the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Globally Applicable Discharge Reanalysis using SWOT observations
Abstract. Global river discharge observations are critical for climate and hydrological research, used for water resource management, risk mitigation, infrastructure and environment conservation, among many other areas. However, existing observations are limited in availability, accuracy and spatial extent, with uneven geographical distribution and high levels of uncertainty often recorded. The NASA SWOT mission provides the opportunity to fill this gap, providing water level observations for all rivers exceeding 100 m in width worldwide. Combined with the daily discharge model GRADES-hydroDL, we present a statistical method to produce a set of global virtual gauging stations with the same temporal resolution as the satellite observations. The high level of accuracy that the SWOT water surface elevation observations allows us to improve the dynamics of discharge estimation over the input discharge model. For our validation gauges, where we compared modelled discharge to observed values, 66 % of Pearson R values are larger than 0.9, showing the method’s skill at replicating temporal patterns in recorded flow. The median Root Mean Square Error, RMSE, of the input discharge set is 36.3 m3 s−1 larger than that of our proposed method, and the NSE 0.3 lower. However, our method fails to improve the bias; the median absolute normalised bias is 0.10 (10 %) higher in our model than the input model, indicating that while the inclusion of Earth Observation can greatly improve the discharge time series dynamics, the trade-off is an increased bias in the distribution. Nevertheless, as the record of SWOT observations increases in length, these results should improve and the margins of bias difference decrease. The result is a globally applicable reanalysis dataset of discharge, which will complement existing physically based models and ground observations, and can be widely used within global hydrological models.
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Status: open (until 26 Oct 2026)
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RC1: 'Comment on egusphere-2026-3843', Xiang Zheng, 29 Aug 2026
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AC1: 'Reply on RC1', Izzy Probyn, 18 Sep 2026
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Thank you very much for your comment and constructive feedback. This is my first paper, so I really appreciate the help, and the speed with which you returned your thoughts. We agree with all of your comments, and hope that our changes, as described below, will address all the issues and provide a clearer explanation of this method, and where it is most suitable.
- Is “reanalysis” the right term? In hydrology, reanalysis usually implies temporally and spatially continuous products with data assimilation. However, SWOT-DR estimates discharge only at SWOT overpass times and only for non-extreme conditions, without assimilation. I therefore question whether “reanalysis” is an appropriate label for this product.
Thank you for raising this; we spent a long time looking for the right word to describe it, thinking it would be clearer to use one word to keep it short. However, as you point out, this could cause some confusion, so we suggest renaming it to SWOT-DQA; SWOT Discharge Quantile Analysis. We have also changed all references to “discharge reanalysis” to “discharge quantile analysis”.
- The monotonicity assumption. The method structurally assumes a strictly monotonic WSE–discharge relationship (Sect. 3.4), but this assumption is only tested indirectly— via monotonicity between gauge and SWOT water levels (Sect. 2.4.1) at 399 gauged reaches. For the global 92,955 reaches the assumption remains unverified. Backwater, tidal, ice, dam regulation, and hysteresis can all violate it; river width is available but unused. I recommend stating this assumption explicitly, discussing its failure modes, and tempering the “globally applicable” claim.
You are completely correct; we have missed out an explanation of this fact. We have added a discussion point on this, explaining where this method is suitable and where it is likely to fail.
Added at line 205:
This method assumes monotonicity between water surface elevation and discharge. Many rating curves use this assumption, representing an ideal state primarily under steady, uniform flow, to produce single-valued mapping between stage and discharge. However, this is not always the case, and this method may therefore not always accurately represent flow patterns. This is particularly prevalent for high flows, and where river discharge is dominated by the effects of a confluence, backwater, tides, ice, dam regulation, or hysteresis (Geertsema et al., 2018; Muste et al., 2020; Simonovic et al., 2022). In these cases, an alternative method, that does not rely on stage-discharge monotonicity may be more appropriate.
