SWOT river observations
The SWOT mission uses a wide-swath Ka-band radar interferometer (KaRIn) to collect global measurements of key terrestrial surface-water features, such as extent, elevation and slope, with an average revisit frequency of 10 days over its full 21-day cycle27,30,32,33. In this study, we use observations from the SWOT Level 2 KaRIn High Rate River Single Pass data product (RiverSP, version C PIC0 and PGC0), which provides node-averaged and reach-averaged measurements of river elevation and width from individual satellite passes51. We use the reach-averaged measurements, with a nominal length of 10 km. The RiverSP observations are aggregated to vector reaches in the SWOT River Database (SWORD)34 v16, which contains approximately 240,000 global river reaches wider than about 30 m.
We retrieve single-pass SWOT observations of river width, WSE and associated observation attributes at all global SWORD reaches from 1 October 2023 to 30 September 2024, corresponding to the satellite nominal orbit with a 21-day cycle, using NASA PO.DAAC’s Hydrocron API service. To ensure the reliability of our analysis of SWOT observations, we apply a series of data quality filters to remove potentially erroneous measurements. We only compute river storage change at SWORD reaches representing rivers (type 1 and type 5), removing reaches corresponding to lakes, reservoirs, dams and waterfalls, and ghost reaches34. We acknowledge that as SWORD reflects reservoir extents at the time of its input compilation, reservoirs constructed more recently may be treated as river reaches, potentially introducing local uncertainties in SWOT data. We filter out SWOT observations with a summary quality indicator (reach_q) of ‘bad’ (3% of observations), retaining observations deemed ‘good’ (0.03%), ‘suspect’ (31%) and ‘degraded’ (66%). We only retain SWOT observations with ‘good’ cross-over calibration (xovr_cal_q = 0). We exclude those affected by dark water conditions (dark_frac > 0.3), and reach-level measurements with substantial missing node data (obs_frac_n < 0.5). Observations where external climate indicators imply the presence of ice or snow (ice_clim_f > 0) are also filtered. As SWOT struggles to produce accurate observations both in close proximity and far from the nadir track of the satellite owing to the angle of radar echoes, we filter observations with a cross-track distance within 10 km or outside of 60 km of the nadir track. In some cases, the range of WSEs measured by SWOT at a given reach are implausibly large. We therefore filter SWORD reaches from further storage computation if the range of elevation observations exceed 20 m, which surpass most of the largest flood height variations observed in the Amazon52. After filtering, we only compute river storage at the 126,674 SWORD reaches with at least 5 valid SWOT observations of WSE and width during the study period (Extended Data Table 1).
We note that the SWOT version D products, forward-processed from April 2025 onwards, resolve several known issues in the version C products used in this study. However, the reprocessing of version D products for science orbit observations between July 2023 and April 2025 is only scheduled to complete in 2026, so that only one full annual cycle is available at the time of this study (autumn 2023 to autumn 2024).
Effective SWOT sampling after quality filtering
The filtering applied to the initial SWOT dataset results in a reduced effective sampling rate, which varies depending on the configuration and quality of the observations. To assess the temporal coverage of the filtered dataset, we evaluate the effective measurement timeline at the basin level (Extended Data Fig. 1). On average, after quality filtering, SWOT provides 1 valid observation every 28 ± 4.6 days (mean ± standard deviation across basins), with well over half of the expected measurements being excluded during the filtering process. A key limitation arises in regions affected by seasonal ice cover, such as over Arctic rivers and high mountainous basins, where no acquisitions are retained from approximately November to May. This absence of data in winter results in annual time series that are biased towards summer and early autumn months, and are likely partly unreliable or misleading for hydrological analysis.
