Machine learning reveals how monsoon seasons bend the tide in a Thai estuary

Deep in the inner Gulf of Thailand, where the Bang Pakong River meets the sea, the tide does not behave the way textbook tides are supposed to behave. In shallow, funnel-shaped estuaries like this one, the incoming ocean tide is progressively distorted as it shoals, so that water rises faster than it falls, sediment drifts preferentially landward, and salt pushes further upriver than it otherwise would. A new seven-year analysis of the Bang Pakong estuary, published in Ocean Dynamics, has now quantified that distortion with unusual precision and revealed that it is not a fixed property of the estuary at all: it breathes with the monsoon, strengthening dramatically each year between June and August, when river discharge is at its peak and mean water level drops by nearly fifteen centimetres.

The study, carried out by Pattharaporn Thongnim of the Department of Mathematics at Burapha University in Chonburi, Thailand, rests on an extraordinary dataset: 353,644 water-level readings recorded at roughly ten-minute intervals between May 2019 and June 2026, obtained from the Marine Department of Thailand. Before any analysis could begin, the raw record had to be cleaned. Duplicated timestamps were merged, exact zeros removed, and a suspicious plateau in late 2022, during which the sensor was evidently stuck at between 5.67 and 5.69 metres, was discarded. Isolated spikes were excised with a Hampel filter, a robust statistical technique that rejects values deviating by more than 0.25 metres from a centred 70-minute running median, applied in two passes. Crucially, the threshold was derived from the distribution of the deviations themselves rather than from the residuals of a tidal model, so that genuinely unexplained observations were not thrown away at the screening stage. In total, 1,458 readings were removed, leaving 351,212 clean measurements spanning seven monsoon cycles.

The first analytical step was a classical one. A least-squares harmonic analysis, in the tradition going back to Doodson’s 1921 development of the tide-generating potential, fitted 33 tidal constituents with nodal corrections to the cleaned record. This decomposition explained 94.7 percent of the hourly variance, a remarkably good fit for a shallow tropical estuary. The relative importance of semidiurnal versus diurnal constituents, expressed as a form factor of 1.28, places Bang Pakong firmly in the mixed, mainly semidiurnal regime that characterises the Gulf of Thailand, where the semi-diurnal tide is known to propagate clockwise around the basin.

But the headline finding concerns asymmetry. In a perfectly linear tidal system, flood and ebb would take equal time. In shallow water, nonlinear effects break that symmetry: crests travel faster than troughs, the flood shortens, and the ebb lengthens. At Bang Pakong, measured directly across 7,889 individual tidal cycles, the mean rise takes 6.26 hours while the mean fall takes 8.12 hours, a duration asymmetry of 1.86 hours. That is a strong flood dominance, and it matters enormously for the estuary’s future. Following the framework established by Friedrichs and Aubrey in their 1988 synthesis of tidal distortion in shallow estuaries, flood dominance generally implies net landward sediment transport, which in turn governs whether the channel silts up or scours out, and how far salt intrudes during the dry season.

The real novelty lies in what happens when the analysis is allowed to vary through the year. By permitting annual modulation of the non-degenerate tidal constituents, the study shows that the shallow-water overtides, the harmonic constituents generated by the nonlinear distortion itself, swing seasonally two to three times more than the principal astronomical constituents. Relative seasonal variations of 22 to 37 percent were found for MS4, M4, MO3, MN4 and M6, against just 13 percent for the dominant lunar semidiurnal constituent M2. Every one of these overtides peaks between June and August, precisely when the southwest monsoon drives maximum river discharge and the mean water level sits 14.8 centimetres lower than average. The physical interpretation is compelling: lower mean depth amplifies the nonlinear shallow-water processes that generate the overtides, so the estuary’s tidal distortion is literally modulated by the monsoon.

