Belgian Tide Gauges Reveal Hidden Uncertainty in the Ocean’s Lowest Limits

Along the windswept coast of Belgium, where the North Sea squeezes through shallow channels and surges against some of Europe’s busiest shipping lanes, the difference between a safe voyage and a grounded vessel can come down to a single number: the lowest level the tide can ever reach. That number, known as the Lowest Astronomical Tide, or LAT, is the foundation upon which nautical charts are built and the benchmark against which under-keel clearances are measured. Now, a team of Belgian researchers has delivered the most rigorous station-by-station assessment of LAT ever attempted in Belgian waters, and the results reveal just how sensitive this critical datum is to the choices scientists make when analysing the tide itself.

The study, led by Somayeh Abdollahi of Ghent University together with colleagues from Flanders Hydraulics, the National Geographic Institute, and the Agency for Maritime and Coastal Services, harnessed twenty-three years of high-resolution water-level observations recorded between 2001 and 2023. Four tide gauges anchored the analysis: Nieuwpoort and Oostende on the open coast, the harbour station at Zeebrugge, and the offshore Westhinder platform, designated MP7, which stands sentinel over the shipping approaches far from land. For the first time in Belgian waters, the team systematically compared multiple analysis windows, reconstruction strategies, and tidal-constituent selection procedures, all within the widely used UTide harmonic-analysis framework developed by David Codiga at the University of Rhode Island.

Harmonic analysis is the classical engine of tidal science, tracing its lineage back to Arthur Doodson’s landmark 1921 decomposition of the tide-generating potential. The idea is elegant: the tide at any location can be represented as the sum of dozens of sinusoidal constituents, each with a precisely known astronomical frequency but an amplitude and phase that must be estimated from observations. Once those amplitudes and phases are locked in, the tide can be predicted forward or backward in time indefinitely. LAT is then defined as the lowest water level the astronomical tide alone can produce, excluding the chaotic contributions of storm surges and weather. In practice, however, the answer depends heavily on which constituents are included, how long a record is analysed, and how the reconstruction is performed.

The researchers confronted this methodological fragility head-on. They tested four period-selection approaches, labelled M1 through M4: a single long-record harmonic analysis spanning 2001 to 2019 with annual reconstructions; separate year-by-year analyses; annual analyses used to predict the following nineteen years; and a sophisticated complex averaging of annual harmonic coefficients that preserves the vector nature of tidal amplitudes and phases. Each method was applied at all four stations, and the spread in the resulting LAT estimates turned out to be far from trivial, underscoring that a single ‘correct’ LAT value is an illusion unless the analytical recipe is specified precisely.

Equally consequential was the choice of tidal constituents. The team compared three selection strategies: the default constituent set offered by UTide, a fixed set traditionally used by the Dutch hydrographic service, and a novel iterative procedure guided by the spectrum of the analysis residuals. In the residual-spectrum-guided approach, the researchers analysed the tide, examined the frequency content of what remained unexplained, and added constituents corresponding to prominent residual peaks, repeating the process until the spectrum was clean. This data-driven strategy, implemented entirely with UTide routines, emerged as the preferred configuration, capable of capturing shallow-water constituents that generic or borrowed constituent sets overlook in the complicated hydrodynamics of the southern North Sea.

The preferred configuration, based on the 2001–2019 input window, yielded deterministic LAT values of −0.648 metres at Nieuwpoort, −0.499 metres at Oostende, −0.251 metres at Zeebrugge, and −0.300 metres at the offshore Westhinder station, all expressed relative to the Belgian national height datum TAW/DNG. The pronounced spatial variation, with LAT nearly half a metre deeper at Nieuwpoort than at Zeebrugge, reflects the complex interplay of coastal geometry, bathymetry, and shallow-water tidal dynamics along the Belgian coast. No single conversion grid, the researchers caution, can faithfully represent such station-specific behaviour without careful local calibration.

To quantify how confident one can be in these numbers, the team propagated uncertainty in the harmonic parameters using 1000 Gaussian Monte Carlo realisations, perturbing the estimated amplitudes and phases according to their statistical uncertainties and recomputing the LAT minimum for each realisation. The resulting conditional standard deviations were remarkably tight, ranging from 0.0031 to 0.0034 metres, suggesting that once the harmonic model and constituent set are fixed, the LAT estimate is numerically robust. The authors are careful, however, to frame this spread as conditional on the chosen model rather than a complete uncertainty budget; it captures parameter uncertainty but not the full spectrum of errors that could affect an operational datum.

The Monte Carlo experiments also delivered a reassuring message about computational practicality. Comparing ensembles of 500 and 1000 realisations across the four period-selection methods produced maximum absolute differences of only 0.007 metres in the Monte Carlo mean, 0.009 metres in the conditional standard deviation, and 0.020 metres in one percentile-interval bound. For the preferred residual-spectrum-guided configuration, those differences shrank further to 0.003, 0.004, and 0.006 metres respectively. In other words, halving the ensemble size barely moves the answer, a finding that will ease the computational burden for hydrographic offices considering similar analyses elsewhere.

Throughout the study, the researchers treated existing operational products, including station values published by the Agency for Maritime and Coastal Services and the official LAT conversion grid, as consistency benchmarks rather than independent ground truth. This distinction matters: the operational values were not used to validate the new estimates in an absolute sense, but to check whether the updated analysis remains compatible with the datums that Belgian mariners and coastal engineers rely on today. The deterministic LAT, defined as the minimum of the unperturbed harmonic reconstruction, and the Monte Carlo mean, the average of minima across perturbed realisations, were deliberately reported separately, since the two quantities answer subtly different questions.

The broader significance of the work extends beyond Belgium’s short coastline. The 18.61-year nodal cycle, in which the lunar orbit’s precession modulates tidal amplitudes by up to tens of centimetres, means that short analysis windows can bias LAT estimates substantially, a phenomenon documented in tide-gauge records worldwide. By demonstrating the value of a nineteen-year input window, roughly one full nodal cycle, and by providing a reproducible framework for constituent selection and uncertainty propagation, the Belgian team has offered a template that other hydrographic services can adapt. As sea levels rise and extreme water levels evolve, the low end of the tidal envelope deserves the same scrutiny as the high end, and this study shows exactly how that scrutiny should be applied. The tide-gauge data underpinning the analysis remain freely available through the Meetnet Vlaamse Banken portal, inviting researchers everywhere to test, refine, and extend the approach.

Subject of Research: Assessment of Lowest Astronomical Tide at Belgian North Sea tide gauges using long-term harmonic analysis and residual-spectrum-guided constituent selection

Article Title: Assessment of lowest astronomical tide at belgian north sea tide gauges using long-term harmonic analysis and residual-spectrum-guided constituent selection

Article References: Abdollahi, S., Vanlede, J., Verbeurgt, J., Verstraeten, J., De Kuyper, A., Gurdebeke, P., & De Wulf, A. (2026). Assessment of lowest astronomical tide at belgian north sea tide gauges using long-term harmonic analysis and residual-spectrum-guided constituent selection. Ocean Dynamics, 76(9), Article 96. https://doi.org/10.1007/s10236-026-01850-3

Image Credits: AI Generated

DOI: 10.1007/s10236-026-01850-3

Keywords: Lowest Astronomical Tide, Belgian North Sea, harmonic analysis, tide gauges, tidal constituents, UTide, Monte Carlo uncertainty, vertical datum, ocean dynamics, hydrography, coastal sciences, residual spectrum