River hypsometry
The simultaneous observations of river width and WSE by SWOT offer a valuable opportunity to map the complex active bathymetry of river channels across a range of flow conditions. River hypsometric curves capture the typically monotonic increase between width and WSE and, importantly, enable the calculation of channel cross-sectional area through integration37. By fitting these hypsometric curves to SWOT observations of width and WSE at individual SWORD reaches, we can track changes in channel flow area over time and convert these area estimates into estimates of storage variability. The cross-sectional area of a river channel as observed by SWOT can be represented by the function:
$$A(H)=\,{\text{\AA }}+\,{\int }_{{H}_{\min }}^{H}W({H}^{{\prime} }){\rm{d}}{H}^{{\prime} }$$
(1)
where H is the WSE, W is the river width, Hmin is the lowest WSE observed by SWOT, Å is the unobserved cross-sectional area below the lowest observed WSE, and W(H′) is the hypsometric function between width and WSE37,53,54. SWOT is unable to capture the entire wetted channel below baseflow levels. Therefore, a portion of the channel cross-section, denoted as area Å in Extended Data Fig. 2a, remains unobserved below the lowest recorded river height. Although the official SWOT mission discharge product currently involves the estimation of full channel geometry53, these estimates require further validation at the global scale. Therefore, we do not attempt to use them here. We note that equation (1) is only an approximation as measurements are averaged at the reach scale, overlooking finer-scale longitudinal variations in width and height. This approach forms the basis for the estimation of river discharge from SWOT53 and has been implemented in the Confluence software engine (https://github.com/swot-confluence/) used to produce SWOT discharge products and the Flow Law Parameter Estimation library FlaPE-Byrd (https://github.com/mikedurand/FLaPE-Byrd).
As SWOT observations of both width and WSE include associated measurement error, standard regression approaches are not suitable for accurately fitting hypsometric functions. Instead, we fit river hypsometric curves to SWOT observations of width and WSE using an ‘errors-in-variable’ approach, as implemented by the FLaPE-Byrd repository and detailed in ref. 37. Originally introduced in ref. 38, errors-in-variables alters the standard least squares regression to explicitly account for measurement uncertainty in both width and WSE37. Reference 37 showed that constraining elevation–width observations with hypsometric curves using errors-in-variable regression reduces the variance in both measurements and improves precision of cross-area estimates. Although measurement uncertainty is included in the SWOT product for each river observation, we find that at the time of this study, the mission’s error estimates remain unreliable. When applying the errors-in-variable approach, we use an assumed WSE uncertainty of 0.1 m and a width uncertainty of 30 m, reflecting the science requirements of the SWOT mission30. A sensitivity analysis of active riverbed shapes and resulting RSAs to SWOT width and elevation uncertainties is presented in Supplementary Information section 4, documenting the impact of these input uncertainties.
Owing to the evolution of channel bathymetry across flow regimes, the relationship between river width and WSE is frequently nonlinear37. Following ref. 37, we fit a three-part piecewise linear relationship to SWOT observations of width and WSE of the form:
$$W(H)=\left\{\begin{array}{cc}{y}_{1}+{m}_{1}H & H < {H}_{1}\\ {y}_{2}+{m}_{2}H & {H}_{1}\le H < {H}_{2}\\ {y}_{3}+{m}_{3}H & {H}_{2} < H\end{array}\right.$$
(2)
where yi are the intercepts of the linear regression segments, mi are the slopes of the linear regression segments and Hi are the WSE breakpoints between subdomains for regions i = 1, 2, 3 (Extended Data Fig. 2b). The subdomains ideally reflect distinct hypsometric relationships across three potential flow regimes: within-bank flow, the transition to out of bank flow and out of bank flow (floodplain)37. Depending on what SWOT sampled, only within-bank flow may have been captured or kept post-filtering, and the three subdomains will then represent different in-bank shapes. When fitting the hypsometric curves, the piecewise linear segments are constrained to be continuous. In some circumstances, the initial errors-in-variable regression fails to converge or produces implausible results (mi terms either greater than 10,000 or negative), often owing to unreliable width measurements. In such situations, we instead fit a simplified rectangular hypsometric curve using the reach’s median width. This approach relies on the more reliable WSE observations to capture flow variability, although it sacrifices detail in representing the channel’s bathymetry. Of the 126,674 SWORD reaches where we fit hypsometric curves, we resort to rectangular fits at only 3,850 reaches (3.0%), the majority of them being located in river deltas where SWOT measurements feature reduced reliability (Supplementary Information section 5).
After generating a piecewise hypsometric curve, we constrain each paired WSE–width measurement to lie on the curve based on the ratio of assumed measurement error to improve the precision of the observations37,38. Because the hypsometric curve represents the true channel bathymetry while accounting for measurement uncertainty, these adjusted observations more accurately reflect the underlying hydrologic conditions as they would appear with minimal random error in the SWOT data. From the hypsometric curves we fit at each reach, we integrate the WSE–width piecewise functions using equation (1) and constrained WSE–width observations to obtain a channel cross-sectional area anomaly δA (refs. 37,53) corresponding to each SWOT observation. To facilitate the consistent aggregation of area anomalies across reaches, we perform the integrations relative to the median WSE, which we assume to be equivalent to the mean cross-sectional area53. Although this simplification introduces a minor residual error between the actual median area and the area at the median WSE, it enables the generation of cross-sectional area anomalies with a near-zero median (Extended Data Fig. 2c).
