A quadtree-adaptive spectral wave model

A spectral wave model coupling a quadtree-adaptive discretisation of the two spatial dimensions with a standard discretisation of the two spectral dimensions is described. The implementation is greatly simplified by reusing components of the Gerris solver (for spatial advection on quadtrees) and WAVEWATCH III (for spectral advection and source terms). Strict equivalence between the anisotropic diffusion and spatial filtering methods for alleviation of the Garden Sprinkler Effect (GSE) is demonstrated. This equivalence facilitates the generalisation of GSE alleviation techniques to quadtree grids. For the case of a cyclone-generated wave field, the cost of the adaptive method increases linearly with spatial resolution compared to quadratically for constant-resolution methods. This leads to decrease in runtimes of one to two orders of magnitude for practical spatial resolutions. Similar efficiency gains are shown to be possible for global spectral wave forecasting.