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River discharge and bathymetry estimation from SWOT altimetry measurements
Abstract
An inversion algorithm to estimate the discharge of rivers observed by the forthcoming SWOT mission (wide swath altimetry) is developed and assessed in detail. The algorithm relies on an advanced variational data assimilation formulation applied to the Saint-Venant equations (1D shallow-water) combined with a lower complexity model (low Froude assumption and locally stationary). This modeling approach enables to estimate from the altimetry measurements the three flow features: the discharge Q(t) associated with an effective bathymetry b(x) and a (non constant) roughness coefficient K. The river geometry is built up with effective cross sections defined from the altimetry measurements. The numerical results are analyzed for three rivers (\sim100 km long each) presenting rapid flow variations compared to the observation frequency. Two scenarios of observation are considered: frequent satellite overpasses corresponding to the SWOT Cal-Val orbit (\sim1 day period) and SWOT like data corresponding to a \sim21 days period with 1 to 4 passes at mid-latitudes. Given prior mean values (of Q or/and b), the numerical experiments demonstrate that the inference of the river discharge Q(t) and the bathymetry profile b(x) may be accurate. Various prior values sources are investigated in view of worldwide applications. Once the assimilation of a long period of measurements is done (e.g. one year long time series), the low complexity flow model is correctly calibrated and provides accurate di…
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“However, altimetric observations require ancillary data since river surface geometry does not uniquely determine discharge14,15.”
From Global scale river discharge and mean depth from radar altimetry and model (2026) · cites this paper as [15]
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“For SWOT, where instantaneous discharge retrieval remains mathematically underdetermined due to unknown bathymetry and friction15”
From Global scale river discharge and mean depth from radar altimetry and model (2026) · cites this paper as [15]
In the citing paper
“Rivers are vital for water security, yet scalable freshwater monitoring and global knowledge of river mean depth and discharge remains limited by sparse in situ data, satellite observations of river surface only and global river flow estimations relying on models with insufficient hydraulic information.”
From Global scale river discharge and mean depth from radar altimetry and model (2026) · cites this paper as [15]
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“The ARC approach also applies to any hydrological-hydraulic model that integrates altimetry and other data within a hierarchical framework for discharge estimation from space15,47.”
From Global scale river discharge and mean depth from radar altimetry and model (2026) · cites this paper as [15]
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Cited by
Global scale river discharge and mean depth from radar altimetry and model
Paris, A., Garambois, P.-A., Gal, L., Cerbelaud, A., Larnier, K., David, C. H., Jucá Oliveira, R. A., Correa, S. W., Tourian, M. J., & Calmant, S. (2026) · Nature Communications · doi:10.1038/s41467-026-78275-5
Self-citation
Metadata
- Authors
- Larnier, K., Monnier, J., Garambois, P.-A., & Verley, J.
- Affiliations
- Institut de Mathématiques de Toulouse (IMT), Toulouse, France
- ICUBE, Strasbourg, France
- Venue
- Inverse Problems in Science and Engineering
- Publisher
- Informa UK Limited
- Published
- 2020-08-31
- Volume
- 29
- Issue
- 6
- Pages
- 759-789
- ISSN
- 1741-5977
- 1741-5985
- Cited by
- 60
- References
- 1
- Language
- en
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