Nonlinear coastal wave prediction with a hybrid approach using phase-resolving models and machine learning

The topo-bathymetry conditions in the coastal areas lead to nonlinear wave transformations and inhomogeneous wave fields that can not be readily described by offshore wave spectra. These nonlinear wave transformations also pose limitations on phase-averaged modelling approaches that are often used for offshore wave forecasting. For example, wave diffractions around islands and coastal structures can not be sufficiently represented with spectra wave models. Phase-resolving models are required for a more realistic representation of the nonlinear wave transformations in complex coastal topo-bathymetry conditions. However, this endeavour often requires increased computational cost compared to the phase-averaging modelling approach. If a certain area of interest is at the focus, for example, a harbour or an especially vulnerable beach, then a site-specific machine learning (ML) algorithm can be used to develop an offshore-to-coast wave correlation that enables fast coastal wave predictions after the nonlinear wave transformations. As the in-situ data are often scarce, the phase-resolving models can be used to represent the nonlinear coastal waves and produce a large set of synthetic data to train the machine learning algorithms. A trained machine learning model using the phase-resolving numerical data can then predict coastal waves given any offshore condition. The offshore conditions themselves can also be predicted with a machine-learning algorithm based on the hindcast data. In this study, a coastal site in Norway is set at the focus. The hindcast data from the open-access database NORA3 provided by the Norwegian Meteorological Institute are used as inputs for numerical simulations of various sea states. With these inputs, the nonlinear wave transformations are represented with the phase-resolving models within the open-source hydrodynamic framework REEF3D. The simulated post-transformation coastal waves are used to train a feedforward neural network (FNN). The trained algorithm can then give near-instant predictions on the coastal wave properties with any given offshore condition. The offshore hindcast time histories in NORA3 are also used to train a long-term short-term memory (LSTM) ML model to predict future events in 3 months. With the predicted offshore waves using NORA3-LSTM, the FNN algorithm trained with REEF3D simulation data can provide coastal wave forecasting for future events. The hybrid approach of phase-resolving models and machine learning utilizing the NORA3-LSTM-REEF3D-FNN combination demonstrates the possibility of fast nonlinear post-transformation coastal wave forecast at key coastal sites characterized by complex topo-bathymetry conditions.