Adaptive Haar wavelets for the angular discretisation of spectral wave models

A new framework for applying anisotropic angular adaptivity in spectral wave modelling is presented. The angular dimension of the action balance equation is discretised with the use of Haar wavelets, hierarchical piecewise-constant basis functions with compact support, and an adaptive methodology for anisotropically adjusting the resolution of the angular mesh is proposed. This work allows a reduction of computational effort in spectral wave modelling, through a reduction in the degrees of freedom required for a given accuracy, with an automated procedure and minimal cost.