The objective of this study is to assess the impact of freshwater fluxes on the Atlantic Ocean by estimating river discharge using the Water Mass Balance (WMB) approach. This method combines satellite gravimetry data from the GRACE and GRACE-FO missions with atmospheric or land surface reanalyses to quantify river discharge.

To ensure a comprehensive coverage of all major rivers discharging into the Atlantic Ocean, all rivers with an average discharge exceeding 2000 m3s-1 were initially identified using data from the HydroRIVERS database (Lehner and Grill, 2013). From this preliminary selection, only the rivers with a catchment area larger than 100 000 km2 were retained, in order to align with the spatial resolution of GRACE and GRACE-FO measurements, which is approximately 300km×300km. This process resulted in the selection of 18 river basins distributed across four continents – North and South America, Africa, and Europe – and encompassing a wide range of climatic regimes in terms of precipitation and temperature (Fig. 1). The largest river to be excluded (in terms of discharge) is the Rio Atrato, with an average long-term discharge of 3768 m3s-1 (Lehner and Grill, 2013).

The main characteristics of the selected basins are summarized in Table 1. River names and outlet locations are taken from the HydroRIVERS database (Lehner and Grill, 2013). Notably, the Essequibo and Cuyuni Rivers were combined due to their shared outlet. Although the Orange River has an average discharge below the 2000 m3s-1 threshold (∼300m3s-1), it was included in the final selection due to its extensive catchment area, which ensures compatibility with the spatial resolution of satellite gravimetry data. The basin areas are extracted from the Major River Basin database (Federal Institute of Hydrology, 2024). The sum of the average river discharge at the outlet over the 18 studied rivers equals to 389 411 m3s-1, representing 64 % of the total discharge to the Atlantic recorded in the HydroRIVERS database. The total discharge excluded represents 105 % of the Amazon discharge.

The Global Runoff Data Centre (GRDC) Data Download Portal offers the most comprehensive, quality-controlled database of river discharge observations, comprising daily and monthly time series from over 10 800 gauging stations along approximately 7000 rivers worldwide (Federal Institute of Hydrology, 2024). The database incorporates various in situ measurement techniques as described by (Dobriyal et al., 2017). Typically, manual discharge measurements are collected at different river stages using devices such as current meters, Acoustic Doppler Current Profilers (ADCPs), or other flow-measuring instruments. For each stage (water level), the corresponding discharge is recorded. A rating curve – often modeled as a power-law function – is then fitted to these data, enabling continuous estimation of river discharge from continuously monitored stage values. However, this method carries inherent uncertainties, typically around 15 %, and is both time-consuming and labor-intensive (Crétaux et al., 2016). Establishing and maintaining in situ gauging stations is therefore costly, which limits their deployment primarily to main river stems, resulting in sparse coverage and limited data availability for remote rivers and tributaries. Moreover, the number of active gauges in the GRDC database has significantly declined since the 1980s, with only 14 % remaining active by 2020 (Elmi et al., 2024). For example, just 2200 stations have reported discharge data beyond 2015. While some stations provide daily data, others report only monthly values.

To enhance the coverage, the GRDC database has been complemented by the HYBAM (HYdro-géochimie du Bassin AMazonien) project (SO HYBAM, 2025), which provides monthly in situ discharge measurements using the ADCP method (Dobriyal et al., 2017) for 17 stations located in South America and the Congo Basin.

In order to avoid gaps in the Tocantins dataset from GRDC, discharge estimates from (Dai, 2017) have been used as reference. In situ measurements were acquired at the Tuvcurui station located the closest to the river mouth. Temporal gaps are filled with data from nearby gauges if available and otherwise with a regression based on a hydrological model. Additional corrections are detailed in (Dai et al., 2009).

Combining the GRDC, HYBAM and Dai and Trenberth datasets, in situ discharge measurements were available for 11 out of the 18 selected rivers since 2000 (Fig. 2). The Magdalena, Usumacinta, Essequibo, Cuyuni, São Francisco, Uruguay, and Ogooué rivers were not sampled since 2000. The Orange River had the longest observation period, lasting 90 years until today, while the Niger River had only 13 years of intermittent data since 2002. Among the 11 rivers sampled with in situ observations, the Orange, Rhine, Nelson, Saint Lawrence, Paraná, Orinoco, Congo, and Amazon rivers all benefited from long, continuous discharge records spanning over the 16 years of the period covered by the WMB approach using GPCC precipitation and ISBA-CTRIP evapotranspiration.

