The Satellite’s Reading

The height a satellite pass reports carries errors from the spacecraft itself, which shape every reading across the swath before a gauge comes into view, and this page takes them in full, as The Gauge’s Reading takes the gauge's.

Over Bass Strait, the correction SWOT's product supplies for its tilt across the swath (the strip of sea the radar maps on either side of the satellite's path) reached 53 mm per kilometer, more than 3 m across 60 km. With it applied, the mission's reprocessed Level 2 heights differed from nine GNSS buoys by a mean of −10.3 mm and a standard deviation of 33.3 mm across single daily passes⁠¹⁠.

The Error Itself

Imperfect knowledge of the satellite's roll to one side, of the radar's phase and timing, or of its mast's length becomes a height error of a known shape, an offset for each half of the swath, a tilt, and a shallow curve⁠²⁠, so at a distance $x$ across the swath the error reads $a + b\,x + c\,x^2$, with $a$ taking one value for each half. In flight, the tilt dominated, at about 60 cm in its slow changes over the 120-day period of the Sun's angle to the orbit and about 15 cm at the period of one orbit, and the errors mattered only for patterns longer than about 1,000 km along the track⁠³⁠. We read that as the gauges on one pass sharing most of whatever error is left.

Some of these errors change slowly rather than from pass to pass. The mast expands and contracts with heat, and a varying vertical velocity of the spacecraft can leave a slowly changing height error of up to 2.5 cm, which the crossover correction could remove in part. As the team studying the Severn Estuary read the mission's release notes, slow variations of about 1 cm were not yet corrected, and a further calibration of about 1 cm was due in later releases⁠⁴⁠. Near the coast, the satellite's reading degrades for reasons of its own, since land inside the radar's footprint contaminates the returned signal, the dry troposphere correction degrades toward the shore, and the wet troposphere correction varies strongly there⁠⁴⁠.

Left half

Right half

Tilt

Curve

Move a slider

One lane per gauge on the pass, from the swath’s left edge to its right, the dot its error now and the bar its change on the last move. The coast, tracks, and gauges are real, and the shape’s sizes illustrative, not measured.

Commit47945eaDataschedule.jsonUnreleased1.2.0

Its Measured Size

In Flight

The in-flight figures come from comparing SWOT's heights across the swath with each other and with the satellite's nadir altimeter (a conventional radar looking straight down), a test that cannot detect an error both instruments share, such as one in the orbit⁠³⁠. The Bass Strait buoys give an absolute check, because they observe the sea surface in the satellite's own reference frame, and against them, the earlier product version had a mean of −102.2 mm and a standard deviation of 58.7 mm⁠¹⁠. Over eight months of SWOT's data, three of the terms fitted to that error followed the same 120-day cycle, though not exactly from one cycle to the next, and the authors read the low level of the error at short wavelengths as a highly stable instrument. The bias between the swath and the nadir altimeter shrank slightly from the sixth cycle, which they could not yet explain, and they left the seasonal behavior of the calibration over inland water to studies with several years of data⁠³⁠.

Over more than a year, the tilt the crossover correction removes averaged near zero with no apparent trend, though it reached a couple of meters at the swath's edge at some angles of the Sun. The radar's clock drifted by −0.007 parts per million a year, which the authors find negligible for the heights, and the remaining phase error stayed stable from month to month and year to year, varying by less than 1 mm across the Sun's angles. That correction also sets KaRIn's overall bias to agree with the satellite's nadir altimeter, so the absolute level of SWOT's heights follows that altimeter and the orbit⁠⁵⁠. None of the SWOT studies checks that level against an independent reference over the years. Comparisons with the tide gauge network have exposed instrument problems in past altimeter series, a drifting water vapor radiometer among them⁠⁶⁠.

Against the Gauges

SWOT's repeat orbit retraces one path every 21 days, and its swaths overlap enough that most places are measured about every 11 days on average, as the mission overview sets out. For its first three months, SWOT repeated a one-day orbit instead, and over the Severn Estuary, where two swaths cross, those daily passes gave as many matches as about three years of the 21-day orbit, or about 5.6 years where no swaths cross⁠⁴⁠.

The first Severn study, like the second⁠⁷⁠, read those daily passes, taking the Level 3 heights that AVISO builds from SWOT's own. It added back the mean sea surface, the tide, and the sea's response to air pressure and wind, since the global tide models are inaccurate in the estuary and a gauge records the local pressure and wind as well⁠⁴⁠. The Sensor’s Height sets out the chain of references that put this sum and the gauges on one geoid. Rebuilding a Height sets out what Tidemark adds back, and Level 3's Differences sets the product's corrections beside the Level 2 samples it keeps.