We convert the zero-median cross-sectional area anomaly time series δA at each reach to an associated river volume change (δV) by:
$${\rm{\delta }}V=L{\rm{\delta }}A$$
(3)
where L is the length of each SWORD reach. SWORD reach lengths are spatially variable, but the majority of reach lengths are between 10 km and 20 km (ref. 34). Much like the cross-sectional area anomaly, the resulting δV only reflects the variability of storage around the observed median WSE, rather than full storage magnitude. As our quality filtering of SWOT observations creates gaps in the storage anomaly time series, we interpolate δV to dates when the reach was observed by SWOT but the corresponding observation was removed during filtering. This ensures that the resulting δV at each reach is reflective of the observational cadence of SWOT. A forward-filling approach is adopted when water is ‘likely fully ice covered’ (ice_clim_f = 2), to maintain a stable δV during the winter months (for example, from November to May in the Arctic), and a linear interpolation between the two surrounding valid observations is performed otherwise. Then, to enable the comparison of SWOT-derived δV with other datasets, we subtract the mean δV value from each interpolated time series, to produce zero-mean RSAs at SWOT overpass dates tSWOT (equation (4) and Extended Data Fig. 2d). Finally, we calculate the monthly mean RSA at each reach (equation (5)), further allowing for the aggregation of anomalies within each of the 61 Pfafstetter55 basins in MERIT-Basins.
$$\mathrm{RSA}({t}_{\mathrm{SWOT}})={\rm{\delta }}V({t}_{\mathrm{SWOT}})-\overline{{\rm{\delta }}V}$$
(4)
$$\forall m\in [10/23;09/24],\,\mathrm{RSA}(m)=\mathop{\mathrm{mean}}\limits_{{t}_{\mathrm{SWOT}}\in m}\,\{\mathrm{RSA}({t}_{\mathrm{SWOT}})\}$$
(5)
We quantify the timing of the maximum RSA (Fig. 2a) and the annual range in river storage variability (ΔRSA) by computing the peak-to-trough amplitude of monthly RSA (equation (6)) at the reach scale (Fig. 2b) and at the basin scale (Fig. 3).
$$\Delta \mathrm{RSA}=\mathop{\max }\limits_{m\in [10/\mathrm{23;09}/24]}\{\mathrm{RSA}(m)\}-\mathop{\min }\limits_{m\in [10/\mathrm{23;09}/24]}\{\mathrm{RSA}(m)\}$$
(6)
It is noted that: (1) reach-scale monthly RSA values are first summed to obtain basin- and global-scale time series, after which ΔRSA is computed at each aggregation level; and (2) the choice of the median WSE as the reference to present the changes in RSA does not affect the reach-, basin- or global-scale seasonal analysis of RSA nor the estimation of river storage variability ΔRSA.
Uncertainty quantification of RSA from SWOT
The simultaneous measurements of river width and WSE provided by SWOT represent an unprecedented advancement in global hydrology, but their validation remains an ongoing and highly complex effort owing to the mission’s global scope and novel data products40. We provide reliable, conservative uncertainty estimates using error propagation as described in ref. 10. These storage uncertainties have been shown to be reliable in the context of nadir altimetry- and imagery-derived RSA estimates. The computation is based on the calculation of uncertainties in SWOT-derived cross-sectional area changes (δA) at a river reach for a given time, which are propagated to the RSA estimates from: (1) the uncertainty associated with the width/elevation pairs; and (2) the uncertainty in the piecewise linear hypsometric regression coefficients. The reader is referred to the supplementary information of ref. 10 for thorough information and assumptions about uncertainty quantification used in the modules of the FLaPE-Byrd library.
Further details, associated with uncertainty, on the observational and methodological limitations of the dataset, as well as on the presence of outliers, are provided in Supplementary Information sections 3 and 5 with supporting refs. 56,57,58,59,60,61.