Not every seasonal signal is straightforward. The M2 amplitude itself shows a statistically significant decline of 0.55 plus or minus 0.09 centimetres per year, a trend reproduced independently in both the wet and dry seasons and therefore not attributable to errors in the nodal corrections that account for the 18.6-year lunar cycle. Meanwhile, attempts to detect annual modulation in the K1, S2 and P1 constituents proved unidentifiable when the S1 and T2 constituents were retained in the model, a degeneracy that would yield physically meaningless amplitudes if ignored. This is a cautionary tale for anyone fitting seasonal tidal models: some apparent seasonal variability is an artefact of constituent interference rather than real physics.

The second methodological pillar of the study addresses a problem that plagues every long-term observational record: gaps. Some 6.4 percent of the hourly water-level values were missing, and rather than simply interpolating, Thongnim turned to Gaussian process regression, a Bayesian machine-learning technique that treats the unknown function as a draw from a probability distribution over functions defined by a covariance kernel. The Gaussian process reconstruction served two distinct purposes. First, it validated the duration analysis: filling the gaps recovered 11.6 percent more complete tidal cycles, and the asymmetry barely moved, settling at 1.83 hours instead of 1.86, confirming that the flood dominance is robust to missing data.

Second, and more subtly, the reconstruction became a testbed for kernel selection. Seven different covariance structures were compared using three independent criteria: closed-form leave-one-out residuals, the Akaike information criterion, and withheld-data experiments. The winner was a two-scale Matérn 3/2 kernel with a semiannual mean term, a choice that captures both short-term tidal roughness and longer seasonal structure. Perhaps the most striking methodological result is that the choice of kernel changes the predictive uncertainty far more than it changes the reconstructed values themselves. In other words, different reasonable kernels agree on what the missing data probably looked like, but disagree substantially on how confident one should be about that agreement, a distinction with real consequences for downstream uncertainty analysis.

Why does this matter beyond one Thai estuary? Monsoon-influenced shallow estuaries line the coasts of South and Southeast Asia, West Africa and tropical Australia, and they host some of the world’s most productive and most densely populated deltas. Tidal asymmetry is the engine of sediment transport in these systems, and if the asymmetry itself varies seasonally by tens of percent, then annual sediment budgets computed from a single season, or from a time-averaged harmonic analysis, may be systematically biased. The finding that shallow-water constituents respond to river discharge and mean water level also provides a sensitive diagnostic for climate-driven change: as sea level rises or monsoon rainfall patterns shift, the seasonal modulation of tidal distortion should shift with them, offering an early warning signal encoded in the tide gauge record itself.

The study also demonstrates how modern statistical machinery can extract more from classical oceanographic data. The combination of a 33-constituent harmonic fit, direct duration statistics across nearly eight thousand tidal cycles, and a carefully validated Gaussian process reconstruction represents a template that can be applied to any long water-level record with gaps. As coastal managers across monsoon Asia grapple with accelerating subsidence, changing sediment loads and intensifying floods, tools like these, which quantify not just the tide but the tide’s seasonal personality, are likely to become indispensable. The Bang Pakong estuary, it turns out, has been quietly broadcasting the signature of its monsoon all along; it simply needed the right mathematics to listen.

Subject of Research: Seasonal variation of tidal asymmetry and Gaussian process reconstruction of water levels in the Bang Pakong estuary, Thailand

Article Title: Gaussian process reconstruction and seasonal change in tidal non-linearity in a monsoon-influenced estuary

Article References: Thongnim, P. (2026). Gaussian process reconstruction and seasonal change in tidal non-linearity in a monsoon-influenced estuary. Ocean Dynamics, 76(11), Article 114. https://doi.org/10.1007/s10236-026-01869-6

Image Credits: AI Generated

DOI: 10.1007/s10236-026-01869-6

Keywords: tidal asymmetry, estuarine tides, shallow-water constituents, seasonal modulation, Gaussian process, covariance kernel, Bang Pakong, monsoon, harmonic analysis, Gulf of Thailand, flood dominance, ocean dynamics