Estimation of long-term harbour wave climates using spectral transfer functions

Long-term harbour wave climates are normally developed using computationally efficient spectral wave models typically based on an action density equation (i.e. SWAN etc.) The processes of wave shoaling and refraction are modelled explicitly, with reflection and diffraction modelled empirically with structures represented as sub-grid scale elements. Whilst this approach works well for open coastal zones, these models do not resolve the diffraction process accurately in the shadow zone of structures, limiting their application for complex layouts of breakwaters normally present around harbours. This is accomplished using computationally-expensive phase resolving Boussinesq or mild-slope equation wave models. However, the computational time of such models limits their application to a limited set of sea-states such as described by a scatter matrix of Hs and Tp. In addition, complex boundary conditions, or multiple runs, are needed for bi-directional or bi-modal conditions. This can limit their application with hindcast, complex, wave climates. In this paper we detail an approach for generating long-term harbour wave climates in terms of the full directional-frequency spectrum. We develop spectral transfer functions (STFs) through spectral analysis of a discrete number of phase resolving (MIKE21 BW) simulations that partition the offshore wave energy spectra into a series of bins. The STFs are validated against several simulated conditions with very good reproduction of the frequency and directional spectra inside the harbour. The influence of the random seed in the boundary condition generation process on the generated STFs is investigated, with interesting insights into the heterogeneity of wave fields inside a harbour. Finally the STFs are applied to (one year) of a 20-year offshore wave hindcast to demonstrate the efficient development of long term harbour wave climates. The advantages and shortcomings of the STF approach are outlined, with examples of the transfer of (dual-peaked) sea-states not easily reproduced at the boundary of phase resolving models.