The Four Error Sources ​

A satellite can set a tide gauge's elevation only as well as the two instruments can be compared. Tidemark sets the height the Surface Water and Ocean Topography (SWOT) satellite reports for a patch of water beside the distance a low-cost gauge measures down to it, as The Height From Orbit sets out, and checks each pass against the anchors, meaning NOAA's stations and the USGS gauges in the estuaries, whose elevations are already known. An error can enter that comparison through the gauge's own measurement, the satellite's measurement, the height the sensor was installed at, or the water moving between the two readings, and this page sets the four side by side as published studies measured and handled them, none of it a Tidemark result.

One table holds all four, and each of its rows links the page that takes its source in full.

hS − hgPass by pass
d
hS
z
Error Source

Water moving between the readings

How It Shows Up in the Data

A difference that changes with the tide, the distance to the pixels, and the waves

How Studies Handle It

Read the gauge at the instant of the pass, take the median of nearby pixels, and keep one phase of the tide

Studies

⁠1⁠ ⁠11⁠ ⁠16⁠ ⁠17⁠ ⁠12⁠

Illustrative, not measured.

Every value as a table
#Error SourceHow It Shows Up in the DataHow Studies Handle ItStudies
1The gauge's own measurementScatter from one reading to the next, beside a shift with the conditions that averaging never removesPair two instruments, solve for each series' random error, correct the speed of sound for the air temperature, and budget for the gauge's noise⁠1⁠ ⁠2⁠ ⁠3⁠ ⁠4⁠ ⁠5⁠ ⁠6⁠ ⁠7⁠
2The satellite's measurementA tilt and an offset across the swath that change from pass to passApply the crossover correction, use the reprocessed product, and model the water vapor near the coast⁠8⁠ ⁠9⁠ ⁠2⁠ ⁠10⁠ ⁠11⁠ ⁠12⁠ ⁠13⁠
3The sensor's installed heightA constant offset at one gauge, which averaging never removesLevel again after a disturbance, look for a step from orbit, and carry the offset as an unknown⁠14⁠ ⁠4⁠ ⁠15⁠ ⁠12⁠
4Water moving between the readingsA difference that changes with the tide, the distance to the pixels, and the wavesRead the gauge at the instant of the pass, take the median of nearby pixels, and keep one phase of the tide⁠1⁠ ⁠11⁠ ⁠16⁠ ⁠17⁠ ⁠12⁠

One Study's Budget ​

Before comparing SWOT with the gauges around the Severn Estuary, the team there listed what each source could add in that estuary, drawing most figures from earlier work, and their list falls under three of the same four sources⁠1⁠, leaving out the gauge's own scatter.

SourceTheir EstimateFalls Under
The satellite's orbitAbout 1 cmThe satellite's measurement
Residual error in the spacecraft's roll, the length of its antenna mast, and the drift between its two radar channelsA few cmThe satellite's measurement
The dry and wet troposphere correctionsA few cm to tens of cmThe satellite's measurement
Currents and waves moving the water during the measurementUnder 1 cmThe satellite's measurement
The leveling of each gauge and the motion of the structure it stands on0.1 mThe sensor's installed height
The EGM2008 geoid that both series are moved onto5 to 10 cmThe sensor's installed height
Land moving under the gaugesAbout 1 cm over ten yearsThe sensor's installed height
Shallow water, waves, wind, tides trapped against the coast, intertidal flats, and river outflowUp to tens of cmWater moving between the readings
The sea state bias correction, from an algorithm not tuned to the coastA few cm, since the waves there are smallWater moving between the readings

Taking the Sources Together ​

The sources divide by whether more passes help, which is the division the Bass Strait error budget makes between errors that average with time and errors that do not⁠4⁠. Scatter in the gauge, noise in a single pass, and waves belong to the first kind, whereas an installed height that is off, a bias in the satellite, a datum conversion, and a mean slope between the gauge and its pixels all leave one constant offset⁠1⁠. That constant is what a comparison like Tidemark's has to read as the sensor's elevation, so the work lies in ruling out the other constants. A gauge's own reading sits on both sides of that division, as The Gauge’s Reading sets out.

The anchors show what the comparison leaves over when the installation is not in doubt. An error that every gauge on a pass shares can also be solved for across a whole network at once, as one sky-wide fit did for every night's calibration and every star's brightness, with the caution that a fit built on differences cannot set the overall level without references of known value⁠18⁠.

Offset100%Scatter100%Gauge level
Passes averaged
Pass11248163264

Illustrative, not measured.

Unmeasured Effects ​

None of the studies read here sets a gauge's level from orbit rather than checking it for a change from a number a survey already fixed, and the pages on the gauge and the satellite name what else their studies leave unmeasured. The Severn and East Coast teams did measure each gauge's constant offset from SWOT, the quantity Tidemark estimates, but read it as an error to explain, and at a single gauge it holds the survey's error and any fixed bias in the satellite together, which their comparisons left unseparated⁠112⁠.

  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. 2Hay 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↩︎ ↩︎

  3. 3Zhu et al. 2025 Validation of Sea Level Anomalies From the SWOT Altimetry Mission Around the Coastal Regions of East Asia and the US West Coast Water 17(21): 3066. https://doi.org/10.3390/w17213066↩︎

  4. 4Watson 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↩︎ ↩︎ ↩︎

  5. 5Theodoro et al. 2023 Low-Cost Ultrasonic Sensors for In-Field Experimentation Data Collection Ciência e Agrotecnologia 47: e013422. https://doi.org/10.1590/1413-7054202347013422↩︎

  6. 6Panagopoulos et al. 2021 Assessment of an Ultrasonic Water Stage Monitoring Sensor Operating in an Urban Stream Sensors 21(14): 4689. https://doi.org/10.3390/s21144689↩︎

  7. 7Bae & Ji 2019 Outlier Detection and Smoothing Process for Water Level Data Measured by Ultrasonic Sensor in Stream Flows Water 11(5): 951. https://doi.org/10.3390/w11050951↩︎

  8. 8Dibarboure 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↩︎

  9. 9Ubelmann 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↩︎

  10. 10Gómez-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↩︎

  11. 11Rong 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↩︎ ↩︎

  12. 12Fan 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↩︎ ↩︎ ↩︎ ↩︎

  13. 13Chen 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↩︎

  14. 14Ray 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↩︎

  15. 15Piecuch 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↩︎

  16. 16Vega-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↩︎

  17. 17Oelsmann 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↩︎

  18. 18Padmanabhan et al. 2008 An Improved Photometric Calibration of the Sloan Digital Sky Survey Imaging Data The Astrophysical Journal 674(2): 1217–1233. https://doi.org/10.1086/524677↩︎