The Moving Water ​

The sources before this one sit in an instrument or in its installation, from the gauge’s reading to the sensor’s height, whereas the water itself keeps moving between one instrument’s reading and the other’s, and the tide, the waves, and the slope from a harbor out to open sea each open a gap of their own.

In the Severn Estuary, the tidal range grows by more than 1.5 m between the gauges at Hinkley Point and Avonmouth⁠1⁠, and the tide moved the water level by up to 60 cm within the 20 minutes a flight of airborne LiDAR (a laser scanner flown over the water, which maps the surface at about 0.5 m) took to cover what SWOT collects in 21 seconds⁠2⁠.

The Error Itself ​

The satellite and the gauge never read the same water, since an altimeter cannot measure right at the coast, whereas a gauge often sits in a harbor or a river mouth⁠1⁠, so sloping water separates the two. At Mayport in Florida, the nearest valid pixel lay only 1.06 km from a gauge in the lower estuary of the St. Johns River, yet the two differed by the largest root mean square of the East Coast's 12 gauges, which the authors put down to salt and fresh water mixing as the tide reverses there, so that the pixel and the gauge read different water. At St. Petersburg, the nearest valid pixel lay 46.9 km away, in a different part of Tampa Bay with a circulation of its own⁠3⁠.

The water between them does not lie flat. In shallow water near the shore, waves steepening as they come in raise and lower the mean level, and in an enclosed bay or estuary a tide trapped against the coast tilts the water across the channel, as the tide circulating around the Bristol Channel does⁠1⁠. The tide also changes the level during the gap in time between the two readings, since the satellite images the water at one instant whereas the Severn's gauges sampled it every 10 or 15 minutes⁠1⁠.

Waves affect the radar and the gauge in different ways. The troughs of waves bias the radar's measured range, which the sea state bias correction removes⁠1⁠. SWOT's sampling can also cross a train of waves, alternately landing on crests and troughs, so that a slight offset in timing or position against the LiDAR left bands of difference about 50 m wide and up to ±2 m at single pixels, which averaging the pixels brings down, as Errors Across the Estuary sets out⁠2⁠. At a gauge itself, breaking waves can raise the water, as at the atoll of Minamitorishima, where a gauge behind a reef saw wave setup at the meter level and was later moved⁠4⁠.

Its Measured Size ​

SWOT's daily images measured those tilts directly. Along the Severn's channel, the slope averaged 0.016 m per km and reached 0.038, whereas across it the slope averaged 0.008 m per km and reached 0.027, both steepest around mid-tide, and the team expected up to 0.08 m of uncertainty over 2 km from the slope across the channel⁠1⁠.

The Severn team also plotted the difference between SWOT and each gauge against the water level, a Van de Casteele diagram, long used to check one gauge against another. Two series measuring the same water at the same place would fall on a vertical line, meaning no difference at any level, just as a plot of one series against the other would fall on the 1:1 line. A slope showed instead a difference growing with the tide, a scaling error. They traced it to the distance between each gauge and the pixels, since the tide's range grows up the estuary and any small offset east or west between the two scales the difference with the tide, and assumed it came mainly from the shallow seabed around each gauge. A loop showed the rising and the falling tide disagreeing. Even the gauge at Hinkley Point C, at the end of a 460 m pier where SWOT's pixels surround it more evenly than at a gauge on the shore, showed the slope, beside more scatter at low water and between the two phases of the tide⁠1⁠.

GaugePixelsHigh waterLow waterNo differencePixels higher ▸
Vertical line
Slope
Loop

A scaling error, the difference growing with the tide as its range grows up the estuary.

The tide and distances are illustrative, not measured, sized to show the shape.

Errors Across the Estuary ​

The second Severn study checked two of SWOT's finer products against the LiDAR, the pixel cloud and the raster. The error shrank as the pixels were averaged, from a standard deviation of 37 cm in the pixel cloud to 9 cm over areas of 1 km²⁠2⁠.

The same study found the estuary's slopes in how SWOT's errors vary across space. Measured against the LiDAR, the errors in pixels across the estuary lost their correlation within about 20 to 50 m and leveled off near 0.1 m², whereas along the estuary they ran larger, at 0.2 to 0.4 m², and cycled without leveling off. The authors traced the difference to the persistent tidal slope, the currents, and the wave trains along the channel, and to the swath's orientation, since the flights across the estuary ran parallel to the swath⁠2⁠.

From that spatial structure, the second Severn team recommends that coastal processing of SWOT model its errors as anisotropic, meaning different along one direction than another, taking in the alignment between the swath and the channel, the effect of the tidal and intertidal seabed on the radar's returns, and the different distances over which errors stay correlated across and along an estuary. Averaging across the estuary reduces the error over a short distance, whereas averaging along it has to allow for errors that stay correlated much farther⁠2⁠.

The Search Radius ​

Other teams removed the tide from both series and tested how far from a gauge to take the satellite's points. Radii from 0.25 to 100 km around gauges in the Baltic, the North Sea, and the Gulf of Mexico gave the smallest differences between 40 and 60 km, in a comparison that estimated no datum, so the authors kept the points within 50 km and took their median there for the 250 m product as well, counting a pass only where it held valid data within 10 km of the gauge⁠5⁠. At Barcelona, narrowing from 100 to 25 km lowered the spread by 22 and 13 percent on two tracks, where long-lived eddies far from the gauge had raised it⁠6⁠.