Seasonal validation against global river gauges
As a result of the mission’s novelty, fine-scale global coverage and the limited range of dynamics covered so far (with only 1 year of measurements), direct validation of the SWOT-derived RSA time series is not yet genuinely feasible. Nevertheless, indirect consistency checks can be performed by comparing SWOT RSA with in situ river discharge records close to the basin outlet, even though the two variables are only loosely related owing to differences in flow velocity and hydrological response times, and water resource management.
To evaluate this consistency, we rely on global in situ river discharge records from the Global Runoff Data Centre62 (GRDC), selecting 61 gauges, each carefully and manually chosen to be representative of a distinct SWORD basin. For each pair, we compute the correlation between the SWOT basin-scale RSA and the mean monthly discharge time series (Extended Data Fig. 3). This seasonal validation emphasizes the reliability of SWOT across most regions (equatorial, tropical and mid-latitude basins), while also highlighting its current difficulties in reliably monitoring Arctic rivers (for example, the Lena, Khatanga, Glomma and Thelon). These low correlations in high-latitude basins are consistent with the difficulty in determining the exact extent of a river in snowy and wetland environments from SWOT, and the overall lack of usable measurements over frozen rivers (Extended Data Fig. 1), and suggest limitations of interpolating RSA during the winter months. Discrepancies in basins such as the Paraná or the Colorado could indicate limitations in the current ability of SWOT to consistently delineate water extent in complex and heavily managed hydrological settings. This seasonal validation probably also reflects actual hydrologic and hydrographic mismatches between variations measured in river water storage at a basin scale and in river discharge at a representative gauge.
Hydrography translations
Details on the Mean Discharge Runoff and Storage (MeanDRS)3 dataset, used in this study as prior knowledge for global river water storage change comparison, can be found in Supplementary Information section 1, with supporting refs. 63,64,65,66,67. As SWOT observations are made along SWORD reaches, whereas the MeanDRS simulations are made along MERIT-Basins reaches, the fundamental differences between the two hydrographic networks pose challenges for directly comparing river storage estimates. To overcome these differences, we leverage translations between individual reaches in MERIT-Basins and SWORD from the MERIT–SWORD dataset45 to facilitate the transfer of hydrologic information between networks. We use translations from the MERIT–SWORD dataset to identify reaches in MERIT-Basins (and therefore, storage simulations in MeanDRS) that directly correspond to SWOT-observed reaches in SWORD. For each SWORD reach where we compute RSA from SWOT, we retrieve the associated MERIT-Basins reaches from MERIT–SWORD and store the degree of overlap between the associated reaches. This subset of selected reaches from MERIT-Basins, and their associated storage time series from MeanDRS, represents a benchmark for comparison with SWOT-derived RSA estimates.
Comparison with global simulations
To enable a consistent comparison between SWOT observations and MeanDRS simulations, we compute the total MeanDRS RSA time series for each basin by aggregating the storages from all corresponding MERIT-Basins reaches over the 30-year simulation period and across the 3 residence time scenarios. When a MERIT-Basins reach only partially overlaps with a SWORD reach, we apply a weighting based on the fractional overlap of reaches provided by the MERIT–SWORD dataset. This ensures that only the storage from the portion of the MERIT-Basins reach that corresponds to an observed SWORD reach is included. As MERIT-Basins reaches are generally more sinuous and therefore longer than SWORD reaches, we apply a global scaling factor during the weighting process. This factor, equal to 1.13 and calculated from the ratio of MERIT-Basins to SWORD reach lengths, helps to more accurately represent the actual extent of overlap between the two networks45. In rare cases where no equivalent MERIT-Basins reach exists for a given observed SWORD reach, we exclude the storage obtained from SWOT for that reach from comparison.
We calculate the RSA for each of the 3 residence time scenarios by subtracting the 30-year mean from the retrieved MeanDRS river storage time series corresponding to the observed SWORD reaches. As the original MeanDRS dataset estimates river storage at all approximately 3 million MERIT-Basins reaches, we note that the variability of the MeanDRS storage anomalies that we calculate is smaller in magnitude than those reported in ref. 3. To enable comparison with SWOT-observed storages, we summarize the MeanDRS RSA time series by calculating global monthly means and standard deviations over the 30-year period. These metrics characterize the typical magnitude and variability of anomalies for each month, allowing for a direct comparison between SWOT-derived monthly RSA values at observed reaches and the modelled storages from MeanDRS in a typical year (Fig. 4a).
