پیش بینی جریان های جزر و مدی با استفاده از یادگیری ماشین بیزی Prediction of tidal currents using Bayesian machine learning

1. Introduction Tidal waves are produced by changes in the gravitational forces of the sun and the moon. Prediction of tidal currents are necessitated by practical requirements like navigation, protection from flooding, coastal management to recent developments of energy extraction. Theoretical understanding of the tidal phenomenon began with Newton pioneering the gravitational theory and then later, Laplace deriving the expression for the tidal potential. There have been many advances in methodologies for tidal analysis since then. The most widely used method is that of the harmonic analysis (HA), where the observed tidal variations are considered as a resultant of various periodic components of known frequencies, with the amplitudes and phases determined using the leastsquares fitting procedure. Computer codes based on HA have been used for decades for the prediction of tidal heights (1-D) and currents (2- D). Over the years various advances have been made to HA approach [see e.g. Pawlowicz et al., 2002; Foreman et al., 2009; Leffler and Jay, 2009]. Other techniques include tidal spectroscopy (Munk and Cartwright, 1966), and response method for unified tide and surge prediction (Cartwright, 1968), however they have not been widely adopted. HA has been extensively used in the analysis of stationary tidal (height) records, providing insights into the tidal dynamics. However, there are several shortcomings of this methodology. One of the challenging tasks in HA is the selection of tidal constituents, which if inaccurate can lead to overfitting of data or numerical issues (Jay and Flinchem, 1999). Appropriate modelling of noise is another issue. In tidal analysis, signals which do not contribute to the tidal variations are classified as ‘noise. In reality, there can be cases where the non-tidal signal is much stronger than the tidal e.g. the occurrence of a stormy event, and many of such effects are non-harmonic. It is difficult to incorporate such effects in the tidal HA formulation. In general, the technique is not suitable for application to non-stationary data (Jay and Flinchem, 1999). HA is also incapable of modelling the spatial variability of tides – this is not a big issue in modelling tidal heights which changes slowly in space, however tidal currents can vary sharply within short distances due to changes in bathymetry and topography. As tides move into shallow waters, they are distorted resulting in overtides (higher harmonics of principal constituents) and compound tides (interaction between different constituents). Such interactions can lead to asymmetry in the flood and ebb magnitudes of the current, depending on the phase relationship (Friedrichs and Aubrey, 1988). In HA, nonlinear characteristics are incorporated with the inclusion of shallow water constituents, some of which may need to be inferred, and such operations are often difficult. Even more complexities can result near headlands (Geyer, 1993), where complex flow structures can result in additional frequencies, which are not necessarily sinusoidal. In relation to the uncertainty estimation, HA generates confidence intervals for the current ellipse parameters (which are often large (Leffler and Jay, 2009)). However, in a lot of practical applications it is more useful to generate confidence interval estimates directly in the time domain.