The river discharge can be estimated using the water mass balance equation, expressed as: 1dSdt=P-ET-R where dS/dt are the changes in land water storage in time, P the precipitation, ET the evapotranspiration and R the river discharge.

Terrestrial Water Storage (TWS) anomalies have been estimated from April 2002–August 2023 at monthly timescales and with a spatial resolution of 1° using an ensemble of GRACE and GRACE-FO solutions derived from (Blazquez et al., 2018). The GRACE and GRACE-FO ensemble comprises 120 solutions, allowing the estimation of uncertainties associated with different processing strategies and geophysical corrections needed for hydrological applications. The ensemble is based on coefficients of the Earth's gravitational potential anomalies estimated by five centers (CNES, CSR, JPL, GFZ, ITSG). A large variety of post-processing corrections are applied to the ensemble, including two models of the geocentre motions (Lemoine and Reinquin, 2017; Sun et al., 2016), three models of the oblateness (C20) of the Earth (Cheng et al., 2013; Lemoine and Reinquin, 2017; Loomis et al., 2019), and two Glacial Isostatic Adjustment (GIA) models (Caron et al., 2018; Peltier et al., 2018). To reduce the anisotropic noise, denoising and decorrelation kernel (DDK) filters (Kusche et al., 2009), are applied to GRACE solutions, using two different orders (DDK3 and DDK6) corresponding to different levels of filtering. The ensemble of 120 solutions results from combining these five processing centers, two geocenter models, three oblateness models, two GIA corrections, and two filters.

The monthly TWS anomalies are then averaged at river basin scale. To compute the first derivative of TWS changes (dS/dt), the GRACE and GRACE-FO time series need to be processed in order to fill data gaps ranging from 1 (satellite operations) to 11 (time gap between the two missions) months. In our dynamic interpolation, we first remove the seasonal terms (annual and semi-annual sinusoids) and linear trends estimated by least squares adjustments, we then use linear interpolation to reconstruct residual TWS times series at the start of each month, and finally we add the seasonal terms and linear trends back to the reconstructed TWS time series. The first derivative of TWS changes (dS/dt) can then be computed as the difference between two consecutive TWS estimates. As noted by (Chen et al., 2020), it is important to interpolate terrestrial water storage (TWS) anomalies to the start of each month. This ensures that the differentiation between consecutive months yields a first-order estimate of TWS changes that is consistent with precipitation and evapotranspiration data averaged over calendar months.

The precipitation (P) is averaged by calendar month and by basin, using the GPCC observational product (Schneider et al., 2015) spanning over 1980–2022 or with the ERA5 reanalysis (Hersbach et al., 2020) spanning over 1980–today. The mean evapotranspiration is estimated with the ERA5 reanalysis spanning over 1980-today, or with the ISBA-CTRIP hydrological model (Decharme et al., 2019) spanning over 1979–2019. Two combinations of river discharge (R) are then calculated based on the difference between the net precipitation (P - ET) and the first derivative of terrestrial water storage changes (dS/dt) for each river basin. The first combination uses ERA5 precipitation and evapotranspiration and will be referred to hereafter as WMB1. It should be noted that the ERA5 water budget is not globally closed, with precipitation exceeding evaporation and spurious variability associated with changes in the assimilation system (Hersbach et al., 2020; Mayer et al., 2021). At the river-basin scale considered here, ERA5 budget residuals are considerably smaller than in previous reanalyses (Mayer et al., 2021), but any remaining regional bias of net freshwater maps directly onto the WMB discharge estimates and contributes to its errors. The second uses GPCC precipitation together with ISBA-CTRIP evapotranspiration and will be referred to hereafter as WMB2. It may be noted that the ISBA-CTRIP hydrological model is forced with GPCC precipitation, ensuring consistency at the model scale, between the atmospheric fluxes considered. The combination using ERA5 atmospheric fluxes spans over the full GRACE and GRACE-FO observation period considered in this study (i.e. April 2022–May 2021), while the combination using GPCC and ISBA-CTRIP spans over April 2002 until July 2019.