Those heights matched the gauges about as closely as CryoSat-2, an older radar altimeter built to measure ice that also measures water. CryoSat-2's heights from 2012 to 2023 differed from every gauge around the estuary, those outside SWOT's swath included, by a root mean square of 0.165 m, beside SWOT's uncorrected figure in the table below. The authors judged SWOT of similar quality rather than better, and the two comparisons covered different years and gauges⁠⁴⁠.

SWOT's own figure depends on which gauges each comparison keeps and what it removes from them. Every row below reads the Level 3 Expert heights at 2 km, version 2.0.1, against the gauges inside SWOT's swath, leaving out those the river flow and the seabed affected, on the rising tide alone, from 31 March to 10 July 2023, with the outliers removed⁠⁴⁠.

Gauges	Removed From Each Gauge	Root Mean Square	In the Study
Every gauge	Nothing	0.128 m	Section 3.5, Figure S2
Every gauge	Its slope against the water level	0.137 m	Section 3.5, Figure 8
Every gauge	Its slope and its offset	0.101 m	Section 3.5, Figure S3
Every gauge but the low-cost ones	Its slope	0.102 m	Section 4, Figure S4
One gauge at a time	Its slope	0.059 to 0.150 m	Section 3.5, Figures S12 to S18

The 0.101 m and 0.102 m figures come out close while measuring different things, since the first removes each gauge's offset and keeps the low-cost gauges, whereas the second leaves those gauges out, and the study's text names no offset removal for it. A figure numbered with an S sits in the study's supporting information.

Over the 21-day orbit that followed, about 40 cycles from August 2023 to December 2025, the mission's Level 2 KaRIn Low Rate Expert product, Version D, whose Expert and Unsmoothed files Tidemark fetches, differed from 12 NOAA gauges from Rhode Island to Florida's Gulf coast by a root mean square of 0.295 m across every pass, with a correlation of 0.998. Station by station, the figure ran from 0.146 m at Lewes to its highest at Mayport. It sits well above the Severn figures partly because the East Coast team compared each gauge with the single nearest valid pixel, and corrected no station for an offset of its own, so each station's constant difference stays inside the figure⁠⁸⁠.

Workarounds in the Studies

The correction is fitted at crossovers, the regions where a northbound and a southbound pass overlap, where the difference between the two cancels the slow part of the ocean and leaves the tilt and the curve to be estimated:

• In simulations before launch, that fit left 1.5 to 2.2 cm over the ocean, with the hard part being to tell the error from a real slope of the sea surface⁠²⁠.
• The Level 2 product from PO.DAAC carries the correction as a separate field, which three of the teams added to the heights themselves⁠¹⁹⁸⁠.
• AVISO's Level 3 product instead applies a research correction, which left less variability than the Level 2 one in flight⁠³⁠.
• The East Coast team kept only the pixels that passed the Level 2 product's quality flags, whereas the Severn team applied none of the Level 3 product's flags, which are tuned for the open ocean and would remove most points near the coast⁠⁸⁴⁠. The second Severn study, on AVISO's Level 3 Unsmoothed product at 250 m, could apply no quality flags either, since fill values near the coast had already excluded some of the pairs⁠⁷⁠.
• The first Severn team pointed to the Level 3 handbook and the product's release notes for each version's corrections and known problems, and version 2.0.1 lost data over the estuary on 78 of 97 daily passes to a processing fault, leaving about 75 percent fewer points at Newport and Avonmouth than version 0.3⁠⁴⁠.
• Near the coast, a weather model's correction for the wet troposphere (water vapor in the lower atmosphere, which delays the radar pulse) matched the onboard radiometer's accuracy and kept many more valid cells, because land in the radiometer's view contaminates its reading, in a study that left out everything within 5 km of the coast, where every gauge Tidemark reads sits⁠⁹⁠.

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1. 1Hay 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↩︎ ↩︎ ↩︎

2. 2Dibarboure et al. 2022. "Data-Driven Calibration Algorithm and Pre-Launch Performance Simulations for the SWOT Mission." Remote Sensing 14(23): 6070. https://doi.org/10.3390/rs14236070↩︎ ↩︎

3. 3Ubelmann et al. 2024. "Data-Driven Calibration of SWOT's Systematic Errors: First In-Flight Assessment." Remote Sensing 16(19): 3558. https://doi.org/10.3390/rs16193558↩︎ ↩︎ ↩︎ ↩︎

4. 4Lichtman 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↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎ ↩︎

5. 5Chen et al. 2026. "Static Calibration of the KaRIn Radar for the SWOT Mission." IEEE Transactions on Geoscience and Remote Sensing 64: 5209715. https://doi.org/10.1109/TGRS.2026.3698772↩︎

6. 6Ray 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↩︎

7. 7Rong 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↩︎ ↩︎

8. 8Fan 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↩︎ ↩︎ ↩︎

9. 9Gómez-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↩︎ ↩︎