Spatiotemporal tidal prediction and analysis through physics-informed machine learning

Thesis

Tidal processes—those driven by gravitational forcing from the Earth, Moon, and Sun—shape coastal environments and significantly impact infrastructure. While conventional methods of tidal analysis and prediction perform well for barotropic tides sampled at high temporal resolution, major challenges arise when exogenous non-tidal forcing is present or temporal sampling becomes sparse and irregular. Under these conditions, the accuracy of empirical methods degrades as their underlying assumptions are violated.

This thesis introduces four novel methodologies that advance the prediction and analysis of tidal and tidally driven processes across diverse spatiotemporal scales. Central to each is the augmentation of classical empirical techniques with modern machine learning, reducing reliance on inaccurate assumptions and improving both predictive power and physical interpretability.

The work focuses on two classical approaches to tidal analysis: harmonic analysis and the response method. Each has strengths that suit particular challenges. For harmonic analysis, I develop a Bayesian framework tailored to sparse, noisy satellite altimetry data. This approach enables the exploitation of Surface Water and Ocean Topography (SWOT) mission data, provides uncertainty estimates lacking in existing models, and led to the discovery of an earth-shaking wave using this dataset.

For the response method, I develop an automated, non-parametric procedure—overcoming a major limitation of the classical approach. It is the only method capable of analyzing and predicting arbitrary tidal processes, including tidal rivers and storm surges. I further propose a coupled response theory for predicting tidal currents. This method offers superior predictive accuracy to harmonic analysis and reduces the required time-series duration by nearly an order of magnitude -- a feature that can enhance harmonic analysis as well.

Finally, I consider augmenting all classical methods -- including harmonic, response, and numerical models -- with short-term forecasting using recent data via an online training procedure. These contributions address long-standing limitations in empirical tidal analysis and have broad applications -- from improving satellite data usage to enhancing operational storm surge forecasting. This thesis argues that the `tide problem' remains unsolved and offers tools and solutions to some of its most pressing challenges.

Authors: Monahan, T

• Alternative title: Spatiotemporal tidal prediction and analysis through physics-informed ML
• DOI: 10.5287/ora-ga6zbany4
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: physics-informed machine learning; tidal energy; tides
• Subjects: Machine learning; Civil engineering; Oceanography