GoKawiilThe importance of tides is embodied in the origins of the word ‘estuary’, which comes from the Latin word ‘aestuarium’, meaning the place of the tide. Along coastlines, where tides are typically magnified11, they profoundly affect navigation, commerce, coastal flooding, water properties and sediment transport12. Tides impact the flooding of rivers and, thus, influence the extent of their floodplain, which has cascading effects on biogeochemical and ecological processes13. Flood cycles, modulated by tides and sea-level rises, are a key factor in the dieback or persistence of saltmarsh systems14. Tidal flooding also accelerates both nitrification and denitrification in soils, leading to variable effects on nutrient levels and coastal water quality15,16. Tides enhance the mixing of saline and freshwater along river channels, which affects water security in coastal cities and food security for agricultural deltas that use river water for irrigation17. Moreover, tides are a critical factor in compound coastal flooding, as demonstrated by the devastating combination of storm surge and high tide that hit New York City during Hurricane Sandy in 201218. Despite their importance, the extent of tides in coastal rivers is poorly known on a global scale because tidal propagation depends on the unique morphologic and hydrologic conditions of each river as well as the magnitude of the tidal signal at the river mouth19. The relative importance of these controls on tidal extent—indeed, the extent itself—has not been unravelled on a global scale, primarily due to limitations of observational coverage.
The combination of numerical modelling and satellite altimetry20 now gives us the ability to predict tidal elevations anywhere in the open ocean with accuracies approaching 1 cm (ref. 21). However, coastal regions and connected inland water bodies remain the Achilles heel for tidal prediction6. The challenge largely stems from two constraints of traditional nadir altimetry: land contamination of radar returns and inadequate density of satellite overpasses. Moreover, nonlinear effects of the shallow water in rivers and estuaries drive complex tidal behaviours22,23, which are best described with physics-based models. Yet adequately resolved models exist only for a handful of locations, owing to the scarcity of bathymetric and water-level data to constrain models and the complexity of the dynamics, which vary from river to river19,24,25.
The highly anticipated Surface Water and Ocean Topography (SWOT) satellite provides two-dimensional swath observations of both ocean and inland water surfaces26. SWOT has the potential to revolutionize the scientific understanding of water-related physical processes27 and to open new avenues of scientific research across the land–ocean–aquatic continuum28,29. Early studies have shown that SWOT can improve the accuracy of tidal estimates in coastal regions, and they have hinted at the potential of using these data to study tidal processes within inland water bodies, including rivers30,31.
The question then becomes, can SWOT be used to pioneer a deeper understanding of tidal dynamics within coastal rivers worldwide? If so, could these insights support the creation of the first-ever global atlas of tidal extent within rivers? By exploiting the observational capabilities of SWOT at the land–ocean interface, we address both these questions and produce a global atlas of tidal rivers, which could radically expand our understanding of the fundamental tidal force that controls land–ocean interactions.
Observing river tides from space
To assess the feasibility of using SWOT data to estimate tides within rivers, we conducted a harmonic analysis on the SWOT River Single-Pass Vector Data Product (RiverSP) from March 2023 to May 2025 to estimate the diurnal O 1 and semi-diurnal M 2 tidal constituents for all observed rivers. Global amplitude results are available at the Database for Hydrological Time Series of Inland Waters (DAHITI): https://dahiti.dgfi.tum.de/en/products/river-tides/map/. Selected rivers are presented in Fig. 1.
Fig. 1: Summed M 2 and O 1 tidal amplitudes within three selected river networks, estimated from SWOT elevation measurements. a–c, The three selected regions are the Gironde Estuary (a), the Seine River (b) and the Elbe River (c). Stars with black borders along the trajectory of the rivers represent the summed M 2 and O 1 amplitude calculated from in situ river gauge observations. The white squares mark the location of dams. Satellite base maps powered by Esri. Full size image
We validated our tidal amplitude estimates from SWOT data using records from 622 globally distributed, in situ tide and river gauge stations. Median and mean amplitude differences for the 622 sites were only 5.53 cm and 9.23 cm for M 2 and 3.23 cm and 5.75 cm for O 1 . In Fig. 2 we present a scatter plot of both SWOT and tide gauge estimates for both constituents, as well as the median error as a function of distance to river mouth. Additionally, we present the respective tide gauge amplitude errors in Fig. 3 for M 2 . The error for O 1 is in Extended Data Fig. 1. We observe errors ranging between 0 cm and 30 cm across the globe, with the largest errors being observed at higher latitudes, where the effects of sea ice may influence the estimates. Amplitude errors of both constituents consistently increase the further upstream the observations are made (Fig. 2), which is expected due to the decreasing signal-to-noise ratio as tidal amplitudes diminish19.
Fig. 2: Error statistics of SWOT tidal estimates compared with tide gauge observations. a,b, Scatter of M 2 (a) and O 1 (b) amplitude estimates from tide gauges (x-axis) and SWOT observations (y-axis). c, The median error as a function of distance to the river mouth. d, The number of in situ observations used in the distance to mouth bins. Full size image
Fig. 3: The amplitude error of the M 2 tide mapped with respect to in situ observations from TICON-4, with several zoom-ins to different regions. a–d, Regional zooms are provided into the west coast (a) and east coast (b) of the USA, the northern coastline of Europe (c) and the coast of Japan (d). The error for O 1 can be found in Extended Data Fig. 1. Base map from Natural Earth. Full size image
... continue reading