RTide: Machine learning enhanced response method for the analysis and prediction of estuarine tides and storm surge

Tides pose significant operational and engineering challenges and are critical drivers of many natural processes. Accurate tidal predictions are important for modeling these phenomena. Conventionally, tidal prediction is carried out using harmonic analysis, the accuracy of which degrades when non-stationary and nontidal forcing are present. While Munk and Cartwright’s response method avoids the assumptions that give rise to this degradation, the difficulty of defining realistic interactions between inputs has inhibited automated applications. Here, we develop a non-parametric framework for tidal analysis and prediction of sea levels under compound forcing. The approach embeds a class of neural networks capable of representing any arbitrary Volterra series—the mathematical basis of the response method—within the classic method. The new ML Response Framework overcomes the automation challenges imposed by the original method and can directly infer high-order nonlinear interactions. This makes the inclusion of meteorological and other non-tidal forcing straightforward. Furthermore, we show that by accounting for this nonstationarity explicitly, a better astronomical tidal estimate is obtained. A method is devised to obtain physical insights from the learned model, illustrating how it can be used to study the interaction and modulation of astronomical tides by external forcing. By taking a nonparametric approach, our framework makes the study of phenomena that heretofore could not be accounted for straightforward. We provide several case studies, including the analysis and prediction of tide-surge interaction, riverine tides, and nuisance flooding. These applications, and more, can be replicated using only three lines of code with the open-source Python package (RTide).