Monotonicity between WSE and discharge relies on the kinematic wave approximation, where the friction slope Sf equals the bed slope S. The full Saint-Venant one-dimensional shallow water momentum equation to relate Sf and S can be written as:
Sf = S - ∂y/∂x - v/g ∂v/∂x - 1/g ∂v/∂t
When the pressure gradients and acceleration terms are (relatively) small, Sf ≈ S, and therefore this is a reasonable assumption to make. Formulas such as Manning’s and Chezy’s Equations rely on this assumption, as do many other single-valued, monotonic stage-discharge rating curve methods (Gehring et al., 2022; Gleason & Smith, 2014). The DAWG algorithms, for example, parameterise different flow laws; those which use the 1D uniform flow equations or empirical At-Many-Stations Hydraulic Geometry (AMHG) scaling relationships will produce this monotonic relationship, while the hydrodynamic methods, such as SIC4Dvar and MetroMan, will not enforce this (Durand et al., 2014, 2023; Oubanas et al., 2018). Situations where this assumption of monotonicity applies includes low-to-moderate in-bank flows, where there is a stable flow geometry, and at rivers with steep bed slopes, where the pressure and acceleration terms are negligible relative to S. On the other hand, flows over lower bed slopes are often controlled by downstream and backwater effects, resulting in larger pressure gradient and acceleration terms, which therefore breaks the kinematic wave approximation. For out-of-bank flows, the increased roughness , momentum exchange with floodplains, and hysteresis have the same effect (Schumann et al., 2016). Since we focus on lower, in-bank flows with this method, we adopt this assumption, but it must be acknowledged that this will therefore not necessarily represent flow for all rivers.
- High R is partly inherited, not an independent contribution of the method. Because SWOT-DR discharge is a monotonic transform of observed WSE, its high correlation with gauged discharge largely reflects the information content of SWOT WSE itself, rather than independent model skill. I suggest explicitly separating observation information content from method gain, e.g., by benchmarking against a null model (direct WSE–discharge regression or a rank-matching version of GRADES) and by softening abstract wording such as "showing the method's skill."
We agree with your point; the correlation is entirely inherited from SWOT. This is the essence of our method, and the reason it performs well. The explanations aren’t clear enough, however, that this is the case. We have rephrased our point where relevant, making sure to either say that the high R shows SWOT’s skill, or state that it is inherited from SWOT.
Changed at line 8:
For our validation gauges, where we compared modelled discharge to observed values, 66% of Pearson R values are larger than 0.9, showing SWOT's skill, and therefore that of our method, at replicating temporal patterns in recorded flow.
Changed at line 312:
By formulation of SWOT-DR, all R values are inherited from the SWOT WSE levels, and are therefore predictably high for our validation reaches, with 66% above 0.9, while only 20% of GRADES R values reach this mark.
References
Durand, M., Gleason, C. J., Pavelsky, T. M., Prata de Moraes Frasson, R., Turmon, M., David, C. H., Altenau, E. H., Tebaldi, N., Larnier, K., Monnier, J., Malaterre, P. O., Oubanas, H., Allen, G. H., Astifan, B., Brinkerhoff, C., Bates, P. D., Bjerklie, D., Coss, S., Dudley, R., … Wang, J. (2023). A Framework for Estimating Global River Discharge From the Surface Water and Ocean Topography Satellite Mission. Water Resources Research, 59(4), e2021WR031614. https://doi.org/10.1029/2021WR031614
Durand, M., Neal, J., Rodríguez, E., Andreadis, K. M., Smith, L. C., & Yoon, Y. (2014). Estimating reach-averaged discharge for the River Severn from measurements of river water surface elevation and slope. Journal of Hydrology, 511, 92–104. https://doi.org/10.1016/J.JHYDROL.2013.12.050