The WMB approach is evaluated using several performance metrics: percent bias (PBias) for the temporal mean, the correlation coefficient (R), the variability ratio (γ), and the modified Kling–Gupta Efficiency (KGE′). The R score is Pearson's correlation coefficient, ranging between -1 (perfect anti-correlation), and +1 (perfect correlation) highlights the strength of the linear relationship between two datasets. The proportional bias corresponds to the sum of the differences between the predicted and observed values, normalized by the average of observed values. It ranges between -∞ and +∞, 0 corresponding to no bias. It is computed as follows: 2PBias=∑i=1N(Pi-Oi)∑i=1NOi Where Pi refers to a predicted value at time i, and Oi to the reference value at the same timestep. The variability ratio is computed as follows: γ=σs/μsσo/μo with σs the standard deviation of the predicted values and σo the standard deviation of the reference data.

The modified Kling–Gupta Efficiency index (KGE′) balances correlation, bias, and variability and is widely used in hydrological studies as a goodness-of-fit criterion. It was proposed by (Kling et al., 2012) as an updated version of the original KGE metric (Gupta et al., 2009) ranging between -∞ and 1, where 1 indicates the perfect fit. 3KGE′=1-(R-1)2+(PBias-1)2+(γ-1)2

To assess the impact of river discharge estimates on ocean model simulations, this study employs the NEMO ocean model (version 4.0.7, Madec et al., 2017), which includes the sea-ice dynamic and thermodynamic model SI3. The model is configured on the ORCA1 grid, featuring a horizontal resolution of 1°, with 1/3° meridional resolution enhancement in the tropical belt, and 75 vertical depth levels with partial steps (Bernard et al., 2006). The surface boundary conditions are computed using the CORE bulk formulas (Large and Yeager, 2009), implemented via the AEROBULK package (Brodeau et al., 2017). Meteorological forcing data are derived from the ECMWF ERA5 atmospheric reanalysis (Hersbach et al., 2020) at hourly frequency. The model setup is the same as the CIGAR reanalysis (Storto and Yang, 2024). It incorporates a 3-band RGB scheme for net shortwave radiation, with extinction coefficients based on a monthly climatology of chlorophyll. Vertical mixing is parameterized using the TKE scheme (Gaspar et al., 1990), and tracers and momentum are diffused using Laplacian and bi-Laplacian operators, respectively.

The experiments we present do not include any data assimilation or bias correction. This approach allows us to evaluate the impact of the river discharge dataset without any interplay with observations. The experiments cover the period from January 2003–December 2020 and are all initialized from the same initial conditions, taken from the CIGAR reanalysis.

We configured several experiments to assess the impact of different river discharge inputs on ocean modeling, summarized in Table 2. The reference experiment (REF) uses the standard NEMO monthly climatology of river discharge from the (Dai and Trenberth, 2002) dataset, as compiled by (Bourdalle-Badie and Treguier, 2006). A second experiment (J5) uses daily varying runoff from the JRA-55-do dataset (Tsujino et al., 2018), based on a bias-corrected land component of the JRA-55 atmospheric reanalysis (using ERA5 as atmospheric forcing as all the other experiments). Although also JRA-55-do relies on an atmospheric reanalyses, its approach is intrinsically different from our WMB data: the JRA55-do runoff is produced by a river routing model forced by JRA-55 land-surface runoff, whose input is adjusted to match the Dai et al. (2009) estimates, with no information from satellite gravimetry.

In addition, we conducted four experiments that incorporate Water Mass Balance (WMB)-derived discharge estimates in place of the monthly climatology for the Atlantic Ocean. Experiments A1 and A2 replace the discharge climatology with WMB estimates for all 18 major rivers listed in Table 1. A1 uses precipitation and evapotranspiration from the ECMWF ERA5 reanalysis (WMB1), while A2 uses fields from GPCC and ISBA (WMB2), respectively. Experiments S1 and S2 focus on isolating the impact of the Amazon, Orinoco, and Tocantins rivers, which show high-confidence results under the WMB approach. In these experiments, WMB estimates are used only for those three rivers, while discharge from all other rivers follows the reference climatology. As with A1/A2, S1 uses ERA5 while S2 uses GPCC and ISBA..

