A comparison of two spectral wave models in the Southern California Bight

Abstract

Two models, a spectral refraction model (Longuet-Higgins) and a parabolic equation method (PEM) refraction-diffraction model (Kirby), are used to simulate the propagation of surface gravity waves across the Southern California Bight. The Bight contains numerous offshore islands and shoals and is significantly larger (≈ 300 km by 300 km) than regions typically studied with these models. The effects of complex bathymetry on the transformation of incident wave directional spectra, S 0( f, θ 0), which are very narrow in both frequency and direction are difficult to model accurately. As S 0( f, θ 0) becomes broader in both dimensions, agreement between the models improves and the spectra predicted at coastal sites become less sensitive to errors in the bathymetry grid, to tidal changes in the mean water depth, and to uncertainty in S 0( f, θ 0) itself. The smoothing associated with even relatively narrow (0.01 Hz-5° bandwidth) S 0( f, θ 0) is usually sufficient to bring the model predictions of shallow water energy into at least qualitative agreement. However, neither model is accurate at highly sheltered sites. The importance of diffraction degrades the predictions of the refraction model, and a positive bias [O (10%) of the deep ocean energy] in the refraction-diffraction model estimates, believed to stem from numerical “noise” (Kirby), may be comparable to the low wave energy. The best agreement between the predicted spectra generally occurs at moderately exposed locations in deeper waters within the Bight, away from shallow water diffractive effects and in the far-field of the islands. In these cases, the differences between the models are small, comparable to the errors caused by tidal fluctuations in water depth as waves propagate across the Bight. The accuracy of predicted energies at these sites is likely to be limited by the uncertainty in specifying S 0( f, θ 0).