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

Assessment of ERS synthetic aperture radar wave spectra retrieved from the Max-Planck-Institut (MPI) scheme through intercomparisons of 1 year of directional buoy measurements

One year of directional buoy measurements comprising the period from May 1994 to April 1995 acquired in deep ocean waters by an offshore heave-pitch-roll buoy are used for the assessment of the directional wave spectra retrieved from synthetic aperture radar (SAR) images using the Max-Planck-Institut (MPI) scheme. SAR is the only sensor so far deployed from satellites that can provide measurements of the directional wave spectrum with high spatial and temporal coverage when operating in the so-called SAR wave mode. Millions of SAR wave mode imagettes have been and are still being acquired over all oceanic basins yielding a powerful data set for investigating wind waves. However, directional spectral information retrieved from SAR images has not yet been assessed against in situ measurements. For the first time, detailed validations of the main wave parameters, that is, significant wave height, mean direction of propagation, and mean wavelength, are performed. It is shown that in terms of these parameters the first-guess spectra taken from the wave model WAM are in better agreement with the buoy measurements than the MPI scheme retrievals. When considering only the longer waves in the part of the spectrum observed by SAR, on the other hand, the algorithm performs at least as well as the third-generation WAM wave model. In addition to the limitations of the MPI scheme in extending the spectral information beyond the high wave number cut-off, an observed misinterpretation of wind sea energy as swell by the MPI scheme is shown to be caused by the use of a quasi-linear approximation of the imaging model in the numerical iteration procedure