The Gauge’s Reading ​

This page takes in full the first of The Four Error Sources, the error a tide gauge brings to the comparison before any satellite enters it, in the scatter of each reading and in whatever shift the conditions around its sensor add.

The Error Itself ​

The shift the conditions around the sensor add matters more than the scatter from one sample to the next, since it repeats rather than averaging away. Maine's low-cost gauges are ultrasonic and radar sensors that report the distance down to the water⁠1⁠, and the station catalog holds the type where a source states it. An ultrasonic sensor's distance depends on the air beneath it, whereas a radar sensor's does not. Hohonu's Quality Control Procedures for Real-Time Water Level Data give MaxBotix's HRXL-MaxSonar-WR datasheet as its ultrasonic sensors' specifications, and the datasheet states that the sensor corrects the speed of sound with a temperature sensor inside its own housing. The same datasheet warns that the air between the sensor and its target can differ from the air at the sensor, and recommends for the best accuracy an optional external temperature sensor mounted midway along the path. Hohonu's procedures add that each ultrasonic sensor samples once a second and averages every 30 seconds onboard, dropping the samples more than three standard deviations from that mean, whereas its radar sensors apply no such step. Neither document says whether a Hohonu gauge carries the external sensor or corrects its readings after they reach the server.

The low-cost gauges in a study of the Severn Estuary in the United Kingdom instead read the water level from navigation-satellite signals reflected off the surface⁠2⁠, so the size of their scatter does not carry over. Their scatter came from the patch of water each one reads moving as the navigation satellites pass overhead, from wind and waves roughening the surface, and from the delay in the troposphere, reflections off other surfaces, and the time each reading aggregates, and it grew at the gauge mounted higher, since it samples a wider area⁠2⁠.

UltrasonicRadarHousing 20 °CAir 32 °C3.1 cm shortreads true

Illustrative, not measured, on a 3 m path with sound at 331.85√(1 + 0.00183 T) m/s, after Theodoro et al. 2023.

Its Measured Size ​

Every approach in the studies needs a second series of the same water. In Bass Strait, Australia, pairs of GNSS buoys (floats that fix the sea surface's height from navigation satellites) moored less than 400 m apart differed by a standard deviation of 6.5 mm⁠3⁠. Along the coast of East Asia, triple collocation, which solves for the random error of each of three independent series without taking any as the truth, gave hourly tide gauges an error variance of 0.005 m² beside 0.010 m² for SWOT⁠4⁠.

Two field tests measure what the air temperature does to a low-cost ultrasonic water level sensor. On a farm in Brazil, the uncorrected distance from an HC-SR04 sensor fixed above a concrete slab fell as the air warmed, with a Spearman correlation of −0.933 over a year spanning 0 to 44.6 °C, and recomputing the speed of sound from a separate reading of the air temperature kept its readings on dry days within 5 mm of their mean of 41.48 cm, against an installed height of 41.45 cm⁠5⁠.

Over a stream in Athens, an HRXL-MaxSonar-WR correcting for temperature inside its own housing still differed from a pressure transducer beside it by an amount that followed the air temperature, with a correlation of 0.67, though never by more than 7 percent of the stage. Through the warm dry months it read the water higher than the transducer, by up to about 6 percent overnight, which the authors put down to the speed of sound rising despite the correction, whereas on afternoons above 30 °C its stage dipped by 2 to 3 cm toward the transducer's, which they partly attribute to the sensor's own calibration⁠6⁠. We read that daily dip as a correction that overshoots once the sun heats the sensor's housing, since an uncorrected sensor would read the water higher as the air warms.

Over an outdoor test channel in Korea, about 2 cm of scatter remained in an ultrasonic sensor's readings once the outliers were removed, which the authors attribute to waves on the flowing water, citing earlier work, and treat as random, so averaging narrows it. They did not test whether the waves leave a reading consistently high or low, and their waves were far smaller than swell or wakes on a coast⁠7⁠. Temperature appears once more, as "unresolved temperature related effects within the tide gauge" among the possible causes of a 27 mm residual between an acoustic tide gauge in Bass Strait and a mooring offshore⁠8⁠. None of the studies measures what humidity does to an ultrasonic gauge, what temperature or waves do to a radar gauge, or whether waves bias an ultrasonic one, and the published account of Maine's network reports no accuracy figure for its sensors⁠1⁠.

Workarounds in the Studies ​

Most teams carry the gauge's noise inside the comparison rather than correcting it:

  • The Severn team reported its result with and without the noisier gauges, and since the figure without them holds each gauge's error as well as SWOT's, it bounds the conventional network's own uncertainty, which sits close to the 0.1 m limit set for the UK's network⁠2⁠.
  • The same team dropped each gauge whose matches all fell below the 1:1 line of a plot of one series against the other, which they traced to river flow and the seabed around it rather than to either instrument⁠2⁠.
  • At gauges that dry out at low water, where the series flattens at the river or bed level while the satellite still measures water offshore, they found that level from the bottom half of each tide and dropped the satellite's points below it⁠2⁠.
  • The Bass Strait comparison entered its acoustic gauge's residual into its error budget as the gauge's precision⁠8⁠.
  • A second Severn study treated its gauges as error free, which assigns its whole 13 cm standard deviation to SWOT, across 98 matches at six gauges with a slope of 0.99, a root mean square (the typical size of the gap between two series) of 0.13 m, and a small bias at every tidal range from 4 to 12 m⁠9⁠.
  • The same study's two pressure sensors on the seabed, corrected for air pressure from nearby stations, differed from SWOT by a root mean square of 0.35 m, which the authors put down to their moorings swaying in the waves and currents and to the 10-minute mean of their readings not landing on the instant of the pass⁠9⁠.
  • Both ultrasonic studies corrected the speed of sound from the air temperature, and the Athens team recommends a temperature sensor out of direct sun that reads the air along the sound's whole path. It also reports a thesis from Iowa, where bridge-mounted ultrasonic sensors carried an instability of about 7 cm either way on a strong daily cycle, which the air temperature from a nearby weather station cut by only about 2 cm and a model of the channel's own air temperature cut to about 1 cm⁠56⁠.
  • Maine's network allows the side-by-side test, since an ultrasonic and a radar gauge were installed together at Machias⁠1⁠, which the station catalog carries as two datasets.

  1. 1Baranes et al. 2026 Supporting Coastal Flood Forecasting and Community-Led Adaptation With Tide Gauges, Community Science and Youth Engagement Frontiers in Climate 8: 1757212. https://doi.org/10.3389/fclim.2026.1757212↩︎ ↩︎ ↩︎

  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. 3Hay 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↩︎

  4. 4Zhu 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↩︎

  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. 8Watson 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↩︎ ↩︎

  9. 9Rong 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↩︎ ↩︎