The WMB provides a single discharge time series at the mouth of each of the 18 rivers, whereas NEMO requires runoff to be prescribed as a freshwater flux on ocean grid points. To adopt the WMB-derived dataset in the NEMO simulations, for each of the 18 rivers, we retained this spatial distribution unchanged from the climatology of Bourdalle-Badie and Tréguier (2006), and rescaled it at every month so that the runoff integrated over the corresponding grid points equals the WMB discharge, thus conserving the total freshwater volume delivered to the ocean; runoff at all other grid points is left at its climatological value. Note also that river runoff in the ocean simulations is all injected at the sea surface (first model level).

The Amazon River has a mean discharge more than four times greater than that of the next largest river flowing into the Atlantic – the Congo River (Table 1). Accurately estimating the Amazon River discharge is therefore crucial for assessing the impact of freshwater fluxes on the ocean. This assessment is carried out by comparing river discharge estimated with the WMB approach to in situ measurements at the Óbidios gauging station, located approximately 500 km upstream of the Amazon delta (Fig. 3). To ensure consistency between the WMB-derived and observed discharge, TWS anomalies, precipitation (P), and evapotranspiration (ET) were averaged over the station drainage area, as defined by the Global Runoff Data Centre (GRDC).

Overall, excellent agreement can be observed between the WMB estimates and in situ measurements acquired at the Obidios gauge, with Pearson's correlation coefficient reaching 0.87 when ERA5 is used to constrain atmospheric fluxes (WMB1) and 0.88 when GPCC and ISBA-CTRIP are used (WMB2) (Fig. 3). When excluding the strong seasonal cycle, the WMB discharge still exhibits good agreement with the GRDC reference, with Pearson's correlation coefficient of 0.45 for WMB1 and 0.47 for WMB2. The average river discharge (1.734×105m3s-1) is well captured by the WMB approach, with a difference of only +2% in WMB1 and -3% in WMB2.

Differences between both WMB approaches appear in their ability to retrieve the seasonal cycle amplitude. While excellent agreement (+ 5 %) with in situ data is retrieved in WMB1, more significant discrepancies occur in WMB2, leading to an overestimation of the annual cycle of the river discharge by 46 % when compared with in situ data. The differences between WMB1 and WMB2 arise from differences in the estimated net precipitation, primarily due to lower mean, higher noise and greater variability in ISBA evapotranspiration, including at annual timescales, when compared with ERA5 (Fig. A1). The phase of the seasonal cycle is also well captured by the WMB approach. The months of the highest and lowest discharge are May and November, both for in situ measurements and the WMB1 approach. By comparison, the highest discharge is two months late when comparing WMB2 to in situ measurements.

Linear trends have also been computed by ordinary least square adjustment over April 2002–December 2019. Linear trends shown in Fig. 3a were calculated and found to be statistically insignificant. Both WMB approaches exhibit stronger high frequency variability compared to in situ measurements with extreme events more marked with WMB2 than WMB1.

Overall, the WMB approach using ERA5 data (WMB1) shows excellent agreement with in situ measurements, yielding a KGE′ score of 0.84. In contrast, using GPCC precipitation and ISBA-CTRIP evapotranspiration (WMB2) results in more pronounced discrepancies – both in the annual cycle and higher-frequency variations – leading to a lower KGE′ score of 0.53. These results confirm the reliability of the WMB approach for estimating Amazon River discharge but highlight the sensitivity of the method to the choice of datasets used to estimate vertical atmospheric fluxes as shown previously by Chen et al. (2020). Biases in net precipitation (P-E), in particular, directly affect the accuracy of discharge estimates. The differences between WMB1 and WMB2 highlight the sensitivity to atmospheric forcing, as precipitation and evapotranspiration are derived using substantially different approaches, including reanalyses, in situ observations, and hydrological models. Although only three sources are considered (ERA5, GPCC, and ISBA-CTRIP), their methodological diversity likely provides a realistic representation of the dispersion among atmospheric flux estimates. Thus, the spread between WMB1 and WMB2 provides a meaningful indication of the uncertainty associated with the choice of atmospheric forcing, consistent with the findings of Lehmann et al. (2022) demonstrating that ERA5-Land generally performs well for water-budget closure, but shows larger discrepancies over regions such as the Amazon.

