Stochastic simulations of ocean waves: An uncertainty quantification study

Keywords: Ocean wave modeling Uncertainty quantification Generalized polynomial chaos Sparse grid collocation Sensitivity analysis Karhunen–Loeve decomposition a b s t r a c t The primary objective of this study is to introduce a stochastic framework based on generalized polynomial chaos (gPC) for uncertainty quantification in numerical ocean wave simulations. The techniques we present can be easily extended to other numerical ocean simulation applications. We perform stochastic simulations using a relatively new numerical method to simulate the HISWA (Hindcasting Shallow Water Waves) laboratory experiment for directional near-shore wave propagation and induced currents in a shallow-water wave basin. We solve the phased-averaged equation with hybrid discretization based on discontinuous Galerkin projections, spectral elements, and Fourier expansions. We first validate the deterministic solver by comparing our simulation results against the HISWA experimental data as well as against the numerical model SWAN (Simulating Waves Nearshore). We then perform sensitivity analysis to assess the effects of the parametrized source terms, current field, and boundary conditions. We employ an efficient sparse-grid stochastic collocation method that can treat many uncertain parameters simultaneously. We find that the depth-induced wave-breaking coefficient is the most important parameter compared to other tunable parameters in the source terms. The current field is modeled as random process with large variation but it does not seem to have a significant effect. Uncertainty in the source terms does not influence significantly the region before the submerged breaker whereas uncertainty in the incoming boundary conditions does. Considering simultaneously the uncertainties from the source terms and boundary conditions, we obtain numerical error bars that contain almost all experimental data, hence identifying the proper range of parameters in the action balance equation. We first present an overview of the action balance equation along with the numerical model, a description of the HISWA experiment, and a review of the stochastic modeling approach we employ. We then present the objectives of this work and the organization of the rest of the paper. 1.1. Phase-averaged equation and source terms We model ocean waves through the spectral ocean wave equation (Holthuijsen, 2007; Young, 1999) also referred to it as phased-averaged model. We solve for the energy density (or action density) to obtain important statistical wave parameters, such as the significant wave height, mean wave period, etc. The phase-averaged model is well suited for slowly varying wave fields, such as ocean waves in deep water, and it is more appropriate for large …