Geertsema, T. J., Teuling, A. J., Uijlenhoet, R., Torfs, P. J. J. F., & Hoitink, A. J. F. (2018). Anatomy of simultaneous flood peaks at a lowland confluence. Hydrology and Earth System Sciences, 22(10), 5599–5613. https://doi.org/10.5194/HESS-22-5599-2018
Gehring, J., Duvvuri, B., & Beighley, E. (2022). Deriving River Discharge Using Remotely Sensed Water Surface Characteristics and Satellite Altimetry in the Mississippi River Basin. Remote Sensing 2022, Vol. 14, Page 3541, 14(15), 3541. https://doi.org/10.3390/RS14153541
Gleason, C. J., & Smith, L. C. (2014). Toward global mapping of river discharge using satellite images and at-many-stations hydraulic geometry. Proceedings of the National Academy of Sciences of the United States of America, 111(13), 4788–4791. https://doi.org/10.1073/PNAS.1317606111
Muste, M., Lee, K., Kim, D., Bacotiu, C., Oliveros, M. R., Cheng, Z., & Quintero, F. (2020). Revisiting hysteresis of flow variables in monitoring unsteady streamflows. Journal of Hydraulic Research, 58(6), 867–887. https://doi.org/10.1080/00221686.2020.1786742
Oubanas, H., Gejadze, I., Malaterre, P. O., Durand, M., Wei, R., Frasson, R. P. M., & Domeneghetti, A. (2018). Discharge Estimation in Ungauged Basins Through Variational Data Assimilation: The Potential of the SWOT Mission. Water Resources Research, 54(3), 2405–2423. https://doi.org/10.1002/2017WR021735;PAGE:STRING:ARTICLE/CHAPTER
Schumann, G. J. P., Stampoulis, D., Smith, A. M., Sampson, C. C., Andreadis, K. M., Neal, J. C., & Bates, P. D. (2016). Rethinking flood hazard at the global scale. Geophysical Research Letters, 43(19), 10,249-10,256. https://doi.org/10.1002/2016GL070260;WGROUP:STRING:PUBLICATION
Simonovic, P., Karmakar, S., Cheng, Z., Muste, M., Kim, D., & Kim, K. (2022). Insights into Flood Wave Propagation in Natural Streams as Captured with Acoustic Profilers at an Index-Velocity Gaging Station. Water 2022, Vol. 14, Page 1380, 14(9), 1380. https://doi.org/10.3390/W14091380
Citation: https://doi.org/10.5194/egusphere-2026-3843-AC1
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AC1: 'Reply on RC1', Izzy Probyn, 18 Sep 2026
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This paper presents a simple, transparent statistical baseline for global discharge estimation from SWOT observations, complementing the more complex DAWG algorithms and greatly expanding spatial coverage. The data preprocessing is careful and the sensitivity analysis is systematic. The evaluation is also honest: a broad set of metrics, performance classification, R_G-stratified analysis, and clear acknowledgment of the bias trade-off and the uneven distribution of validation gauges. However, I have a few comments on this paper.
1. Is “reanalysis” the right term? In hydrology, reanalysis usually implies temporally and spatially continuous products with data assimilation. However, SWOT-DR estimates discharge only at SWOT overpass times and only for non-extreme conditions, without assimilation. I therefore question whether “reanalysis” is an appropriate label for this product.
2. The monotonicity assumption. The method structurally assumes a strictly monotonic WSE–discharge relationship (Sect. 3.4), but this assumption is only tested indirectly— via monotonicity between gauge and SWOT water levels (Sect. 2.4.1) at 399 gauged reaches. For the global 92,955 reaches the assumption remains unverified. Backwater, tidal, ice, dam regulation, and hysteresis can all violate it; river width is available but unused. I recommend stating this assumption explicitly, discussing its failure modes, and tempering the “globally applicable” claim.
3. High R is partly inherited, not an independent contribution of the method. Because SWOT-DR discharge is a monotonic transform of observed WSE, its high correlation with gauged discharge largely reflects the information content of SWOT WSE itself, rather than independent model skill. I suggest explicitly separating observation information content from method gain, e.g., by benchmarking against a null model (direct WSE–discharge regression or a rank-matching version of GRADES) and by softening abstract wording such as "showing the method's skill."