River discharge estimates based on in situ measurements can underestimate the total freshwater flux entering the ocean when gauging stations are located far upstream from the river mouth, as they capture only a portion of the full basin's drainage area. This is the case for the Óbidos station, located approximately 500 km upstream of the Amazon Delta (Fig. 4a). The Water Mass Balance (WMB) approach enables discharge estimation over any drainage area large enough to be resolved by GRACE and GRACE-FO satellite observations. In this study, we compare discharge estimates for the entire Amazon Basin and the Óbidos drainage area using the WMB method, driven by ERA5 atmospheric fluxes – a configuration shown to provide accurate results at Óbidos.

The Óbidos drainage area is approximately 22 % smaller than the entire Amazon River Basin, excluding several major tributaries such as the Tapajos, Xingu, and Jari (Fig. 4a). As a result, the mean river discharge at Óbidos is 15 % lower than at the river mouth. Similarly, the amplitude of the annual discharge cycle is underestimated by 20 % when using data from Óbidos instead of the full basin. Peak flow – defined as the maximum discharge – also shows an underestimation of 15 % at Óbidos compared to the river outlet. These discrepancies are substantial and must be considered when assessing the influence of Amazonian freshwater fluxes on the Atlantic Ocean. For context, a 10 % underestimation in the Amazon's mean discharge is equivalent to omitting the entire flow of the Mississippi River (Table 1).

River discharge was estimated at the outlet of each of the 18 selected rivers (Fig. 1) using the Water Mass Balance (WMB) approach, driven by two combinations of vertical atmospheric fluxes: ERA5 reanalysis (WMB1), and GPCC precipitation with ISBA evapotranspiration (WMB2) (Table 3). The results show significant discrepancies in both mean discharge and seasonal variability depending on the dataset used to represent atmospheric fluxes.

The largest difference in mean discharge was observed for the Congo River, where WMB2 yielded a discharge of 58 537 m3s-1, compared to 27 801 m3s-1 with WMB1–representing a 53 % difference. For smaller rivers, relative differences are even more pronounced. In the Niger River, the choice of dataset results in a 74 % difference, while the Magdalena River shows an 87 % difference. In extreme cases, such as the São Francisco River, the WMB method produced a negative mean discharge when forced with GPCC and ISBA, clearly highlighting the method's failure to capture river discharge. These discrepancies stem from excessive noise or biases in one or more components of the WMB equation and emphasize the method's sensitivity to the quality of regional atmospheric data.

The largest difference in seasonal discharge amplitude was found in the Amazon River, where the seasonal variation amplitude is larger by 56 844 m3s-1, or 31 % in WMB2 compared to WMB1. Significant differences in seasonal variability were also found between WMB2 and WMB1 for other rivers, such as the Orinoco: 19 506 m3s-1 (55 % of WMB1 amplitude), Mississippi: 13 982 m3s-1 (48 %), and Nelson: 10 909 m3s-1 (134 %) Rivers. Such discrepancies underscore the limitations of the WMB method, which is highly sensitive to uncertainties in atmospheric forcing. Improving the accuracy of net precipitation estimates (P–E) at regional scales would directly enhance the reliability of WMB-based discharge estimates.

The discharge estimates from the WMB approach are generally lower than the Dai and Trenberth (2002) climatology used in the REF experiment. WMB1 and WMB2 discharges are lower than the reference climatology for 13 out of 18 rivers. The total freshwater fluxes are reduced by 28 % in WMB1 and 22 % in WMB2 compared to the REF experiment. However, no general pattern emerges regarding the comparison of seasonal discharge amplitudes.

