figure 7: River basin trends and annual signal amplitudes. Upper panels: maps showing the trend (a) and amplitude (b) values derived from the C3S TWSA dataset. Basins with hatched patterns indicate where the C3S-derived value falls outside the confidence interval of the values from all other TWSA datasets. Lower panels: trend (c) and amplitude (d) values for each basin, plotted for all datasets. Blue dots represent the C3S-derived values, while red dots indicate cases where the value lies outside the confidence interval—corresponding to the hatched basins in the upper panels.

Table 3: River basins in which the C3S values fall outside the confidence interval.

Signal-to-noise ratio over the river basins

The signal-to-noise ratio (S2N) is, by itself, difficult to interpret. Therefore, Figure 8 presents a direct comparison of the C3S TWSA S2N with those of all other TWSA datasets. For each basin, the number of datasets for which the C3S S2N exceeds their value is counted. The results are evenly distributed, with an equal number of basins where the C3S S2N is higher and lower than the majority of the other datasets. It should be noted that in many basins the S2N are very close together. For example, in the Mississippi basin, where C3S has a lower S2N than all other datasets, the values range only from 1.51 to 1.65. On the other hand, in some basins the scatter of S2N is larger, e.g., for the Orinoco Basin 2.10 - 2.65 (C3S best) or the Kura Basin 2.33 - 4.23 (C3S intermediate). In general, we do not find any clear relationship between the S2N of C3S in comparison to S2N of all other data sets and geographic basin characteristics such as size or region. This further confirms that the C3S TWSA dataset lies within the quality range of the other operational TWSA datasets.

Figure 8: For each river basin, the number of TWSA datasets for which the S2N value is lower than that of the C3S TWSA dataset. Distribution of counts per class: 0 – 12 basins; 1 – 8 basins; 2 – 21 basins; 3 – 21 basins; 4 – 19 basins; 5 – 14 basins; 6 – 20 basins; 7 – 6 basins.

Uncertainty validation

The uncertainty provided with the C3S TWSA dataset, twsa_uncertainty, is compared to the empirical standard deviation, σ, across four desert regions presented in Figure 9. The presented data indicate that the provided twsa_uncertainty of the C3S TWSA dataset is reasonable, because a) it matches the magnitude of σ_phase closely across all regions, and b) it captures the temporal variability of σ_phase. However, σ_phase is generally larger than twsa_uncertainty, likely due to residual hydrological signals present. This effect is most pronounced in the Gobi Desert, which is adjacent to the Himalayas. From there, relatively strong hydrological signals from snow and glaciers leak into the Gobi Desert (see definition of "Leakage" above).

Figure 9:  Time series of the C3S-provided uncertainty, twsa_uncertainty, compared with the empirical standard deviations per mission phase, σ_phase, for the four desert regions.

Results of the comparison to hydrological models

Noise level over desert regions

For each modelled TWSA dataset, the noise level—defined as the empirical standard deviation (σ)—is calculated over the four desert regions and compared with that of the C3S TWSA (see Figure 10). The noise level of the C3S TWSA falls well within the range of the modelled TWSA noise levels, despite the latter being affected by less measurement noise. This indicates that, over desert regions, the C3S TWSA dataset aligns well with the six modelled TWSA datasets.

Figure 10:  Time series of the noise level, i.e. the empirical standard deviations, σ, for all hydrological model outputs and the C3S TWSA dataset in the four desert regions.

Comparison of time series in the river basins

For each of the 121 major river basins, the normalised differences between the C3S TWSA dataset and the ensemble mean of the modelled TWSA are calculated. Figure 11 presents the distribution of these differences across all basins using a box-and-whisker plot. In the majority of basins (82 in total), the median of the normalised differences lies below 1. A median below 1 indicates a strong agreement between the C3S TWSA data set and the ensemble of the modelled TWSA. The larger the median value of the normalised differences, the larger the mismatch of the time series.

Figure 11: Box-and-whisker plot showing the normalised differences between the basin time series of the C3S TWSA and all modelled TWSA datasets. The upper and lower edges of the coloured boxes represent the third and first quartiles, respectively. Colours correspond to those used in the basin map in Figure 3.