Along the US East Coast, where the tide stayed in both series, averaging the pixels within 5 to 50 km of each gauge by inverse distance helped at some stations and hurt at others. The root mean square changed little with the radius at three stations, was lowest between 10 and 20 km at three more, and rose sharply beyond 30 km at two, and the authors put part of that rise down to a growing offset rather than to scatter. At Mayport, it reached 1.757 m at 20 km whereas the unbiased figure stayed at 0.295 m, and at Lake Worth Pier it rose from 0.257 to 0.984 m between 5 and 50 km whereas the unbiased figure rose only from 0.135 to 0.162 m. The authors conclude that the best radius depends on how many valid pixels a gauge has and on the coast around it rather than on any one distance⁠3⁠.

Workarounds in the Studies ​

The workarounds bring the two readings closer in time and in place before any height is compared, collecting the gauge's side over time and the satellite's over space.

A physical basis for the moving water has entered these designs through models, within limits. The method that found the Rodrigues step removes one model of the sea's response to wind and air pressure from both series, evaluated for the gauge at its exact position⁠4⁠, yet in Bass Strait, the global tide models missed the buoys' tide by a standard deviation of 59 to 76 mm, more toward the coast⁠7⁠.

Matching the Instant ​

  • Each gauge is read at the instant of the pass, by interpolating a two-hour window of its readings in the Severn, and linearly between the two 6-minute readings on either side along the US East Coast, at the time the nearest pixel was acquired to the millisecond⁠13⁠.
  • The Severn team dropped spikes beyond three median absolute deviations from that window and then interpolated with a modified Akima method, which follows both the oscillating and the flat stretches of a series, since a gauge in the intertidal zone or on a river records only part of the tide. The median slope of the same window marked each match as rising or falling tide⁠1⁠.
  • The second Severn team read its gauges with the same Akima method, but took the 10-minute mean just before each pass from its seabed pressure sensors, whose rapid fluctuations ruled out interpolating them, and moved each LiDAR height to the instant of the pass with the change in tide the NEMO-UK500 model predicted⁠2⁠.

Choosing the Pixels ​

  • Before matching, the Severn team removed land with a shoreline mask drawn from the UK's high-water line at about 30 m, dropped heights beyond 9 m on either side of the geoid, dropped the sea state bias data above a wave height of 8 m, and dropped spikes beyond three median absolute deviations within each pass. After matching, they dropped any pair differing by more than 1 m, and then any beyond three median absolute deviations once the slope with the water level was removed⁠1⁠.
  • The second Severn team kept the comparison to open water with a coastline mask that removed land, small islands, and everything within 50 m of the shore⁠2⁠.
  • Both Severn teams took the median of the pixels close to the gauge, within 6 km and 3 km⁠12⁠. The second chose 3 km to stay close to the gauge, given the lag in the tide's phase between a gauge and SWOT, and the spread of the pixels within it stayed below 0.1 m on most passes⁠2⁠. The first team's 6 km reached the track of CryoSat-2, which they compared as well, and took between 2 and 17 of SWOT's pixels per pass. The median outperformed linear and cubic extrapolation and several forms of kriging, with regression kriging a close second, which they put down to the median cancelling the slope along the channel while no method captured the processes across it near the shore. Because most gauges sit on the shore, the median cannot cancel the slope across the channel, which was about half the size⁠1⁠.
  • Keeping only the rising tide and correcting each gauge for its slope gave the single-gauge figures that Against the Gauges lists. The team recommends keeping one phase of the tide, rising or falling, when a coastal gauge validates altimetry, and correcting each gauge for its own slope and offset, which a linear fit to its Van de Casteele diagram gives⁠1⁠.
  • With older altimeters, keeping the 20 percent of points within 300 km that followed the gauge's series most closely made land-motion trends 15 percent more accurate than averaging all points within 250 km⁠8⁠.

  1. 1Lichtman et al. 2025 Evaluating Water Levels From the Surface Water and Ocean Topography (SWOT) Mission in a Hyper-Tidal Coastal and Estuarine Environment Earth and Space Science 12(7): e2024EA004104. https://doi.org/10.1029/2024EA004104↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎

  2. 2Rong et al. 2026 Evaluating SWOT in the Coastal Zone: Comparisons With Tide Gauge and Airborne LiDAR in the Bristol Channel and Severn Estuary, UK Geophysical Research Letters 53(2): e2025GL116590. https://doi.org/10.1029/2025GL116590↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎

  3. 3Fan et al. 2026 Assessing the Consistency of Coastal Sea Surface Height Measurements From SWOT Altimetry and Tide Gauges Along the U.S. East Coast Acta Geodynamica et Geomaterialia 23(3): 393–402. https://doi.org/10.13168/agg.2026.0026↩︎ ↩︎ ↩︎

  4. 4Ray et al. 2023 Offsets in Tide-Gauge Reference Levels Detected by Satellite Altimetry: Ten Case Studies Journal of Geodesy 97(12): 110. https://doi.org/10.1007/s00190-023-01800-7↩︎ ↩︎

  5. 5Vega-Gimenez et al. 2025 Expanding the Coastal Observation Frontier: SWOT Reveals the Spatial Footprint of Storm Surges Geophysical Research Letters 52(24): e2025GL117299. https://doi.org/10.1029/2025GL117299↩︎

  6. 6Gómez-Enri et al. 2026 Validation of the Surface Water and Ocean Topography (SWOT) KaRIn Sea Level Data IEEE Transactions on Geoscience and Remote Sensing 64: 4205911. https://doi.org/10.1109/TGRS.2026.3679467↩︎

  7. 7Hay et al. 2025 In Situ Geometric Validation of SWOT Satellite Observations in Bass Strait, Australia Earth and Space Science 12(8): e2025EA004326. https://doi.org/10.1029/2025EA004326↩︎

  8. 8Oelsmann et al. 2021 The Zone of Influence: Matching Sea Level Variability From Coastal Altimetry and Tide Gauges for Vertical Land Motion Estimation Ocean Science 17(1): 35–57. https://doi.org/10.5194/os-17-35-2021↩︎