A data-driven analysis of inhomogeneous wave field based on two-dimensional Hilbert–Huang transform

Quantitative characterization of the wave field nearshore is critical for coastal applications. The spatial inhomogeneity of the coastal wave field poses challenges to conventional Fourier analysis. To address this issue, we propose a data-driven analysis framework based on the adaptive two-dimensional Hilbert–Huang transform, the accuracy of which is first demonstrated using synthetic wave data. We then conduct wave-phase-resolved simulations based on a high-order spectral method, where the initial wave conditions are constructed for sea states with various wave field properties and the bathymetry profile varies continuously from deep water to shallow water. The impact of varying bathymetry is observed on the raw data obtained from the simulation and the large-scale components obtained from the empirical mode decomposition of the raw data. We also calculate the Hilbert spectrum and identify the features of coastal wave processes including refraction, shoaling and breaking. We propose three integral quantities to characterize the spatially-variant wave field, including the direction angle, the characteristic wavenumber, and the wave energy. Further discussions on the limitations of the conventional Fourier analysis and the Hilbert–Huang transform are also provided.