The Sensor’s Height ​

Beyond what either instrument gets wrong, which The Gauge’s Reading and The Satellite’s Reading take, every height a gauge reports rests on the elevation its sensor was installed at.

At Rodrigues in the Indian Ocean, two calibration cables switched during a site visit in October 2013 made a radar gauge report the sea 43 mm too high, and the cause came to light only after a comparison with satellite altimetry found a step of 32 ± 6 mm in the series⁠1⁠.

The Error Itself ​

The elevation of a sensor above a datum (the reference level that heights are measured from) is one surveyed number, and an error in it is the same at every reading, so nothing in the gauge's own series reveals it. Against a satellite, it appears as a fixed offset at that gauge, and around the Severn Estuary, where only some of the gauges had leveling reports of a known standard, One Study’s Budget lists the size the team expected of such an error⁠2⁠.

Other constant errors look the same, as 12 NOAA gauges along the US East Coast show. Each gauge's readings went from NAVD 88 onto the NAD83(2011) ellipsoid through VDatum and the GEOID18 model, then into ITRF2014 through NOAA's time-dependent positioning model, and were then corrected for the land sinking beneath every one of them, at 0.3 to 2.5 mm a year from the Nevada Geodetic Laboratory's GNSS rates. Even so, each kept a mean difference of its own (gauge minus SWOT), which the authors put down to land in the radar's view, to the datum conversion, and to pixels as far as 50 km from the gauge⁠3⁠. Offset Beside Scatter gives its extremes, at Mayport and Lake Worth Pier.

Land moving under a gauge shifts its sensor in the same way, although slowly. Around the Severn, the same budget lists its trend, and the GNSS stations at Newport and Swansea recorded ranges of about 20 mm and 25 mm over the years each ran. The team left it uncorrected, since it was small over three months of data and the nearest GNSS station, at Newport, had closed in 2009, whereas GNSS stations near each gauge could correct it over a longer comparison⁠2⁠.

The gauge’s recordThe satelliteSensorOn record43 mmThe same gap at every passThe record alone looks right
Drag On record

The tide and passes are illustrative, not measured, the gap drawn far larger against the tide than in life. It starts at Rodrigues’s 43 mm and runs over the 12 to 104 mm the method found at ten gauges in one altimetry product.

Its Measured Size ​

The Rodrigues step came from a method applied at ten gauges, which forms the satellite-minus-gauge series, removes the seasonal rise and fall of sea level, and fits the step and a linear trend together by least squares. The steps ran from 12 to 104 mm in one altimetry product and from 5 to 103 mm in the other. Altimetry alone cannot tell a lost reference level from sudden land movement, so each step was checked against nearby geodetic stations, which record land motion, and against maintenance logs. A step of 1 to 2 cm is also detectable only where the satellite and the gauge record the same ocean signal, which is likeliest at small islands in the open ocean⁠1⁠.

In the Severn, removing each gauge's own offset along with its slope against the water level brought the whole network to its lowest root mean square against SWOT, which Against the Gauges sets beside the study's other figures. That offset takes up a gauge's leveling error and any bias in the satellite's orbit together⁠2⁠.

The Severn team's chain of references shows where such constants enter. Each gauge's series went from Ordnance Datum Newlyn onto the ellipsoid through the Ordnance Survey's own tool and then onto the EGM2008 geoid, as SWOT's heights did. That geoid, whose accuracy the budget lists, has a resolution near 2 km in an area where it rises and falls by about 1.5 m over 50 km. The geoid model a gauge was surveyed on mattered by itself, since moving the Severn Bridge gauge from the Ordnance Survey's 2002 model to its 2015 one shifted it by 0.03 m⁠2⁠. The second Severn study made the same conversion from Ordnance Datum Newlyn to EGM2008 with PyProj and the Ordnance Survey's transformation grids, noting that the transformation's accuracy has not been validated more than 1 or 2 km offshore, and put the leveling of the network's gauges at better than 0.1 m. The same study notes that Version C of the pixel cloud and the raster interpolates the geoid with an offset of half an arcminute, which shifted heights by typically less than 5 cm over the Severn, and it does not say whether the Level 3 heights behind its gauge comparison carry the same offset⁠4⁠.

Offset Beside Scatter ​

The East Coast study reported each station's root mean square beside an unbiased root mean square, the same figure computed after removing the mean difference, and the two split each station's error in two, since the square of the first is the square of the mean difference plus the square of the second. At Mayport, the 0.459 m total holds a constant offset of −0.371 m beside 0.270 m of scatter from pass to pass, and at Lake Worth Pier the 0.292 m total holds an offset of 0.252 m beside 0.148 m of scatter⁠3⁠. We read that split as the one Tidemark's estimate rests on, because the scatter shrinks as passes accumulate while the offset stays, and the offset is the constant the sensor's height and every other fixed error share.

Workarounds in the Studies ​

The studies either send someone back to the site or keep the offset inside the analysis:

  • A step found from orbit leads back to the station's logs and equipment, where the Rodrigues fault was found and corrected, and an adjustment those logs cannot explain stays out of the gauge archives⁠1⁠.
  • The Burnie gauge in Bass Strait is tied to benchmarks by regular leveling (surveying a gauge's height against marks on land), which was repeated after tug boats struck the gauge in January and July 2007⁠5⁠.
  • A Bayesian model of 36 gauges from the northeast coast of North America treats each gauge's datum offset as an unknown. On synthetic data, fixing the model's parameters made its 95 percent intervals hold the true values 77.1 percent of the time, against 95.6 percent with them free, and the datum parameters accounted for most of the loss⁠6⁠.

However the offset is handled, it limits the error budget. At Bass Strait, the standard error of each altimeter's mean bias came to 2 to 4 mm, whereas the realistic total was 16 to 20 mm, dominated by errors in the reference's own datum, which do not average away⁠5⁠.

  1. 1Ray 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↩︎ ↩︎ ↩︎

  2. 2Lichtman 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↩︎ ↩︎ ↩︎ ↩︎

  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. 4Rong 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↩︎

  5. 5Watson et al. 2011 Absolute Calibration in Bass Strait, Australia: TOPEX, Jason-1 and OSTM/Jason-2 Marine Geodesy 34(3–4): 242–260. https://doi.org/10.1080/01490419.2011.584834↩︎ ↩︎

  6. 6Piecuch et al. 2017 Comparison of Full and Empirical Bayes Approaches for Inferring Sea-Level Changes From Tide-Gauge Data Journal of Geophysical Research: Oceans 122(3): 2243–2258. https://doi.org/10.1002/2016JC012506↩︎