Regional hydroclimatic variability (for example, El Niño periods) exerts a substantial influence on comparisons between a single year of SWOT observations and long-term gauge-corrected simulated means, as the study period captured by SWOT (2023–2024) may represent conditions that are substantially different from climatological averages. The exceptional drought in the Amazon Basin since 2023, with record lows observed in several major rivers including the Negro, which hit century-low levels16,47, probably resulted in SWOT-observed variability for 2023–2024 being much lower than that of the 30-year MeanDRS average. To explore whether the storage anomaly derived from SWOT observations aligns with specific historical years in the MeanDRS record, we compare the SWOT-derived RSA to the 30 individual annual time slices of MeanDRS storage simulations across all 3 residence time scenarios (Fig. 4b and Extended Data Figs. 4 and 5). Although the SWOT-derived RSA is generally lower in magnitude than the simulated anomalies in each scenario, we observe the closest agreement during the least variable, and probably driest, years within the historical record for the lowest-volume MeanDRS scenario (Fig. 4b). This suggests that either the period of SWOT observations used in this study coincided with unusually low global river storage variability, or, alternatively, that even the lowest-volume MeanDRS scenario may overestimate the true variability in river storage. The persistent divergence between SWOT observations and the normal and high-volume MeanDRS scenarios, even during years of minimal variability, could further indicate that the land run-off inputs and residence time assumptions underlying these scenarios may not be valid at the global scale. In particular, it is possible that the upper bound for celerity in the model runs (1.4 m s−1), underlying the low-volume scenario (Fig. 4b), remains too low, or that assuming spatiotemporally constant global celerity values is overly unrealistic.
Quantifying agreement with simulations
To assess spatial variations in the agreement between SWOT and MeanDRS RSA, we compare the Pfafstetter basins with the largest SWOT-observed river storage variability (Extended Data Fig. 6). The Amazon River Basin and the Yenisei and Lena River basins show some of the largest differences between SWOT and MeanDRS, probably owing to a record drought in the Amazon and challenges in resolving partially to fully frozen Arctic rivers from SWOT, respectively. The Nile River Basin features the most striking discrepancy with a SWOT-observed ΔRSA of only 8.5 ± 1.6 km3 in 2023–2024, much lower than previous knowledge estimates (93 km3 for the MeanDRS low-volume scenario; 160 km3 referenced in ref. 2). We note that the MeanDRS simulations over the Nile Basin were not bias-corrected owing to the lack of long-term in situ observations and appear to overestimate river discharge by a factor of 3 to 6 (compared with older in situ data from the GRDC), and therefore overestimate storage variations accordingly. With more SWOT observations spanning full annual cycles (when version D products are available) and more local validation endeavours, clearer explanations will emerge.
We also compute several metrics of difference between the 2 volume estimates in each of the 61 Pfafstetter basins. First, we determine the ratio of ΔRSA between SWOT and the MeanDRS low-volume scenario, which shows the highest global agreement with SWOT (Extended Data Fig. 7). In addition, we compute this variability ratio for each of the 3 MeanDRS residence time scenarios and identify the scenario with a ratio closest to 1 for each basin, indicating the best agreement with SWOT (Extended Data Fig. 8).
We evaluate the temporal alignment between SWOT and MeanDRS RSA by calculating both unlagged and circularly lagged Pearson correlation coefficients. We compute the unlagged Pearson correlation between the SWOT and MeanDRS RSA time series within each basin to evaluate their agreement in time (Extended Data Fig. 9). We also perform a circular lag analysis by incrementally shifting the MeanDRS time series by 1 month and recalculating the correlation at each step, covering all 12 possible monthly lags. This approach quantifies the extent to which the SWOT and MeanDRS volume anomalies may be temporally offset. For each region, we identify and plot the lag that yields the highest correlation, indicating the best temporal alignment (Extended Data Fig. 10). Correlations between SWOT-derived RSA and both representative in situ discharge (Extended Data Fig. 3) and MeanDRS RSA (Extended Data Fig. 9) show strong and regionally consistent agreement. We note that lags between SWOT and MeanDRS RSA time series can also be the result of monthly lumped routing in MeanDRS, where run-off is accumulated from upstream to downstream without accounting for horizontal travel time from land to rivers or within the river system.
