Statistical Tests for the Comparison of Surface Gravity Wave Spectra with Application to Model Validation

Abstract

A new second generation deep-water ocean wave model VAG is presented and several modifications are tested on a one month hindcast. On the same period and with the same windfields a version of the third generation model WAM is also tested. All the results are compared with the data of a pitch-roll-heave buoy moored at the entrance of the English Channel in 110 meters depth. This necessitates a preliminary investigation of existing tools to carry such comparisons. Based on commonly used criteria in model testing VAG and WAM achieve similar results. New tests are defined. For the significant wave heights, the use of the scatter index is criticized and the notion of relative error is introduced. For the mean wave directions, a weighted mean angular gap is defined which minimizes the impact of the direction errors of the low waves. From the theory of stationary random processes applied to waves, a criterion is proposed for frequency spectrum comparisons. Some diagrams are designed for the comparisons of more directional information. The sensitivity of the new tests to small differences in the modeling of the spectra attests to their suitability for model comparisons. Their application to the various runs shows that 1) In VAG, the swell modeling is improved by reducing the directional resolution of the spectrum and the grid mesh size. A reshaping of the windsea with f?4 power law for the high frequencies gives better results. 2) Swells are better modeled with WAM. 3) For both models, the direction of the high waves are better predicted. 4) In wind turning situations, a lag time between wind turning and wave turning is observed by the buoy even for rather high frequency waves. This lag time is correctly reproduced with VAG, but is too long with WAM.