While the WMB method is sensitive to the choice of atmospheric forcing data, it offers the significant advantage of enhanced spatial coverage. Specifically, it enables discharge estimates at the outlets of all 18 rivers – whereas in situ gauging stations exist for only 11, and usually not at the river mouths (e.g., Óbidos). Relying solely on these limited observations would lead to an underestimation of the total mean freshwater flux by 21 % with respect to the total flux estimated at the outlets, and an underestimation of the seasonal amplitude by 27 % (Fig. 5). This estimate is based on river discharge values resulting from the WMB1 approach, considering (i) the full drainage area of all 18 river basins and (ii) the drainage areas corresponding to the 11 gauging stations located closest to the river mouths (Fig. 1).

River discharge estimates derived from the WMB approach are subject to significant uncertainties, as evidenced by the large variability associated with the choice of atmospheric forcing data. As no reference discharge measurements are available at the river's outlets, the method's performance is further evaluated over the drainage areas of the 11 selected gauging stations. River discharge estimated using the WMB approach was compared with the corresponding in situ measurements. The resulting mean and annual discharge amplitudes are listed in Table 4. The amplitude and mean discharge are computed over the longest uninterrupted common interval between the in situ, WMB1 and WMB2 time series. These statistics can therefore not be directly compared between rivers. The “Total” row refers to the sum WMB1 and WMB2 time series over the 11 stations during the 2002–2019 period. As the in situ measurements' time coverage is not consistent between rivers, no total value is provided.

The largest errors in the mean discharge are obtained for the Congo river which is overestimated relative to the in situ observations by 17 784 m3s-1 (+45%) in WMB2 and underestimated by 12 156 m3s-1 (-31%) in WMB1. The errors in the mean discharge are generally higher with WMB2, though there are no systematic biases: for some rivers the mean discharge is overestimated (e.g. Congo, Parana, Tocantins, Niger and Orange) and for some others it is underestimated (e.g. Amazon, Orinoco, Mississippi, Saint Lawrence, Nelson, Rhine). The absolute and relative amplitude of the errors is also variable depending on the river selected. In WMB1, the relative error on the mean river discharge is under 15 % for 5 out of 11 rivers, namely the Amazon, Orinoco, Parana, Tocantins and Saint-Lawrence.

Similarly, for the annual cycle, WMB2 generally results in larger deviations from in situ measurements compared to WMB1. The most pronounced errors in the mean annual amplitude occur for the Amazon (+62991m3s-1, or +46% relative to in situ) and the Parana (+39615m3s-1, or +1237%) in WMB2. Notable errors are also observed in WMB1, particularly for the Congo (-33308m3s-1, or -51%), Paraná (+33564m3s-1, or +1048 %) and Niger (+19580m3s-1, or 158 %) Rivers. The error in the annual amplitude of river discharge remains below 15 % for only the Amazon, and only when using ERA5 forcing. Once again, no systematic bias is apparent, as both the magnitude and direction of the errors vary depending on the river and the atmospheric dataset used.

The WMB approach is further evaluated using the PBias for the temporal mean, the correlation coefficient (R), the variability ratio (γ), and the modified Kling–Gupta Efficiency (KGE′). All metric values are provided in Table B1 of the Appendix, while PBias and R are illustrated in Fig. 5.

The WMB approach yields reasonable performance for South American rivers – particularly the Amazon – when forced with ERA5 atmospheric fluxes, as indicated by PBias values close to zero and R scores above 0.5. In contrast, results are more variable and generally less satisfactory for rivers in Africa and North America. Both WMB configurations struggle to capture the mean discharge of African rivers: values are typically underestimated in WMB1 (ranging from -31% to -112%) and overestimated in WMB2 (ranging from +45% to +580%). Overall, the correlation (R score) is higher when using ERA5 than GPCC-ISBA for 8 out of the 11 rivers analyzed.

The variability ratio highlights the substantial high-frequency noise present in the WMB estimates compared to other metrics (PBias, R Score, KGE′). Although the WMB approach generally captures the mean discharge adequately, its high-frequency variability is considerably greater than that observed in in situ data. Across both atmospheric datasets, the median variability ratio is 2.2 for WMB1 and 1.9 for WMB2.