To examine the basins, where the median is greater than one, more closely, Figure 12 displays a spatial map of these 121 median values. The basins showing the largest discrepancies between the C3S TWSA and modelled TWSA time series are those dominated by strong trends (see Figure 7 for trend values), particularly those containing glaciated regions. This outcome is expected, as none of the hydrological models explicitly account for glacier mass changes and therefore do not accurately capture the trends of ice melting. In basins where the dominant signal is annual variability, the C3S TWSA and modelled TWSA datasets exhibit strong agreement.

Figure 12: Map of the median of the normalised differences between the basin time series of the C3S TWSA and all modelled TWSA datasets. 

Agreement in amplitude in the river basins

The annual signal amplitudes are compared between the C3S TWSA and the modelled TWSA, with an additional assessment of whether the amplitude derived from the C3S dataset falls within the confidence interval defined by the modelled TWSA values. Figure 13 presents the results of this comparison across all basins. Overall, in seven basins, the C3S TWSA amplitude lies outside the confidence interval, with detailed values provided in Table 4. In most of these cases, the C3S values are close to the interval bounds, with the notable exception of the Mobile River basin in the United States. Once again, this highlights the strong agreement between the annual signals of the C3S TWSA and the modelled TWSA datasets.

Figure 13: River basin annual amplitudes.Upper panels (a): map showing the amplitude values derived from the C3S TWSA dataset. Basins with hatched patterns indicate where the C3S-derived value falls outside the confidence interval. Lower panels (b) amplitude values for each basin, plotted for all datasets. Grey dots represent values derived from all hydrological model outputs. Blue dots show the C3S-derived values, while red dots highlight cases where these values fall outside the confidence interval—corresponding to the hatched basins in the upper panels. 

Table 4: River basins in which the C3S values fall outside the confidence interval.

Assessment of the Product Stability

Assessment of signal stability

Of the 121 river basins investigated, the annual signal amplitude does not change between the GRACE and GRACE-FO periods in 54 of the cases. The mean difference between the amplitudes across all basins is 15% of the amplitude or absolut 10mm.  Figure 14 displays the amplitudes of the GRACE period against the amplitudes of the GRACE-FO period. The differences between the amplitudes increase with increasing amplitudes. Overall, no systematic shift in amplitude is detectable between the two phases. Thus, the changes in amplitude are most likely caused by natural variability.

Figure 14: Annual amplitudes of the GRACE mission phase vs. the GRACE-FO mission phase for 121 river basins. Marked in green are the amplitude pairs where no significant difference is detectable.

The comparison with all six subsets of GRACE-REC also did not indicate any offset between the GRACE and GRACE-FO periods. Thus, the signals remain stable across the GRACE to GRACE-FO transition with respect to the signal level, i.e., absence of bias.

Assessment of the noise stability

According to the Mann–Whitney U test, the noise level during the GRACE-FO period is significantly higher than that of the GRACE period. The mean noise of the GRACE period is 16.87mm and 18.30mm for the GRACE-FO period. However, this does not necessarily imply a lack of stability between GRACE and GRACE-FO. The noise level is strongly correlated with solar activity (solar cycle #25  [URL last accessed 03/12/2025]), which was exceptionally high in 2024. Elevated solar activity increases radiation pressure and atmospheric drag on the satellites, both of which must be modelled to separate them from the gravitational signals. Any remaining unmodelled forces  —such as residual atmospheric drag or radiation pressure — can increase the noise in the TWSA data.

Compliance with user requirements concerning data quality

The product target requirements have been defined by the Global Climate Observing System (GCOS) (WMO, 2025). Table 5 summarises the requirements and characteristics of the C3S TWSA product.

For each requirement, a threshold and a goal value are defined as listed in Table 5. The goal is the ideal level. Once this is met, further improvements in that criterion are not strictly necessary for most applications.  Threshold is the minimum acceptable requirement. 

Table 5: GCOS goal and threshold requirements for the ECV TWSA. Colours: green - within goal, yellow - within threshold, red - does not meet threshold, grey - not applicable

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Appendix A: List of river basins

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