Learning extreme wave run-up conditions

Wave inundation in coastal regions is an ubiquitous hazard, and near-shore bathymetric variations can significantly influence the dynamics of such events. A multifaceted approach is developed in this work to identify environmental conditions, primarily the coastal profiles, aiding in extreme wave run-ups. The near-shore bathymetry profile is approximated using a Gaussian process model. The latter is then used for simulation of waves using a finite-volume based numerical approach approximating nonlinear shallow water equations. Optimization is performed in the framework of Bayesian optimization which uses the generated information to build a surrogate model for the wave run-up objective function, and then uses an acquisition function to sequentially determine the next-best query point in its feature space. We show that certain bathymetry geometries can lead to resonant run-ups that are larger than known results of maximum run-up on a plane beach. Another mechanism, possibly resulting from the interaction of the trailing and the preceding bore, can also lead to extreme run-ups, although much lower in magnitude than in the resonant case. We also perform a few case studies with N waves, as well as on bathymetric conditions for least wave-run ups. Application of the approach in conceptual designing of coastal structures is also demonstrated.