A Novel Similarity Index for Wave Spectra Comparison

Abstract

This paper introduces a spectral similarity index based on an optimal-approximationprocedure combined with an energy-weighted residual penalty. The method identifies thesubset of wave systems from one directional wave spectrum whose spectral content consti-tutes the optimal approximation to a second directional wave spectrum, while penalizingunmatched residual energy, thereby ensuring sensitivity to both structural agreementand energetic consistency. The framework is symmetrized by construction, invariant topartition ordering, and designed to emphasize dominant discrepancies while remainingresilient to weak perturbations. Systematic experiments demonstrate the ability of theindex to distinguish differences arising from directional misalignment, energy scaling, andmultimodal spectral composition. Owing to its physically interpretable formulation andrigorous treatment of spectral similarity, the proposed index provides a robust and ob-jective tool for the quantitative comparison of directional wave spectra, with potentialapplications in wave model validation, remote sensing calibration, spectral assimilation,and the assessment of spatial and temporal wave-field homogeneity.